id	sid	tid	token	lemma	pos
ap-7684	1	1	acta	acta	PROPN
ap-7684	1	2	polytechnica	polytechnica	PROPN
ap-7684	1	3	https://doi.org/10.14311/ap.2022.62.0293	https://doi.org/10.14311/ap.2022.62.0293	PROPN
ap-7684	1	4	acta	acta	PROPN
ap-7684	1	5	polytechnica	polytechnica	PROPN
ap-7684	1	6	62(2):293–302	62(2):293–302	PROPN
ap-7684	1	7	,	,	PUNCT
ap-7684	1	8	2022	2022	NUM
ap-7684	1	9	©	©	ADP
ap-7684	1	10	2022	2022	NUM
ap-7684	1	11	the	the	DET
ap-7684	1	12	author(s	author(s	NOUN
ap-7684	1	13	)	)	PUNCT
ap-7684	1	14	.	.	PUNCT
ap-7684	2	1	licensed	license	VERB
ap-7684	2	2	under	under	ADP
ap-7684	2	3	a	a	DET
ap-7684	2	4	cc	cc	NOUN
ap-7684	2	5	-	-	PUNCT
ap-7684	2	6	by	by	ADP
ap-7684	2	7	4.0	4.0	NUM
ap-7684	2	8	licence	licence	NOUN
ap-7684	2	9	published	publish	VERB
ap-7684	2	10	by	by	ADP
ap-7684	2	11	the	the	DET
ap-7684	2	12	czech	czech	PROPN
ap-7684	2	13	technical	technical	PROPN
ap-7684	2	14	university	university	PROPN
ap-7684	2	15	in	in	ADP
ap-7684	2	16	prague	prague	PROPN
ap-7684	2	17	a	a	DET
ap-7684	2	18	mindlin	mindlin	PROPN
ap-7684	2	19	shell	shell	PROPN
ap-7684	2	20	finite	finite	PROPN
ap-7684	2	21	element	element	NOUN
ap-7684	2	22	for	for	ADP
ap-7684	2	23	stone	stone	NOUN
ap-7684	2	24	masonry	masonry	NOUN
ap-7684	2	25	bridges	bridge	NOUN
ap-7684	2	26	with	with	ADP
ap-7684	2	27	backfill	backfill	NOUN
ap-7684	2	28	petr	petr	PROPN
ap-7684	2	29	řeřicha	řeřicha	PROPN
ap-7684	2	30	czech	czech	PROPN
ap-7684	2	31	technical	technical	PROPN
ap-7684	2	32	university	university	PROPN
ap-7684	2	33	in	in	ADP
ap-7684	2	34	prague	prague	PROPN
ap-7684	2	35	,	,	PUNCT
ap-7684	2	36	faculty	faculty	NOUN
ap-7684	2	37	of	of	ADP
ap-7684	2	38	civil	civil	ADJ
ap-7684	2	39	engineering	engineering	NOUN
ap-7684	2	40	,	,	PUNCT
ap-7684	2	41	thákurova	thákurova	PROPN
ap-7684	2	42	7	7	NUM
ap-7684	2	43	,	,	PUNCT
ap-7684	2	44	prague	prague	NOUN
ap-7684	2	45	,	,	PUNCT
ap-7684	2	46	czech	czech	PROPN
ap-7684	2	47	republic	republic	NOUN
ap-7684	2	48	correspondence	correspondence	NOUN
ap-7684	2	49	:	:	PUNCT
ap-7684	2	50	petr.rericha@fsv.cvut.cz	petr.rericha@fsv.cvut.cz	NOUN
ap-7684	2	51	abstract	abstract	ADJ
ap-7684	2	52	.	.	PUNCT
ap-7684	3	1	stone	stone	NOUN
ap-7684	3	2	masonry	masonry	NOUN
ap-7684	3	3	bridges	bridge	NOUN
ap-7684	3	4	are	be	AUX
ap-7684	3	5	difficult	difficult	ADJ
ap-7684	3	6	to	to	PART
ap-7684	3	7	analyse	analyse	VERB
ap-7684	3	8	with	with	ADP
ap-7684	3	9	commercial	commercial	ADJ
ap-7684	3	10	finite	finite	PROPN
ap-7684	3	11	element	element	NOUN
ap-7684	3	12	(	(	PUNCT
ap-7684	3	13	fe	fe	NOUN
ap-7684	3	14	)	)	PUNCT
ap-7684	3	15	packages	package	NOUN
ap-7684	3	16	for	for	ADP
ap-7684	3	17	their	their	PRON
ap-7684	3	18	specific	specific	ADJ
ap-7684	3	19	heterogeneous	heterogeneous	ADJ
ap-7684	3	20	composition	composition	NOUN
ap-7684	3	21	.	.	PUNCT
ap-7684	4	1	the	the	DET
ap-7684	4	2	stone	stone	NOUN
ap-7684	4	3	arch	arch	NOUN
ap-7684	4	4	is	be	AUX
ap-7684	4	5	best	well	ADV
ap-7684	4	6	modelled	model	VERB
ap-7684	4	7	as	as	ADP
ap-7684	4	8	a	a	DET
ap-7684	4	9	thick	thick	ADJ
ap-7684	4	10	shell	shell	NOUN
ap-7684	4	11	where	where	SCONJ
ap-7684	4	12	there	there	PRON
ap-7684	4	13	are	be	VERB
ap-7684	4	14	predestined	predestine	VERB
ap-7684	4	15	directions	direction	NOUN
ap-7684	4	16	of	of	ADP
ap-7684	4	17	tension	tension	NOUN
ap-7684	4	18	failure	failure	NOUN
ap-7684	4	19	,	,	PUNCT
ap-7684	4	20	normal	normal	ADJ
ap-7684	4	21	to	to	ADP
ap-7684	4	22	the	the	DET
ap-7684	4	23	bed	bed	NOUN
ap-7684	4	24	joints	joint	NOUN
ap-7684	4	25	.	.	PUNCT
ap-7684	5	1	a	a	PRON
ap-7684	5	2	dedicated	dedicated	ADJ
ap-7684	5	3	,	,	PUNCT
ap-7684	5	4	very	very	ADV
ap-7684	5	5	simple	simple	ADJ
ap-7684	5	6	,	,	PUNCT
ap-7684	5	7	mindlin	mindlin	PROPN
ap-7684	5	8	shell	shell	PROPN
ap-7684	5	9	finite	finite	PROPN
ap-7684	5	10	element	element	NOUN
ap-7684	5	11	is	be	AUX
ap-7684	5	12	developed	develop	VERB
ap-7684	5	13	with	with	ADP
ap-7684	5	14	five	five	NUM
ap-7684	5	15	translational	translational	ADJ
ap-7684	5	16	degrees	degree	NOUN
ap-7684	5	17	of	of	ADP
ap-7684	5	18	freedom	freedom	NOUN
ap-7684	5	19	per	per	ADP
ap-7684	5	20	node	node	NOUN
ap-7684	5	21	.	.	PUNCT
ap-7684	6	1	it	it	PRON
ap-7684	6	2	features	feature	VERB
ap-7684	6	3	compatibility	compatibility	NOUN
ap-7684	6	4	with	with	ADP
ap-7684	6	5	linear	linear	ADJ
ap-7684	6	6	isoparametric	isoparametric	ADJ
ap-7684	6	7	or	or	CCONJ
ap-7684	6	8	constant	constant	ADJ
ap-7684	6	9	strain	strain	NOUN
ap-7684	6	10	elements	element	NOUN
ap-7684	6	11	for	for	ADP
ap-7684	6	12	the	the	DET
ap-7684	6	13	backfill	backfill	NOUN
ap-7684	6	14	.	.	PUNCT
ap-7684	7	1	most	most	ADJ
ap-7684	7	2	bridges	bridge	NOUN
ap-7684	7	3	can	can	AUX
ap-7684	7	4	be	be	AUX
ap-7684	7	5	analysed	analyse	VERB
ap-7684	7	6	with	with	ADP
ap-7684	7	7	a	a	DET
ap-7684	7	8	sufficient	sufficient	ADJ
ap-7684	7	9	accuracy	accuracy	NOUN
ap-7684	7	10	assuming	assume	VERB
ap-7684	7	11	plain	plain	ADJ
ap-7684	7	12	strain	strain	NOUN
ap-7684	7	13	conditions	condition	NOUN
ap-7684	7	14	.	.	PUNCT
ap-7684	8	1	the	the	DET
ap-7684	8	2	element	element	NOUN
ap-7684	8	3	then	then	ADV
ap-7684	8	4	simplifies	simplify	VERB
ap-7684	8	5	to	to	ADP
ap-7684	8	6	a	a	DET
ap-7684	8	7	timoshenko	timoshenko	ADJ
ap-7684	8	8	beam	beam	NOUN
ap-7684	8	9	element	element	NOUN
ap-7684	8	10	with	with	ADP
ap-7684	8	11	three	three	NUM
ap-7684	8	12	translational	translational	ADJ
ap-7684	8	13	degrees	degree	NOUN
ap-7684	8	14	of	of	ADP
ap-7684	8	15	freedom	freedom	NOUN
ap-7684	8	16	per	per	ADP
ap-7684	8	17	node	node	NOUN
ap-7684	8	18	.	.	PUNCT
ap-7684	9	1	an	an	DET
ap-7684	9	2	application	application	NOUN
ap-7684	9	3	of	of	ADP
ap-7684	9	4	the	the	DET
ap-7684	9	5	latter	latter	ADJ
ap-7684	9	6	one	one	NUM
ap-7684	9	7	to	to	ADP
ap-7684	9	8	the	the	DET
ap-7684	9	9	bridge	bridge	NOUN
ap-7684	9	10	at	at	ADP
ap-7684	9	11	poniklá	poniklá	NOUN
ap-7684	9	12	is	be	AUX
ap-7684	9	13	presented	present	VERB
ap-7684	9	14	.	.	PUNCT
ap-7684	10	1	keywords	keyword	NOUN
ap-7684	10	2	:	:	PUNCT
ap-7684	10	3	masonry	masonry	NOUN
ap-7684	10	4	arches	arch	NOUN
ap-7684	10	5	,	,	PUNCT
ap-7684	10	6	no	no	DET
ap-7684	10	7	tension	tension	NOUN
ap-7684	10	8	joints	joint	NOUN
ap-7684	10	9	,	,	PUNCT
ap-7684	10	10	thick	thick	ADJ
ap-7684	10	11	shell	shell	NOUN
ap-7684	10	12	elements	element	NOUN
ap-7684	10	13	,	,	PUNCT
ap-7684	10	14	octave	octave	NOUN
ap-7684	10	15	script	script	NOUN
ap-7684	10	16	.	.	PUNCT
ap-7684	11	1	1	1	X
ap-7684	11	2	.	.	X
ap-7684	11	3	introduction	introduction	NOUN
ap-7684	11	4	masonry	masonry	NOUN
ap-7684	11	5	arch	arch	NOUN
ap-7684	11	6	bridges	bridge	NOUN
ap-7684	11	7	still	still	ADV
ap-7684	11	8	constitute	constitute	VERB
ap-7684	11	9	a	a	DET
ap-7684	11	10	considerable	considerable	ADJ
ap-7684	11	11	part	part	NOUN
ap-7684	11	12	of	of	ADP
ap-7684	11	13	the	the	DET
ap-7684	11	14	bridge	bridge	NOUN
ap-7684	11	15	stock	stock	NOUN
ap-7684	11	16	of	of	ADP
ap-7684	11	17	the	the	DET
ap-7684	11	18	transport	transport	NOUN
ap-7684	11	19	infrastructure	infrastructure	NOUN
ap-7684	11	20	in	in	ADP
ap-7684	11	21	czechia	czechia	NOUN
ap-7684	11	22	.	.	PUNCT
ap-7684	12	1	many	many	ADJ
ap-7684	12	2	of	of	ADP
ap-7684	12	3	them	they	PRON
ap-7684	12	4	are	be	AUX
ap-7684	12	5	valueable	valueable	ADJ
ap-7684	12	6	monuments	monument	NOUN
ap-7684	12	7	of	of	ADP
ap-7684	12	8	the	the	DET
ap-7684	12	9	technical	technical	ADJ
ap-7684	12	10	expertise	expertise	NOUN
ap-7684	12	11	and	and	CCONJ
ap-7684	12	12	craftsmenship	craftsmenship	NOUN
ap-7684	12	13	of	of	ADP
ap-7684	12	14	the	the	DET
ap-7684	12	15	past	past	ADJ
ap-7684	12	16	generations	generation	NOUN
ap-7684	12	17	as	as	ADV
ap-7684	12	18	well	well	ADV
ap-7684	12	19	.	.	PUNCT
ap-7684	13	1	design	design	NOUN
ap-7684	13	2	standards	standard	NOUN
ap-7684	13	3	for	for	ADP
ap-7684	13	4	this	this	DET
ap-7684	13	5	sort	sort	NOUN
ap-7684	13	6	of	of	ADP
ap-7684	13	7	bridges	bridge	NOUN
ap-7684	13	8	do	do	AUX
ap-7684	13	9	not	not	PART
ap-7684	13	10	exist	exist	VERB
ap-7684	13	11	worlwide	worlwide	NOUN
ap-7684	13	12	,	,	PUNCT
ap-7684	13	13	guides	guide	NOUN
ap-7684	13	14	and	and	CCONJ
ap-7684	13	15	manuals	manual	NOUN
ap-7684	13	16	for	for	ADP
ap-7684	13	17	load	load	NOUN
ap-7684	13	18	rating	rating	NOUN
ap-7684	13	19	are	be	AUX
ap-7684	13	20	provided	provide	VERB
ap-7684	13	21	instead	instead	ADV
ap-7684	13	22	,	,	PUNCT
ap-7684	13	23	like	like	ADP
ap-7684	13	24	[	[	X
ap-7684	13	25	1	1	NUM
ap-7684	13	26	]	]	PUNCT
ap-7684	13	27	or	or	CCONJ
ap-7684	13	28	[	[	X
ap-7684	13	29	2	2	NUM
ap-7684	13	30	]	]	PUNCT
ap-7684	13	31	.	.	PUNCT
ap-7684	14	1	they	they	PRON
ap-7684	14	2	usually	usually	ADV
ap-7684	14	3	contain	contain	VERB
ap-7684	14	4	conservative	conservative	ADJ
ap-7684	14	5	approximate	approximate	ADJ
ap-7684	14	6	methods	method	NOUN
ap-7684	14	7	for	for	ADP
ap-7684	14	8	a	a	DET
ap-7684	14	9	routine	routine	ADJ
ap-7684	14	10	assessment	assessment	NOUN
ap-7684	14	11	and	and	CCONJ
ap-7684	14	12	some	some	DET
ap-7684	14	13	guidance	guidance	NOUN
ap-7684	14	14	and	and	CCONJ
ap-7684	14	15	recommendations	recommendation	NOUN
ap-7684	14	16	for	for	ADP
ap-7684	14	17	more	more	ADV
ap-7684	14	18	complicated	complicated	ADJ
ap-7684	14	19	individual	individual	ADJ
ap-7684	14	20	assessments	assessment	NOUN
ap-7684	14	21	based	base	VERB
ap-7684	14	22	on	on	ADP
ap-7684	14	23	advanced	advanced	ADJ
ap-7684	14	24	structural	structural	ADJ
ap-7684	14	25	analysis	analysis	NOUN
ap-7684	14	26	methods	method	NOUN
ap-7684	14	27	.	.	PUNCT
ap-7684	15	1	a	a	DET
ap-7684	15	2	structural	structural	ADJ
ap-7684	15	3	analysis	analysis	NOUN
ap-7684	15	4	of	of	ADP
ap-7684	15	5	masonry	masonry	NOUN
ap-7684	15	6	arch	arch	NOUN
ap-7684	15	7	bridges	bridge	NOUN
ap-7684	15	8	is	be	AUX
ap-7684	15	9	specific	specific	ADJ
ap-7684	15	10	in	in	SCONJ
ap-7684	15	11	that	that	SCONJ
ap-7684	15	12	the	the	DET
ap-7684	15	13	ultimate	ultimate	ADJ
ap-7684	15	14	limit	limit	NOUN
ap-7684	15	15	state	state	NOUN
ap-7684	15	16	forces	force	NOUN
ap-7684	15	17	and	and	CCONJ
ap-7684	15	18	stresses	stress	NOUN
ap-7684	15	19	can	can	AUX
ap-7684	15	20	not	not	PART
ap-7684	15	21	be	be	AUX
ap-7684	15	22	solved	solve	VERB
ap-7684	15	23	for	for	ADP
ap-7684	15	24	assuming	assume	VERB
ap-7684	15	25	homogeneous	homogeneous	ADJ
ap-7684	15	26	isotropic	isotropic	ADJ
ap-7684	15	27	linear	linear	ADJ
ap-7684	15	28	elastic	elastic	ADJ
ap-7684	15	29	material	material	NOUN
ap-7684	15	30	.	.	PUNCT
ap-7684	16	1	in	in	ADP
ap-7684	16	2	contrast	contrast	NOUN
ap-7684	16	3	to	to	ADP
ap-7684	16	4	that	that	PRON
ap-7684	16	5	,	,	PUNCT
ap-7684	16	6	design	design	NOUN
ap-7684	16	7	standards	standard	NOUN
ap-7684	16	8	for	for	ADP
ap-7684	16	9	reinforced	reinforce	VERB
ap-7684	16	10	concrete	concrete	ADJ
ap-7684	16	11	and	and	CCONJ
ap-7684	16	12	steel	steel	NOUN
ap-7684	16	13	structures	structure	NOUN
ap-7684	16	14	admit	admit	VERB
ap-7684	16	15	such	such	ADJ
ap-7684	16	16	solutions	solution	NOUN
ap-7684	16	17	.	.	PUNCT
ap-7684	17	1	en	en	ADP
ap-7684	17	2	1996	1996	NUM
ap-7684	17	3	-	-	SYM
ap-7684	17	4	1	1	NUM
ap-7684	17	5	-	-	SYM
ap-7684	17	6	1	1	NUM
ap-7684	17	7	codifies	codifie	NOUN
ap-7684	17	8	in	in	ADP
ap-7684	17	9	clause	clause	NOUN
ap-7684	17	10	6.1.1(2	6.1.1(2	NUM
ap-7684	17	11	)	)	PUNCT
ap-7684	17	12	that	that	SCONJ
ap-7684	17	13	plane	plane	NOUN
ap-7684	17	14	sections	section	NOUN
ap-7684	17	15	remain	remain	VERB
ap-7684	17	16	plane	plane	NOUN
ap-7684	17	17	and	and	CCONJ
ap-7684	17	18	the	the	DET
ap-7684	17	19	tensile	tensile	NOUN
ap-7684	17	20	strength	strength	NOUN
ap-7684	17	21	of	of	ADP
ap-7684	17	22	masonry	masonry	NOUN
ap-7684	17	23	perpendicular	perpendicular	ADJ
ap-7684	17	24	to	to	ADP
ap-7684	17	25	bed	bed	NOUN
ap-7684	17	26	joints	joint	NOUN
ap-7684	17	27	is	be	AUX
ap-7684	17	28	zero	zero	NUM
ap-7684	17	29	in	in	ADP
ap-7684	17	30	the	the	DET
ap-7684	17	31	ultimate	ultimate	ADJ
ap-7684	17	32	limit	limit	NOUN
ap-7684	17	33	state	state	NOUN
ap-7684	17	34	.	.	PUNCT
ap-7684	18	1	the	the	DET
ap-7684	18	2	standard	standard	NOUN
ap-7684	18	3	is	be	AUX
ap-7684	18	4	not	not	PART
ap-7684	18	5	compulsory	compulsory	ADJ
ap-7684	18	6	for	for	ADP
ap-7684	18	7	bridges	bridge	NOUN
ap-7684	18	8	but	but	CCONJ
ap-7684	18	9	its	its	PRON
ap-7684	18	10	conditions	condition	NOUN
ap-7684	18	11	should	should	AUX
ap-7684	18	12	be	be	AUX
ap-7684	18	13	perceived	perceive	VERB
ap-7684	18	14	as	as	ADP
ap-7684	18	15	the	the	DET
ap-7684	18	16	minimum	minimum	NOUN
ap-7684	18	17	for	for	ADP
ap-7684	18	18	them	they	PRON
ap-7684	18	19	.	.	PUNCT
ap-7684	19	1	cracks	crack	NOUN
ap-7684	19	2	in	in	ADP
ap-7684	19	3	the	the	DET
ap-7684	19	4	bed	bed	NOUN
ap-7684	19	5	joints	joint	NOUN
ap-7684	19	6	of	of	ADP
ap-7684	19	7	the	the	DET
ap-7684	19	8	masonry	masonry	NOUN
ap-7684	19	9	arches	arch	NOUN
ap-7684	19	10	affect	affect	VERB
ap-7684	19	11	the	the	DET
ap-7684	19	12	stress	stress	NOUN
ap-7684	19	13	distribution	distribution	NOUN
ap-7684	19	14	in	in	ADP
ap-7684	19	15	a	a	DET
ap-7684	19	16	way	way	NOUN
ap-7684	19	17	that	that	PRON
ap-7684	19	18	does	do	AUX
ap-7684	19	19	not	not	PART
ap-7684	19	20	admit	admit	VERB
ap-7684	19	21	a	a	DET
ap-7684	19	22	linear	linear	ADJ
ap-7684	19	23	solution	solution	NOUN
ap-7684	19	24	.	.	PUNCT
ap-7684	20	1	the	the	DET
ap-7684	20	2	simplest	simple	ADJ
ap-7684	20	3	material	material	NOUN
ap-7684	20	4	model	model	NOUN
ap-7684	20	5	that	that	PRON
ap-7684	20	6	can	can	AUX
ap-7684	20	7	be	be	AUX
ap-7684	20	8	accepted	accept	VERB
ap-7684	20	9	is	be	AUX
ap-7684	20	10	the	the	DET
ap-7684	20	11	no	no	DET
ap-7684	20	12	-	-	PUNCT
ap-7684	20	13	tension	tension	NOUN
ap-7684	20	14	linear	linear	ADJ
ap-7684	20	15	material	material	NOUN
ap-7684	20	16	where	where	SCONJ
ap-7684	20	17	the	the	DET
ap-7684	20	18	no	no	DET
ap-7684	20	19	-	-	PUNCT
ap-7684	20	20	tension	tension	NOUN
ap-7684	20	21	condition	condition	NOUN
ap-7684	20	22	applies	apply	VERB
ap-7684	20	23	to	to	ADP
ap-7684	20	24	the	the	DET
ap-7684	20	25	normal	normal	ADJ
ap-7684	20	26	stress	stress	NOUN
ap-7684	20	27	in	in	ADP
ap-7684	20	28	the	the	DET
ap-7684	20	29	planes	plane	NOUN
ap-7684	20	30	parallel	parallel	NOUN
ap-7684	20	31	to	to	ADP
ap-7684	20	32	the	the	DET
ap-7684	20	33	bed	bed	NOUN
ap-7684	20	34	joints	joint	NOUN
ap-7684	20	35	.	.	PUNCT
ap-7684	21	1	this	this	DET
ap-7684	21	2	specific	specific	ADJ
ap-7684	21	3	behaviour	behaviour	NOUN
ap-7684	21	4	is	be	AUX
ap-7684	21	5	difficult	difficult	ADJ
ap-7684	21	6	to	to	PART
ap-7684	21	7	simulate	simulate	VERB
ap-7684	21	8	by	by	ADP
ap-7684	21	9	material	material	NOUN
ap-7684	21	10	models	model	NOUN
ap-7684	21	11	available	available	ADJ
ap-7684	21	12	in	in	ADP
ap-7684	21	13	general	general	ADJ
ap-7684	21	14	purpose	purpose	NOUN
ap-7684	21	15	program	program	NOUN
ap-7684	21	16	packages	package	NOUN
ap-7684	21	17	,	,	PUNCT
ap-7684	21	18	[	[	X
ap-7684	21	19	3	3	NUM
ap-7684	21	20	]	]	PUNCT
ap-7684	21	21	.	.	PUNCT
ap-7684	22	1	commercial	commercial	ADJ
ap-7684	22	2	packages	package	NOUN
ap-7684	22	3	do	do	AUX
ap-7684	22	4	not	not	PART
ap-7684	22	5	include	include	VERB
ap-7684	22	6	such	such	ADJ
ap-7684	22	7	material	material	NOUN
ap-7684	22	8	models	model	NOUN
ap-7684	22	9	.	.	PUNCT
ap-7684	23	1	there	there	PRON
ap-7684	23	2	were	be	VERB
ap-7684	23	3	attempts	attempt	NOUN
ap-7684	23	4	to	to	PART
ap-7684	23	5	achieve	achieve	VERB
ap-7684	23	6	the	the	DET
ap-7684	23	7	specific	specific	ADJ
ap-7684	23	8	properties	property	NOUN
ap-7684	23	9	of	of	ADP
ap-7684	23	10	the	the	DET
ap-7684	23	11	masonry	masonry	NOUN
ap-7684	23	12	arches	arch	VERB
ap-7684	23	13	with	with	ADP
ap-7684	23	14	a	a	DET
ap-7684	23	15	trivial	trivial	ADJ
ap-7684	23	16	model	model	NOUN
ap-7684	23	17	of	of	ADP
ap-7684	23	18	a	a	DET
ap-7684	23	19	heterogeneous	heterogeneous	ADJ
ap-7684	23	20	material	material	NOUN
ap-7684	23	21	–	–	PUNCT
ap-7684	23	22	individual	individual	ADJ
ap-7684	23	23	meshing	meshing	NOUN
ap-7684	23	24	of	of	ADP
ap-7684	23	25	voussoirs	voussoir	NOUN
ap-7684	23	26	and	and	CCONJ
ap-7684	23	27	joints	joint	NOUN
ap-7684	23	28	by	by	ADP
ap-7684	23	29	standard	standard	ADJ
ap-7684	23	30	continuum	continuum	ADJ
ap-7684	23	31	finite	finite	ADJ
ap-7684	23	32	elements	element	NOUN
ap-7684	23	33	with	with	ADP
ap-7684	23	34	homogeneous	homogeneous	ADJ
ap-7684	23	35	material	material	NOUN
ap-7684	23	36	models	model	NOUN
ap-7684	23	37	.	.	PUNCT
ap-7684	24	1	it	it	PRON
ap-7684	24	2	is	be	AUX
ap-7684	24	3	possible	possible	ADJ
ap-7684	24	4	in	in	ADP
ap-7684	24	5	academic	academic	ADJ
ap-7684	24	6	works	work	NOUN
ap-7684	24	7	but	but	CCONJ
ap-7684	24	8	not	not	PART
ap-7684	24	9	acceptable	acceptable	ADJ
ap-7684	24	10	in	in	ADP
ap-7684	24	11	design	design	NOUN
ap-7684	24	12	practice	practice	NOUN
ap-7684	24	13	for	for	ADP
ap-7684	24	14	demands	demand	NOUN
ap-7684	24	15	on	on	ADP
ap-7684	24	16	the	the	DET
ap-7684	24	17	labour	labour	NOUN
ap-7684	24	18	,	,	PUNCT
ap-7684	24	19	software	software	NOUN
ap-7684	24	20	and	and	CCONJ
ap-7684	24	21	input	input	NOUN
ap-7684	24	22	data	datum	NOUN
ap-7684	24	23	on	on	ADP
ap-7684	24	24	materials	material	NOUN
ap-7684	24	25	properties	property	NOUN
ap-7684	24	26	.	.	PUNCT
ap-7684	25	1	this	this	DET
ap-7684	25	2	experience	experience	NOUN
ap-7684	25	3	testifies	testify	VERB
ap-7684	25	4	that	that	SCONJ
ap-7684	25	5	shell	shell	NOUN
ap-7684	25	6	/	/	SYM
ap-7684	25	7	beam	beam	NOUN
ap-7684	25	8	elements	element	NOUN
ap-7684	25	9	using	use	VERB
ap-7684	25	10	the	the	DET
ap-7684	25	11	rigid	rigid	ADJ
ap-7684	25	12	normals	normal	NOUN
ap-7684	25	13	assumption	assumption	NOUN
ap-7684	25	14	(	(	PUNCT
ap-7684	25	15	timoshenko	timoshenko	NOUN
ap-7684	25	16	,	,	PUNCT
ap-7684	25	17	mindlin	mindlin	NOUN
ap-7684	25	18	,	,	PUNCT
ap-7684	25	19	bernoulli	bernoulli	NOUN
ap-7684	25	20	-	-	PUNCT
ap-7684	25	21	navier	navier	NOUN
ap-7684	25	22	and	and	CCONJ
ap-7684	25	23	other	other	ADJ
ap-7684	25	24	assumptions	assumption	NOUN
ap-7684	25	25	)	)	PUNCT
ap-7684	25	26	are	be	AUX
ap-7684	25	27	indispensable	indispensable	ADJ
ap-7684	25	28	for	for	ADP
ap-7684	25	29	the	the	DET
ap-7684	25	30	solution	solution	NOUN
ap-7684	25	31	of	of	ADP
ap-7684	25	32	the	the	DET
ap-7684	25	33	masonry	masonry	NOUN
ap-7684	25	34	arch	arch	ADJ
ap-7684	25	35	bridges	bridge	NOUN
ap-7684	25	36	.	.	PUNCT
ap-7684	26	1	several	several	ADJ
ap-7684	26	2	dedicated	dedicated	ADJ
ap-7684	26	3	codes	code	NOUN
ap-7684	26	4	have	have	AUX
ap-7684	26	5	been	be	AUX
ap-7684	26	6	written	write	VERB
ap-7684	26	7	around	around	ADP
ap-7684	26	8	1990	1990	NUM
ap-7684	26	9	for	for	ADP
ap-7684	26	10	the	the	DET
ap-7684	26	11	analysis	analysis	NOUN
ap-7684	26	12	of	of	ADP
ap-7684	26	13	masonry	masonry	NOUN
ap-7684	26	14	arches	arch	NOUN
ap-7684	26	15	based	base	VERB
ap-7684	26	16	on	on	ADP
ap-7684	26	17	the	the	DET
ap-7684	26	18	castigliano	castigliano	PROPN
ap-7684	26	19	principle	principle	NOUN
ap-7684	26	20	,	,	PUNCT
ap-7684	26	21	ctap	ctap	ADJ
ap-7684	26	22	[	[	X
ap-7684	26	23	4	4	NUM
ap-7684	26	24	]	]	PUNCT
ap-7684	26	25	,	,	PUNCT
ap-7684	26	26	[	[	X
ap-7684	26	27	5	5	NUM
ap-7684	26	28	]	]	PUNCT
ap-7684	26	29	,	,	PUNCT
ap-7684	26	30	rigid	rigid	ADJ
ap-7684	26	31	block	block	NOUN
ap-7684	26	32	assumption	assumption	NOUN
ap-7684	26	33	ring	ring	NOUN
ap-7684	26	34	,	,	PUNCT
ap-7684	26	35	[	[	X
ap-7684	26	36	6	6	NUM
ap-7684	26	37	]	]	PUNCT
ap-7684	26	38	,	,	PUNCT
ap-7684	26	39	mechanism	mechanism	NOUN
ap-7684	26	40	based	base	VERB
ap-7684	26	41	archie	archie	NOUN
ap-7684	26	42	,	,	PUNCT
ap-7684	26	43	[	[	X
ap-7684	26	44	7	7	NUM
ap-7684	26	45	]	]	PUNCT
ap-7684	26	46	and	and	CCONJ
ap-7684	26	47	others	other	NOUN
ap-7684	26	48	.	.	PUNCT
ap-7684	27	1	all	all	PRON
ap-7684	27	2	of	of	ADP
ap-7684	27	3	them	they	PRON
ap-7684	27	4	assume	assume	VERB
ap-7684	27	5	plane	plane	NOUN
ap-7684	27	6	strain	strain	NOUN
ap-7684	27	7	conditions	condition	NOUN
ap-7684	27	8	.	.	PUNCT
ap-7684	28	1	these	these	DET
ap-7684	28	2	models	model	NOUN
ap-7684	28	3	simulate	simulate	VERB
ap-7684	28	4	very	very	ADV
ap-7684	28	5	well	well	ADV
ap-7684	28	6	the	the	DET
ap-7684	28	7	observed	observed	ADJ
ap-7684	28	8	behaviour	behaviour	NOUN
ap-7684	28	9	of	of	ADP
ap-7684	28	10	masonry	masonry	NOUN
ap-7684	28	11	arches	arch	VERB
ap-7684	28	12	in	in	ADP
ap-7684	28	13	situ	situ	NOUN
ap-7684	28	14	and	and	CCONJ
ap-7684	28	15	in	in	ADP
ap-7684	28	16	large	large	ADJ
ap-7684	28	17	scale	scale	NOUN
ap-7684	28	18	model	model	NOUN
ap-7684	28	19	tests	test	NOUN
ap-7684	28	20	.	.	PUNCT
ap-7684	29	1	they	they	PRON
ap-7684	29	2	have	have	AUX
ap-7684	29	3	been	be	AUX
ap-7684	29	4	applied	apply	VERB
ap-7684	29	5	worldwide	worldwide	ADV
ap-7684	29	6	in	in	ADP
ap-7684	29	7	practice	practice	NOUN
ap-7684	29	8	despite	despite	SCONJ
ap-7684	29	9	their	their	PRON
ap-7684	29	10	common	common	ADJ
ap-7684	29	11	drawback	drawback	NOUN
ap-7684	29	12	that	that	PRON
ap-7684	29	13	they	they	PRON
ap-7684	29	14	underestimate	underestimate	VERB
ap-7684	29	15	the	the	DET
ap-7684	29	16	interaction	interaction	NOUN
ap-7684	29	17	of	of	ADP
ap-7684	29	18	the	the	DET
ap-7684	29	19	barrel	barrel	NOUN
ap-7684	29	20	,	,	PUNCT
ap-7684	29	21	backfill	backfill	NOUN
ap-7684	29	22	and	and	CCONJ
ap-7684	29	23	pavement	pavement	NOUN
ap-7684	29	24	.	.	PUNCT
ap-7684	30	1	two	two	NUM
ap-7684	30	2	simple	simple	ADJ
ap-7684	30	3	finite	finite	ADJ
ap-7684	30	4	elements	element	NOUN
ap-7684	30	5	for	for	ADP
ap-7684	30	6	thick	thick	ADJ
ap-7684	30	7	shells	shell	NOUN
ap-7684	30	8	are	be	AUX
ap-7684	30	9	developed	develop	VERB
ap-7684	30	10	based	base	VERB
ap-7684	30	11	on	on	ADP
ap-7684	30	12	the	the	DET
ap-7684	30	13	timoshenko	timoshenko	NOUN
ap-7684	30	14	/	/	SYM
ap-7684	30	15	mindlin	mindlin	NOUN
ap-7684	30	16	kinematic	kinematic	PROPN
ap-7684	30	17	assumptions	assumption	NOUN
ap-7684	30	18	,	,	PUNCT
ap-7684	30	19	one	one	NUM
ap-7684	30	20	for	for	ADP
ap-7684	30	21	plane	plane	NOUN
ap-7684	30	22	stress	stress	NOUN
ap-7684	30	23	/	/	SYM
ap-7684	30	24	plane	plane	NOUN
ap-7684	30	25	strain	strain	NOUN
ap-7684	30	26	conditions	condition	NOUN
ap-7684	30	27	,	,	PUNCT
ap-7684	30	28	the	the	DET
ap-7684	30	29	other	other	ADJ
ap-7684	30	30	for	for	ADP
ap-7684	30	31	3d	3d	NUM
ap-7684	30	32	shells	shell	NOUN
ap-7684	30	33	.	.	PUNCT
ap-7684	31	1	in	in	ADP
ap-7684	31	2	order	order	NOUN
ap-7684	31	3	to	to	PART
ap-7684	31	4	facilitate	facilitate	VERB
ap-7684	31	5	a	a	DET
ap-7684	31	6	seamless	seamless	ADJ
ap-7684	31	7	interaction	interaction	NOUN
ap-7684	31	8	with	with	ADP
ap-7684	31	9	the	the	DET
ap-7684	31	10	backfill	backfill	NOUN
ap-7684	31	11	continuum	continuum	ADJ
ap-7684	31	12	,	,	PUNCT
ap-7684	31	13	only	only	ADV
ap-7684	31	14	translational	translational	ADJ
ap-7684	31	15	degrees	degree	NOUN
ap-7684	31	16	of	of	ADP
ap-7684	31	17	freedom	freedom	NOUN
ap-7684	31	18	(	(	PUNCT
ap-7684	31	19	dofs	dof	NOUN
ap-7684	31	20	)	)	PUNCT
ap-7684	31	21	are	be	AUX
ap-7684	31	22	employed	employ	VERB
ap-7684	31	23	.	.	PUNCT
ap-7684	32	1	the	the	DET
ap-7684	32	2	no	no	DET
ap-7684	32	3	-	-	PUNCT
ap-7684	32	4	tension	tension	NOUN
ap-7684	32	5	linear	linear	ADJ
ap-7684	32	6	elastic	elastic	ADJ
ap-7684	32	7	constitutive	constitutive	ADJ
ap-7684	32	8	equations	equation	NOUN
ap-7684	32	9	are	be	AUX
ap-7684	32	10	integrated	integrate	VERB
ap-7684	32	11	in	in	ADP
ap-7684	32	12	a	a	DET
ap-7684	32	13	closed	closed	ADJ
ap-7684	32	14	form	form	NOUN
ap-7684	32	15	for	for	ADP
ap-7684	32	16	the	the	DET
ap-7684	32	17	normal	normal	ADJ
ap-7684	32	18	stress	stress	NOUN
ap-7684	32	19	in	in	ADP
ap-7684	32	20	planes	plane	NOUN
ap-7684	32	21	parallel	parallel	NOUN
ap-7684	32	22	to	to	ADP
ap-7684	32	23	the	the	DET
ap-7684	32	24	bed	bed	NOUN
ap-7684	32	25	joints	joint	NOUN
ap-7684	32	26	.	.	PUNCT
ap-7684	33	1	the	the	DET
ap-7684	33	2	shape	shape	NOUN
ap-7684	33	3	functions	function	NOUN
ap-7684	33	4	of	of	ADP
ap-7684	33	5	the	the	DET
ap-7684	33	6	elements	element	NOUN
ap-7684	33	7	are	be	AUX
ap-7684	33	8	2d	2d	NUM
ap-7684	33	9	and	and	CCONJ
ap-7684	33	10	3d	3d	NUM
ap-7684	33	11	variants	variant	NOUN
ap-7684	33	12	of	of	ADP
ap-7684	33	13	the	the	DET
ap-7684	33	14	same	same	ADJ
ap-7684	33	15	concept	concept	NOUN
ap-7684	33	16	.	.	PUNCT
ap-7684	34	1	the	the	DET
ap-7684	34	2	simpler	simple	ADJ
ap-7684	34	3	2d	2d	NOUN
ap-7684	34	4	variant	variant	NOUN
ap-7684	34	5	is	be	AUX
ap-7684	34	6	presented	present	VERB
ap-7684	34	7	first	first	ADV
ap-7684	34	8	with	with	ADP
ap-7684	34	9	an	an	DET
ap-7684	34	10	application	application	NOUN
ap-7684	34	11	to	to	ADP
ap-7684	34	12	a	a	DET
ap-7684	34	13	bridge	bridge	NOUN
ap-7684	34	14	,	,	PUNCT
ap-7684	34	15	a	a	DET
ap-7684	34	16	triangle	triangle	NOUN
ap-7684	34	17	thick	thick	ADJ
ap-7684	34	18	shell	shell	NOUN
ap-7684	34	19	element	element	NOUN
ap-7684	34	20	follows	follow	VERB
ap-7684	34	21	.	.	PUNCT
ap-7684	35	1	2	2	X
ap-7684	35	2	.	.	X
ap-7684	35	3	the	the	DET
ap-7684	35	4	tt	tt	PROPN
ap-7684	35	5	element	element	NOUN
ap-7684	35	6	,	,	PUNCT
ap-7684	35	7	timoshenko	timoshenko	NOUN
ap-7684	35	8	beam	beam	NOUN
ap-7684	35	9	with	with	ADP
ap-7684	35	10	translational	translational	ADJ
ap-7684	35	11	dofs	dof	NOUN
ap-7684	35	12	the	the	DET
ap-7684	35	13	displacement	displacement	ADJ
ap-7684	35	14	shape	shape	NOUN
ap-7684	35	15	functions	function	NOUN
ap-7684	35	16	are	be	AUX
ap-7684	35	17	sketched	sketch	VERB
ap-7684	35	18	in	in	ADP
ap-7684	35	19	figure	figure	NOUN
ap-7684	35	20	1	1	NUM
ap-7684	35	21	for	for	ADP
ap-7684	35	22	the	the	DET
ap-7684	35	23	axial	axial	ADJ
ap-7684	35	24	displacement	displacement	NOUN
ap-7684	35	25	ui	ui	PROPN
ap-7684	35	26	,	,	PUNCT
ap-7684	35	27	t	t	PROPN
ap-7684	35	28	of	of	ADP
ap-7684	35	29	node	node	PROPN
ap-7684	35	30	i	i	PROPN
ap-7684	35	31	,	,	PUNCT
ap-7684	35	32	for	for	ADP
ap-7684	35	33	the	the	DET
ap-7684	35	34	293	293	NUM
ap-7684	35	35	https://doi.org/10.14311/ap.2022.62.0293	https://doi.org/10.14311/ap.2022.62.0293	NOUN
ap-7684	35	36	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7684	35	37	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-7684	35	38	petr	petr	PROPN
ap-7684	35	39	řeřicha	řeřicha	PROPN
ap-7684	35	40	acta	acta	PROPN
ap-7684	35	41	polytechnica	polytechnica	PROPN
ap-7684	35	42	u	u	PROPN
ap-7684	35	43	i	i	PROPN
ap-7684	35	44	,	,	PUNCT
ap-7684	35	45	b	b	PROPN
ap-7684	35	46	u	u	X
ap-7684	35	47	i	i	PROPN
ap-7684	35	48	,	,	PUNCT
ap-7684	35	49	b	b	PROPN
ap-7684	35	50	u	u	X
ap-7684	35	51	u	u	X
ap-7684	35	52	i	i	PROPN
ap-7684	35	53	,	,	PUNCT
ap-7684	35	54	t	t	PROPN
ap-7684	35	55	j	j	PROPN
ap-7684	35	56	,	,	PUNCT
ap-7684	35	57	b	b	PROPN
ap-7684	35	58	x	x	SYM
ap-7684	35	59	xx	xx	NUM
ap-7684	36	1	i	i	PROPN
ap-7684	36	2	,	,	PUNCT
ap-7684	36	3	b	b	PROPN
ap-7684	36	4	j	j	PROPN
ap-7684	36	5	,	,	PUNCT
ap-7684	36	6	b	b	PROPN
ap-7684	36	7	j	j	PROPN
ap-7684	36	8	,	,	PUNCT
ap-7684	36	9	ti	ti	PROPN
ap-7684	36	10	,	,	PUNCT
ap-7684	36	11	t	t	PROPN
ap-7684	36	12	u	u	PROPN
ap-7684	36	13	j	j	PROPN
ap-7684	36	14	,	,	PUNCT
ap-7684	36	15	t	t	PROPN
ap-7684	36	16	v	v	NOUN
ap-7684	36	17	vi	vi	PROPN
ap-7684	36	18	y	y	PROPN
ap-7684	36	19	yi	yi	PROPN
ap-7684	37	1	j	j	PROPN
ap-7684	37	2	l	l	PROPN
ap-7684	38	1	i	i	PROPN
ap-7684	38	2	,	,	PUNCT
ap-7684	38	3	j	j	PROPN
ap-7684	38	4	d	d	PROPN
ap-7684	38	5	i	i	PROPN
ap-7684	38	6	,	,	PUNCT
ap-7684	38	7	j	j	PROPN
ap-7684	38	8	vj	vj	INTJ
ap-7684	38	9	i	i	PRON
ap-7684	38	10	j	j	PROPN
ap-7684	38	11	x	x	PUNCT
ap-7684	38	12	x	x	X
ap-7684	38	13	y	y	PROPN
ap-7684	38	14	figure	figure	NOUN
ap-7684	38	15	1	1	NUM
ap-7684	38	16	.	.	PUNCT
ap-7684	38	17	shape	shape	NOUN
ap-7684	38	18	functions	function	NOUN
ap-7684	38	19	,	,	PUNCT
ap-7684	38	20	dofs	dof	NOUN
ap-7684	38	21	and	and	CCONJ
ap-7684	38	22	conjugate	conjugate	ADJ
ap-7684	38	23	nodal	nodal	NOUN
ap-7684	38	24	forces	force	NOUN
ap-7684	38	25	of	of	ADP
ap-7684	38	26	the	the	DET
ap-7684	38	27	tt	tt	PROPN
ap-7684	38	28	element	element	PROPN
ap-7684	38	29	lateral	lateral	ADJ
ap-7684	38	30	displacement	displacement	NOUN
ap-7684	38	31	vj	vj	NOUN
ap-7684	38	32	of	of	ADP
ap-7684	38	33	node	node	PROPN
ap-7684	38	34	j	j	PROPN
ap-7684	38	35	and	and	CCONJ
ap-7684	38	36	for	for	ADP
ap-7684	38	37	the	the	DET
ap-7684	38	38	axial	axial	ADJ
ap-7684	38	39	displacement	displacement	NOUN
ap-7684	38	40	ui	ui	PROPN
ap-7684	38	41	,	,	PUNCT
ap-7684	38	42	b.	b.	PROPN
ap-7684	38	43	axial	axial	ADJ
ap-7684	38	44	and	and	CCONJ
ap-7684	38	45	lateral	lateral	ADJ
ap-7684	38	46	directions	direction	NOUN
ap-7684	38	47	denote	denote	VERB
ap-7684	38	48	the	the	DET
ap-7684	38	49	element	element	NOUN
ap-7684	38	50	local	local	ADJ
ap-7684	38	51	x	x	X
ap-7684	38	52	and	and	CCONJ
ap-7684	38	53	y	y	PROPN
ap-7684	38	54	directions	direction	NOUN
ap-7684	38	55	,	,	PUNCT
ap-7684	38	56	indices	indice	VERB
ap-7684	38	57	t	t	PROPN
ap-7684	38	58	and	and	CCONJ
ap-7684	38	59	b	b	PROPN
ap-7684	38	60	denote	denote	VERB
ap-7684	38	61	the	the	DET
ap-7684	38	62	top	top	ADJ
ap-7684	38	63	and	and	CCONJ
ap-7684	38	64	bottom	bottom	ADJ
ap-7684	38	65	faces	face	NOUN
ap-7684	38	66	later	later	ADV
ap-7684	38	67	also	also	ADV
ap-7684	38	68	extrados	extrado	VERB
ap-7684	38	69	and	and	CCONJ
ap-7684	38	70	intrados	intrado	NOUN
ap-7684	38	71	of	of	ADP
ap-7684	38	72	the	the	DET
ap-7684	38	73	arch	arch	NOUN
ap-7684	38	74	.	.	PUNCT
ap-7684	39	1	the	the	DET
ap-7684	39	2	local	local	ADJ
ap-7684	39	3	x	x	VERB
ap-7684	39	4	axis	axis	NOUN
ap-7684	39	5	goes	go	VERB
ap-7684	39	6	from	from	ADP
ap-7684	39	7	node	node	PROPN
ap-7684	39	8	i	i	PRON
ap-7684	39	9	to	to	PART
ap-7684	39	10	node	node	VERB
ap-7684	39	11	j.	j.	PROPN
ap-7684	40	1	the	the	DET
ap-7684	40	2	deflection	deflection	NOUN
ap-7684	40	3	line	line	NOUN
ap-7684	40	4	is	be	AUX
ap-7684	40	5	parabolic	parabolic	ADJ
ap-7684	40	6	and	and	CCONJ
ap-7684	40	7	symmetric	symmetric	ADJ
ap-7684	40	8	.	.	PUNCT
ap-7684	41	1	it	it	PRON
ap-7684	41	2	’s	’	VERB
ap-7684	41	3	single	single	ADJ
ap-7684	41	4	free	free	ADJ
ap-7684	41	5	parameter	parameter	NOUN
ap-7684	41	6	is	be	AUX
ap-7684	41	7	determined	determine	VERB
ap-7684	41	8	so	so	SCONJ
ap-7684	41	9	that	that	SCONJ
ap-7684	41	10	the	the	DET
ap-7684	41	11	shear	shear	NOUN
ap-7684	41	12	strain	strain	NOUN
ap-7684	41	13	energy	energy	NOUN
ap-7684	41	14	is	be	AUX
ap-7684	41	15	minimum	minimum	ADJ
ap-7684	41	16	for	for	ADP
ap-7684	41	17	any	any	DET
ap-7684	41	18	imposed	impose	VERB
ap-7684	41	19	node	node	ADJ
ap-7684	41	20	displacements	displacement	NOUN
ap-7684	41	21	.	.	PUNCT
ap-7684	42	1	analogous	analogous	ADJ
ap-7684	42	2	shape	shape	NOUN
ap-7684	42	3	functions	function	NOUN
ap-7684	42	4	are	be	AUX
ap-7684	42	5	valid	valid	ADJ
ap-7684	42	6	for	for	ADP
ap-7684	42	7	all	all	PRON
ap-7684	42	8	four	four	NUM
ap-7684	42	9	axial	axial	ADJ
ap-7684	42	10	dofs	dof	NOUN
ap-7684	42	11	ui	ui	PROPN
ap-7684	42	12	/	/	SYM
ap-7684	42	13	j	j	PROPN
ap-7684	42	14	,	,	PUNCT
ap-7684	42	15	t	t	PROPN
ap-7684	42	16	/	/	SYM
ap-7684	42	17	b	b	PROPN
ap-7684	42	18	and	and	CCONJ
ap-7684	42	19	the	the	DET
ap-7684	42	20	same	same	ADJ
ap-7684	42	21	applies	apply	VERB
ap-7684	42	22	to	to	ADP
ap-7684	42	23	the	the	DET
ap-7684	42	24	two	two	NUM
ap-7684	42	25	lateral	lateral	ADJ
ap-7684	42	26	dofs	dof	NOUN
ap-7684	42	27	vi	vi	PROPN
ap-7684	42	28	/	/	SYM
ap-7684	42	29	j	j	PROPN
ap-7684	42	30	.	.	PUNCT
ap-7684	43	1	the	the	DET
ap-7684	43	2	cross	cross	ADJ
ap-7684	43	3	-	-	ADJ
ap-7684	43	4	sections	section	NOUN
ap-7684	43	5	remain	remain	VERB
ap-7684	43	6	straight	straight	ADJ
ap-7684	43	7	but	but	CCONJ
ap-7684	43	8	not	not	PART
ap-7684	43	9	normal	normal	ADJ
ap-7684	43	10	to	to	ADP
ap-7684	43	11	the	the	DET
ap-7684	43	12	deflected	deflected	ADJ
ap-7684	43	13	beam	beam	NOUN
ap-7684	43	14	axis	axis	NOUN
ap-7684	43	15	.	.	PUNCT
ap-7684	44	1	in	in	ADP
ap-7684	44	2	an	an	DET
ap-7684	44	3	isoparametric	isoparametric	ADJ
ap-7684	44	4	beam	beam	NOUN
ap-7684	44	5	element	element	NOUN
ap-7684	44	6	(	(	PUNCT
ap-7684	44	7	linear	linear	ADJ
ap-7684	44	8	variation	variation	NOUN
ap-7684	44	9	of	of	ADP
ap-7684	44	10	the	the	DET
ap-7684	44	11	cross	cross	NOUN
ap-7684	44	12	-	-	NOUN
ap-7684	44	13	section	section	NOUN
ap-7684	44	14	rotations	rotation	NOUN
ap-7684	44	15	and	and	CCONJ
ap-7684	44	16	shear	shear	NOUN
ap-7684	44	17	deformation	deformation	NOUN
ap-7684	44	18	,	,	PUNCT
ap-7684	44	19	axial	axial	ADJ
ap-7684	44	20	strain	strain	NOUN
ap-7684	44	21	and	and	CCONJ
ap-7684	44	22	lateral	lateral	ADJ
ap-7684	44	23	deflections	deflection	NOUN
ap-7684	44	24	along	along	ADP
ap-7684	44	25	the	the	DET
ap-7684	44	26	beam	beam	NOUN
ap-7684	44	27	axis	axis	NOUN
ap-7684	44	28	)	)	PUNCT
ap-7684	44	29	,	,	PUNCT
ap-7684	44	30	there	there	PRON
ap-7684	44	31	would	would	AUX
ap-7684	44	32	be	be	AUX
ap-7684	44	33	no	no	DET
ap-7684	44	34	deflections	deflection	NOUN
ap-7684	44	35	for	for	ADP
ap-7684	44	36	the	the	DET
ap-7684	44	37	ui	ui	PROPN
ap-7684	44	38	/	/	SYM
ap-7684	44	39	j	j	PROPN
ap-7684	44	40	,	,	PUNCT
ap-7684	44	41	t	t	PROPN
ap-7684	44	42	dofs	dof	NOUN
ap-7684	44	43	.	.	PUNCT
ap-7684	45	1	the	the	DET
ap-7684	45	2	element	element	NOUN
ap-7684	45	3	is	be	AUX
ap-7684	45	4	known	know	VERB
ap-7684	45	5	to	to	PART
ap-7684	45	6	lock	lock	VERB
ap-7684	45	7	for	for	ADP
ap-7684	45	8	small	small	ADJ
ap-7684	45	9	depths	depth	NOUN
ap-7684	45	10	of	of	ADP
ap-7684	45	11	the	the	DET
ap-7684	45	12	beam	beam	NOUN
ap-7684	45	13	owing	owe	VERB
ap-7684	45	14	to	to	ADP
ap-7684	45	15	excessive	excessive	ADJ
ap-7684	45	16	work	work	NOUN
ap-7684	45	17	of	of	ADP
ap-7684	45	18	the	the	DET
ap-7684	45	19	shear	shear	NOUN
ap-7684	45	20	deformation	deformation	NOUN
ap-7684	45	21	.	.	PUNCT
ap-7684	46	1	the	the	DET
ap-7684	46	2	present	present	ADJ
ap-7684	46	3	element	element	NOUN
ap-7684	46	4	features	feature	VERB
ap-7684	46	5	a	a	DET
ap-7684	46	6	constant	constant	ADJ
ap-7684	46	7	shear	shear	NOUN
ap-7684	46	8	deformation	deformation	NOUN
ap-7684	46	9	since	since	SCONJ
ap-7684	46	10	the	the	DET
ap-7684	46	11	antisymmetric	antisymmetric	NOUN
ap-7684	46	12	(	(	PUNCT
ap-7684	46	13	with	with	ADP
ap-7684	46	14	respect	respect	NOUN
ap-7684	46	15	to	to	ADP
ap-7684	46	16	the	the	DET
ap-7684	46	17	element	element	ADJ
ap-7684	46	18	centre	centre	NOUN
ap-7684	46	19	)	)	PUNCT
ap-7684	46	20	part	part	NOUN
ap-7684	46	21	of	of	ADP
ap-7684	46	22	the	the	DET
ap-7684	46	23	cross	cross	NOUN
ap-7684	46	24	-	-	NOUN
ap-7684	46	25	section	section	NOUN
ap-7684	46	26	rotations	rotation	NOUN
ap-7684	46	27	is	be	AUX
ap-7684	46	28	assigned	assign	VERB
ap-7684	46	29	to	to	ADP
ap-7684	46	30	a	a	DET
ap-7684	46	31	constant	constant	ADJ
ap-7684	46	32	curvature	curvature	NOUN
ap-7684	46	33	of	of	ADP
ap-7684	46	34	the	the	DET
ap-7684	46	35	deflection	deflection	NOUN
ap-7684	46	36	line	line	NOUN
ap-7684	46	37	.	.	PUNCT
ap-7684	47	1	the	the	DET
ap-7684	47	2	element	element	NOUN
ap-7684	47	3	dofs	dof	NOUN
ap-7684	47	4	are	be	AUX
ap-7684	47	5	ordered	order	VERB
ap-7684	47	6	in	in	ADP
ap-7684	47	7	the	the	DET
ap-7684	47	8	{	{	PUNCT
ap-7684	47	9	u	u	NOUN
ap-7684	47	10	}	}	PUNCT
ap-7684	47	11	matrix	matrix	NOUN
ap-7684	47	12	,	,	PUNCT
ap-7684	47	13	{	{	PUNCT
ap-7684	47	14	u	u	NOUN
ap-7684	47	15	}	}	PUNCT
ap-7684	47	16	=	=	SYM
ap-7684	47	17	{	{	PUNCT
ap-7684	47	18	{	{	PUNCT
ap-7684	47	19	u}i	u}i	NOUN
ap-7684	47	20	{	{	PUNCT
ap-7684	47	21	u}j	u}j	PROPN
ap-7684	47	22	}	}	PUNCT
ap-7684	47	23	,	,	PUNCT
ap-7684	47	24	{	{	PUNCT
ap-7684	47	25	u}n	u}n	ADP
ap-7684	47	26	=	=	PUNCT
ap-7684	47	27			NOUN
ap-7684	47	28	un	un	PROPN
ap-7684	47	29	,	,	PUNCT
ap-7684	47	30	t	t	PROPN
ap-7684	47	31	vn	vn	PROPN
ap-7684	47	32	un	un	PROPN
ap-7684	47	33	,	,	PUNCT
ap-7684	47	34	b	b	X
ap-7684	47	35			NOUN
ap-7684	47	36	,	,	PUNCT
ap-7684	47	37	n	n	PROPN
ap-7684	47	38	=	=	SYM
ap-7684	47	39	i	i	PROPN
ap-7684	47	40	,	,	PUNCT
ap-7684	48	1	j	j	PROPN
ap-7684	48	2	linear	linear	VERB
ap-7684	48	3	normal	normal	ADJ
ap-7684	48	4	and	and	CCONJ
ap-7684	48	5	constant	constant	ADJ
ap-7684	48	6	shear	shear	NOUN
ap-7684	48	7	element	element	NOUN
ap-7684	48	8	strains	strain	NOUN
ap-7684	48	9	are	be	AUX
ap-7684	48	10	specified	specify	VERB
ap-7684	48	11	by	by	ADP
ap-7684	48	12	top	top	ADJ
ap-7684	48	13	and	and	CCONJ
ap-7684	48	14	bottom	bottom	ADJ
ap-7684	48	15	face	face	NOUN
ap-7684	48	16	normal	normal	ADJ
ap-7684	48	17	strains	strain	NOUN
ap-7684	49	1	εt	εt	INTJ
ap-7684	49	2	,	,	PUNCT
ap-7684	49	3	εb	εb	PRON
ap-7684	49	4	and	and	CCONJ
ap-7684	49	5	shear	shear	NOUN
ap-7684	49	6	strain	strain	NOUN
ap-7684	49	7	γ	γ	PROPN
ap-7684	49	8	,	,	PUNCT
ap-7684	49	9	ordered	order	VERB
ap-7684	49	10	in	in	ADP
ap-7684	49	11	the	the	DET
ap-7684	49	12	matrix	matrix	NOUN
ap-7684	49	13	of	of	ADP
ap-7684	49	14	internal	internal	ADJ
ap-7684	49	15	strains	strain	NOUN
ap-7684	49	16	ε	ε	PROPN
ap-7684	49	17	=	=	SYM
ap-7684	49	18	{	{	PUNCT
ap-7684	49	19	εt	εt	PROPN
ap-7684	49	20	,	,	PUNCT
ap-7684	49	21	εb	εb	ADP
ap-7684	49	22	,	,	PUNCT
ap-7684	49	23	γ}t	γ}t	PROPN
ap-7684	49	24	.	.	PUNCT
ap-7684	50	1	shear	shear	NOUN
ap-7684	50	2	strain	strain	VERB
ap-7684	50	3	γ	γ	NOUN
ap-7684	50	4	and	and	CCONJ
ap-7684	50	5	conjugate	conjugate	ADJ
ap-7684	50	6	shear	shear	NOUN
ap-7684	50	7	stress	stress	NOUN
ap-7684	50	8	τ	τ	PROPN
ap-7684	50	9	have	have	VERB
ap-7684	50	10	opposite	opposite	ADJ
ap-7684	50	11	signs	sign	NOUN
ap-7684	50	12	than	than	ADP
ap-7684	50	13	usual	usual	ADJ
ap-7684	50	14	in	in	ADP
ap-7684	50	15	elasticity	elasticity	NOUN
ap-7684	50	16	,	,	PUNCT
ap-7684	50	17	γ	γ	PROPN
ap-7684	50	18	=	=	SYM
ap-7684	50	19	−(∂ux/∂y+∂uy/∂x)/2	−(∂ux/∂y+∂uy/∂x)/2	PROPN
ap-7684	50	20	.	.	PUNCT
ap-7684	51	1	the	the	DET
ap-7684	51	2	element	element	ADJ
ap-7684	51	3	geometric	geometric	ADJ
ap-7684	51	4	matrix	matrix	NOUN
ap-7684	51	5	[	[	X
ap-7684	51	6	b	b	X
ap-7684	51	7	]	]	X
ap-7684	51	8	reads	read	VERB
ap-7684	51	9	:	:	PUNCT
ap-7684	52	1	[	[	X
ap-7684	52	2	b	b	X
ap-7684	52	3	]	]	X
ap-7684	52	4	=	=	SYM
ap-7684	52	5	1	1	NUM
ap-7684	52	6	l	l	NOUN
ap-7684	52	7	[	[	PUNCT
ap-7684	52	8	−1	−1	NOUN
ap-7684	52	9	0	0	NUM
ap-7684	52	10	0	0	NUM
ap-7684	52	11	1	1	NUM
ap-7684	52	12	0	0	NUM
ap-7684	52	13	0	0	NUM
ap-7684	52	14	0	0	NUM
ap-7684	52	15	0	0	NUM
ap-7684	52	16	−1	−1	NOUN
ap-7684	52	17	0	0	NUM
ap-7684	52	18	0	0	NUM
ap-7684	52	19	1	1	NUM
ap-7684	52	20	l/2	l/2	NUM
ap-7684	52	21	/	/	SYM
ap-7684	52	22	d	d	NOUN
ap-7684	52	23	−1	−1	NOUN
ap-7684	52	24	−l/2	−l/2	PROPN
ap-7684	52	25	/	/	SYM
ap-7684	52	26	d	d	X
ap-7684	52	27	l/2	l/2	PROPN
ap-7684	52	28	/	/	SYM
ap-7684	52	29	d	d	PROPN
ap-7684	52	30	1	1	NUM
ap-7684	52	31	−l/2	−l/2	PROPN
ap-7684	52	32	/	/	SYM
ap-7684	52	33	d	d	NOUN
ap-7684	52	34	]	]	PUNCT
ap-7684	52	35	conjugate	conjugate	ADJ
ap-7684	52	36	to	to	ADP
ap-7684	52	37	node	node	ADJ
ap-7684	52	38	displacements	displacement	NOUN
ap-7684	52	39	{	{	PUNCT
ap-7684	52	40	u	u	NOUN
ap-7684	52	41	}	}	PUNCT
ap-7684	52	42	are	be	AUX
ap-7684	52	43	the	the	DET
ap-7684	52	44	nodal	nodal	ADJ
ap-7684	52	45	forces	force	NOUN
ap-7684	52	46	{	{	PUNCT
ap-7684	52	47	x	x	NOUN
ap-7684	52	48	}	}	PUNCT
ap-7684	52	49	,	,	PUNCT
ap-7684	52	50	conjugate	conjugate	ADJ
ap-7684	52	51	to	to	ADP
ap-7684	52	52	{	{	PUNCT
ap-7684	52	53	ε	ε	PROPN
ap-7684	52	54	}	}	PUNCT
ap-7684	52	55	is	be	AUX
ap-7684	52	56	the	the	DET
ap-7684	52	57	matrix	matrix	NOUN
ap-7684	52	58	of	of	ADP
ap-7684	52	59	internal	internal	ADJ
ap-7684	52	60	forces	force	NOUN
ap-7684	52	61	{	{	PUNCT
ap-7684	52	62	s	s	NOUN
ap-7684	52	63	}	}	PUNCT
ap-7684	52	64	.	.	PUNCT
ap-7684	53	1	the	the	DET
ap-7684	53	2	nodal	nodal	NOUN
ap-7684	53	3	forces	force	NOUN
ap-7684	53	4	in	in	ADP
ap-7684	53	5	terms	term	NOUN
ap-7684	53	6	of	of	ADP
ap-7684	53	7	nodal	nodal	NOUN
ap-7684	53	8	displacements	displacement	NOUN
ap-7684	53	9	read	read	VERB
ap-7684	53	10	{	{	PUNCT
ap-7684	53	11	x	x	NOUN
ap-7684	53	12	}	}	PUNCT
ap-7684	53	13	=	=	PUNCT
ap-7684	54	1	[	[	X
ap-7684	54	2	b]t	b]t	NOUN
ap-7684	54	3	{	{	PUNCT
ap-7684	54	4	s}({ε	s}({ε	NOUN
ap-7684	54	5	}	}	PUNCT
ap-7684	54	6	)	)	PUNCT
ap-7684	54	7	=	=	PUNCT
ap-7684	55	1	[	[	X
ap-7684	55	2	b]t	b]t	X
ap-7684	55	3	{	{	PUNCT
ap-7684	55	4	s}([b]{u	s}([b]{u	NOUN
ap-7684	55	5	}	}	PUNCT
ap-7684	55	6	)	)	PUNCT
ap-7684	55	7	(	(	PUNCT
ap-7684	55	8	1	1	X
ap-7684	55	9	)	)	PUNCT
ap-7684	55	10	constitutive	constitutive	ADJ
ap-7684	55	11	equations	equation	NOUN
ap-7684	55	12	for	for	ADP
ap-7684	55	13	the	the	DET
ap-7684	55	14	cross	cross	NOUN
ap-7684	55	15	-	-	NOUN
ap-7684	55	16	section	section	NOUN
ap-7684	55	17	are	be	AUX
ap-7684	55	18	developed	develop	VERB
ap-7684	55	19	separately	separately	ADV
ap-7684	55	20	for	for	ADP
ap-7684	55	21	the	the	DET
ap-7684	55	22	bending	bending	NOUN
ap-7684	55	23	,	,	PUNCT
ap-7684	55	24	the	the	DET
ap-7684	55	25	first	first	ADJ
ap-7684	55	26	two	two	NUM
ap-7684	55	27	members	member	NOUN
ap-7684	55	28	of	of	ADP
ap-7684	55	29	{	{	PUNCT
ap-7684	55	30	ε	ε	PROPN
ap-7684	55	31	}	}	PUNCT
ap-7684	55	32	and	and	CCONJ
ap-7684	55	33	{	{	PUNCT
ap-7684	55	34	s}int	s}int	NOUN
ap-7684	55	35	.	.	PUNCT
ap-7684	56	1	ε	ε	PROPN
ap-7684	56	2	ξ	ξ	PROPN
ap-7684	56	3	d	d	PROPN
ap-7684	56	4	d	d	X
ap-7684	56	5	ζ	ζ	PROPN
ap-7684	56	6	t	t	PROPN
ap-7684	56	7	σ	σ	PROPN
ap-7684	56	8	:	:	PUNCT
ap-7684	56	9	>	>	SYM
ap-7684	56	10	0	0	PUNCT
ap-7684	56	11	ε	ε	PROPN
ap-7684	56	12	σ	σ	PROPN
ap-7684	56	13	:	:	PUNCT
ap-7684	56	14	εt<0	εt<0	PROPN
ap-7684	56	15	tz	tz	PROPN
ap-7684	56	16	(	(	PUNCT
ap-7684	56	17	)	)	PUNCT
ap-7684	56	18	z	z	NOUN
ap-7684	56	19	(	(	PUNCT
ap-7684	56	20	)	)	PUNCT
ap-7684	56	21	ζ	ζ	PROPN
ap-7684	56	22	b	b	PROPN
ap-7684	56	23	b	b	PROPN
ap-7684	56	24	σ	σ	PROPN
ap-7684	56	25	:	:	PUNCT
ap-7684	56	26	0	0	NUM
ap-7684	56	27	ε	ε	PROPN
ap-7684	56	28	1	1	NUM
ap-7684	56	29	1	1	NUM
ap-7684	56	30	ξ	ξ	SYM
ap-7684	56	31	1	1	NUM
ap-7684	56	32	1	1	NUM
ap-7684	56	33	ε	ε	PROPN
ap-7684	56	34	b	b	PROPN
ap-7684	56	35	>	>	X
ap-7684	56	36	0<0	0<0	X
ap-7684	56	37	ξ	ξ	PROPN
ap-7684	56	38	d	d	X
ap-7684	56	39	ξ	ξ	PRON
ap-7684	56	40	ζ	ζ	NOUN
ap-7684	56	41	figure	figure	NOUN
ap-7684	56	42	2	2	NUM
ap-7684	56	43	.	.	PUNCT
ap-7684	56	44	stress	stress	NOUN
ap-7684	56	45	/	/	SYM
ap-7684	56	46	strain	strain	NOUN
ap-7684	56	47	diagram	diagram	NOUN
ap-7684	56	48	,	,	PUNCT
ap-7684	56	49	strain	strain	NOUN
ap-7684	56	50	shape	shape	NOUN
ap-7684	56	51	functions	function	NOUN
ap-7684	56	52	and	and	CCONJ
ap-7684	56	53	normal	normal	ADJ
ap-7684	56	54	stress	stress	NOUN
ap-7684	56	55	diagrams	diagram	NOUN
ap-7684	56	56	of	of	ADP
ap-7684	56	57	the	the	DET
ap-7684	56	58	tt	tt	PROPN
ap-7684	56	59	element	element	NOUN
ap-7684	56	60	2.1	2.1	NUM
ap-7684	56	61	.	.	PUNCT
ap-7684	57	1	constitutive	constitutive	ADJ
ap-7684	57	2	equations	equation	NOUN
ap-7684	57	3	for	for	ADP
ap-7684	57	4	bending	bend	VERB
ap-7684	57	5	no	no	DET
ap-7684	57	6	-	-	PUNCT
ap-7684	57	7	tension	tension	NOUN
ap-7684	57	8	linear	linear	ADJ
ap-7684	57	9	elastic	elastic	ADJ
ap-7684	57	10	material	material	NOUN
ap-7684	57	11	is	be	AUX
ap-7684	57	12	assumed	assume	VERB
ap-7684	57	13	,	,	PUNCT
ap-7684	57	14	see	see	VERB
ap-7684	57	15	the	the	DET
ap-7684	57	16	stress	stress	NOUN
ap-7684	57	17	-	-	PUNCT
ap-7684	57	18	strain	strain	NOUN
ap-7684	57	19	diagram	diagram	NOUN
ap-7684	57	20	in	in	ADP
ap-7684	57	21	figure	figure	NOUN
ap-7684	57	22	2	2	NUM
ap-7684	57	23	.	.	PUNCT
ap-7684	58	1	the	the	DET
ap-7684	58	2	no	no	DET
ap-7684	58	3	-	-	PUNCT
ap-7684	58	4	tension	tension	NOUN
ap-7684	58	5	condition	condition	NOUN
ap-7684	58	6	is	be	AUX
ap-7684	58	7	applied	apply	VERB
ap-7684	58	8	to	to	ADP
ap-7684	58	9	the	the	DET
ap-7684	58	10	normal	normal	ADJ
ap-7684	58	11	stress	stress	NOUN
ap-7684	58	12	in	in	ADP
ap-7684	58	13	crosssections	crosssection	NOUN
ap-7684	58	14	and	and	CCONJ
ap-7684	58	15	bed	bed	NOUN
ap-7684	58	16	joints	joint	NOUN
ap-7684	58	17	of	of	ADP
ap-7684	58	18	the	the	DET
ap-7684	58	19	arch	arch	NOUN
ap-7684	58	20	.	.	PUNCT
ap-7684	59	1	though	though	SCONJ
ap-7684	59	2	simple	simple	ADJ
ap-7684	59	3	,	,	PUNCT
ap-7684	59	4	it	it	PRON
ap-7684	59	5	makes	make	VERB
ap-7684	59	6	possible	possible	ADJ
ap-7684	59	7	the	the	DET
ap-7684	59	8	most	most	ADV
ap-7684	59	9	frequent	frequent	ADJ
ap-7684	59	10	type	type	NOUN
ap-7684	59	11	of	of	ADP
ap-7684	59	12	failure	failure	NOUN
ap-7684	59	13	of	of	ADP
ap-7684	59	14	the	the	DET
ap-7684	59	15	stone	stone	NOUN
ap-7684	59	16	masonry	masonry	NOUN
ap-7684	59	17	arch	arch	ADJ
ap-7684	59	18	bridges	bridge	NOUN
ap-7684	59	19	.	.	PUNCT
ap-7684	60	1	the	the	DET
ap-7684	60	2	normal	normal	ADJ
ap-7684	60	3	strain	strain	NOUN
ap-7684	60	4	ε	ε	PROPN
ap-7684	60	5	is	be	AUX
ap-7684	60	6	determined	determine	VERB
ap-7684	60	7	by	by	ADP
ap-7684	60	8	the	the	DET
ap-7684	60	9	top	top	ADJ
ap-7684	60	10	and	and	CCONJ
ap-7684	60	11	bottom	bottom	ADJ
ap-7684	60	12	face	face	NOUN
ap-7684	60	13	strains	strain	VERB
ap-7684	61	1	εt	εt	PROPN
ap-7684	61	2	,	,	PUNCT
ap-7684	61	3	εb	εb	ADP
ap-7684	61	4	through	through	ADP
ap-7684	61	5	the	the	DET
ap-7684	61	6	shape	shape	NOUN
ap-7684	61	7	functions	function	NOUN
ap-7684	61	8	shown	show	VERB
ap-7684	61	9	in	in	ADP
ap-7684	61	10	the	the	DET
ap-7684	61	11	centre	centre	NOUN
ap-7684	61	12	of	of	ADP
ap-7684	61	13	figure	figure	NOUN
ap-7684	61	14	2	2	NUM
ap-7684	61	15	.	.	PUNCT
ap-7684	61	16	ε	ε	PROPN
ap-7684	61	17	=	=	SYM
ap-7684	61	18	zt(ζ)εt	zt(ζ)εt	PROPN
ap-7684	62	1	+	+	CCONJ
ap-7684	62	2	zb(ζ)εb	zb(ζ)εb	NUM
ap-7684	62	3	constitutive	constitutive	ADJ
ap-7684	62	4	equations	equation	NOUN
ap-7684	62	5	of	of	ADP
ap-7684	62	6	the	the	DET
ap-7684	62	7	cross	cros	NOUN
ap-7684	62	8	-	-	NOUN
ap-7684	62	9	sections	section	NOUN
ap-7684	62	10	are	be	AUX
ap-7684	62	11	defined	define	VERB
ap-7684	62	12	in	in	ADP
ap-7684	62	13	terms	term	NOUN
ap-7684	62	14	of	of	ADP
ap-7684	62	15	dimensionless	dimensionless	NOUN
ap-7684	62	16	functions	function	NOUN
ap-7684	62	17	st	st	PROPN
ap-7684	62	18	(	(	PUNCT
ap-7684	62	19	)	)	PUNCT
ap-7684	62	20	and	and	CCONJ
ap-7684	62	21	sb	sb	PROPN
ap-7684	62	22	(	(	PUNCT
ap-7684	62	23	)	)	PUNCT
ap-7684	62	24	of	of	ADP
ap-7684	62	25	dimensionless	dimensionless	NOUN
ap-7684	62	26	arguments	argument	NOUN
ap-7684	62	27	:	:	PUNCT
ap-7684	62	28	st(εt	st(εt	NOUN
ap-7684	62	29	,	,	PUNCT
ap-7684	62	30	εb	εb	ADP
ap-7684	62	31	)	)	PUNCT
ap-7684	62	32	=	=	SYM
ap-7684	63	1	∫	∫	PROPN
ap-7684	63	2	1	1	NUM
ap-7684	63	3	0	0	NUM
ap-7684	63	4	zt(ζ)s(εtzt(ζ	zt(ζ)s(εtzt(ζ	NUM
ap-7684	63	5	)	)	PUNCT
ap-7684	64	1	+	+	CCONJ
ap-7684	64	2	εb	εb	ADP
ap-7684	64	3	,	,	PUNCT
ap-7684	64	4	xzb(ζ))dζ	xzb(ζ))dζ	NOUN
ap-7684	64	5	sb(εt	sb(εt	NOUN
ap-7684	64	6	,	,	PUNCT
ap-7684	64	7	εb	εb	ADP
ap-7684	64	8	)	)	PUNCT
ap-7684	64	9	=	=	SYM
ap-7684	64	10	∫	∫	PROPN
ap-7684	64	11	1	1	NUM
ap-7684	64	12	0	0	NUM
ap-7684	64	13	zb(ζ)s(εtzt(ζ	zb(ζ)s(εtzt(ζ	NUM
ap-7684	64	14	)	)	PUNCT
ap-7684	65	1	+	+	NUM
ap-7684	65	2	εbzb(ζ))dζ	εbzb(ζ))dζ	NOUN
ap-7684	65	3	,	,	PUNCT
ap-7684	65	4	(	(	PUNCT
ap-7684	65	5	2	2	X
ap-7684	65	6	)	)	PUNCT
ap-7684	65	7	the	the	DET
ap-7684	65	8	cross	cross	ADJ
ap-7684	65	9	-	-	ADJ
ap-7684	65	10	section	section	ADJ
ap-7684	65	11	forces	force	NOUN
ap-7684	65	12	are	be	AUX
ap-7684	65	13	st	st	PROPN
ap-7684	65	14	/	/	SYM
ap-7684	65	15	b	b	PROPN
ap-7684	65	16	=	=	PUNCT
ap-7684	65	17	ebdst	ebdst	NOUN
ap-7684	65	18	/	/	SYM
ap-7684	65	19	b	b	PROPN
ap-7684	65	20	=	=	SYM
ap-7684	65	21	east	east	PROPN
ap-7684	65	22	/	/	SYM
ap-7684	65	23	b	b	PROPN
ap-7684	65	24	(	(	PUNCT
ap-7684	65	25	valid	valid	ADJ
ap-7684	65	26	for	for	ADP
ap-7684	65	27	both	both	DET
ap-7684	65	28	t	t	PROPN
ap-7684	65	29	and	and	CCONJ
ap-7684	65	30	b	b	NOUN
ap-7684	65	31	subscripts	subscript	NOUN
ap-7684	65	32	,	,	PUNCT
ap-7684	65	33	where	where	SCONJ
ap-7684	65	34	e	e	NOUN
ap-7684	65	35	is	be	AUX
ap-7684	65	36	the	the	DET
ap-7684	65	37	young	young	ADJ
ap-7684	65	38	modulus	modulus	NOUN
ap-7684	65	39	,	,	PUNCT
ap-7684	65	40	b	b	X
ap-7684	65	41	the	the	DET
ap-7684	65	42	cross	cross	ADJ
ap-7684	65	43	-	-	ADJ
ap-7684	65	44	section	section	ADJ
ap-7684	65	45	width	width	NOUN
ap-7684	65	46	,	,	PUNCT
ap-7684	65	47	d	d	X
ap-7684	65	48	the	the	DET
ap-7684	65	49	crosssection	crosssection	NOUN
ap-7684	65	50	depth	depth	NOUN
ap-7684	65	51	and	and	CCONJ
ap-7684	65	52	a	a	DET
ap-7684	65	53	its	its	PRON
ap-7684	65	54	area	area	NOUN
ap-7684	65	55	.	.	PUNCT
ap-7684	66	1	functions	function	NOUN
ap-7684	66	2	st	st	PROPN
ap-7684	66	3	/	/	SYM
ap-7684	66	4	b	b	PROPN
ap-7684	66	5	(	(	PUNCT
ap-7684	66	6	)	)	PUNCT
ap-7684	66	7	and	and	CCONJ
ap-7684	66	8	their	their	PRON
ap-7684	66	9	derivatives	derivative	NOUN
ap-7684	66	10	with	with	ADP
ap-7684	66	11	respect	respect	NOUN
ap-7684	66	12	to	to	ADP
ap-7684	66	13	εt	εt	PROPN
ap-7684	66	14	,	,	PUNCT
ap-7684	66	15	εb	εb	PRON
ap-7684	66	16	have	have	VERB
ap-7684	66	17	to	to	PART
ap-7684	66	18	be	be	AUX
ap-7684	66	19	developed	develop	VERB
ap-7684	66	20	separately	separately	ADV
ap-7684	66	21	for	for	ADP
ap-7684	66	22	four	four	NUM
ap-7684	66	23	possible	possible	ADJ
ap-7684	66	24	strain	strain	NOUN
ap-7684	66	25	states	state	NOUN
ap-7684	66	26	:	:	PUNCT
ap-7684	66	27	algorithm	algorithm	NOUN
ap-7684	66	28	start	start	VERB
ap-7684	66	29	when	when	SCONJ
ap-7684	66	30	εt	εt	PROPN
ap-7684	66	31	>	>	X
ap-7684	66	32	0	0	PUNCT
ap-7684	66	33	and	and	CCONJ
ap-7684	66	34	εb	εb	ADP
ap-7684	66	35	>	>	X
ap-7684	66	36	0	0	PUNCT
ap-7684	67	1	then	then	ADV
ap-7684	67	2	all	all	DET
ap-7684	67	3	internal	internal	ADJ
ap-7684	67	4	forces	force	NOUN
ap-7684	67	5	are	be	AUX
ap-7684	67	6	0	0	NUM
ap-7684	67	7	,	,	PUNCT
ap-7684	67	8	the	the	DET
ap-7684	67	9	cross	cross	NOUN
ap-7684	67	10	-	-	NOUN
ap-7684	67	11	section	section	NOUN
ap-7684	67	12	is	be	AUX
ap-7684	67	13	totally	totally	ADV
ap-7684	67	14	disintegrated	disintegrate	VERB
ap-7684	67	15	.	.	PUNCT
ap-7684	68	1	all	all	DET
ap-7684	68	2	stresses	stress	NOUN
ap-7684	68	3	and	and	CCONJ
ap-7684	68	4	internal	internal	ADJ
ap-7684	68	5	forces	force	NOUN
ap-7684	68	6	vanish	vanish	VERB
ap-7684	68	7	in	in	ADP
ap-7684	68	8	the	the	DET
ap-7684	68	9	element	element	NOUN
ap-7684	68	10	.	.	PUNCT
ap-7684	69	1	when	when	SCONJ
ap-7684	69	2	εt	εt	PROPN
ap-7684	69	3	>	>	X
ap-7684	69	4	0	0	PUNCT
ap-7684	69	5	and	and	CCONJ
ap-7684	69	6	εb	εb	ADP
ap-7684	69	7	<	<	X
ap-7684	69	8	0	0	NUM
ap-7684	69	9	,	,	PUNCT
ap-7684	69	10	then	then	ADV
ap-7684	69	11	(	(	PUNCT
ap-7684	69	12	see	see	VERB
ap-7684	69	13	the	the	DET
ap-7684	69	14	left	left	ADJ
ap-7684	69	15	strain	strain	NOUN
ap-7684	69	16	diagram	diagram	NOUN
ap-7684	69	17	in	in	ADP
ap-7684	69	18	figure	figure	NOUN
ap-7684	69	19	2	2	NUM
ap-7684	69	20	):	):	PUNCT
ap-7684	69	21	ξ	ξ	X
ap-7684	69	22	=	=	PUNCT
ap-7684	69	23	εb	εb	ADP
ap-7684	69	24	εb	εb	ADP
ap-7684	69	25	−	−	PROPN
ap-7684	69	26	εt	εt	INTJ
ap-7684	69	27	st	st	PROPN
ap-7684	69	28	=	=	PROPN
ap-7684	69	29	εbξ	εbξ	PROPN
ap-7684	69	30	2/6	2/6	NUM
ap-7684	69	31	,	,	PUNCT
ap-7684	69	32	sb	sb	PROPN
ap-7684	69	33	=	=	PROPN
ap-7684	69	34	(	(	PUNCT
ap-7684	69	35	0.5	0.5	NUM
ap-7684	69	36	−	−	PROPN
ap-7684	69	37	ξ/6)ξεb	ξ/6)ξεb	PROPN
ap-7684	69	38	∂st	∂st	PROPN
ap-7684	69	39	∂εt	∂εt	NOUN
ap-7684	69	40	=	=	PUNCT
ap-7684	69	41	ξ3/3	ξ3/3	NOUN
ap-7684	69	42	,	,	PUNCT
ap-7684	69	43	∂st	∂st	PROPN
ap-7684	69	44	∂εb	∂εb	NOUN
ap-7684	69	45	=	=	SYM
ap-7684	69	46	(	(	PUNCT
ap-7684	69	47	1	1	NUM
ap-7684	69	48	−	−	PROPN
ap-7684	69	49	2ξ	2ξ	NUM
ap-7684	69	50	εt	εt	INTJ
ap-7684	69	51	εb	εb	ADP
ap-7684	69	52	)	)	PUNCT
ap-7684	69	53	ξ2	ξ2	NOUN
ap-7684	69	54	6	6	NUM
ap-7684	70	1	∂sb	∂sb	PROPN
ap-7684	70	2	∂εt	∂εt	NOUN
ap-7684	70	3	=	=	SYM
ap-7684	70	4	(	(	PUNCT
ap-7684	70	5	0.5−ξ/3)ξ2	0.5−ξ/3)ξ2	NUM
ap-7684	70	6	,	,	PUNCT
ap-7684	70	7	∂sb	∂sb	PROPN
ap-7684	70	8	∂εb	∂εb	PROPN
ap-7684	70	9	=	=	SYM
ap-7684	70	10	(	(	PUNCT
ap-7684	70	11	0.5−	0.5−	X
ap-7684	70	12	ξ	ξ	SYM
ap-7684	70	13	6)ξ−(0.5−	6)ξ−(0.5−	NUM
ap-7684	70	14	ξ	ξ	SYM
ap-7684	70	15	3)ξ2	3)ξ2	NUM
ap-7684	70	16	εt	εt	INTJ
ap-7684	70	17	εb	εb	ADP
ap-7684	70	18	when	when	SCONJ
ap-7684	70	19	εt	εt	PROPN
ap-7684	70	20	<	<	X
ap-7684	70	21	0	0	PUNCT
ap-7684	70	22	and	and	CCONJ
ap-7684	70	23	εb	εb	ADP
ap-7684	70	24	>	>	X
ap-7684	70	25	0	0	NUM
ap-7684	70	26	,	,	PUNCT
ap-7684	70	27	then	then	ADV
ap-7684	70	28	(	(	PUNCT
ap-7684	70	29	see	see	VERB
ap-7684	70	30	the	the	DET
ap-7684	70	31	right	right	ADJ
ap-7684	70	32	strain	strain	NOUN
ap-7684	70	33	diagram	diagram	NOUN
ap-7684	70	34	in	in	ADP
ap-7684	70	35	figure	figure	NOUN
ap-7684	70	36	2	2	NUM
ap-7684	70	37	):	):	PUNCT
ap-7684	71	1	ξ	ξ	X
ap-7684	71	2	=	=	SYM
ap-7684	71	3	εt	εt	INTJ
ap-7684	71	4	εt	εt	PROPN
ap-7684	71	5	−	−	PROPN
ap-7684	71	6	εb	εb	ADP
ap-7684	71	7	294	294	NUM
ap-7684	71	8	vol	vol	NOUN
ap-7684	71	9	.	.	PUNCT
ap-7684	72	1	62	62	NUM
ap-7684	72	2	no	no	INTJ
ap-7684	72	3	.	.	PUNCT
ap-7684	73	1	2/2022	2/2022	PROPN
ap-7684	74	1	a	a	DET
ap-7684	74	2	mindlin	mindlin	PROPN
ap-7684	74	3	shell	shell	PROPN
ap-7684	74	4	finite	finite	PROPN
ap-7684	74	5	element	element	NOUN
ap-7684	74	6	for	for	ADP
ap-7684	74	7	stone	stone	NOUN
ap-7684	74	8	masonry	masonry	NOUN
ap-7684	74	9	bridges	bridge	NOUN
ap-7684	74	10	with	with	ADP
ap-7684	74	11	backfill	backfill	NOUN
ap-7684	74	12	i	i	NOUN
ap-7684	74	13	x	x	PUNCT
ap-7684	75	1	=	=	NOUN
ap-7684	75	2	s	s	NOUN
ap-7684	75	3	+	+	NOUN
ap-7684	75	4	vl/(2d)x	vl/(2d)x	NOUN
ap-7684	75	5	=	=	NOUN
ap-7684	75	6	−s	−s	NOUN
ap-7684	75	7	+	+	NOUN
ap-7684	75	8	vl/(2d	vl/(2d	ADJ
ap-7684	75	9	)	)	PUNCT
ap-7684	76	1	x	x	PUNCT
ap-7684	77	1	=	=	NOUN
ap-7684	77	2	−s	−s	NOUN
ap-7684	77	3	−vl/(2d)b	−vl/(2d)b	PROPN
ap-7684	77	4	t	t	NOUN
ap-7684	77	5	l	l	NOUN
ap-7684	78	1	d	d	X
ap-7684	78	2	x	x	PUNCT
ap-7684	79	1	=	=	NOUN
ap-7684	79	2	s	s	NOUN
ap-7684	79	3	−vl/(2d	−vl/(2d	NOUN
ap-7684	79	4	)	)	PUNCT
ap-7684	79	5	bj	bj	ADP
ap-7684	79	6	tjti	tjti	ADP
ap-7684	79	7	bi	bi	PROPN
ap-7684	79	8	v	v	PROPN
ap-7684	79	9	y	y	PROPN
ap-7684	79	10	=	=	NOUN
ap-7684	79	11	−vi	−vi	NUM
ap-7684	79	12	j	j	X
ap-7684	79	13	y	y	PROPN
ap-7684	79	14	=	=	PROPN
ap-7684	79	15	vj	vj	PROPN
ap-7684	79	16	t	t	PROPN
ap-7684	79	17	b	b	PROPN
ap-7684	79	18	figure	figure	NOUN
ap-7684	79	19	3	3	NUM
ap-7684	79	20	.	.	PUNCT
ap-7684	79	21	element	element	ADJ
ap-7684	79	22	internal	internal	ADJ
ap-7684	79	23	forces	force	NOUN
ap-7684	79	24	{	{	PUNCT
ap-7684	79	25	s	s	NOUN
ap-7684	79	26	}	}	PUNCT
ap-7684	79	27	and	and	CCONJ
ap-7684	79	28	nodal	nodal	ADJ
ap-7684	79	29	forces	force	NOUN
ap-7684	79	30	{	{	PUNCT
ap-7684	79	31	x	x	NOUN
ap-7684	79	32	}	}	PUNCT
ap-7684	79	33	st	st	PROPN
ap-7684	79	34	=	=	SYM
ap-7684	79	35	(	(	PUNCT
ap-7684	79	36	0.5	0.5	NUM
ap-7684	79	37	−	−	PROPN
ap-7684	79	38	ξ	ξ	PROPN
ap-7684	79	39	6)ξεt	6)ξεt	PROPN
ap-7684	79	40	,	,	PUNCT
ap-7684	79	41	sb	sb	PROPN
ap-7684	79	42	=	=	PROPN
ap-7684	79	43	εtξ	εtξ	PROPN
ap-7684	79	44	2/6	2/6	NUM
ap-7684	79	45	∂st	∂st	NOUN
ap-7684	79	46	∂εt	∂εt	NOUN
ap-7684	79	47	=	=	SYM
ap-7684	79	48	(	(	PUNCT
ap-7684	79	49	0.5−	0.5−	X
ap-7684	79	50	ξ	ξ	SYM
ap-7684	79	51	6)ξ−(0.5−	6)ξ−(0.5−	NUM
ap-7684	79	52	ξ	ξ	X
ap-7684	79	53	3)ξ2	3)ξ2	NUM
ap-7684	79	54	εb	εb	ADP
ap-7684	79	55	εt	εt	PROPN
ap-7684	79	56	,	,	PUNCT
ap-7684	79	57	∂st	∂st	PROPN
ap-7684	79	58	∂εb	∂εb	NOUN
ap-7684	79	59	=	=	SYM
ap-7684	79	60	(	(	PUNCT
ap-7684	79	61	0.5−ξ/3)ξ2	0.5−ξ/3)ξ2	NUM
ap-7684	79	62	∂sb	∂sb	PROPN
ap-7684	79	63	∂εt	∂εt	NOUN
ap-7684	79	64	=	=	SYM
ap-7684	79	65	(	(	PUNCT
ap-7684	79	66	1	1	NUM
ap-7684	79	67	−	−	PROPN
ap-7684	79	68	2ξ	2ξ	NUM
ap-7684	79	69	εb	εb	ADP
ap-7684	79	70	εt	εt	PROPN
ap-7684	79	71	)	)	PUNCT
ap-7684	79	72	ξ2	ξ2	NOUN
ap-7684	79	73	6	6	NUM
ap-7684	79	74	,	,	PUNCT
ap-7684	79	75	∂sb	∂sb	PROPN
ap-7684	79	76	∂εb	∂εb	NOUN
ap-7684	79	77	=	=	SYM
ap-7684	79	78	ξ3/3	ξ3/3	NOUN
ap-7684	79	79	when	when	SCONJ
ap-7684	79	80	εt	εt	PROPN
ap-7684	79	81	<	<	X
ap-7684	79	82	0	0	PUNCT
ap-7684	79	83	and	and	CCONJ
ap-7684	79	84	εb	εb	ADP
ap-7684	79	85	<	<	X
ap-7684	79	86	0	0	NUM
ap-7684	79	87	,	,	PUNCT
ap-7684	79	88	then	then	ADV
ap-7684	79	89	the	the	DET
ap-7684	79	90	cross	cross	NOUN
ap-7684	79	91	-	-	NOUN
ap-7684	79	92	section	section	NOUN
ap-7684	79	93	is	be	AUX
ap-7684	79	94	linear	linear	ADJ
ap-7684	79	95	elastic	elastic	ADJ
ap-7684	79	96	and	and	CCONJ
ap-7684	79	97	dimensionless	dimensionless	ADJ
ap-7684	79	98	generalised	generalise	VERB
ap-7684	79	99	forces	force	NOUN
ap-7684	79	100	are	be	AUX
ap-7684	79	101	st	st	PROPN
ap-7684	79	102	/	/	SYM
ap-7684	79	103	b	b	PROPN
ap-7684	79	104	=	=	PUNCT
ap-7684	79	105	(	(	PUNCT
ap-7684	79	106	2εt	2εt	NOUN
ap-7684	79	107	/	/	SYM
ap-7684	79	108	b	b	NOUN
ap-7684	80	1	+	+	CCONJ
ap-7684	80	2	εb	εb	ADP
ap-7684	80	3	/	/	SYM
ap-7684	80	4	t)/6	t)/6	VERB
ap-7684	80	5	the	the	DET
ap-7684	80	6	cross	cross	ADJ
ap-7684	80	7	-	-	ADJ
ap-7684	80	8	section	section	ADJ
ap-7684	80	9	stiffness	stiffness	NOUN
ap-7684	80	10	matrix	matrix	NOUN
ap-7684	80	11	:	:	PUNCT
ap-7684	80	12	∂{sbend	∂{sbend	AUX
ap-7684	80	13	}	}	PUNCT
ap-7684	80	14	∂{εbend	∂{εbend	VERB
ap-7684	80	15	}	}	PUNCT
ap-7684	80	16	=	=	SYM
ap-7684	80	17	1	1	NUM
ap-7684	80	18	6	6	NUM
ap-7684	80	19	[	[	PUNCT
ap-7684	80	20	2	2	NUM
ap-7684	80	21	1	1	NUM
ap-7684	80	22	1	1	NUM
ap-7684	80	23	2	2	NUM
ap-7684	80	24	]	]	PUNCT
ap-7684	80	25	(	(	PUNCT
ap-7684	80	26	3	3	X
ap-7684	80	27	)	)	PUNCT
ap-7684	80	28	algorithm	algorithm	NOUN
ap-7684	80	29	end	end	VERB
ap-7684	80	30	the	the	DET
ap-7684	80	31	bending	bend	VERB
ap-7684	80	32	stiffness	stiffness	ADJ
ap-7684	80	33	tangent	tangent	NOUN
ap-7684	80	34	matrix	matrix	NOUN
ap-7684	80	35	of	of	ADP
ap-7684	80	36	the	the	DET
ap-7684	80	37	crosssection	crosssection	NOUN
ap-7684	80	38	is	be	AUX
ap-7684	80	39	denoted	denote	VERB
ap-7684	80	40	for	for	ADP
ap-7684	80	41	a	a	DET
ap-7684	80	42	later	later	ADJ
ap-7684	80	43	reference	reference	NOUN
ap-7684	80	44	[	[	X
ap-7684	80	45	dbend	dbend	X
ap-7684	80	46	]	]	X
ap-7684	80	47	=	=	SYM
ap-7684	80	48	∂{sbend	∂{sbend	ADJ
ap-7684	80	49	}	}	PUNCT
ap-7684	80	50	∂{εbend	∂{εbend	VERB
ap-7684	80	51	}	}	PUNCT
ap-7684	80	52	=	=	SYM
ap-7684	80	53	ebd	ebd	PROPN
ap-7684	81	1	[	[	PUNCT
ap-7684	81	2	∂st	∂st	NOUN
ap-7684	81	3	∂εt	∂εt	NOUN
ap-7684	81	4	∂st	∂st	VERB
ap-7684	81	5	∂εb	∂εb	NOUN
ap-7684	81	6	∂sb	∂sb	PROPN
ap-7684	81	7	∂εt	∂εt	NOUN
ap-7684	81	8	∂sb	∂sb	PROPN
ap-7684	81	9	∂εb	∂εb	PROPN
ap-7684	81	10	]	]	X
ap-7684	81	11	(	(	PUNCT
ap-7684	81	12	4	4	NUM
ap-7684	81	13	)	)	PUNCT
ap-7684	81	14	2.2	2.2	NUM
ap-7684	81	15	.	.	PUNCT
ap-7684	82	1	full	full	ADJ
ap-7684	82	2	cross	cross	ADJ
ap-7684	82	3	-	-	ADJ
ap-7684	82	4	section	section	ADJ
ap-7684	82	5	stiffness	stiffness	NOUN
ap-7684	82	6	matrix	matrix	NOUN
ap-7684	82	7	the	the	DET
ap-7684	82	8	shear	shear	NOUN
ap-7684	82	9	force	force	NOUN
ap-7684	82	10	v	v	NOUN
ap-7684	82	11	is	be	AUX
ap-7684	82	12	computed	compute	VERB
ap-7684	82	13	from	from	ADP
ap-7684	82	14	the	the	DET
ap-7684	82	15	shear	shear	NOUN
ap-7684	82	16	deformation	deformation	NOUN
ap-7684	82	17	γ	γ	NOUN
ap-7684	82	18	in	in	ADP
ap-7684	82	19	the	the	DET
ap-7684	82	20	timoshenko	timoshenko	ADJ
ap-7684	82	21	beam	beam	NOUN
ap-7684	82	22	.	.	PUNCT
ap-7684	83	1	linear	linear	ADJ
ap-7684	83	2	elastic	elastic	ADJ
ap-7684	83	3	behaviour	behaviour	NOUN
ap-7684	83	4	v	v	ADP
ap-7684	83	5	=	=	PUNCT
ap-7684	83	6	gebdγ	gebdγ	PROPN
ap-7684	83	7	is	be	AUX
ap-7684	83	8	assumed	assume	VERB
ap-7684	83	9	in	in	ADP
ap-7684	83	10	the	the	DET
ap-7684	83	11	model	model	NOUN
ap-7684	83	12	,	,	PUNCT
ap-7684	83	13	independent	independent	ADJ
ap-7684	83	14	on	on	ADP
ap-7684	83	15	the	the	DET
ap-7684	83	16	normal	normal	ADJ
ap-7684	83	17	stress	stress	NOUN
ap-7684	83	18	in	in	ADP
ap-7684	83	19	the	the	DET
ap-7684	83	20	cross	cross	NOUN
ap-7684	83	21	-	-	NOUN
ap-7684	83	22	sections	section	NOUN
ap-7684	83	23	.	.	PUNCT
ap-7684	84	1	this	this	DET
ap-7684	84	2	assumption	assumption	NOUN
ap-7684	84	3	is	be	AUX
ap-7684	84	4	mostly	mostly	ADV
ap-7684	84	5	sufficient	sufficient	ADJ
ap-7684	84	6	for	for	ADP
ap-7684	84	7	cross	cros	NOUN
ap-7684	84	8	-	-	NOUN
ap-7684	84	9	sections	section	NOUN
ap-7684	84	10	of	of	ADP
ap-7684	84	11	the	the	DET
ap-7684	84	12	stone	stone	NOUN
ap-7684	84	13	masonry	masonry	NOUN
ap-7684	84	14	arch	arch	ADJ
ap-7684	84	15	bridges	bridge	NOUN
ap-7684	84	16	.	.	PUNCT
ap-7684	85	1	the	the	DET
ap-7684	85	2	full	full	ADJ
ap-7684	85	3	cross	cross	ADJ
ap-7684	85	4	-	-	ADJ
ap-7684	85	5	section	section	ADJ
ap-7684	85	6	stiffness	stiffness	NOUN
ap-7684	85	7	matrix	matrix	NOUN
ap-7684	85	8	is	be	AUX
ap-7684	85	9	then	then	ADV
ap-7684	85	10	[	[	X
ap-7684	85	11	dcs	dcs	X
ap-7684	85	12	]	]	X
ap-7684	85	13	=	=	PUNCT
ap-7684	86	1	[	[	PUNCT
ap-7684	86	2	[	[	X
ap-7684	86	3	dbend	dbend	X
ap-7684	86	4	]	]	X
ap-7684	86	5	{	{	PUNCT
ap-7684	86	6	0	0	NUM
ap-7684	86	7	}	}	PUNCT
ap-7684	86	8	{	{	PUNCT
ap-7684	86	9	0}t	0}t	NOUN
ap-7684	86	10	gebd	gebd	NOUN
ap-7684	86	11	]	]	PUNCT
ap-7684	86	12	the	the	DET
ap-7684	86	13	matrix	matrix	NOUN
ap-7684	86	14	has	have	VERB
ap-7684	86	15	to	to	PART
ap-7684	86	16	be	be	AUX
ap-7684	86	17	adapted	adapt	VERB
ap-7684	86	18	when	when	SCONJ
ap-7684	86	19	more	more	ADV
ap-7684	86	20	involved	involve	VERB
ap-7684	86	21	cross	cross	ADJ
ap-7684	86	22	-	-	ADJ
ap-7684	86	23	section	section	ADJ
ap-7684	86	24	constitutive	constitutive	ADJ
ap-7684	86	25	equations	equation	NOUN
ap-7684	86	26	are	be	AUX
ap-7684	86	27	necessary	necessary	ADJ
ap-7684	86	28	,	,	PUNCT
ap-7684	86	29	for	for	ADP
ap-7684	86	30	instance	instance	NOUN
ap-7684	86	31	,	,	PUNCT
ap-7684	86	32	shear	shear	ADJ
ap-7684	86	33	failure	failure	NOUN
ap-7684	86	34	of	of	ADP
ap-7684	86	35	bed	bed	NOUN
ap-7684	86	36	joints	joint	NOUN
ap-7684	86	37	.	.	PUNCT
ap-7684	87	1	the	the	DET
ap-7684	87	2	nodal	nodal	NOUN
ap-7684	87	3	forces	force	NOUN
ap-7684	87	4	{	{	PUNCT
ap-7684	87	5	x	x	NOUN
ap-7684	87	6	}	}	PUNCT
ap-7684	87	7	=	=	SYM
ap-7684	87	8	{	{	PUNCT
ap-7684	87	9	xi	xi	PROPN
ap-7684	87	10	,	,	PUNCT
ap-7684	87	11	t	t	PROPN
ap-7684	87	12	,	,	PUNCT
ap-7684	87	13	yi	yi	PROPN
ap-7684	87	14	,	,	PUNCT
ap-7684	87	15	xi	xi	PROPN
ap-7684	87	16	,	,	PUNCT
ap-7684	87	17	b	b	PROPN
ap-7684	87	18	,	,	PUNCT
ap-7684	87	19	xj	xj	PROPN
ap-7684	87	20	,	,	PUNCT
ap-7684	87	21	t	t	PROPN
ap-7684	87	22	,	,	PUNCT
ap-7684	87	23	yj	yj	PROPN
ap-7684	87	24	,	,	PUNCT
ap-7684	87	25	xj	xj	PROPN
ap-7684	87	26	,	,	PUNCT
ap-7684	87	27	b}t	b}t	NOUN
ap-7684	87	28	of	of	ADP
ap-7684	87	29	the	the	DET
ap-7684	87	30	element	element	NOUN
ap-7684	87	31	can	can	AUX
ap-7684	87	32	be	be	AUX
ap-7684	87	33	obtained	obtain	VERB
ap-7684	87	34	in	in	ADP
ap-7684	87	35	terms	term	NOUN
ap-7684	87	36	of	of	ADP
ap-7684	87	37	the	the	DET
ap-7684	87	38	internal	internal	ADJ
ap-7684	87	39	forces	force	NOUN
ap-7684	87	40	{	{	PUNCT
ap-7684	87	41	s	s	SYM
ap-7684	87	42	}	}	PUNCT
ap-7684	87	43	either	either	CCONJ
ap-7684	87	44	by	by	ADP
ap-7684	87	45	expansion	expansion	NOUN
ap-7684	87	46	of	of	ADP
ap-7684	87	47	[	[	X
ap-7684	87	48	b]t	b]t	X
ap-7684	87	49	{	{	PUNCT
ap-7684	87	50	s	s	NOUN
ap-7684	87	51	}	}	PUNCT
ap-7684	87	52	or	or	CCONJ
ap-7684	87	53	by	by	ADP
ap-7684	87	54	the	the	DET
ap-7684	87	55	equilibrium	equilibrium	NOUN
ap-7684	87	56	conditions	condition	NOUN
ap-7684	87	57	of	of	ADP
ap-7684	87	58	the	the	DET
ap-7684	87	59	element	element	NOUN
ap-7684	87	60	in	in	ADP
ap-7684	87	61	figure	figure	NOUN
ap-7684	87	62	3	3	NUM
ap-7684	87	63	:	:	PUNCT
ap-7684	87	64	the	the	DET
ap-7684	87	65	dimensionless	dimensionless	ADJ
ap-7684	87	66	cross	cross	ADJ
ap-7684	87	67	-	-	ADJ
ap-7684	87	68	section	section	ADJ
ap-7684	87	69	stiffness	stiffness	NOUN
ap-7684	87	70	matrix	matrix	NOUN
ap-7684	87	71	for	for	ADP
ap-7684	87	72	bending	bend	VERB
ap-7684	87	73	[	[	X
ap-7684	87	74	dbend	dbend	X
ap-7684	87	75	]	]	X
ap-7684	87	76	=	=	SYM
ap-7684	87	77	∂{sbend/∂{εbend	∂{sbend/∂{εbend	PROPN
ap-7684	87	78	}	}	PUNCT
ap-7684	87	79	is	be	AUX
ap-7684	87	80	not	not	PART
ap-7684	87	81	symmetric	symmetric	ADJ
ap-7684	87	82	when	when	SCONJ
ap-7684	87	83	the	the	DET
ap-7684	87	84	neutral	neutral	ADJ
ap-7684	87	85	axis	axis	NOUN
ap-7684	87	86	lies	lie	VERB
ap-7684	87	87	inside	inside	ADP
ap-7684	87	88	the	the	DET
ap-7684	87	89	cross	cross	NOUN
ap-7684	87	90	-	-	NOUN
ap-7684	87	91	section	section	NOUN
ap-7684	87	92	so	so	SCONJ
ap-7684	87	93	that	that	SCONJ
ap-7684	87	94	the	the	DET
ap-7684	87	95	x	x	SYM
ap-7684	87	96	xe	xe	PROPN
ap-7684	87	97	f	f	PROPN
ap-7684	87	98	bottom	bottom	PROPN
ap-7684	87	99	face	face	NOUN
ap-7684	87	100	bottom	bottom	ADJ
ap-7684	87	101	face	face	NOUN
ap-7684	87	102	element	element	NOUN
ap-7684	87	103	e	e	PROPN
ap-7684	87	104	node	node	NOUN
ap-7684	88	1	i	i	PRON
ap-7684	88	2	element	element	NOUN
ap-7684	88	3	f	f	PROPN
ap-7684	88	4	t	t	PROPN
ap-7684	88	5	t	t	PROPN
ap-7684	88	6	r	r	NOUN
ap-7684	88	7	rr	rr	NOUN
ap-7684	88	8	1	1	NUM
ap-7684	88	9	1	1	NUM
ap-7684	88	10	r	r	NOUN
ap-7684	88	11	b	b	NOUN
ap-7684	88	12	i	i	NOUN
ap-7684	88	13	xb	xb	X
ap-7684	88	14	x	x	PUNCT
ap-7684	88	15	b	b	X
ap-7684	88	16	xb	xb	X
ap-7684	88	17	x	x	SYM
ap-7684	88	18	b	b	PROPN
ap-7684	88	19	x	x	SYM
ap-7684	88	20	b	b	PROPN
ap-7684	88	21	xb	xb	X
ap-7684	88	22	f	f	PROPN
ap-7684	88	23	e	e	PROPN
ap-7684	88	24	f	f	AUX
ap-7684	88	25	f	f	PROPN
ap-7684	88	26	e	e	X
ap-7684	88	27	e	e	PRON
ap-7684	88	28	figure	figure	VERB
ap-7684	88	29	4	4	NUM
ap-7684	88	30	.	.	PUNCT
ap-7684	88	31	equilibrium	equilibrium	NOUN
ap-7684	88	32	of	of	ADP
ap-7684	88	33	node	node	PROPN
ap-7684	88	34	i	i	PROPN
ap-7684	88	35	element	element	NOUN
ap-7684	88	36	and	and	CCONJ
ap-7684	88	37	structure	structure	NOUN
ap-7684	88	38	matrices	matrix	NOUN
ap-7684	88	39	will	will	AUX
ap-7684	88	40	not	not	PART
ap-7684	88	41	be	be	AUX
ap-7684	88	42	symmetric	symmetric	ADJ
ap-7684	88	43	,	,	PUNCT
ap-7684	88	44	too	too	ADV
ap-7684	88	45	.	.	PUNCT
ap-7684	89	1	the	the	DET
ap-7684	89	2	element	element	ADJ
ap-7684	89	3	stiffness	stiffness	NOUN
ap-7684	89	4	matrix	matrix	NOUN
ap-7684	89	5	is	be	AUX
ap-7684	89	6	[	[	X
ap-7684	89	7	k]straight	k]straight	X
ap-7684	89	8	=	=	PUNCT
ap-7684	89	9	ebdl[b]t	ebdl[b]t	PROPN
ap-7684	90	1	[	[	X
ap-7684	90	2	dcs][b	dcs][b	X
ap-7684	90	3	]	]	X
ap-7684	90	4	it	it	PRON
ap-7684	90	5	is	be	AUX
ap-7684	90	6	ready	ready	ADJ
ap-7684	90	7	for	for	ADP
ap-7684	90	8	application	application	NOUN
ap-7684	90	9	in	in	ADP
ap-7684	90	10	straight	straight	ADJ
ap-7684	90	11	beams	beam	NOUN
ap-7684	90	12	,	,	PUNCT
ap-7684	90	13	but	but	CCONJ
ap-7684	90	14	for	for	ADP
ap-7684	90	15	arches	arch	NOUN
ap-7684	90	16	and	and	CCONJ
ap-7684	90	17	other	other	ADJ
ap-7684	90	18	curved	curved	ADJ
ap-7684	90	19	beams	beam	NOUN
ap-7684	90	20	,	,	PUNCT
ap-7684	90	21	it	it	PRON
ap-7684	90	22	must	must	AUX
ap-7684	90	23	be	be	AUX
ap-7684	90	24	modified	modify	VERB
ap-7684	90	25	.	.	PUNCT
ap-7684	91	1	2.3	2.3	NUM
ap-7684	91	2	.	.	PUNCT
ap-7684	92	1	arch	arch	NOUN
ap-7684	92	2	nodes	node	NOUN
ap-7684	92	3	equilibrium	equilibrium	NOUN
ap-7684	92	4	the	the	DET
ap-7684	92	5	equilibrium	equilibrium	NOUN
ap-7684	92	6	of	of	ADP
ap-7684	92	7	the	the	DET
ap-7684	92	8	nodal	nodal	NOUN
ap-7684	92	9	forces	force	NOUN
ap-7684	92	10	x⃗ibe	x⃗ibe	PROPN
ap-7684	92	11	=	=	SYM
ap-7684	92	12	xibex⃗e	xibex⃗e	PROPN
ap-7684	92	13	,	,	PUNCT
ap-7684	92	14	x⃗ibf	x⃗ibf	PROPN
ap-7684	92	15	=	=	SYM
ap-7684	93	1	xibf	xibf	PROPN
ap-7684	94	1	x⃗f	x⃗f	PROPN
ap-7684	94	2	of	of	ADP
ap-7684	94	3	the	the	DET
ap-7684	94	4	adjacent	adjacent	ADJ
ap-7684	94	5	elements	element	NOUN
ap-7684	94	6	e	e	NOUN
ap-7684	94	7	and	and	CCONJ
ap-7684	94	8	f	f	PROPN
ap-7684	94	9	at	at	ADP
ap-7684	94	10	arch	arch	ADJ
ap-7684	94	11	node	node	NOUN
ap-7684	94	12	i	i	PRON
ap-7684	94	13	simplifies	simplify	VERB
ap-7684	94	14	to	to	PART
ap-7684	94	15	xibe	xibe	VERB
ap-7684	94	16	+	+	CCONJ
ap-7684	94	17	xibf	xibf	NOUN
ap-7684	95	1	=	=	SYM
ap-7684	95	2	0	0	NUM
ap-7684	95	3	when	when	SCONJ
ap-7684	95	4	the	the	DET
ap-7684	95	5	element	element	NOUN
ap-7684	95	6	’s	’s	PART
ap-7684	95	7	unit	unit	NOUN
ap-7684	95	8	length	length	NOUN
ap-7684	95	9	direction	direction	NOUN
ap-7684	95	10	vectors	vector	NOUN
ap-7684	95	11	x⃗l	x⃗l	PROPN
ap-7684	95	12	,	,	PUNCT
ap-7684	95	13	e	e	NOUN
ap-7684	95	14	and	and	CCONJ
ap-7684	95	15	x⃗l	x⃗l	PROPN
ap-7684	95	16	,	,	PUNCT
ap-7684	95	17	f	f	PROPN
ap-7684	95	18	coincide	coincide	NOUN
ap-7684	95	19	,	,	PUNCT
ap-7684	95	20	see	see	VERB
ap-7684	95	21	the	the	DET
ap-7684	95	22	figure	figure	NOUN
ap-7684	95	23	4	4	NUM
ap-7684	95	24	.	.	PUNCT
ap-7684	96	1	the	the	DET
ap-7684	96	2	node	node	ADJ
ap-7684	96	3	index	index	NOUN
ap-7684	96	4	i	i	PRON
ap-7684	96	5	is	be	AUX
ap-7684	96	6	omitted	omit	VERB
ap-7684	96	7	for	for	ADP
ap-7684	96	8	brevity	brevity	NOUN
ap-7684	96	9	as	as	ADV
ap-7684	96	10	long	long	ADV
ap-7684	96	11	as	as	SCONJ
ap-7684	96	12	the	the	DET
ap-7684	96	13	the	the	DET
ap-7684	96	14	development	development	NOUN
ap-7684	96	15	concerns	concern	NOUN
ap-7684	96	16	just	just	ADV
ap-7684	96	17	a	a	DET
ap-7684	96	18	single	single	ADJ
ap-7684	96	19	node	node	PROPN
ap-7684	96	20	i.	i.	PROPN
ap-7684	96	21	xbe	xbe	PROPN
ap-7684	96	22	and	and	CCONJ
ap-7684	96	23	xbf	xbf	PROPN
ap-7684	96	24	are	be	AUX
ap-7684	96	25	the	the	DET
ap-7684	96	26	magnitudes	magnitude	NOUN
ap-7684	96	27	of	of	ADP
ap-7684	96	28	the	the	DET
ap-7684	96	29	respective	respective	ADJ
ap-7684	96	30	forces	force	NOUN
ap-7684	96	31	with	with	ADP
ap-7684	96	32	positive	positive	ADJ
ap-7684	96	33	senses	sense	NOUN
ap-7684	96	34	in	in	ADP
ap-7684	96	35	element	element	NOUN
ap-7684	96	36	’s	’s	PART
ap-7684	96	37	direction	direction	NOUN
ap-7684	96	38	vectors	vector	NOUN
ap-7684	96	39	.	.	PUNCT
ap-7684	97	1	these	these	DET
ap-7684	97	2	forces	force	NOUN
ap-7684	97	3	are	be	AUX
ap-7684	97	4	stored	store	VERB
ap-7684	97	5	in	in	ADP
ap-7684	97	6	the	the	DET
ap-7684	97	7	third	third	ADJ
ap-7684	97	8	components	component	NOUN
ap-7684	97	9	of	of	ADP
ap-7684	97	10	the	the	DET
ap-7684	97	11	element	element	NOUN
ap-7684	97	12	nodal	nodal	NOUN
ap-7684	97	13	forces	force	NOUN
ap-7684	97	14	matrices	matrix	NOUN
ap-7684	97	15	and	and	CCONJ
ap-7684	97	16	in	in	ADP
ap-7684	97	17	case	case	NOUN
ap-7684	97	18	of	of	ADP
ap-7684	97	19	parallel	parallel	ADJ
ap-7684	97	20	elements	element	NOUN
ap-7684	97	21	,	,	PUNCT
ap-7684	97	22	the	the	DET
ap-7684	97	23	equilibrium	equilibrium	NOUN
ap-7684	97	24	equation	equation	NOUN
ap-7684	97	25	at	at	ADP
ap-7684	97	26	a	a	DET
ap-7684	97	27	node	node	NOUN
ap-7684	97	28	is	be	AUX
ap-7684	97	29	{	{	PUNCT
ap-7684	97	30	x}e	x}e	PROPN
ap-7684	97	31	+	+	CCONJ
ap-7684	97	32	{	{	PUNCT
ap-7684	97	33	x}f	x}f	NOUN
ap-7684	97	34	=	=	PROPN
ap-7684	97	35	{	{	PUNCT
ap-7684	97	36	0	0	NUM
ap-7684	97	37	}	}	PUNCT
ap-7684	97	38	,	,	PUNCT
ap-7684	97	39	where	where	SCONJ
ap-7684	97	40	indices	index	NOUN
ap-7684	97	41	e	e	NOUN
ap-7684	97	42	and	and	CCONJ
ap-7684	97	43	f	f	PROPN
ap-7684	97	44	indicate	indicate	VERB
ap-7684	97	45	the	the	DET
ap-7684	97	46	left	left	ADJ
ap-7684	97	47	and	and	CCONJ
ap-7684	97	48	right	right	ADJ
ap-7684	97	49	element	element	NOUN
ap-7684	97	50	,	,	PUNCT
ap-7684	97	51	respectively	respectively	ADV
ap-7684	97	52	.	.	PUNCT
ap-7684	98	1	when	when	SCONJ
ap-7684	98	2	the	the	DET
ap-7684	98	3	adjacent	adjacent	ADJ
ap-7684	98	4	elements	element	NOUN
ap-7684	98	5	are	be	AUX
ap-7684	98	6	not	not	PART
ap-7684	98	7	parallel	parallel	ADJ
ap-7684	98	8	,	,	PUNCT
ap-7684	98	9	the	the	DET
ap-7684	98	10	resultants	resultant	NOUN
ap-7684	98	11	of	of	ADP
ap-7684	98	12	the	the	DET
ap-7684	98	13	two	two	NUM
ap-7684	98	14	forces	force	NOUN
ap-7684	98	15	add	add	VERB
ap-7684	98	16	up	up	ADP
ap-7684	98	17	to	to	PART
ap-7684	98	18	force	force	VERB
ap-7684	98	19	r⃗.	r⃗.	VERB
ap-7684	98	20	the	the	DET
ap-7684	98	21	force	force	NOUN
ap-7684	98	22	is	be	AUX
ap-7684	98	23	decomposed	decompose	VERB
ap-7684	98	24	into	into	ADP
ap-7684	98	25	component	component	NOUN
ap-7684	98	26	r	r	NOUN
ap-7684	98	27	in	in	ADP
ap-7684	98	28	the	the	DET
ap-7684	98	29	direction	direction	NOUN
ap-7684	98	30	r	r	NOUN
ap-7684	98	31	and	and	CCONJ
ap-7684	98	32	force	force	NOUN
ap-7684	98	33	t	t	PROPN
ap-7684	98	34	in	in	ADP
ap-7684	98	35	the	the	DET
ap-7684	98	36	t	t	NOUN
ap-7684	98	37	direction	direction	NOUN
ap-7684	98	38	.	.	PUNCT
ap-7684	99	1	the	the	DET
ap-7684	99	2	component	component	NOUN
ap-7684	99	3	r	r	NOUN
ap-7684	99	4	can	can	AUX
ap-7684	99	5	act	act	VERB
ap-7684	99	6	anywhere	anywhere	ADV
ap-7684	99	7	on	on	ADP
ap-7684	99	8	ray	ray	NOUN
ap-7684	99	9	r	r	NOUN
ap-7684	99	10	since	since	SCONJ
ap-7684	99	11	the	the	DET
ap-7684	99	12	arch	arch	NOUN
ap-7684	99	13	is	be	AUX
ap-7684	99	14	considered	consider	VERB
ap-7684	99	15	rigid	rigid	ADJ
ap-7684	99	16	in	in	ADP
ap-7684	99	17	the	the	DET
ap-7684	99	18	transverse	transverse	NOUN
ap-7684	99	19	direction	direction	NOUN
ap-7684	99	20	.	.	PUNCT
ap-7684	100	1	it	it	PRON
ap-7684	100	2	is	be	AUX
ap-7684	100	3	thus	thus	ADV
ap-7684	100	4	added	add	VERB
ap-7684	100	5	to	to	ADP
ap-7684	100	6	forces	force	NOUN
ap-7684	100	7	acting	act	VERB
ap-7684	100	8	at	at	ADP
ap-7684	100	9	node	node	PROPN
ap-7684	100	10	i.	i.	PROPN
ap-7684	100	11	component	component	PROPN
ap-7684	100	12	t	t	PROPN
ap-7684	100	13	must	must	AUX
ap-7684	100	14	vanish	vanish	VERB
ap-7684	100	15	to	to	PART
ap-7684	100	16	keep	keep	VERB
ap-7684	100	17	the	the	DET
ap-7684	100	18	null	null	ADJ
ap-7684	100	19	moment	moment	NOUN
ap-7684	100	20	with	with	ADP
ap-7684	100	21	respect	respect	NOUN
ap-7684	100	22	to	to	ADP
ap-7684	100	23	joint	joint	ADJ
ap-7684	100	24	i.	i.	NOUN
ap-7684	100	25	t	t	PROPN
ap-7684	100	26	=	=	PUNCT
ap-7684	100	27	(	(	PUNCT
ap-7684	100	28	xbex⃗e	xbex⃗e	PROPN
ap-7684	101	1	+	+	ADJ
ap-7684	101	2	xbf	xbf	PROPN
ap-7684	101	3	x⃗f	x⃗f	PROPN
ap-7684	101	4	)	)	PUNCT
ap-7684	101	5	·	·	PUNCT
ap-7684	101	6	⃗t	⃗t	X
ap-7684	101	7	=	=	PUNCT
ap-7684	101	8	=	=	SYM
ap-7684	101	9	(	(	PUNCT
ap-7684	101	10	xbex⃗e	xbex⃗e	PROPN
ap-7684	102	1	+	+	ADJ
ap-7684	102	2	xbf	xbf	PROPN
ap-7684	102	3	x⃗f	x⃗f	PROPN
ap-7684	102	4	)	)	PUNCT
ap-7684	102	5	·	·	PUNCT
ap-7684	102	6	(	(	PUNCT
ap-7684	102	7	x⃗e	x⃗e	X
ap-7684	102	8	+	+	CCONJ
ap-7684	102	9	x⃗f	x⃗f	PROPN
ap-7684	102	10	)	)	PUNCT
ap-7684	102	11	/|x⃗e	/|x⃗e	PUNCT
ap-7684	103	1	+	+	CCONJ
ap-7684	104	1	x⃗f	x⃗f	INTJ
ap-7684	104	2	|	|	ADV
ap-7684	104	3	=	=	SYM
ap-7684	104	4	0	0	NUM
ap-7684	104	5	,	,	PUNCT
ap-7684	104	6	which	which	PRON
ap-7684	104	7	implies	imply	VERB
ap-7684	104	8	xbe	xbe	PROPN
ap-7684	105	1	+	+	NOUN
ap-7684	105	2	xbf	xbf	NOUN
ap-7684	105	3	=	=	SYM
ap-7684	105	4	0	0	NUM
ap-7684	105	5	,	,	PUNCT
ap-7684	105	6	provided	provide	VERB
ap-7684	105	7	the	the	DET
ap-7684	105	8	two	two	NUM
ap-7684	105	9	elements	element	NOUN
ap-7684	105	10	are	be	AUX
ap-7684	105	11	not	not	PART
ap-7684	105	12	normal	normal	ADJ
ap-7684	105	13	to	to	ADP
ap-7684	105	14	each	each	DET
ap-7684	105	15	other	other	ADJ
ap-7684	105	16	.	.	PUNCT
ap-7684	106	1	force	force	NOUN
ap-7684	106	2	r	r	NOUN
ap-7684	106	3	is	be	AUX
ap-7684	106	4	r	r	NOUN
ap-7684	106	5	=	=	PUNCT
ap-7684	106	6	(	(	PUNCT
ap-7684	106	7	xbex⃗e	xbex⃗e	PROPN
ap-7684	106	8	−xbf	−xbf	NOUN
ap-7684	106	9	x⃗f	x⃗f	PROPN
ap-7684	106	10	)	)	PUNCT
ap-7684	106	11	·	·	PUNCT
ap-7684	106	12	r⃗	r⃗	NOUN
ap-7684	106	13	=	=	SYM
ap-7684	106	14	(	(	PUNCT
ap-7684	106	15	xbex⃗e	xbex⃗e	PROPN
ap-7684	106	16	−xbf	−xbf	NOUN
ap-7684	106	17	x⃗f	x⃗f	PROPN
ap-7684	106	18	)	)	PUNCT
ap-7684	106	19	·	·	PUNCT
ap-7684	106	20	(	(	PUNCT
ap-7684	106	21	x⃗e	x⃗e	PROPN
ap-7684	106	22	−	−	PROPN
ap-7684	107	1	x⃗f	x⃗f	PROPN
ap-7684	107	2	)	)	PUNCT
ap-7684	107	3	/|x⃗e	/|x⃗e	PUNCT
ap-7684	108	1	−	−	PROPN
ap-7684	109	1	x⃗f	x⃗f	INTJ
ap-7684	110	1	|	|	ADV
ap-7684	110	2	=	=	SYM
ap-7684	110	3	(	(	PUNCT
ap-7684	110	4	xbe	xbe	PROPN
ap-7684	110	5	−xbf	−xbf	PUNCT
ap-7684	110	6	)	)	PUNCT
ap-7684	110	7	√	√	CCONJ
ap-7684	110	8	(	(	PUNCT
ap-7684	110	9	1	1	NUM
ap-7684	110	10	−	−	NUM
ap-7684	110	11	x⃗e·x⃗f	x⃗e·x⃗f	NUM
ap-7684	110	12	)	)	PUNCT
ap-7684	110	13	/2	/2	PROPN
ap-7684	111	1	and	and	CCONJ
ap-7684	111	2	its	its	PRON
ap-7684	111	3	vector	vector	NOUN
ap-7684	111	4	r⃗	r⃗	NOUN
ap-7684	111	5	=	=	SYM
ap-7684	111	6	rr⃗	rr⃗	NOUN
ap-7684	111	7	=	=	PUNCT
ap-7684	111	8	0.5(xbe	0.5(xbe	NUM
ap-7684	111	9	−xbf	−xbf	NUM
ap-7684	111	10	)	)	PUNCT
ap-7684	111	11	(	(	PUNCT
ap-7684	111	12	x⃗e	x⃗e	PROPN
ap-7684	111	13	−	−	PROPN
ap-7684	112	1	x⃗f	x⃗f	PROPN
ap-7684	112	2	)	)	PUNCT
ap-7684	112	3	295	295	NUM
ap-7684	112	4	petr	petr	PROPN
ap-7684	112	5	řeřicha	řeřicha	PROPN
ap-7684	112	6	acta	acta	PROPN
ap-7684	112	7	polytechnica	polytechnica	PROPN
ap-7684	112	8	the	the	DET
ap-7684	112	9	ray	ray	NOUN
ap-7684	112	10	r	r	NOUN
ap-7684	112	11	of	of	ADP
ap-7684	112	12	the	the	DET
ap-7684	112	13	force	force	NOUN
ap-7684	112	14	must	must	AUX
ap-7684	112	15	connect	connect	VERB
ap-7684	112	16	points	point	NOUN
ap-7684	112	17	i	i	PRON
ap-7684	112	18	and	and	CCONJ
ap-7684	112	19	bi	bi	PROPN
ap-7684	112	20	,	,	PUNCT
ap-7684	112	21	the	the	DET
ap-7684	112	22	intersection	intersection	NOUN
ap-7684	112	23	of	of	ADP
ap-7684	112	24	the	the	DET
ap-7684	112	25	x⃗be	x⃗be	PROPN
ap-7684	112	26	and	and	CCONJ
ap-7684	112	27	x⃗bf	x⃗bf	PROPN
ap-7684	112	28	forces	force	NOUN
ap-7684	112	29	rays	ray	NOUN
ap-7684	112	30	,	,	PUNCT
ap-7684	112	31	otherwise	otherwise	ADV
ap-7684	112	32	node	node	VERB
ap-7684	112	33	i	i	PRON
ap-7684	112	34	would	would	AUX
ap-7684	112	35	not	not	PART
ap-7684	112	36	be	be	AUX
ap-7684	112	37	in	in	ADP
ap-7684	112	38	equilibrium	equilibrium	NOUN
ap-7684	112	39	.	.	PUNCT
ap-7684	113	1	ray	ray	NOUN
ap-7684	113	2	r	r	NOUN
ap-7684	113	3	is	be	AUX
ap-7684	113	4	approximately	approximately	ADV
ap-7684	113	5	radial	radial	ADJ
ap-7684	113	6	to	to	ADP
ap-7684	113	7	the	the	DET
ap-7684	113	8	arch	arch	NOUN
ap-7684	113	9	.	.	PUNCT
ap-7684	114	1	vector	vector	NOUN
ap-7684	114	2	g⃗	g⃗	PROPN
ap-7684	114	3	=	=	SYM
ap-7684	114	4	0.5(x⃗e	0.5(x⃗e	PROPN
ap-7684	115	1	−	−	PUNCT
ap-7684	116	1	x⃗f	x⃗f	INTJ
ap-7684	116	2	)	)	PUNCT
ap-7684	116	3	(	(	PUNCT
ap-7684	116	4	5	5	X
ap-7684	116	5	)	)	PUNCT
ap-7684	116	6	is	be	AUX
ap-7684	116	7	an	an	DET
ap-7684	116	8	important	important	ADJ
ap-7684	116	9	property	property	NOUN
ap-7684	116	10	of	of	ADP
ap-7684	116	11	node	node	PROPN
ap-7684	116	12	i.	i.	NOUN
ap-7684	116	13	the	the	DET
ap-7684	116	14	matrix	matrix	NOUN
ap-7684	116	15	expression	expression	NOUN
ap-7684	116	16	for	for	ADP
ap-7684	116	17	vector	vector	NOUN
ap-7684	116	18	r⃗	r⃗	NOUN
ap-7684	116	19	is	be	AUX
ap-7684	116	20	in	in	ADP
ap-7684	116	21	terms	term	NOUN
ap-7684	116	22	of	of	ADP
ap-7684	116	23	g⃗	g⃗	PROPN
ap-7684	116	24	r⃗	r⃗	ADJ
ap-7684	116	25	=	=	PUNCT
ap-7684	116	26	{	{	PUNCT
ap-7684	116	27	g⃗,−g⃗	g⃗,−g⃗	NOUN
ap-7684	116	28	}	}	PUNCT
ap-7684	116	29	{	{	PUNCT
ap-7684	116	30	xbe	xbe	PROPN
ap-7684	116	31	xbf	xbf	PROPN
ap-7684	116	32	}	}	PUNCT
ap-7684	116	33	recall	recall	VERB
ap-7684	116	34	that	that	SCONJ
ap-7684	116	35	xbe	xbe	PROPN
ap-7684	116	36	denotes	denote	VERB
ap-7684	116	37	the	the	DET
ap-7684	116	38	third	third	ADJ
ap-7684	116	39	element	element	NOUN
ap-7684	116	40	of	of	ADP
ap-7684	116	41	the	the	DET
ap-7684	116	42	nodal	nodal	NOUN
ap-7684	116	43	forces	force	NOUN
ap-7684	116	44	matrix	matrix	NOUN
ap-7684	116	45	of	of	ADP
ap-7684	116	46	element	element	NOUN
ap-7684	116	47	e	e	NOUN
ap-7684	116	48	at	at	ADP
ap-7684	116	49	node	node	PROPN
ap-7684	116	50	i	i	PROPN
ap-7684	116	51	and	and	CCONJ
ap-7684	116	52	the	the	DET
ap-7684	116	53	analogue	analogue	NOUN
ap-7684	116	54	holds	hold	VERB
ap-7684	116	55	for	for	ADP
ap-7684	116	56	xbf	xbf	NOUN
ap-7684	116	57	.	.	PUNCT
ap-7684	117	1	conjugate	conjugate	ADJ
ap-7684	117	2	displacements	displacement	NOUN
ap-7684	117	3	to	to	ADP
ap-7684	117	4	xbe	xbe	PROPN
ap-7684	117	5	and	and	CCONJ
ap-7684	117	6	xbf	xbf	NOUN
ap-7684	117	7	are	be	AUX
ap-7684	117	8	ube	ube	ADJ
ap-7684	117	9	and	and	CCONJ
ap-7684	117	10	ubf	ubf	ADJ
ap-7684	117	11	,	,	PUNCT
ap-7684	117	12	conjugate	conjugate	ADJ
ap-7684	117	13	to	to	ADP
ap-7684	117	14	r⃗	r⃗	NOUN
ap-7684	117	15	is	be	AUX
ap-7684	117	16	the	the	DET
ap-7684	117	17	displacement	displacement	ADJ
ap-7684	117	18	vector	vector	NOUN
ap-7684	117	19	u⃗	u⃗	PROPN
ap-7684	117	20	of	of	ADP
ap-7684	117	21	node	node	PROPN
ap-7684	117	22	i.	i.	PROPN
ap-7684	117	23	the	the	DET
ap-7684	117	24	principle	principle	NOUN
ap-7684	117	25	of	of	ADP
ap-7684	117	26	virtual	virtual	ADJ
ap-7684	117	27	work	work	NOUN
ap-7684	117	28	thus	thus	ADV
ap-7684	117	29	implies	imply	VERB
ap-7684	117	30	{	{	PUNCT
ap-7684	117	31	ube	ube	PRON
ap-7684	117	32	ubf	ubf	ADJ
ap-7684	117	33	}	}	PUNCT
ap-7684	118	1	=	=	SYM
ap-7684	118	2	{	{	PUNCT
ap-7684	118	3	g⃗	g⃗	PROPN
ap-7684	118	4	−g⃗	−g⃗	PROPN
ap-7684	118	5	}	}	PUNCT
ap-7684	118	6	·	·	PUNCT
ap-7684	118	7	u⃗	u⃗	PROPN
ap-7684	118	8	the	the	DET
ap-7684	118	9	same	same	ADJ
ap-7684	118	10	result	result	NOUN
ap-7684	118	11	can	can	AUX
ap-7684	118	12	be	be	AUX
ap-7684	118	13	obtained	obtain	VERB
ap-7684	118	14	when	when	SCONJ
ap-7684	118	15	the	the	DET
ap-7684	118	16	part	part	NOUN
ap-7684	118	17	of	of	ADP
ap-7684	118	18	u⃗	u⃗	PROPN
ap-7684	118	19	in	in	ADP
ap-7684	118	20	r⃗	r⃗	ADJ
ap-7684	118	21	direction	direction	NOUN
ap-7684	118	22	,	,	PUNCT
ap-7684	118	23	(	(	PUNCT
ap-7684	118	24	u⃗·r⃗)r⃗	u⃗·r⃗)r⃗	NOUN
ap-7684	118	25	,	,	PUNCT
ap-7684	118	26	is	be	AUX
ap-7684	118	27	projected	project	VERB
ap-7684	118	28	on	on	ADP
ap-7684	118	29	the	the	DET
ap-7684	118	30	x⃗e	x⃗e	PROPN
ap-7684	118	31	direction	direction	NOUN
ap-7684	118	32	to	to	PART
ap-7684	118	33	obtain	obtain	VERB
ap-7684	118	34	ube	ube	NOUN
ap-7684	118	35	:	:	PUNCT
ap-7684	118	36	ube	ube	NOUN
ap-7684	118	37	=	=	SYM
ap-7684	118	38	(	(	PUNCT
ap-7684	118	39	u⃗·r⃗)r⃗·x⃗e	u⃗·r⃗)r⃗·x⃗e	PROPN
ap-7684	118	40	=	=	SYM
ap-7684	118	41	g⃗·u⃗.	g⃗·u⃗.	PROPN
ap-7684	118	42	projection	projection	NOUN
ap-7684	118	43	on	on	ADP
ap-7684	118	44	x⃗e	x⃗e	PROPN
ap-7684	118	45	yields	yield	VERB
ap-7684	118	46	the	the	DET
ap-7684	118	47	same	same	ADJ
ap-7684	118	48	expression	expression	NOUN
ap-7684	118	49	but	but	CCONJ
ap-7684	118	50	for	for	ADP
ap-7684	118	51	a	a	DET
ap-7684	118	52	negative	negative	ADJ
ap-7684	118	53	sign	sign	NOUN
ap-7684	118	54	at	at	ADP
ap-7684	118	55	g⃗.	g⃗.	NOUN
ap-7684	118	56	expression	expression	NOUN
ap-7684	118	57	for	for	ADP
ap-7684	118	58	εb	εb	ADV
ap-7684	118	59	becomes	become	VERB
ap-7684	118	60	εb	εb	ADP
ap-7684	118	61	=(	=(	NOUN
ap-7684	118	62	ub	ub	PROPN
ap-7684	118	63	,	,	PUNCT
ap-7684	118	64	j	j	PROPN
ap-7684	118	65	+	+	CCONJ
ap-7684	118	66	g⃗j	g⃗j	PROPN
ap-7684	118	67	·	·	PUNCT
ap-7684	118	68	u⃗j	u⃗j	PROPN
ap-7684	118	69	−	−	PROPN
ap-7684	118	70	ub	ub	PROPN
ap-7684	118	71	,	,	PUNCT
ap-7684	118	72	i	i	PROPN
ap-7684	118	73	+	+	CCONJ
ap-7684	119	1	g⃗i·u⃗i)/li	g⃗i·u⃗i)/li	PROPN
ap-7684	119	2	,	,	PUNCT
ap-7684	119	3	j	j	PROPN
ap-7684	119	4	=(	=(	PROPN
ap-7684	119	5	ub	ub	PROPN
ap-7684	119	6	,	,	PUNCT
ap-7684	119	7	j	j	PROPN
ap-7684	119	8	+	+	CCONJ
ap-7684	119	9	{	{	PUNCT
ap-7684	119	10	gj}t	gj}t	PROPN
ap-7684	119	11	{	{	PUNCT
ap-7684	119	12	ut	ut	PROPN
ap-7684	119	13	,	,	PUNCT
ap-7684	119	14	j	j	PROPN
ap-7684	119	15	vj	vj	INTJ
ap-7684	119	16	}	}	PUNCT
ap-7684	119	17	−	−	PROPN
ap-7684	119	18	ub	ub	PROPN
ap-7684	119	19	,	,	PUNCT
ap-7684	119	20	i	i	PRON
ap-7684	119	21	+	+	CCONJ
ap-7684	119	22	{	{	PUNCT
ap-7684	119	23	gi}t	gi}t	PROPN
ap-7684	119	24	{	{	PUNCT
ap-7684	119	25	ut	ut	PROPN
ap-7684	119	26	,	,	PUNCT
ap-7684	119	27	i	i	PRON
ap-7684	119	28	vi	vi	VERB
ap-7684	119	29	}	}	PUNCT
ap-7684	119	30	)	)	PUNCT
ap-7684	119	31	/li	/li	PROPN
ap-7684	119	32	,	,	PUNCT
ap-7684	119	33	j	j	PROPN
ap-7684	119	34	(	(	PUNCT
ap-7684	119	35	6	6	NUM
ap-7684	119	36	)	)	PUNCT
ap-7684	119	37	where	where	SCONJ
ap-7684	119	38	indices	indice	VERB
ap-7684	119	39	i	i	PRON
ap-7684	119	40	and	and	CCONJ
ap-7684	119	41	j	j	PROPN
ap-7684	119	42	denote	denote	VERB
ap-7684	119	43	the	the	DET
ap-7684	119	44	nodes	node	NOUN
ap-7684	119	45	of	of	ADP
ap-7684	119	46	the	the	DET
ap-7684	119	47	element	element	NOUN
ap-7684	119	48	with	with	ADP
ap-7684	119	49	the	the	DET
ap-7684	119	50	element	element	NOUN
ap-7684	119	51	local	local	ADJ
ap-7684	119	52	x	x	VERB
ap-7684	119	53	axis	axis	NOUN
ap-7684	119	54	from	from	ADP
ap-7684	119	55	i	i	PRON
ap-7684	119	56	to	to	ADP
ap-7684	119	57	j.	j.	PROPN
ap-7684	119	58	in	in	ADP
ap-7684	119	59	the	the	DET
ap-7684	119	60	wake	wake	NOUN
ap-7684	119	61	of	of	ADP
ap-7684	119	62	it	it	PRON
ap-7684	119	63	,	,	PUNCT
ap-7684	119	64	the	the	DET
ap-7684	119	65	geometric	geometric	ADJ
ap-7684	119	66	matrix	matrix	NOUN
ap-7684	119	67	is	be	AUX
ap-7684	119	68	modified	modify	VERB
ap-7684	119	69	to	to	ADP
ap-7684	119	70	[	[	X
ap-7684	119	71	b	b	X
ap-7684	119	72	]	]	X
ap-7684	119	73	=	=	SYM
ap-7684	119	74	1	1	NUM
ap-7684	119	75	l	l	NOUN
ap-7684	119	76			NOUN
ap-7684	119	77	−1	−1	NOUN
ap-7684	119	78	0	0	NUM
ap-7684	119	79	0	0	NUM
ap-7684	119	80	1	1	NUM
ap-7684	119	81	0	0	NUM
ap-7684	119	82	0	0	NUM
ap-7684	119	83	gi	gi	NOUN
ap-7684	119	84	,	,	PUNCT
ap-7684	119	85	x	x	SYM
ap-7684	119	86	gi	gi	INTJ
ap-7684	119	87	,	,	PUNCT
ap-7684	119	88	y	y	PROPN
ap-7684	119	89	−1	−1	NOUN
ap-7684	119	90	gj	gj	PROPN
ap-7684	119	91	,	,	PUNCT
ap-7684	119	92	x	x	PROPN
ap-7684	119	93	gj	gj	PROPN
ap-7684	119	94	,	,	PUNCT
ap-7684	119	95	y	y	PROPN
ap-7684	119	96	1	1	NUM
ap-7684	119	97	λ	λ	SYM
ap-7684	119	98	−1	−1	NOUN
ap-7684	119	99	−λ	−λ	PROPN
ap-7684	119	100	λ	λ	PROPN
ap-7684	119	101	1	1	NUM
ap-7684	119	102	−λ	−λ	ADJ
ap-7684	119	103			NOUN
ap-7684	119	104	(	(	PUNCT
ap-7684	119	105	7	7	NUM
ap-7684	119	106	)	)	PUNCT
ap-7684	119	107	with	with	ADP
ap-7684	119	108	λ	λ	X
ap-7684	119	109	=	=	SYM
ap-7684	119	110	l	l	X
ap-7684	119	111	/	/	SYM
ap-7684	119	112	d/2	d/2	PROPN
ap-7684	119	113	and	and	CCONJ
ap-7684	119	114	subscripts	subscript	VERB
ap-7684	119	115	x	x	PUNCT
ap-7684	119	116	and	and	CCONJ
ap-7684	119	117	y	y	PROPN
ap-7684	119	118	indicating	indicate	VERB
ap-7684	119	119	components	component	NOUN
ap-7684	119	120	of	of	ADP
ap-7684	119	121	the	the	DET
ap-7684	119	122	vectors	vector	NOUN
ap-7684	119	123	g⃗	g⃗	PROPN
ap-7684	119	124	in	in	ADP
ap-7684	119	125	the	the	DET
ap-7684	119	126	global	global	ADJ
ap-7684	119	127	coordinate	coordinate	NOUN
ap-7684	119	128	system	system	NOUN
ap-7684	119	129	.	.	PUNCT
ap-7684	120	1	different	different	ADJ
ap-7684	120	2	element	element	NOUN
ap-7684	120	3	lengths	length	NOUN
ap-7684	120	4	have	have	VERB
ap-7684	120	5	to	to	PART
ap-7684	120	6	be	be	AUX
ap-7684	120	7	used	use	VERB
ap-7684	120	8	in	in	ADP
ap-7684	120	9	the	the	DET
ap-7684	120	10	geometric	geometric	ADJ
ap-7684	120	11	equation	equation	NOUN
ap-7684	120	12	7	7	NUM
ap-7684	120	13	and	and	CCONJ
ap-7684	120	14	the	the	DET
ap-7684	120	15	volume	volume	NOUN
ap-7684	120	16	integration	integration	NOUN
ap-7684	120	17	implicit	implicit	ADJ
ap-7684	120	18	in	in	ADP
ap-7684	120	19	8	8	NUM
ap-7684	120	20	.	.	PUNCT
ap-7684	121	1	the	the	DET
ap-7684	121	2	top	top	ADJ
ap-7684	121	3	face	face	NOUN
ap-7684	121	4	nodes	node	NOUN
ap-7684	121	5	distance	distance	NOUN
ap-7684	121	6	l	l	NOUN
ap-7684	121	7	is	be	AUX
ap-7684	121	8	used	use	VERB
ap-7684	121	9	in	in	ADP
ap-7684	121	10	the	the	DET
ap-7684	121	11	former	former	ADJ
ap-7684	121	12	case	case	NOUN
ap-7684	121	13	,	,	PUNCT
ap-7684	121	14	the	the	DET
ap-7684	121	15	reduced	reduce	VERB
ap-7684	121	16	length	length	NOUN
ap-7684	121	17	lred	lre	VERB
ap-7684	121	18	=	=	SYM
ap-7684	121	19	lrax	lrax	PROPN
ap-7684	121	20	/	/	SYM
ap-7684	121	21	rt	rt	PROPN
ap-7684	121	22	=	=	PUNCT
ap-7684	121	23	lrratio	lrratio	PROPN
ap-7684	121	24	is	be	AUX
ap-7684	121	25	used	use	VERB
ap-7684	121	26	in	in	ADP
ap-7684	121	27	the	the	DET
ap-7684	121	28	latter	latter	ADJ
ap-7684	121	29	case	case	NOUN
ap-7684	121	30	.	.	PUNCT
ap-7684	122	1	rax	rax	NOUN
ap-7684	122	2	denotes	denote	VERB
ap-7684	122	3	the	the	DET
ap-7684	122	4	radius	radius	NOUN
ap-7684	122	5	of	of	ADP
ap-7684	122	6	the	the	DET
ap-7684	122	7	arch	arch	ADJ
ap-7684	122	8	central	central	ADJ
ap-7684	122	9	axis	axis	NOUN
ap-7684	122	10	,	,	PUNCT
ap-7684	122	11	rt	rt	PROPN
ap-7684	122	12	is	be	AUX
ap-7684	122	13	the	the	DET
ap-7684	122	14	radius	radius	NOUN
ap-7684	122	15	of	of	ADP
ap-7684	122	16	the	the	DET
ap-7684	122	17	top	top	ADJ
ap-7684	122	18	face	face	NOUN
ap-7684	122	19	curve	curve	NOUN
ap-7684	122	20	.	.	PUNCT
ap-7684	123	1	the	the	DET
ap-7684	123	2	element	element	ADJ
ap-7684	123	3	stiffness	stiffness	NOUN
ap-7684	123	4	matrix	matrix	NOUN
ap-7684	123	5	for	for	ADP
ap-7684	123	6	an	an	DET
ap-7684	123	7	arch	arch	ADJ
ap-7684	123	8	element	element	NOUN
ap-7684	123	9	is	be	AUX
ap-7684	123	10	[	[	X
ap-7684	123	11	k]e	k]e	X
ap-7684	123	12	=	=	X
ap-7684	123	13	ebdlred[b]t	ebdlred[b]t	X
ap-7684	124	1	[	[	X
ap-7684	124	2	dcs][b	dcs][b	X
ap-7684	124	3	]	]	X
ap-7684	124	4	(	(	PUNCT
ap-7684	124	5	8)	8)	NUM
ap-7684	124	6	-4	-4	INTJ
ap-7684	124	7	-2	-2	NOUN
ap-7684	124	8	0	0	NUM
ap-7684	124	9	2	2	NUM
ap-7684	124	10	4	4	NUM
ap-7684	124	11	-32	-32	SYM
ap-7684	124	12	-30	-30	NUM
ap-7684	124	13	-28	-28	PROPN
ap-7684	124	14	-26	-26	PROPN
ap-7684	124	15	-24	-24	PUNCT
ap-7684	124	16	2587	2587	NUM
ap-7684	124	17	2176183115011182	2176183115011182	NUM
ap-7684	124	18	930.6114613401500164117861889188917731596141512561104963.2840.8739.7	930.6114613401500164117861889188917731596141512561104963.2840.8739.7	NUM
ap-7684	124	19	732.1810873.5924.2963.4992.210121024102910301027102310181014	732.1810873.5924.2963.4992.210121024102910301027102310181014	NUM
ap-7684	124	20	1013	1013	NUM
ap-7684	124	21	1015	1015	NUM
ap-7684	124	22	1021	1021	NUM
ap-7684	124	23	1031	1031	NUM
ap-7684	124	24	1043	1043	NUM
ap-7684	124	25	32.79	32.79	NUM
ap-7684	124	26	33.3625.514.772.337	33.3625.514.772.337	NUM
ap-7684	124	27	10.6723.2834.9345.5855.4464.5973.7681.7488.2593.2895.794.1388.34	10.6723.2834.9345.5855.4464.5973.7681.7488.2593.2895.794.1388.34	NUM
ap-7684	124	28	122.6162.2170.4	122.6162.2170.4	NUM
ap-7684	124	29	173.1318.9525.3723.4734.6209.217011612	173.1318.9525.3723.4734.6209.217011612	NUM
ap-7684	124	30	211.5125.5	211.5125.5	NUM
ap-7684	124	31	1667171753.04490.5563.2447.9301.5190.5135.7	1667171753.04490.5563.2447.9301.5190.5135.7	NUM
ap-7684	124	32	figure	figure	NOUN
ap-7684	124	33	5	5	NUM
ap-7684	124	34	.	.	PUNCT
ap-7684	124	35	bridge	bridge	NOUN
ap-7684	124	36	at	at	ADP
ap-7684	124	37	ponikla	ponikla	NOUN
ap-7684	124	38	,	,	PUNCT
ap-7684	124	39	compression	compression	NOUN
ap-7684	124	40	stresses	stress	VERB
ap-7684	125	1	[	[	X
ap-7684	125	2	kpa	kpa	X
ap-7684	125	3	]	]	X
ap-7684	125	4	and	and	CCONJ
ap-7684	125	5	depths	depth	NOUN
ap-7684	125	6	of	of	ADP
ap-7684	125	7	the	the	DET
ap-7684	125	8	cracks	crack	NOUN
ap-7684	125	9	in	in	ADP
ap-7684	125	10	the	the	DET
ap-7684	125	11	bed	bed	NOUN
ap-7684	125	12	joints	joint	NOUN
ap-7684	125	13	3	3	NUM
ap-7684	125	14	.	.	X
ap-7684	125	15	application	application	NOUN
ap-7684	125	16	to	to	ADP
ap-7684	125	17	an	an	DET
ap-7684	125	18	arch	arch	ADJ
ap-7684	125	19	bridge	bridge	NOUN
ap-7684	125	20	exclusive	exclusive	ADJ
ap-7684	125	21	translational	translational	ADJ
ap-7684	125	22	dofs	dof	NOUN
ap-7684	125	23	facilitate	facilitate	VERB
ap-7684	125	24	the	the	DET
ap-7684	125	25	combination	combination	NOUN
ap-7684	125	26	of	of	ADP
ap-7684	125	27	the	the	DET
ap-7684	125	28	tt	tt	PROPN
ap-7684	125	29	element	element	NOUN
ap-7684	125	30	with	with	ADP
ap-7684	125	31	simple	simple	ADJ
ap-7684	125	32	2d	2d	NUM
ap-7684	125	33	continuum	continuum	ADJ
ap-7684	125	34	elements	element	NOUN
ap-7684	125	35	.	.	PUNCT
ap-7684	126	1	a	a	DET
ap-7684	126	2	dedicated	dedicated	ADJ
ap-7684	126	3	matlab	matlab	NOUN
ap-7684	126	4	/	/	SYM
ap-7684	126	5	octave	octave	NOUN
ap-7684	126	6	code	code	NOUN
ap-7684	126	7	has	have	AUX
ap-7684	126	8	been	be	AUX
ap-7684	126	9	written	write	VERB
ap-7684	126	10	to	to	PART
ap-7684	126	11	utilize	utilize	VERB
ap-7684	126	12	this	this	DET
ap-7684	126	13	combination	combination	NOUN
ap-7684	126	14	for	for	ADP
ap-7684	126	15	the	the	DET
ap-7684	126	16	analysis	analysis	NOUN
ap-7684	126	17	of	of	ADP
ap-7684	126	18	masonry	masonry	NOUN
ap-7684	126	19	arch	arch	ADJ
ap-7684	126	20	bridges	bridge	NOUN
ap-7684	126	21	.	.	PUNCT
ap-7684	127	1	the	the	DET
ap-7684	127	2	code	code	NOUN
ap-7684	127	3	features	feature	VERB
ap-7684	127	4	the	the	DET
ap-7684	127	5	simplest	simple	ADJ
ap-7684	127	6	possible	possible	ADJ
ap-7684	127	7	way	way	NOUN
ap-7684	127	8	how	how	SCONJ
ap-7684	127	9	the	the	DET
ap-7684	127	10	interaction	interaction	NOUN
ap-7684	127	11	of	of	ADP
ap-7684	127	12	the	the	DET
ap-7684	127	13	masonry	masonry	NOUN
ap-7684	127	14	arch	arch	NOUN
ap-7684	127	15	,	,	PUNCT
ap-7684	127	16	backfill	backfill	NOUN
ap-7684	127	17	and	and	CCONJ
ap-7684	127	18	pavement	pavement	NOUN
ap-7684	127	19	can	can	AUX
ap-7684	127	20	be	be	AUX
ap-7684	127	21	assessed	assess	VERB
ap-7684	127	22	parallel	parallel	NOUN
ap-7684	127	23	with	with	ADP
ap-7684	127	24	the	the	DET
ap-7684	127	25	principal	principal	ADJ
ap-7684	127	26	pattern	pattern	NOUN
ap-7684	127	27	of	of	ADP
ap-7684	127	28	failure	failure	NOUN
ap-7684	127	29	of	of	ADP
ap-7684	127	30	the	the	DET
ap-7684	127	31	masonry	masonry	NOUN
ap-7684	127	32	arch	arch	VERB
ap-7684	127	33	.	.	PUNCT
ap-7684	128	1	the	the	DET
ap-7684	128	2	arch	arch	NOUN
ap-7684	128	3	and	and	CCONJ
ap-7684	128	4	pavement	pavement	NOUN
ap-7684	128	5	are	be	AUX
ap-7684	128	6	modelled	model	VERB
ap-7684	128	7	by	by	ADP
ap-7684	128	8	the	the	DET
ap-7684	128	9	tt	tt	PROPN
ap-7684	128	10	elements	element	NOUN
ap-7684	128	11	,	,	PUNCT
ap-7684	128	12	the	the	DET
ap-7684	128	13	backfill	backfill	NOUN
ap-7684	128	14	by	by	ADP
ap-7684	128	15	the	the	DET
ap-7684	128	16	classic	classic	ADJ
ap-7684	128	17	constant	constant	ADJ
ap-7684	128	18	strain	strain	NOUN
ap-7684	128	19	triangle	triangle	NOUN
ap-7684	128	20	(	(	PUNCT
ap-7684	128	21	cst	cst	PROPN
ap-7684	128	22	)	)	PUNCT
ap-7684	128	23	elements	element	NOUN
ap-7684	128	24	.	.	PUNCT
ap-7684	129	1	meshing	meshing	NOUN
ap-7684	129	2	of	of	ADP
ap-7684	129	3	the	the	DET
ap-7684	129	4	backfill	backfill	NOUN
ap-7684	129	5	provides	provide	VERB
ap-7684	129	6	the	the	DET
ap-7684	129	7	persson	persson	PROPN
ap-7684	129	8	and	and	CCONJ
ap-7684	129	9	strang	strang	PROPN
ap-7684	129	10	mesh	mesh	PROPN
ap-7684	129	11	generator	generator	PROPN
ap-7684	129	12	,	,	PUNCT
ap-7684	129	13	[	[	X
ap-7684	129	14	8	8	NUM
ap-7684	129	15	]	]	PUNCT
ap-7684	129	16	.	.	PUNCT
ap-7684	130	1	the	the	DET
ap-7684	130	2	no	no	DET
ap-7684	130	3	-	-	PUNCT
ap-7684	130	4	tension	tension	NOUN
ap-7684	130	5	cross	cross	ADJ
ap-7684	130	6	-	-	ADJ
ap-7684	130	7	section	section	ADJ
ap-7684	130	8	model	model	NOUN
ap-7684	130	9	defined	define	VERB
ap-7684	130	10	in	in	ADP
ap-7684	130	11	section	section	NOUN
ap-7684	130	12	2.1	2.1	NUM
ap-7684	130	13	supports	support	VERB
ap-7684	130	14	the	the	DET
ap-7684	130	15	cracking	cracking	NOUN
ap-7684	130	16	of	of	ADP
ap-7684	130	17	the	the	DET
ap-7684	130	18	arch	arch	ADJ
ap-7684	130	19	bed	bed	NOUN
ap-7684	130	20	joints	joint	NOUN
ap-7684	130	21	,	,	PUNCT
ap-7684	130	22	which	which	PRON
ap-7684	130	23	is	be	AUX
ap-7684	130	24	the	the	DET
ap-7684	130	25	dominant	dominant	ADJ
ap-7684	130	26	pattern	pattern	NOUN
ap-7684	130	27	of	of	ADP
ap-7684	130	28	the	the	DET
ap-7684	130	29	masonry	masonry	PROPN
ap-7684	130	30	arch	arch	PROPN
ap-7684	130	31	bridge	bridge	NOUN
ap-7684	130	32	failure	failure	NOUN
ap-7684	130	33	.	.	PUNCT
ap-7684	131	1	the	the	DET
ap-7684	131	2	code	code	NOUN
ap-7684	131	3	includes	include	VERB
ap-7684	131	4	a	a	DET
ap-7684	131	5	simple	simple	ADJ
ap-7684	131	6	,	,	PUNCT
ap-7684	131	7	purely	purely	ADV
ap-7684	131	8	vector	vector	NOUN
ap-7684	131	9	graphics	graphic	NOUN
ap-7684	131	10	output	output	NOUN
ap-7684	131	11	.	.	PUNCT
ap-7684	132	1	it	it	PRON
ap-7684	132	2	consists	consist	VERB
ap-7684	132	3	of	of	ADP
ap-7684	132	4	1150	1150	NUM
ap-7684	132	5	octave	octave	NOUN
ap-7684	132	6	command	command	NOUN
ap-7684	132	7	lines	line	NOUN
ap-7684	132	8	,	,	PUNCT
ap-7684	132	9	not	not	PART
ap-7684	132	10	including	include	VERB
ap-7684	132	11	the	the	DET
ap-7684	132	12	mesh	mesh	NOUN
ap-7684	132	13	generator	generator	NOUN
ap-7684	132	14	.	.	PUNCT
ap-7684	133	1	an	an	DET
ap-7684	133	2	application	application	NOUN
ap-7684	133	3	to	to	ADP
ap-7684	133	4	the	the	DET
ap-7684	133	5	sandstone	sandstone	NOUN
ap-7684	133	6	arch	arch	NOUN
ap-7684	133	7	bridge	bridge	NOUN
ap-7684	133	8	at	at	ADP
ap-7684	133	9	ponikla	ponikla	NOUN
ap-7684	133	10	in	in	ADP
ap-7684	133	11	north	north	NOUN
ap-7684	133	12	bohemia	bohemia	NOUN
ap-7684	133	13	illustrates	illustrate	VERB
ap-7684	133	14	the	the	DET
ap-7684	133	15	code	code	NOUN
ap-7684	133	16	output	output	NOUN
ap-7684	133	17	in	in	ADP
ap-7684	133	18	figure	figure	NOUN
ap-7684	133	19	5	5	NUM
ap-7684	133	20	.	.	PUNCT
ap-7684	134	1	the	the	DET
ap-7684	134	2	span	span	NOUN
ap-7684	134	3	of	of	ADP
ap-7684	134	4	the	the	DET
ap-7684	134	5	arch	arch	NOUN
ap-7684	134	6	is	be	AUX
ap-7684	134	7	11.4	11.4	NUM
ap-7684	134	8	m.	m.	NOUN
ap-7684	134	9	two	two	NUM
ap-7684	134	10	principal	principal	ADJ
ap-7684	134	11	quantities	quantity	NOUN
ap-7684	134	12	are	be	AUX
ap-7684	134	13	shown	show	VERB
ap-7684	134	14	in	in	ADP
ap-7684	134	15	each	each	DET
ap-7684	134	16	arch	arch	ADJ
ap-7684	134	17	element	element	NOUN
ap-7684	134	18	,	,	PUNCT
ap-7684	134	19	the	the	DET
ap-7684	134	20	maximum	maximum	ADJ
ap-7684	134	21	compression	compression	NOUN
ap-7684	134	22	normal	normal	ADJ
ap-7684	134	23	stress	stress	NOUN
ap-7684	134	24	value	value	NOUN
ap-7684	134	25	inserted	insert	VERB
ap-7684	134	26	at	at	ADP
ap-7684	134	27	the	the	DET
ap-7684	134	28	arch	arch	ADJ
ap-7684	134	29	face	face	NOUN
ap-7684	134	30	where	where	SCONJ
ap-7684	134	31	it	it	PRON
ap-7684	134	32	occurs	occur	VERB
ap-7684	134	33	and	and	CCONJ
ap-7684	134	34	the	the	DET
ap-7684	134	35	depth	depth	NOUN
ap-7684	134	36	of	of	ADP
ap-7684	134	37	the	the	DET
ap-7684	134	38	cracks	crack	NOUN
ap-7684	134	39	in	in	ADP
ap-7684	134	40	the	the	DET
ap-7684	134	41	bed	bed	NOUN
ap-7684	134	42	joint	joint	NOUN
ap-7684	134	43	.	.	PUNCT
ap-7684	135	1	the	the	DET
ap-7684	135	2	load	load	NOUN
ap-7684	135	3	case	case	NOUN
ap-7684	135	4	is	be	AUX
ap-7684	135	5	the	the	DET
ap-7684	135	6	design	design	NOUN
ap-7684	135	7	dead	dead	ADJ
ap-7684	135	8	load	load	NOUN
ap-7684	135	9	combined	combine	VERB
ap-7684	135	10	with	with	ADP
ap-7684	135	11	the	the	DET
ap-7684	135	12	tandem	tandem	NOUN
ap-7684	135	13	axle	axle	NOUN
ap-7684	135	14	live	live	VERB
ap-7684	135	15	loads	load	NOUN
ap-7684	135	16	with	with	ADP
ap-7684	135	17	twice	twice	DET
ap-7684	135	18	the	the	DET
ap-7684	135	19	design	design	NOUN
ap-7684	135	20	intensity	intensity	NOUN
ap-7684	135	21	level	level	NOUN
ap-7684	135	22	,	,	PUNCT
ap-7684	135	23	i.e.	i.e.	X
ap-7684	135	24	,	,	PUNCT
ap-7684	135	25	360	360	NUM
ap-7684	135	26	kn	kn	NOUN
ap-7684	135	27	per	per	ADP
ap-7684	135	28	wheel	wheel	NOUN
ap-7684	135	29	in	in	ADP
ap-7684	135	30	lane	lane	NOUN
ap-7684	135	31	1	1	NUM
ap-7684	135	32	according	accord	VERB
ap-7684	135	33	to	to	ADP
ap-7684	135	34	en	en	ADP
ap-7684	135	35	1991	1991	NUM
ap-7684	135	36	-	-	SYM
ap-7684	135	37	2	2	NUM
ap-7684	135	38	.	.	PUNCT
ap-7684	136	1	the	the	DET
ap-7684	136	2	tt	tt	PROPN
ap-7684	136	3	element	element	NOUN
ap-7684	136	4	and	and	CCONJ
ap-7684	136	5	the	the	DET
ap-7684	136	6	masonry	masonry	NOUN
ap-7684	136	7	arch	arch	PROPN
ap-7684	136	8	fem	fem	NOUN
ap-7684	136	9	models	model	NOUN
ap-7684	136	10	based	base	VERB
ap-7684	136	11	on	on	ADP
ap-7684	136	12	it	it	PRON
ap-7684	136	13	claim	claim	VERB
ap-7684	136	14	to	to	PART
ap-7684	136	15	be	be	AUX
ap-7684	136	16	the	the	DET
ap-7684	136	17	simplest	simple	ADJ
ap-7684	136	18	models	model	NOUN
ap-7684	136	19	available	available	ADJ
ap-7684	136	20	to	to	PART
ap-7684	136	21	assess	assess	VERB
ap-7684	136	22	the	the	DET
ap-7684	136	23	most	most	ADV
ap-7684	136	24	frequent	frequent	ADJ
ap-7684	136	25	failure	failure	NOUN
ap-7684	136	26	mode	mode	NOUN
ap-7684	136	27	of	of	ADP
ap-7684	136	28	the	the	DET
ap-7684	136	29	stone	stone	NOUN
ap-7684	136	30	masonry	masonry	NOUN
ap-7684	136	31	arches	arch	NOUN
ap-7684	136	32	and	and	CCONJ
ap-7684	136	33	the	the	DET
ap-7684	136	34	interaction	interaction	NOUN
ap-7684	136	35	of	of	ADP
ap-7684	136	36	the	the	DET
ap-7684	136	37	arch	arch	NOUN
ap-7684	136	38	with	with	ADP
ap-7684	136	39	backfill	backfill	NOUN
ap-7684	136	40	and	and	CCONJ
ap-7684	136	41	pavement	pavement	NOUN
ap-7684	136	42	.	.	PUNCT
ap-7684	137	1	4	4	X
ap-7684	137	2	.	.	X
ap-7684	137	3	3d	3d	PROPN
ap-7684	137	4	mindlin	mindlin	PROPN
ap-7684	137	5	shell	shell	PROPN
ap-7684	137	6	element	element	NOUN
ap-7684	137	7	tm	tm	ADP
ap-7684	137	8	the	the	DET
ap-7684	137	9	2d	2d	NOUN
ap-7684	137	10	models	model	NOUN
ap-7684	137	11	are	be	AUX
ap-7684	137	12	often	often	ADV
ap-7684	137	13	not	not	PART
ap-7684	137	14	adequate	adequate	ADJ
ap-7684	137	15	for	for	SCONJ
ap-7684	137	16	the	the	DET
ap-7684	137	17	solution	solution	NOUN
ap-7684	137	18	of	of	ADP
ap-7684	137	19	masonry	masonry	NOUN
ap-7684	137	20	arches	arch	VERB
ap-7684	137	21	whose	whose	DET
ap-7684	137	22	widths	width	NOUN
ap-7684	137	23	are	be	AUX
ap-7684	137	24	mostly	mostly	ADV
ap-7684	137	25	comparable	comparable	ADJ
ap-7684	137	26	to	to	ADP
ap-7684	137	27	spans	span	NOUN
ap-7684	137	28	which	which	PRON
ap-7684	137	29	makes	make	VERB
ap-7684	137	30	the	the	DET
ap-7684	137	31	transverse	transverse	ADJ
ap-7684	137	32	variation	variation	NOUN
ap-7684	137	33	of	of	ADP
ap-7684	137	34	stresses	stress	NOUN
ap-7684	137	35	and	and	CCONJ
ap-7684	137	36	displacements	displacement	NOUN
ap-7684	137	37	nonuniform	nonuniform	ADJ
ap-7684	137	38	.	.	PUNCT
ap-7684	138	1	a	a	DET
ap-7684	138	2	3d	3d	NUM
ap-7684	138	3	analogue	analogue	NOUN
ap-7684	138	4	to	to	ADP
ap-7684	138	5	the	the	DET
ap-7684	138	6	2d	2d	NOUN
ap-7684	138	7	tt	tt	PROPN
ap-7684	138	8	element	element	NOUN
ap-7684	138	9	is	be	AUX
ap-7684	138	10	,	,	PUNCT
ap-7684	138	11	therefore	therefore	ADV
ap-7684	138	12	,	,	PUNCT
ap-7684	138	13	derived	derive	VERB
ap-7684	138	14	.	.	PUNCT
ap-7684	139	1	the	the	DET
ap-7684	139	2	mindlin	mindlin	PROPN
ap-7684	139	3	assumptions	assumption	NOUN
ap-7684	139	4	,	,	PUNCT
ap-7684	139	5	[	[	X
ap-7684	139	6	9	9	NUM
ap-7684	139	7	]	]	PUNCT
ap-7684	139	8	,	,	PUNCT
ap-7684	139	9	and	and	CCONJ
ap-7684	139	10	the	the	DET
ap-7684	139	11	simplest	simple	ADJ
ap-7684	139	12	triangular	triangular	NOUN
ap-7684	139	13	facet	facet	ADJ
ap-7684	139	14	shape	shape	NOUN
ap-7684	139	15	are	be	AUX
ap-7684	139	16	adopted	adopt	VERB
ap-7684	139	17	,	,	PUNCT
ap-7684	139	18	see	see	VERB
ap-7684	139	19	figure	figure	NOUN
ap-7684	139	20	6	6	NUM
ap-7684	139	21	.	.	PUNCT
ap-7684	140	1	the	the	DET
ap-7684	140	2	element	element	ADJ
ap-7684	140	3	local	local	ADJ
ap-7684	140	4	coordinate	coordinate	NOUN
ap-7684	140	5	system	system	NOUN
ap-7684	140	6	features	feature	VERB
ap-7684	140	7	z	z	NOUN
ap-7684	140	8	axis	axis	VERB
ap-7684	140	9	normal	normal	ADJ
ap-7684	140	10	to	to	ADP
ap-7684	140	11	the	the	DET
ap-7684	140	12	facet	facet	ADJ
ap-7684	140	13	plane	plane	NOUN
ap-7684	140	14	.	.	PUNCT
ap-7684	141	1	there	there	PRON
ap-7684	141	2	is	be	VERB
ap-7684	141	3	always	always	ADV
ap-7684	141	4	a	a	DET
ap-7684	141	5	preference	preference	NOUN
ap-7684	141	6	direction	direction	NOUN
ap-7684	141	7	in	in	ADP
ap-7684	141	8	the	the	DET
ap-7684	141	9	facet	facet	ADJ
ap-7684	141	10	plane	plane	NOUN
ap-7684	141	11	,	,	PUNCT
ap-7684	141	12	the	the	DET
ap-7684	141	13	direction	direction	NOUN
ap-7684	141	14	closest	close	ADJ
ap-7684	141	15	to	to	ADP
ap-7684	141	16	the	the	DET
ap-7684	141	17	normals	normal	NOUN
ap-7684	141	18	296	296	NUM
ap-7684	141	19	vol	vol	NOUN
ap-7684	141	20	.	.	PUNCT
ap-7684	142	1	62	62	NUM
ap-7684	142	2	no	no	INTJ
ap-7684	142	3	.	.	PUNCT
ap-7684	143	1	2/2022	2/2022	PROPN
ap-7684	144	1	a	a	DET
ap-7684	144	2	mindlin	mindlin	PROPN
ap-7684	144	3	shell	shell	PROPN
ap-7684	144	4	finite	finite	PROPN
ap-7684	144	5	element	element	NOUN
ap-7684	144	6	for	for	ADP
ap-7684	144	7	stone	stone	NOUN
ap-7684	144	8	masonry	masonry	NOUN
ap-7684	144	9	bridges	bridge	NOUN
ap-7684	144	10	with	with	ADP
ap-7684	144	11	backfill	backfill	NOUN
ap-7684	144	12	k	k	NOUN
ap-7684	145	1	x	x	PUNCT
ap-7684	145	2	j	j	PROPN
ap-7684	146	1	d	d	X
ap-7684	146	2	y	y	PROPN
ap-7684	146	3	z	z	NOUN
ap-7684	147	1	i	i	PRON
ap-7684	147	2	u	u	PROPN
ap-7684	147	3	w	w	PROPN
ap-7684	147	4	t	t	PROPN
ap-7684	147	5	,	,	PUNCT
ap-7684	147	6	x	x	PROPN
ap-7684	147	7	ut	ut	PROPN
ap-7684	147	8	,	,	PUNCT
ap-7684	147	9	y	y	PROPN
ap-7684	147	10	u	u	NOUN
ap-7684	147	11	u	u	PROPN
ap-7684	147	12	b	b	PROPN
ap-7684	147	13	,	,	PUNCT
ap-7684	147	14	x	x	PROPN
ap-7684	147	15	b	b	X
ap-7684	147	16	,	,	PUNCT
ap-7684	147	17	y	y	PROPN
ap-7684	147	18	figure	figure	NOUN
ap-7684	147	19	6	6	NUM
ap-7684	147	20	.	.	PUNCT
ap-7684	148	1	geometry	geometry	NOUN
ap-7684	148	2	of	of	ADP
ap-7684	148	3	the	the	DET
ap-7684	148	4	shell	shell	ADJ
ap-7684	148	5	facet	facet	ADJ
ap-7684	148	6	triangle	triangle	NOUN
ap-7684	148	7	element	element	NOUN
ap-7684	148	8	,	,	PUNCT
ap-7684	148	9	the	the	DET
ap-7684	148	10	element	element	ADJ
ap-7684	148	11	local	local	ADJ
ap-7684	148	12	coordinate	coordinate	NOUN
ap-7684	148	13	system	system	NOUN
ap-7684	148	14	and	and	CCONJ
ap-7684	148	15	the	the	DET
ap-7684	148	16	dofs	dof	NOUN
ap-7684	148	17	at	at	ADP
ap-7684	148	18	node	node	PROPN
ap-7684	148	19	i	i	PRON
ap-7684	148	20	to	to	ADP
ap-7684	148	21	the	the	DET
ap-7684	148	22	bed	bed	NOUN
ap-7684	148	23	joints	joint	NOUN
ap-7684	148	24	planes	plane	NOUN
ap-7684	148	25	of	of	ADP
ap-7684	148	26	the	the	DET
ap-7684	148	27	masonry	masonry	NOUN
ap-7684	148	28	arch	arch	VERB
ap-7684	148	29	.	.	PUNCT
ap-7684	149	1	it	it	PRON
ap-7684	149	2	is	be	AUX
ap-7684	149	3	assumed	assume	VERB
ap-7684	149	4	forthwith	forthwith	NOUN
ap-7684	149	5	that	that	SCONJ
ap-7684	149	6	the	the	DET
ap-7684	149	7	arch	arch	NOUN
ap-7684	149	8	is	be	AUX
ap-7684	149	9	a	a	DET
ap-7684	149	10	cylindric	cylindric	ADJ
ap-7684	149	11	segment	segment	NOUN
ap-7684	149	12	shell	shell	NOUN
ap-7684	149	13	and	and	CCONJ
ap-7684	149	14	the	the	DET
ap-7684	149	15	bed	bed	NOUN
ap-7684	149	16	joints	joint	NOUN
ap-7684	149	17	normals	normal	NOUN
ap-7684	149	18	are	be	AUX
ap-7684	149	19	tangents	tangent	NOUN
ap-7684	149	20	to	to	ADP
ap-7684	149	21	the	the	DET
ap-7684	149	22	directrix	directrix	NOUN
ap-7684	149	23	of	of	ADP
ap-7684	149	24	the	the	DET
ap-7684	149	25	cylinder	cylinder	NOUN
ap-7684	149	26	so	so	SCONJ
ap-7684	149	27	that	that	SCONJ
ap-7684	149	28	their	their	PRON
ap-7684	149	29	directions	direction	NOUN
ap-7684	149	30	lie	lie	VERB
ap-7684	149	31	in	in	ADP
ap-7684	149	32	a	a	DET
ap-7684	149	33	single	single	ADJ
ap-7684	149	34	plane	plane	NOUN
ap-7684	149	35	.	.	PUNCT
ap-7684	150	1	the	the	DET
ap-7684	150	2	global	global	ADJ
ap-7684	150	3	x	x	ADJ
ap-7684	150	4	axis	axis	NOUN
ap-7684	150	5	is	be	AUX
ap-7684	150	6	assumed	assume	VERB
ap-7684	150	7	to	to	PART
ap-7684	150	8	lie	lie	VERB
ap-7684	150	9	in	in	ADP
ap-7684	150	10	that	that	DET
ap-7684	150	11	plane	plane	NOUN
ap-7684	150	12	,	,	PUNCT
ap-7684	150	13	too	too	ADV
ap-7684	150	14	.	.	PUNCT
ap-7684	151	1	in	in	ADP
ap-7684	151	2	terms	term	NOUN
ap-7684	151	3	of	of	ADP
ap-7684	151	4	the	the	DET
ap-7684	151	5	bridge	bridge	NOUN
ap-7684	151	6	nomenclature	nomenclature	NOUN
ap-7684	151	7	,	,	PUNCT
ap-7684	151	8	the	the	DET
ap-7684	151	9	global	global	ADJ
ap-7684	151	10	x	x	ADJ
ap-7684	151	11	axis	axis	NOUN
ap-7684	151	12	is	be	AUX
ap-7684	151	13	in	in	ADP
ap-7684	151	14	the	the	DET
ap-7684	151	15	direction	direction	NOUN
ap-7684	151	16	of	of	ADP
ap-7684	151	17	the	the	DET
ap-7684	151	18	arch	arch	ADJ
ap-7684	151	19	span	span	NOUN
ap-7684	151	20	.	.	PUNCT
ap-7684	152	1	the	the	DET
ap-7684	152	2	element	element	NOUN
ap-7684	152	3	local	local	ADJ
ap-7684	152	4	x	x	VERB
ap-7684	152	5	axis	axis	NOUN
ap-7684	152	6	is	be	AUX
ap-7684	152	7	chosen	choose	VERB
ap-7684	152	8	as	as	ADP
ap-7684	152	9	the	the	DET
ap-7684	152	10	direction	direction	NOUN
ap-7684	152	11	closest	close	ADJ
ap-7684	152	12	to	to	ADP
ap-7684	152	13	the	the	DET
ap-7684	152	14	global	global	ADJ
ap-7684	152	15	x	x	PUNCT
ap-7684	152	16	within	within	ADP
ap-7684	152	17	the	the	DET
ap-7684	152	18	element	element	NOUN
ap-7684	152	19	plane	plane	NOUN
ap-7684	152	20	.	.	PUNCT
ap-7684	153	1	the	the	DET
ap-7684	153	2	no	no	DET
ap-7684	153	3	-	-	PUNCT
ap-7684	153	4	tension	tension	NOUN
ap-7684	153	5	condition	condition	NOUN
ap-7684	153	6	is	be	AUX
ap-7684	153	7	applied	apply	VERB
ap-7684	153	8	to	to	ADP
ap-7684	153	9	the	the	DET
ap-7684	153	10	σx	σx	PROPN
ap-7684	153	11	(	(	PUNCT
ap-7684	153	12	local	local	ADJ
ap-7684	153	13	x	x	NOUN
ap-7684	153	14	)	)	PUNCT
ap-7684	153	15	normal	normal	ADJ
ap-7684	153	16	stress	stress	NOUN
ap-7684	153	17	component	component	NOUN
ap-7684	153	18	.	.	PUNCT
ap-7684	154	1	other	other	ADJ
ap-7684	154	2	options	option	NOUN
ap-7684	154	3	are	be	AUX
ap-7684	154	4	possible	possible	ADJ
ap-7684	154	5	and	and	CCONJ
ap-7684	154	6	can	can	AUX
ap-7684	154	7	be	be	AUX
ap-7684	154	8	rather	rather	ADV
ap-7684	154	9	easily	easily	ADV
ap-7684	154	10	implemented	implement	VERB
ap-7684	154	11	in	in	ADP
ap-7684	154	12	the	the	DET
ap-7684	154	13	code	code	NOUN
ap-7684	154	14	.	.	PUNCT
ap-7684	155	1	it	it	PRON
ap-7684	155	2	may	may	AUX
ap-7684	155	3	be	be	AUX
ap-7684	155	4	necessary	necessary	ADJ
ap-7684	155	5	in	in	ADP
ap-7684	155	6	case	case	NOUN
ap-7684	155	7	of	of	ADP
ap-7684	155	8	other	other	ADJ
ap-7684	155	9	than	than	ADP
ap-7684	155	10	cylindric	cylindric	ADJ
ap-7684	155	11	shells	shell	NOUN
ap-7684	155	12	or	or	CCONJ
ap-7684	155	13	more	more	ADJ
ap-7684	155	14	general	general	ADJ
ap-7684	155	15	failure	failure	NOUN
ap-7684	155	16	modes	mode	NOUN
ap-7684	155	17	and	and	CCONJ
ap-7684	155	18	constitutive	constitutive	ADJ
ap-7684	155	19	equations	equation	NOUN
ap-7684	155	20	.	.	PUNCT
ap-7684	156	1	local	local	ADJ
ap-7684	156	2	y	y	PROPN
ap-7684	156	3	axis	axis	NOUN
ap-7684	156	4	completes	complete	VERB
ap-7684	156	5	the	the	DET
ap-7684	156	6	element	element	NOUN
ap-7684	156	7	local	local	ADJ
ap-7684	156	8	right	right	ADV
ap-7684	156	9	-	-	PUNCT
ap-7684	156	10	handed	handed	ADJ
ap-7684	156	11	cartesian	cartesian	ADJ
ap-7684	156	12	coordinate	coordinate	NOUN
ap-7684	156	13	system	system	NOUN
ap-7684	156	14	.	.	PUNCT
ap-7684	157	1	all	all	DET
ap-7684	157	2	components	component	NOUN
ap-7684	157	3	are	be	AUX
ap-7684	157	4	in	in	ADP
ap-7684	157	5	this	this	DET
ap-7684	157	6	system	system	NOUN
ap-7684	157	7	up	up	ADP
ap-7684	157	8	to	to	ADP
ap-7684	157	9	section	section	NOUN
ap-7684	157	10	4.4	4.4	NUM
ap-7684	157	11	,	,	PUNCT
ap-7684	157	12	where	where	SCONJ
ap-7684	157	13	two	two	NUM
ap-7684	157	14	other	other	ADJ
ap-7684	157	15	systems	system	NOUN
ap-7684	157	16	are	be	AUX
ap-7684	157	17	necessary	necessary	ADJ
ap-7684	157	18	.	.	PUNCT
ap-7684	158	1	five	five	NUM
ap-7684	158	2	translational	translational	ADJ
ap-7684	158	3	dofs	dof	NOUN
ap-7684	158	4	per	per	ADP
ap-7684	158	5	node	node	NOUN
ap-7684	158	6	are	be	AUX
ap-7684	158	7	shown	show	VERB
ap-7684	158	8	in	in	ADP
ap-7684	158	9	figure	figure	NOUN
ap-7684	158	10	6	6	NUM
ap-7684	158	11	for	for	ADP
ap-7684	158	12	node	node	ADJ
ap-7684	158	13	i.	i.	NOUN
ap-7684	158	14	they	they	PRON
ap-7684	158	15	are	be	AUX
ap-7684	158	16	ordered	order	VERB
ap-7684	158	17	in	in	ADP
ap-7684	158	18	matrix	matrix	NOUN
ap-7684	158	19	{	{	PUNCT
ap-7684	158	20	u	u	NOUN
ap-7684	158	21	}	}	PUNCT
ap-7684	158	22	at	at	ADP
ap-7684	158	23	each	each	DET
ap-7684	158	24	node	node	NOUN
ap-7684	158	25	,	,	PUNCT
ap-7684	158	26	with	with	SCONJ
ap-7684	158	27	node	node	ADJ
ap-7684	158	28	index	index	NOUN
ap-7684	158	29	omitted	omit	VERB
ap-7684	158	30	:	:	PUNCT
ap-7684	158	31	{	{	PUNCT
ap-7684	158	32	u}t	u}t	ADJ
ap-7684	158	33	=	=	SYM
ap-7684	158	34	{	{	PUNCT
ap-7684	158	35	ut	ut	PROPN
ap-7684	158	36	,	,	PUNCT
ap-7684	158	37	x	x	NOUN
ap-7684	158	38	,	,	PUNCT
ap-7684	158	39	ut	ut	PROPN
ap-7684	158	40	,	,	PUNCT
ap-7684	158	41	y	y	PROPN
ap-7684	158	42	,	,	PUNCT
ap-7684	158	43	w	w	PROPN
ap-7684	158	44	,	,	PUNCT
ap-7684	158	45	ub	ub	ADP
ap-7684	158	46	,	,	PUNCT
ap-7684	158	47	x	x	X
ap-7684	158	48	,	,	PUNCT
ap-7684	158	49	ub	ub	PROPN
ap-7684	158	50	,	,	PUNCT
ap-7684	158	51	y	y	PROPN
ap-7684	158	52	}	}	PUNCT
ap-7684	158	53	deflection	deflection	NOUN
ap-7684	158	54	w	w	NOUN
ap-7684	158	55	and	and	CCONJ
ap-7684	158	56	in	in	ADP
ap-7684	158	57	-	-	PUNCT
ap-7684	158	58	plane	plane	NOUN
ap-7684	158	59	displacement	displacement	NOUN
ap-7684	158	60	vector	vector	NOUN
ap-7684	158	61	u⃗	u⃗	PROPN
ap-7684	158	62	are	be	AUX
ap-7684	158	63	approximated	approximate	VERB
ap-7684	158	64	by	by	ADP
ap-7684	158	65	linear	linear	ADJ
ap-7684	158	66	independent	independent	ADJ
ap-7684	158	67	functions	function	NOUN
ap-7684	158	68	of	of	ADP
ap-7684	158	69	natural	natural	ADJ
ap-7684	158	70	triangular	triangular	NOUN
ap-7684	158	71	coordinates	coordinate	NOUN
ap-7684	158	72	ξi	ξi	NOUN
ap-7684	158	73	.	.	PUNCT
ap-7684	159	1	w	w	PROPN
ap-7684	159	2	=	=	PUNCT
ap-7684	159	3	∑	∑	PROPN
ap-7684	159	4	i	i	PRON
ap-7684	159	5	wiξi	wiξi	VERB
ap-7684	159	6	,	,	PUNCT
ap-7684	159	7	u⃗	u⃗	PROPN
ap-7684	159	8	=	=	PUNCT
ap-7684	159	9	∑	∑	PUNCT
ap-7684	159	10	i	i	PRON
ap-7684	159	11	u⃗iξi	u⃗iξi	PROPN
ap-7684	159	12	in	in	ADP
ap-7684	159	13	literature	literature	NOUN
ap-7684	159	14	,	,	PUNCT
ap-7684	159	15	a	a	DET
ap-7684	159	16	common	common	ADJ
ap-7684	159	17	term	term	NOUN
ap-7684	159	18	for	for	ADP
ap-7684	159	19	this	this	DET
ap-7684	159	20	kind	kind	NOUN
ap-7684	159	21	of	of	ADP
ap-7684	159	22	approximation	approximation	NOUN
ap-7684	159	23	is	be	AUX
ap-7684	159	24	isoparametric	isoparametric	ADJ
ap-7684	159	25	element	element	NOUN
ap-7684	159	26	,	,	PUNCT
ap-7684	159	27	not	not	PART
ap-7684	159	28	to	to	PART
ap-7684	159	29	be	be	AUX
ap-7684	159	30	confused	confuse	VERB
ap-7684	159	31	with	with	ADP
ap-7684	159	32	true	true	ADJ
ap-7684	159	33	isoparametric	isoparametric	ADJ
ap-7684	159	34	elements	element	NOUN
ap-7684	159	35	for	for	ADP
ap-7684	159	36	2d	2d	NUM
ap-7684	159	37	and	and	CCONJ
ap-7684	159	38	3d	3d	NUM
ap-7684	159	39	continua	continuum	NOUN
ap-7684	159	40	.	.	PUNCT
ap-7684	160	1	derivatives	derivative	NOUN
ap-7684	160	2	of	of	ADP
ap-7684	160	3	ξi	ξi	NOUN
ap-7684	160	4	are	be	AUX
ap-7684	160	5	constants	constant	NOUN
ap-7684	160	6	in	in	ADP
ap-7684	160	7	the	the	DET
ap-7684	160	8	element	element	NOUN
ap-7684	160	9	area	area	NOUN
ap-7684	160	10	,	,	PUNCT
ap-7684	160	11	∂ξi	∂ξi	PROPN
ap-7684	160	12	∂x	∂x	NOUN
ap-7684	160	13	=	=	SYM
ap-7684	160	14	bi	bi	ADJ
ap-7684	160	15	2a	2a	NUM
ap-7684	160	16	,	,	PUNCT
ap-7684	160	17	∂ξi	∂ξi	NOUN
ap-7684	160	18	∂y	∂y	X
ap-7684	161	1	=	=	NOUN
ap-7684	161	2	ai	ai	VERB
ap-7684	161	3	2a	2a	NUM
ap-7684	161	4	or	or	CCONJ
ap-7684	161	5	∂ξi	∂ξi	NOUN
ap-7684	161	6	∂x⃗	∂x⃗	NUM
ap-7684	161	7	=	=	SYM
ap-7684	161	8	−n⃗i	−n⃗i	NUM
ap-7684	161	9	li	li	PROPN
ap-7684	161	10	2a	2a	NUM
ap-7684	161	11	,	,	PUNCT
ap-7684	161	12	where	where	SCONJ
ap-7684	161	13	a	a	PRON
ap-7684	161	14	is	be	AUX
ap-7684	161	15	the	the	DET
ap-7684	161	16	element	element	ADJ
ap-7684	161	17	area	area	NOUN
ap-7684	161	18	(	(	PUNCT
ap-7684	161	19	note	note	VERB
ap-7684	161	20	that	that	PRON
ap-7684	161	21	li/2a	li/2a	PROPN
ap-7684	161	22	is	be	AUX
ap-7684	161	23	the	the	DET
ap-7684	161	24	slope	slope	NOUN
ap-7684	161	25	of	of	ADP
ap-7684	161	26	the	the	DET
ap-7684	161	27	ξi	ξi	NOUN
ap-7684	161	28	surface	surface	NOUN
ap-7684	161	29	upon	upon	SCONJ
ap-7684	161	30	the	the	DET
ap-7684	161	31	element	element	NOUN
ap-7684	161	32	area	area	NOUN
ap-7684	161	33	)	)	PUNCT
ap-7684	161	34	and	and	CCONJ
ap-7684	161	35	n⃗i	n⃗i	PROPN
ap-7684	161	36	=	=	SYM
ap-7684	162	1	−	−	PROPN
ap-7684	162	2	1	1	NUM
ap-7684	162	3	li	li	X
ap-7684	162	4	{	{	PUNCT
ap-7684	162	5	bi	bi	NOUN
ap-7684	162	6	ai	ai	VERB
ap-7684	162	7	}	}	PUNCT
ap-7684	162	8	.	.	PUNCT
ap-7684	163	1	γy	γy	X
ap-7684	163	2	γ	γ	X
ap-7684	163	3	x	x	PROPN
ap-7684	164	1	i	i	PRON
ap-7684	164	2	j	j	PROPN
ap-7684	165	1	k	k	PROPN
ap-7684	165	2	a	a	DET
ap-7684	165	3	aa	aa	PROPN
ap-7684	165	4	b	b	PROPN
ap-7684	165	5	b	b	PROPN
ap-7684	166	1	ij	ij	INTJ
ap-7684	166	2	k	k	NOUN
ap-7684	167	1	i	i	PRON
ap-7684	167	2	k	k	PROPN
ap-7684	168	1	y	y	PROPN
ap-7684	168	2	z	z	PROPN
ap-7684	168	3	w	w	PROPN
ap-7684	169	1	i	i	PRON
ap-7684	169	2	φ	φ	VERB
ap-7684	169	3	i	i	PRON
ap-7684	169	4	wjdw	wjdw	PROPN
ap-7684	169	5	/	/	SYM
ap-7684	169	6	dx	dx	PROPN
ap-7684	170	1	d	d	X
ap-7684	170	2	w	w	PROPN
ap-7684	170	3	/d	/d	PUNCT
ap-7684	170	4	y	y	PROPN
ap-7684	170	5	i	i	PRON
ap-7684	170	6	j	j	PROPN
ap-7684	171	1	k	k	X
ap-7684	171	2	a	a	PRON
ap-7684	171	3	a	a	PRON
ap-7684	171	4	a	a	DET
ap-7684	171	5	s	s	NOUN
ap-7684	171	6	n	n	NOUN
ap-7684	171	7	i	i	PRON
ap-7684	172	1	i	i	PROPN
ap-7684	172	2	b	b	X
ap-7684	173	1	j	j	NOUN
ap-7684	173	2	x	x	X
ap-7684	173	3	w	w	PROPN
ap-7684	173	4	w	w	PROPN
ap-7684	173	5	figure	figure	NOUN
ap-7684	173	6	7	7	NUM
ap-7684	173	7	.	.	NOUN
ap-7684	173	8	triangular	triangular	NOUN
ap-7684	173	9	coordinates	coordinate	NOUN
ap-7684	173	10	and	and	CCONJ
ap-7684	173	11	shear	shear	ADJ
ap-7684	173	12	deformation	deformation	NOUN
ap-7684	173	13	owing	owe	VERB
ap-7684	173	14	to	to	ADP
ap-7684	173	15	deflection	deflection	NOUN
ap-7684	173	16	alone	alone	ADJ
ap-7684	173	17	chain	chain	NOUN
ap-7684	173	18	differentiation	differentiation	NOUN
ap-7684	173	19	yields	yield	NOUN
ap-7684	173	20	then	then	ADV
ap-7684	173	21	γw	γw	VERB
ap-7684	173	22	,	,	PUNCT
ap-7684	173	23	x	x	PUNCT
ap-7684	173	24	=	=	SYM
ap-7684	174	1	−	−	PROPN
ap-7684	174	2	1	1	NUM
ap-7684	174	3	2a	2a	NUM
ap-7684	174	4	∑	∑	PUNCT
ap-7684	174	5	i	i	PRON
ap-7684	174	6	wiai	wiai	VERB
ap-7684	174	7	,	,	PUNCT
ap-7684	174	8	γw	γw	PRON
ap-7684	174	9	,	,	PUNCT
ap-7684	174	10	y	y	PROPN
ap-7684	174	11	=	=	SYM
ap-7684	174	12	1	1	NUM
ap-7684	174	13	2a	2a	NUM
ap-7684	174	14	∑	∑	PUNCT
ap-7684	174	15	i	i	PRON
ap-7684	174	16	wibi	wibi	NOUN
ap-7684	174	17	(	(	PUNCT
ap-7684	174	18	9	9	NUM
ap-7684	174	19	)	)	PUNCT
ap-7684	174	20	the	the	DET
ap-7684	174	21	shear	shear	NOUN
ap-7684	174	22	deformation	deformation	NOUN
ap-7684	174	23	γ⃗w	γ⃗w	NOUN
ap-7684	174	24	owing	owe	VERB
ap-7684	174	25	to	to	ADP
ap-7684	174	26	deflection	deflection	NOUN
ap-7684	174	27	alone	alone	ADV
ap-7684	174	28	is	be	AUX
ap-7684	174	29	γw	γw	PROPN
ap-7684	174	30	,	,	PUNCT
ap-7684	174	31	x	x	PUNCT
ap-7684	175	1	=	=	PUNCT
ap-7684	175	2	−∂w	−∂w	PROPN
ap-7684	175	3	∂y	∂y	PROPN
ap-7684	175	4	,	,	PUNCT
ap-7684	175	5	γw	γw	PROPN
ap-7684	175	6	,	,	PUNCT
ap-7684	175	7	y	y	PROPN
ap-7684	175	8	=	=	SYM
ap-7684	175	9	∂w	∂w	PROPN
ap-7684	175	10	∂x	∂x	PROPN
ap-7684	175	11	,	,	PUNCT
ap-7684	175	12	(	(	PUNCT
ap-7684	175	13	10	10	NUM
ap-7684	175	14	)	)	PUNCT
ap-7684	175	15	note	note	NOUN
ap-7684	175	16	that	that	SCONJ
ap-7684	175	17	positive	positive	ADJ
ap-7684	175	18	sense	sense	NOUN
ap-7684	175	19	is	be	AUX
ap-7684	175	20	indicated	indicate	VERB
ap-7684	175	21	in	in	ADP
ap-7684	175	22	the	the	DET
ap-7684	175	23	figure	figure	NOUN
ap-7684	175	24	for	for	ADP
ap-7684	175	25	each	each	PRON
ap-7684	175	26	of	of	ADP
ap-7684	175	27	the	the	DET
ap-7684	175	28	four	four	NUM
ap-7684	175	29	rotations	rotation	NOUN
ap-7684	175	30	and	and	CCONJ
ap-7684	175	31	γ⃗	γ⃗	NOUN
ap-7684	175	32	is	be	AUX
ap-7684	175	33	the	the	DET
ap-7684	175	34	rotation	rotation	NOUN
ap-7684	175	35	of	of	ADP
ap-7684	175	36	the	the	DET
ap-7684	175	37	normal	normal	ADJ
ap-7684	175	38	to	to	ADP
ap-7684	175	39	the	the	DET
ap-7684	175	40	element	element	NOUN
ap-7684	175	41	plane	plane	NOUN
ap-7684	175	42	embedded	embed	VERB
ap-7684	175	43	in	in	ADP
ap-7684	175	44	the	the	DET
ap-7684	175	45	material	material	NOUN
ap-7684	175	46	before	before	ADP
ap-7684	175	47	deformation	deformation	NOUN
ap-7684	175	48	towards	towards	ADP
ap-7684	175	49	the	the	DET
ap-7684	175	50	normal	normal	ADJ
ap-7684	175	51	to	to	ADP
ap-7684	175	52	the	the	DET
ap-7684	175	53	element	element	NOUN
ap-7684	175	54	plane	plane	NOUN
ap-7684	175	55	after	after	ADP
ap-7684	175	56	deformation	deformation	NOUN
ap-7684	175	57	with	with	ADP
ap-7684	175	58	standard	standard	ADJ
ap-7684	175	59	sign	sign	PROPN
ap-7684	175	60	convention	convention	NOUN
ap-7684	175	61	of	of	ADP
ap-7684	175	62	its	its	PRON
ap-7684	175	63	components	component	NOUN
ap-7684	175	64	.	.	PUNCT
ap-7684	176	1	in	in	ADP
ap-7684	176	2	particular	particular	ADJ
ap-7684	176	3	,	,	PUNCT
ap-7684	176	4	the	the	DET
ap-7684	176	5	motion	motion	NOUN
ap-7684	176	6	(	(	PUNCT
ap-7684	176	7	rotation	rotation	NOUN
ap-7684	176	8	)	)	PUNCT
ap-7684	176	9	shown	show	VERB
ap-7684	176	10	in	in	ADP
ap-7684	176	11	the	the	DET
ap-7684	176	12	section	section	NOUN
ap-7684	176	13	view	view	NOUN
ap-7684	176	14	right	right	ADV
ap-7684	176	15	to	to	PART
ap-7684	176	16	left	leave	VERB
ap-7684	176	17	in	in	ADP
ap-7684	176	18	figure	figure	NOUN
ap-7684	176	19	7	7	NUM
ap-7684	176	20	goes	go	VERB
ap-7684	176	21	from	from	ADP
ap-7684	176	22	the	the	DET
ap-7684	176	23	inclined	inclined	ADJ
ap-7684	176	24	dashed	dash	VERB
ap-7684	176	25	line	line	NOUN
ap-7684	176	26	to	to	ADP
ap-7684	176	27	the	the	DET
ap-7684	176	28	horizontal	horizontal	ADJ
ap-7684	176	29	and	and	CCONJ
ap-7684	176	30	γx	γx	NOUN
ap-7684	176	31	is	be	AUX
ap-7684	176	32	thus	thus	ADV
ap-7684	176	33	negative	negative	ADJ
ap-7684	176	34	.	.	PUNCT
ap-7684	177	1	as	as	ADP
ap-7684	177	2	in	in	ADP
ap-7684	177	3	the	the	DET
ap-7684	177	4	tt	tt	PROPN
ap-7684	177	5	element	element	NOUN
ap-7684	177	6	,	,	PUNCT
ap-7684	177	7	the	the	DET
ap-7684	177	8	bending	bending	NOUN
ap-7684	177	9	and	and	CCONJ
ap-7684	177	10	shear	shear	ADJ
ap-7684	177	11	deformation	deformation	NOUN
ap-7684	177	12	,	,	PUNCT
ap-7684	177	13	are	be	AUX
ap-7684	177	14	treated	treat	VERB
ap-7684	177	15	separately	separately	ADV
ap-7684	177	16	.	.	PUNCT
ap-7684	178	1	4.1	4.1	NUM
ap-7684	178	2	.	.	PUNCT
ap-7684	178	3	bending	bend	VERB
ap-7684	178	4	and	and	CCONJ
ap-7684	178	5	in	in	ADP
ap-7684	178	6	-	-	PUNCT
ap-7684	178	7	plane	plane	NOUN
ap-7684	178	8	deformation	deformation	NOUN
ap-7684	178	9	pseudocurvatures	pseudocurvature	NOUN
ap-7684	178	10	define	define	VERB
ap-7684	178	11	the	the	DET
ap-7684	178	12	bending	bend	VERB
ap-7684	178	13	deformation	deformation	NOUN
ap-7684	178	14	.	.	PUNCT
ap-7684	179	1	they	they	PRON
ap-7684	179	2	are	be	AUX
ap-7684	179	3	the	the	DET
ap-7684	179	4	derivatives	derivative	NOUN
ap-7684	179	5	of	of	ADP
ap-7684	179	6	rotations	rotation	NOUN
ap-7684	179	7	of	of	ADP
ap-7684	179	8	the	the	DET
ap-7684	179	9	normals	normal	NOUN
ap-7684	179	10	to	to	ADP
ap-7684	179	11	the	the	DET
ap-7684	179	12	element	element	NOUN
ap-7684	179	13	plane	plane	NOUN
ap-7684	179	14	.	.	PUNCT
ap-7684	180	1	the	the	DET
ap-7684	180	2	rotations	rotation	NOUN
ap-7684	180	3	of	of	ADP
ap-7684	180	4	the	the	DET
ap-7684	180	5	normals	normal	NOUN
ap-7684	180	6	in	in	ADP
ap-7684	180	7	their	their	PRON
ap-7684	180	8	turn	turn	NOUN
ap-7684	180	9	depend	depend	VERB
ap-7684	180	10	on	on	ADP
ap-7684	180	11	the	the	DET
ap-7684	180	12	in	in	ADP
ap-7684	180	13	-	-	PUNCT
ap-7684	180	14	plane	plane	NOUN
ap-7684	180	15	displacements	displacement	NOUN
ap-7684	180	16	u⃗	u⃗	PROPN
ap-7684	180	17	of	of	ADP
ap-7684	180	18	the	the	DET
ap-7684	180	19	top	top	ADJ
ap-7684	180	20	and	and	CCONJ
ap-7684	180	21	bottom	bottom	ADJ
ap-7684	180	22	faces	face	NOUN
ap-7684	180	23	of	of	ADP
ap-7684	180	24	the	the	DET
ap-7684	180	25	element	element	NOUN
ap-7684	180	26	.	.	PUNCT
ap-7684	181	1	the	the	DET
ap-7684	181	2	element	element	NOUN
ap-7684	181	3	in	in	ADP
ap-7684	181	4	-	-	PUNCT
ap-7684	181	5	plane	plane	NOUN
ap-7684	181	6	strains	strain	NOUN
ap-7684	181	7	are	be	AUX
ap-7684	181	8	specified	specify	VERB
ap-7684	181	9	in	in	ADP
ap-7684	181	10	terms	term	NOUN
ap-7684	181	11	of	of	ADP
ap-7684	181	12	the	the	DET
ap-7684	181	13	top	top	ADJ
ap-7684	181	14	and	and	CCONJ
ap-7684	181	15	bottom	bottom	ADJ
ap-7684	181	16	faces	face	NOUN
ap-7684	181	17	(	(	PUNCT
ap-7684	181	18	extrados	extrado	NOUN
ap-7684	181	19	and	and	CCONJ
ap-7684	181	20	intrados	intrado	NOUN
ap-7684	181	21	)	)	PUNCT
ap-7684	181	22	strain	strain	NOUN
ap-7684	181	23	matrices	matrix	NOUN
ap-7684	181	24	{	{	PUNCT
ap-7684	181	25	εt	εt	X
ap-7684	181	26	}	}	PUNCT
ap-7684	181	27	and	and	CCONJ
ap-7684	181	28	{	{	PUNCT
ap-7684	181	29	εb	εb	ADP
ap-7684	181	30	}	}	PUNCT
ap-7684	181	31	in	in	ADP
ap-7684	181	32	analogy	analogy	NOUN
ap-7684	181	33	to	to	ADP
ap-7684	181	34	the	the	DET
ap-7684	181	35	top	top	ADJ
ap-7684	181	36	and	and	CCONJ
ap-7684	181	37	bottom	bottom	ADJ
ap-7684	181	38	uniaxial	uniaxial	ADJ
ap-7684	181	39	strains	strain	NOUN
ap-7684	181	40	εt	εt	INTJ
ap-7684	181	41	and	and	CCONJ
ap-7684	181	42	εb	εb	ADP
ap-7684	181	43	in	in	ADP
ap-7684	181	44	the	the	DET
ap-7684	181	45	timoshenko	timoshenko	ADJ
ap-7684	181	46	2d	2d	NUM
ap-7684	181	47	beam	beam	NOUN
ap-7684	181	48	element	element	NOUN
ap-7684	181	49	.	.	PUNCT
ap-7684	182	1	the	the	DET
ap-7684	182	2	element	element	NOUN
ap-7684	182	3	triangle	triangle	NOUN
ap-7684	182	4	geometry	geometry	NOUN
ap-7684	182	5	is	be	AUX
ap-7684	182	6	defined	define	VERB
ap-7684	182	7	in	in	ADP
ap-7684	182	8	terms	term	NOUN
ap-7684	182	9	of	of	ADP
ap-7684	182	10	distances	distance	NOUN
ap-7684	182	11	ai	ai	VERB
ap-7684	182	12	=	=	SYM
ap-7684	182	13	xk	xk	PROPN
ap-7684	182	14	−	−	PROPN
ap-7684	182	15	xj	xj	PROPN
ap-7684	182	16	,	,	PUNCT
ap-7684	182	17	bi	bi	NOUN
ap-7684	182	18	=	=	PROPN
ap-7684	182	19	yj	yj	PROPN
ap-7684	182	20	−	−	PROPN
ap-7684	182	21	yk	yk	PROPN
ap-7684	182	22	,	,	PUNCT
ap-7684	182	23	where	where	SCONJ
ap-7684	182	24	indices	indice	VERB
ap-7684	182	25	i	i	PRON
ap-7684	182	26	,	,	PUNCT
ap-7684	182	27	j	j	PROPN
ap-7684	182	28	,	,	PUNCT
ap-7684	182	29	k	k	PROPN
ap-7684	182	30	are	be	AUX
ap-7684	182	31	subjected	subject	VERB
ap-7684	182	32	to	to	ADP
ap-7684	182	33	cyclic	cyclic	ADJ
ap-7684	182	34	permutation	permutation	NOUN
ap-7684	182	35	and	and	CCONJ
ap-7684	182	36	xi	xi	PROPN
ap-7684	182	37	,	,	PUNCT
ap-7684	182	38	yi	yi	PROPN
ap-7684	182	39	specify	specify	VERB
ap-7684	182	40	node	node	PROPN
ap-7684	182	41	’s	’s	PART
ap-7684	183	1	i	i	PRON
ap-7684	183	2	positions	position	NOUN
ap-7684	183	3	in	in	ADP
ap-7684	183	4	the	the	DET
ap-7684	183	5	local	local	ADJ
ap-7684	183	6	system	system	NOUN
ap-7684	183	7	,	,	PUNCT
ap-7684	183	8	see	see	VERB
ap-7684	183	9	figure	figure	NOUN
ap-7684	183	10	7	7	NUM
ap-7684	183	11	.	.	PUNCT
ap-7684	184	1	the	the	DET
ap-7684	184	2	geometric	geometric	ADJ
ap-7684	184	3	equations	equation	NOUN
ap-7684	184	4	297	297	NUM
ap-7684	184	5	petr	petr	PROPN
ap-7684	184	6	řeřicha	řeřicha	PROPN
ap-7684	184	7	acta	acta	PROPN
ap-7684	184	8	polytechnica	polytechnica	PROPN
ap-7684	184	9	of	of	ADP
ap-7684	184	10	the	the	DET
ap-7684	184	11	cst	cst	PROPN
ap-7684	184	12	triangle	triangle	NOUN
ap-7684	184	13	applied	apply	VERB
ap-7684	184	14	to	to	ADP
ap-7684	184	15	the	the	DET
ap-7684	184	16	top	top	ADJ
ap-7684	184	17	face	face	NOUN
ap-7684	184	18	read	read	NOUN
ap-7684	184	19	{	{	PUNCT
ap-7684	184	20	εt	εt	PROPN
ap-7684	184	21	}	}	PUNCT
ap-7684	184	22	=	=	PUNCT
ap-7684	184	23			PROPN
ap-7684	184	24	εt	εt	PROPN
ap-7684	184	25	,	,	PUNCT
ap-7684	184	26	x	x	PROPN
ap-7684	184	27	εt	εt	PROPN
ap-7684	184	28	,	,	PUNCT
ap-7684	185	1	y	y	PROPN
ap-7684	185	2	2εt	2εt	PROPN
ap-7684	185	3	/	/	SYM
ap-7684	185	4	b	b	NOUN
ap-7684	185	5	,	,	PUNCT
ap-7684	185	6	xy	xy	PROPN
ap-7684	186	1			NOUN
ap-7684	186	2	=	=	PUNCT
ap-7684	186	3	1	1	NUM
ap-7684	186	4	2a	2a	NUM
ap-7684	186	5	∑	∑	PUNCT
ap-7684	186	6	i	i	PRON
ap-7684	186	7			VERB
ap-7684	186	8	bi	bi	NOUN
ap-7684	186	9	0	0	NUM
ap-7684	186	10	0	0	NUM
ap-7684	186	11	ai	ai	VERB
ap-7684	186	12	ai	ai	INTJ
ap-7684	186	13	bi	bi	NOUN
ap-7684	186	14			NOUN
ap-7684	186	15	{	{	PUNCT
ap-7684	186	16	ui	ui	PROPN
ap-7684	186	17	,	,	PUNCT
ap-7684	186	18	t	t	PROPN
ap-7684	186	19	,	,	PUNCT
ap-7684	186	20	x	x	PROPN
ap-7684	186	21	ui	ui	PROPN
ap-7684	186	22	,	,	PUNCT
ap-7684	186	23	t	t	PROPN
ap-7684	186	24	,	,	PUNCT
ap-7684	186	25	y	y	PROPN
ap-7684	186	26	}	}	PUNCT
ap-7684	186	27	,	,	PUNCT
ap-7684	186	28	(	(	PUNCT
ap-7684	186	29	11	11	NUM
ap-7684	186	30	)	)	PUNCT
ap-7684	186	31	substitute	substitute	NOUN
ap-7684	186	32	b	b	PROPN
ap-7684	186	33	for	for	ADP
ap-7684	186	34	t	t	PROPN
ap-7684	186	35	subscript	subscript	NOUN
ap-7684	186	36	to	to	PART
ap-7684	186	37	get	get	VERB
ap-7684	186	38	the	the	DET
ap-7684	186	39	bottom	bottom	ADJ
ap-7684	186	40	face	face	NOUN
ap-7684	186	41	strain	strain	NOUN
ap-7684	186	42	matrix	matrix	NOUN
ap-7684	186	43	.	.	PUNCT
ap-7684	187	1	the	the	DET
ap-7684	187	2	in	in	ADP
ap-7684	187	3	-	-	PUNCT
ap-7684	187	4	plane	plane	NOUN
ap-7684	187	5	strains	strain	NOUN
ap-7684	187	6	vary	vary	VERB
ap-7684	187	7	linearly	linearly	ADV
ap-7684	187	8	across	across	ADP
ap-7684	187	9	the	the	DET
ap-7684	187	10	element	element	ADJ
ap-7684	187	11	depth	depth	NOUN
ap-7684	187	12	d	d	NOUN
ap-7684	187	13	,	,	PUNCT
ap-7684	187	14	{	{	PUNCT
ap-7684	187	15	ε	ε	PROPN
ap-7684	187	16	}	}	PUNCT
ap-7684	187	17	=	=	SYM
ap-7684	187	18	zt{εt	zt{εt	NOUN
ap-7684	187	19	}	}	PUNCT
ap-7684	187	20	+	+	NUM
ap-7684	187	21	zb{εb	zb{εb	NUM
ap-7684	187	22	}	}	PUNCT
ap-7684	187	23	(	(	PUNCT
ap-7684	187	24	12	12	NUM
ap-7684	187	25	)	)	PUNCT
ap-7684	187	26	where	where	SCONJ
ap-7684	187	27	zt	zt	PROPN
ap-7684	187	28	=	=	PRON
ap-7684	187	29	(	(	PUNCT
ap-7684	187	30	d	d	X
ap-7684	187	31	+	+	NUM
ap-7684	187	32	z)/d	z)/d	NOUN
ap-7684	187	33	=	=	SYM
ap-7684	188	1	1	1	NUM
ap-7684	188	2	+	+	CCONJ
ap-7684	188	3	ζ	ζ	NOUN
ap-7684	188	4	and	and	CCONJ
ap-7684	188	5	zb	zb	NOUN
ap-7684	188	6	=	=	PUNCT
ap-7684	188	7	−z	−z	NOUN
ap-7684	188	8	/	/	SYM
ap-7684	188	9	d	d	NOUN
ap-7684	188	10	=	=	SYM
ap-7684	188	11	−ζ	−ζ	NOUN
ap-7684	188	12	are	be	AUX
ap-7684	188	13	linear	linear	ADJ
ap-7684	188	14	shape	shape	NOUN
ap-7684	188	15	functions	function	NOUN
ap-7684	188	16	of	of	ADP
ap-7684	188	17	the	the	DET
ap-7684	188	18	element	element	NOUN
ap-7684	188	19	in	in	ADP
ap-7684	188	20	terms	term	NOUN
ap-7684	188	21	of	of	ADP
ap-7684	188	22	the	the	DET
ap-7684	188	23	element	element	NOUN
ap-7684	188	24	local	local	ADJ
ap-7684	188	25	0	0	PUNCT
ap-7684	188	26	>	>	X
ap-7684	188	27	z	z	X
ap-7684	188	28	>	>	X
ap-7684	188	29	−d	−d	ADJ
ap-7684	188	30	coordinate	coordinate	NOUN
ap-7684	188	31	with	with	ADP
ap-7684	188	32	z	z	NOUN
ap-7684	188	33	=	=	SYM
ap-7684	188	34	0	0	NUM
ap-7684	188	35	at	at	ADP
ap-7684	188	36	the	the	DET
ap-7684	188	37	top	top	ADJ
ap-7684	188	38	face	face	NOUN
ap-7684	188	39	of	of	ADP
ap-7684	188	40	the	the	DET
ap-7684	188	41	element	element	NOUN
ap-7684	188	42	or	or	CCONJ
ap-7684	188	43	of	of	ADP
ap-7684	188	44	the	the	DET
ap-7684	188	45	relative	relative	ADJ
ap-7684	188	46	dimensionless	dimensionless	NOUN
ap-7684	188	47	0	0	PUNCT
ap-7684	188	48	>	>	X
ap-7684	188	49	ζ	ζ	PROPN
ap-7684	188	50	>	>	SYM
ap-7684	188	51	−1	−1	NOUN
ap-7684	188	52	coordinate	coordinate	NOUN
ap-7684	188	53	.	.	PUNCT
ap-7684	189	1	plain	plain	ADJ
ap-7684	189	2	stress	stress	NOUN
ap-7684	189	3	conditions	condition	NOUN
ap-7684	189	4	with	with	ADP
ap-7684	189	5	σzz	σzz	NOUN
ap-7684	189	6	=	=	SYM
ap-7684	189	7	0	0	NUM
ap-7684	189	8	are	be	AUX
ap-7684	189	9	assumed	assume	VERB
ap-7684	189	10	in	in	ADP
ap-7684	189	11	the	the	DET
ap-7684	189	12	shell	shell	NOUN
ap-7684	189	13	,	,	PUNCT
ap-7684	189	14	then	then	ADV
ap-7684	189	15	,	,	PUNCT
ap-7684	189	16	the	the	DET
ap-7684	189	17	material	material	ADJ
ap-7684	189	18	stiffness	stiffness	NOUN
ap-7684	189	19	matrix	matrix	NOUN
ap-7684	189	20	is	be	AUX
ap-7684	189	21	[	[	X
ap-7684	189	22	d	d	X
ap-7684	189	23	]	]	X
ap-7684	189	24	=	=	SYM
ap-7684	189	25	e	e	X
ap-7684	189	26	1	1	NUM
ap-7684	189	27	−	−	NOUN
ap-7684	189	28	ν2	ν2	NOUN
ap-7684	189	29			NOUN
ap-7684	189	30	1	1	NUM
ap-7684	189	31	ν	ν	NOUN
ap-7684	189	32	0	0	NUM
ap-7684	189	33	1	1	NUM
ap-7684	189	34	0	0	NUM
ap-7684	189	35	1−ν	1−ν	NUM
ap-7684	189	36	2	2	NUM
ap-7684	189	37			NOUN
ap-7684	189	38	(	(	PUNCT
ap-7684	189	39	13	13	NUM
ap-7684	189	40	)	)	PUNCT
ap-7684	189	41	for	for	ADP
ap-7684	189	42	a	a	DET
ap-7684	189	43	linear	linear	ADJ
ap-7684	189	44	elastic	elastic	ADJ
ap-7684	189	45	isotropic	isotropic	NOUN
ap-7684	189	46	material	material	NOUN
ap-7684	189	47	.	.	PUNCT
ap-7684	190	1	when	when	SCONJ
ap-7684	190	2	cracked	crack	VERB
ap-7684	190	3	bed	bed	NOUN
ap-7684	190	4	joints	joint	NOUN
ap-7684	190	5	occur	occur	VERB
ap-7684	190	6	in	in	ADP
ap-7684	190	7	planes	plane	NOUN
ap-7684	190	8	normal	normal	ADJ
ap-7684	190	9	to	to	PART
ap-7684	190	10	element	element	VERB
ap-7684	190	11	’s	’s	PART
ap-7684	190	12	x	x	NOUN
ap-7684	190	13	axis	axis	NOUN
ap-7684	190	14	,	,	PUNCT
ap-7684	190	15	the	the	DET
ap-7684	190	16	conditions	condition	NOUN
ap-7684	190	17	become	become	VERB
ap-7684	190	18	vague	vague	ADJ
ap-7684	190	19	.	.	PUNCT
ap-7684	191	1	adjacent	adjacent	ADJ
ap-7684	191	2	to	to	ADP
ap-7684	191	3	the	the	DET
ap-7684	191	4	cracked	crack	VERB
ap-7684	191	5	joints	joint	NOUN
ap-7684	191	6	an	an	DET
ap-7684	191	7	approximately	approximately	ADV
ap-7684	191	8	uniaxial	uniaxial	ADJ
ap-7684	191	9	stress	stress	NOUN
ap-7684	191	10	prevails	prevail	VERB
ap-7684	191	11	.	.	PUNCT
ap-7684	192	1	it	it	PRON
ap-7684	192	2	is	be	AUX
ap-7684	192	3	thus	thus	ADV
ap-7684	192	4	assumed	assume	VERB
ap-7684	192	5	forthwith	forthwith	NOUN
ap-7684	192	6	that	that	SCONJ
ap-7684	192	7	the	the	DET
ap-7684	192	8	material	material	ADJ
ap-7684	192	9	stiffness	stiffness	NOUN
ap-7684	192	10	matrix	matrix	NOUN
ap-7684	192	11	in	in	ADP
ap-7684	192	12	the	the	DET
ap-7684	192	13	cracked	crack	VERB
ap-7684	192	14	elements	element	NOUN
ap-7684	192	15	is	be	AUX
ap-7684	192	16	[	[	X
ap-7684	192	17	d({ε	d({ε	NOUN
ap-7684	192	18	}	}	PUNCT
ap-7684	192	19	)	)	PUNCT
ap-7684	192	20	]	]	PUNCT
ap-7684	193	1	=	=	PUNCT
ap-7684	193	2	e	e	X
ap-7684	193	3			PROPN
ap-7684	193	4	s(εx	s(εx	NUM
ap-7684	193	5	)	)	PUNCT
ap-7684	193	6	0	0	NUM
ap-7684	193	7	0	0	NUM
ap-7684	193	8	1	1	NUM
ap-7684	193	9	0	0	NUM
ap-7684	193	10	1−ν	1−ν	NUM
ap-7684	193	11	2	2	NUM
ap-7684	193	12			NOUN
ap-7684	193	13	(	(	PUNCT
ap-7684	193	14	14	14	NUM
ap-7684	193	15	)	)	PUNCT
ap-7684	193	16	where	where	SCONJ
ap-7684	193	17	s	s	X
ap-7684	193	18	(	(	PUNCT
ap-7684	193	19	)	)	PUNCT
ap-7684	193	20	is	be	AUX
ap-7684	193	21	the	the	DET
ap-7684	193	22	normalized	normalize	VERB
ap-7684	193	23	bilinear	bilinear	NOUN
ap-7684	193	24	stress	stress	NOUN
ap-7684	193	25	/	/	SYM
ap-7684	193	26	strain	strain	NOUN
ap-7684	193	27	diagram	diagram	NOUN
ap-7684	193	28	in	in	ADP
ap-7684	193	29	the	the	DET
ap-7684	193	30	left	left	ADJ
ap-7684	193	31	sketch	sketch	NOUN
ap-7684	193	32	of	of	ADP
ap-7684	193	33	figure	figure	NOUN
ap-7684	193	34	2	2	NUM
ap-7684	193	35	.	.	PUNCT
ap-7684	194	1	it	it	PRON
ap-7684	194	2	is	be	AUX
ap-7684	194	3	obvious	obvious	ADJ
ap-7684	194	4	that	that	SCONJ
ap-7684	194	5	the	the	DET
ap-7684	194	6	element	element	NOUN
ap-7684	194	7	local	local	ADJ
ap-7684	194	8	x	x	VERB
ap-7684	194	9	axis	axis	NOUN
ap-7684	194	10	must	must	AUX
ap-7684	194	11	approximately	approximately	ADV
ap-7684	194	12	coincide	coincide	VERB
ap-7684	194	13	with	with	ADP
ap-7684	194	14	the	the	DET
ap-7684	194	15	normals	normal	NOUN
ap-7684	194	16	to	to	ADP
ap-7684	194	17	the	the	DET
ap-7684	194	18	bed	bed	NOUN
ap-7684	194	19	joints	joint	NOUN
ap-7684	194	20	of	of	ADP
ap-7684	194	21	the	the	DET
ap-7684	194	22	arch	arch	ADJ
ap-7684	194	23	barrel	barrel	NOUN
ap-7684	194	24	.	.	PUNCT
ap-7684	195	1	the	the	DET
ap-7684	195	2	virtual	virtual	ADJ
ap-7684	195	3	work	work	NOUN
ap-7684	195	4	equation	equation	NOUN
ap-7684	195	5	for	for	ADP
ap-7684	195	6	cracked	crack	VERB
ap-7684	195	7	elements	element	NOUN
ap-7684	195	8	δw	δw	NOUN
ap-7684	195	9	=	=	PUNCT
ap-7684	195	10	∑	∑	PROPN
ap-7684	195	11	i	i	PRON
ap-7684	195	12	(	(	PUNCT
ap-7684	195	13	δ{ui	δ{ui	PROPN
ap-7684	195	14	,	,	PUNCT
ap-7684	195	15	t}t	t}t	NOUN
ap-7684	195	16	{	{	PUNCT
ap-7684	195	17	gi	gi	PROPN
ap-7684	195	18	,	,	PUNCT
ap-7684	195	19	t	t	PROPN
ap-7684	195	20	}	}	PUNCT
ap-7684	195	21	+	+	CCONJ
ap-7684	195	22	δ{ui	δ{ui	PROPN
ap-7684	195	23	,	,	PUNCT
ap-7684	195	24	b}t	b}t	NOUN
ap-7684	195	25	{	{	PUNCT
ap-7684	195	26	gi	gi	INTJ
ap-7684	195	27	,	,	PUNCT
ap-7684	195	28	b	b	NOUN
ap-7684	195	29	}	}	PUNCT
ap-7684	195	30	)	)	PUNCT
ap-7684	196	1	=	=	SYM
ap-7684	196	2	∫	∫	PROPN
ap-7684	196	3	v	v	INTJ
ap-7684	196	4	δ{ε}t	δ{ε}t	NOUN
ap-7684	197	1	[	[	X
ap-7684	197	2	d({ε})]{ε}dv	d({ε})]{ε}dv	NOUN
ap-7684	197	3	=	=	SYM
ap-7684	197	4	e	e	NOUN
ap-7684	197	5	∫	∫	PROPN
ap-7684	197	6	v	v	PROPN
ap-7684	197	7	(	(	PUNCT
ap-7684	197	8	δεxs(εx	δεxs(εx	PROPN
ap-7684	197	9	)	)	PUNCT
ap-7684	197	10	+	+	NUM
ap-7684	197	11	δεyεy	δεyεy	PROPN
ap-7684	197	12	+	+	CCONJ
ap-7684	197	13	(	(	PUNCT
ap-7684	197	14	1	1	NUM
ap-7684	197	15	−	−	NOUN
ap-7684	197	16	ν)δεxyεxydv	ν)δεxyεxydv	NOUN
ap-7684	197	17	(	(	PUNCT
ap-7684	197	18	15	15	NUM
ap-7684	197	19	)	)	PUNCT
ap-7684	197	20	delivers	deliver	VERB
ap-7684	197	21	the	the	DET
ap-7684	197	22	expressions	expression	NOUN
ap-7684	197	23	for	for	ADP
ap-7684	197	24	the	the	DET
ap-7684	197	25	nodal	nodal	NOUN
ap-7684	197	26	forces	force	NOUN
ap-7684	197	27	{	{	PUNCT
ap-7684	197	28	gi	gi	PROPN
ap-7684	197	29	,	,	PUNCT
ap-7684	197	30	t	t	PROPN
ap-7684	197	31	}	}	PUNCT
ap-7684	197	32	,	,	PUNCT
ap-7684	197	33	{	{	PUNCT
ap-7684	197	34	gi	gi	INTJ
ap-7684	197	35	,	,	PUNCT
ap-7684	197	36	b	b	NOUN
ap-7684	197	37	}	}	PUNCT
ap-7684	197	38	when	when	SCONJ
ap-7684	197	39	strains	strain	NOUN
ap-7684	197	40	are	be	AUX
ap-7684	197	41	expanded	expand	VERB
ap-7684	197	42	in	in	ADP
ap-7684	197	43	terms	term	NOUN
ap-7684	197	44	of	of	ADP
ap-7684	197	45	the	the	DET
ap-7684	197	46	virtual	virtual	ADJ
ap-7684	197	47	nodal	nodal	NOUN
ap-7684	197	48	displacements	displacement	NOUN
ap-7684	197	49	using	use	VERB
ap-7684	197	50	equation	equation	NOUN
ap-7684	197	51	11	11	NUM
ap-7684	197	52	.	.	PUNCT
ap-7684	198	1	functions	function	NOUN
ap-7684	198	2	st(εt	st(εt	PROPN
ap-7684	198	3	,	,	PUNCT
ap-7684	198	4	x	x	NOUN
ap-7684	198	5	,	,	PUNCT
ap-7684	198	6	εb	εb	ADP
ap-7684	198	7	,	,	PUNCT
ap-7684	198	8	x	x	NOUN
ap-7684	198	9	)	)	PUNCT
ap-7684	198	10	and	and	CCONJ
ap-7684	198	11	sb	sb	PROPN
ap-7684	198	12	(	(	PUNCT
ap-7684	198	13	)	)	PUNCT
ap-7684	198	14	,	,	PUNCT
ap-7684	198	15	see	see	VERB
ap-7684	198	16	2	2	NUM
ap-7684	198	17	in	in	ADP
ap-7684	198	18	section	section	NOUN
ap-7684	198	19	2.1	2.1	NUM
ap-7684	198	20	,	,	PUNCT
ap-7684	198	21	return	return	VERB
ap-7684	198	22	dimensionles	dimensionle	NOUN
ap-7684	198	23	top	top	ADJ
ap-7684	198	24	and	and	CCONJ
ap-7684	198	25	bottom	bottom	ADJ
ap-7684	198	26	cross	cross	ADJ
ap-7684	198	27	-	-	ADJ
ap-7684	198	28	section	section	ADJ
ap-7684	198	29	forces	force	NOUN
ap-7684	198	30	conjugate	conjugate	VERB
ap-7684	198	31	to	to	ADP
ap-7684	198	32	top	top	ADJ
ap-7684	198	33	and	and	CCONJ
ap-7684	198	34	bottom	bottom	ADJ
ap-7684	198	35	strains	strain	NOUN
ap-7684	198	36	(	(	PUNCT
ap-7684	198	37	input	input	NOUN
ap-7684	198	38	parameters	parameter	NOUN
ap-7684	198	39	)	)	PUNCT
ap-7684	198	40	of	of	ADP
ap-7684	198	41	a	a	DET
ap-7684	198	42	unit	unit	NOUN
ap-7684	198	43	depth	depth	NOUN
ap-7684	198	44	cross	cross	NOUN
ap-7684	198	45	-	-	NOUN
ap-7684	198	46	section	section	NOUN
ap-7684	198	47	with	with	ADP
ap-7684	198	48	e	e	NOUN
ap-7684	198	49	=	=	SYM
ap-7684	198	50	1	1	NUM
ap-7684	198	51	and	and	CCONJ
ap-7684	198	52	no	no	DET
ap-7684	198	53	-	-	PUNCT
ap-7684	198	54	tension	tension	NOUN
ap-7684	198	55	stress	stress	NOUN
ap-7684	198	56	-	-	PUNCT
ap-7684	198	57	strain	strain	NOUN
ap-7684	198	58	diagram	diagram	NOUN
ap-7684	198	59	.	.	PUNCT
ap-7684	199	1	with	with	ADP
ap-7684	199	2	the	the	DET
ap-7684	199	3	aid	aid	NOUN
ap-7684	199	4	of	of	ADP
ap-7684	199	5	the	the	DET
ap-7684	199	6	functions	function	NOUN
ap-7684	199	7	,	,	PUNCT
ap-7684	199	8	the	the	DET
ap-7684	199	9	integrals	integral	NOUN
ap-7684	199	10	in	in	ADP
ap-7684	199	11	the	the	DET
ap-7684	199	12	virtual	virtual	ADJ
ap-7684	199	13	work	work	NOUN
ap-7684	199	14	expression	expression	NOUN
ap-7684	199	15	can	can	AUX
ap-7684	199	16	be	be	AUX
ap-7684	199	17	expressed	express	VERB
ap-7684	199	18	in	in	ADP
ap-7684	199	19	a	a	DET
ap-7684	199	20	closed	closed	ADJ
ap-7684	199	21	form	form	NOUN
ap-7684	199	22	:	:	PUNCT
ap-7684	199	23	δw	δw	ADP
ap-7684	199	24	=	=	SYM
ap-7684	200	1	ed	ed	NOUN
ap-7684	200	2	2	2	NUM
ap-7684	200	3	(	(	PUNCT
ap-7684	200	4	δεt	δεt	PROPN
ap-7684	200	5	,	,	PUNCT
ap-7684	200	6	xst	xst	PROPN
ap-7684	200	7	+	+	CCONJ
ap-7684	200	8	δεb	δεb	PROPN
ap-7684	200	9	,	,	PUNCT
ap-7684	200	10	xsb	xsb	PROPN
ap-7684	200	11	+	+	X
ap-7684	200	12	δεt	δεt	PROPN
ap-7684	200	13	,	,	PUNCT
ap-7684	200	14	y(εt	y(εt	NOUN
ap-7684	200	15	,	,	PUNCT
ap-7684	200	16	y/3	y/3	NOUN
ap-7684	200	17	+	+	CCONJ
ap-7684	200	18	εb	εb	ADP
ap-7684	200	19	,	,	PUNCT
ap-7684	200	20	y/6	y/6	NOUN
ap-7684	200	21	)	)	PUNCT
ap-7684	201	1	+	+	NUM
ap-7684	201	2	δεb	δεb	NOUN
ap-7684	201	3	,	,	PUNCT
ap-7684	201	4	y(εt	y(εt	NOUN
ap-7684	201	5	,	,	PUNCT
ap-7684	201	6	y/6	y/6	PRON
ap-7684	201	7	+	+	CCONJ
ap-7684	201	8	εb	εb	X
ap-7684	201	9	,	,	PUNCT
ap-7684	201	10	y/3	y/3	NOUN
ap-7684	201	11	)	)	PUNCT
ap-7684	202	1	+	+	CCONJ
ap-7684	202	2	(	(	PUNCT
ap-7684	202	3	δεt	δεt	PROPN
ap-7684	202	4	,	,	PUNCT
ap-7684	202	5	xy(εt	xy(εt	PROPN
ap-7684	202	6	,	,	PUNCT
ap-7684	202	7	xy/3	xy/3	PROPN
ap-7684	202	8	+	+	X
ap-7684	202	9	εb	εb	ADP
ap-7684	202	10	,	,	PUNCT
ap-7684	202	11	xy/6	xy/6	ADJ
ap-7684	202	12	)	)	PUNCT
ap-7684	203	1	+	+	NUM
ap-7684	203	2	δεb	δεb	NOUN
ap-7684	203	3	,	,	PUNCT
ap-7684	203	4	xy(εt	xy(εt	PROPN
ap-7684	203	5	,	,	PUNCT
ap-7684	203	6	xy/6	xy/6	PROPN
ap-7684	203	7	+	+	CCONJ
ap-7684	203	8	εb	εb	ADP
ap-7684	203	9	,	,	PUNCT
ap-7684	203	10	xy/3))(1	xy/3))(1	NOUN
ap-7684	203	11	−	−	PROPN
ap-7684	203	12	ν	ν	NOUN
ap-7684	203	13	)	)	PUNCT
ap-7684	203	14	)	)	PUNCT
ap-7684	203	15	(	(	PUNCT
ap-7684	203	16	16	16	X
ap-7684	203	17	)	)	PUNCT
ap-7684	203	18	substitution	substitution	NOUN
ap-7684	203	19	by	by	ADP
ap-7684	203	20	11	11	NUM
ap-7684	203	21	and	and	CCONJ
ap-7684	203	22	selection	selection	NOUN
ap-7684	203	23	of	of	ADP
ap-7684	203	24	individual	individual	ADJ
ap-7684	203	25	nonzero	nonzero	NOUN
ap-7684	203	26	virtual	virtual	ADJ
ap-7684	203	27	nodal	nodal	NOUN
ap-7684	203	28	displacements	displacement	NOUN
ap-7684	203	29	yields	yield	VERB
ap-7684	203	30	the	the	DET
ap-7684	203	31	expressions	expression	NOUN
ap-7684	203	32	for	for	ADP
ap-7684	203	33	the	the	DET
ap-7684	203	34	element	element	NOUN
ap-7684	203	35	nodal	nodal	NOUN
ap-7684	203	36	forces	force	NOUN
ap-7684	203	37	:	:	PUNCT
ap-7684	203	38	gi	gi	X
ap-7684	203	39	,	,	PUNCT
ap-7684	203	40	t	t	PROPN
ap-7684	203	41	,	,	PUNCT
ap-7684	203	42	x	x	PUNCT
ap-7684	203	43	=	=	PUNCT
ap-7684	203	44	ed	ed	NOUN
ap-7684	203	45	2	2	NUM
ap-7684	203	46	(	(	PUNCT
ap-7684	203	47	bist	bist	NOUN
ap-7684	203	48	+	+	CCONJ
ap-7684	203	49	ai(εt	ai(εt	PROPN
ap-7684	203	50	,	,	PUNCT
ap-7684	203	51	xy/3	xy/3	PROPN
ap-7684	203	52	+	+	X
ap-7684	203	53	εb	εb	ADP
ap-7684	203	54	,	,	PUNCT
ap-7684	203	55	xy/6)(1	xy/6)(1	PROPN
ap-7684	203	56	−	−	NOUN
ap-7684	203	57	ν	ν	NOUN
ap-7684	203	58	)	)	PUNCT
ap-7684	203	59	)	)	PUNCT
ap-7684	204	1	gi	gi	ADP
ap-7684	204	2	,	,	PUNCT
ap-7684	204	3	t	t	PROPN
ap-7684	204	4	,	,	PUNCT
ap-7684	204	5	y	y	PROPN
ap-7684	204	6	=	=	PUNCT
ap-7684	204	7	ed	ed	NOUN
ap-7684	204	8	2	2	NUM
ap-7684	204	9	(	(	PUNCT
ap-7684	204	10	ai(εt	ai(εt	VERB
ap-7684	204	11	,	,	PUNCT
ap-7684	204	12	y/3	y/3	NOUN
ap-7684	204	13	+	+	CCONJ
ap-7684	204	14	εb	εb	ADP
ap-7684	204	15	,	,	PUNCT
ap-7684	204	16	y/6)+	y/6)+	PROPN
ap-7684	204	17	bi(εt	bi(εt	PROPN
ap-7684	204	18	,	,	PUNCT
ap-7684	204	19	xy/3	xy/3	PROPN
ap-7684	204	20	+	+	X
ap-7684	204	21	εb	εb	ADP
ap-7684	204	22	,	,	PUNCT
ap-7684	204	23	xy/6)(1	xy/6)(1	PROPN
ap-7684	204	24	−	−	NOUN
ap-7684	204	25	ν	ν	NOUN
ap-7684	204	26	)	)	PUNCT
ap-7684	204	27	)	)	PUNCT
ap-7684	205	1	gi	gi	ADP
ap-7684	205	2	,	,	PUNCT
ap-7684	205	3	b	b	NOUN
ap-7684	205	4	,	,	PUNCT
ap-7684	205	5	x	x	SYM
ap-7684	205	6	=	=	SYM
ap-7684	205	7	ed	ed	NOUN
ap-7684	205	8	2	2	NUM
ap-7684	205	9	(	(	PUNCT
ap-7684	205	10	bisb	bisb	NOUN
ap-7684	205	11	+	+	CCONJ
ap-7684	205	12	ai(εt	ai(εt	NOUN
ap-7684	205	13	,	,	PUNCT
ap-7684	205	14	xy/6	xy/6	PROPN
ap-7684	205	15	+	+	CCONJ
ap-7684	205	16	εb	εb	ADP
ap-7684	205	17	,	,	PUNCT
ap-7684	205	18	xy/3)(1	xy/3)(1	PROPN
ap-7684	205	19	−	−	NOUN
ap-7684	205	20	ν	ν	NOUN
ap-7684	205	21	)	)	PUNCT
ap-7684	205	22	)	)	PUNCT
ap-7684	206	1	gi	gi	ADP
ap-7684	206	2	,	,	PUNCT
ap-7684	206	3	b	b	NOUN
ap-7684	206	4	,	,	PUNCT
ap-7684	206	5	y	y	PROPN
ap-7684	206	6	=	=	PUNCT
ap-7684	206	7	ed	ed	NOUN
ap-7684	206	8	2	2	NUM
ap-7684	206	9	(	(	PUNCT
ap-7684	206	10	ai(εt	ai(εt	VERB
ap-7684	206	11	,	,	PUNCT
ap-7684	206	12	y/6	y/6	PRON
ap-7684	206	13	+	+	CCONJ
ap-7684	206	14	εb	εb	ADP
ap-7684	206	15	,	,	PUNCT
ap-7684	206	16	y/3)+	y/3)+	PROPN
ap-7684	206	17	bi(εt	bi(εt	PROPN
ap-7684	206	18	,	,	PUNCT
ap-7684	206	19	xy/6	xy/6	PROPN
ap-7684	207	1	+	+	CCONJ
ap-7684	207	2	εb	εb	ADP
ap-7684	207	3	,	,	PUNCT
ap-7684	207	4	xy/3)(1	xy/3)(1	PROPN
ap-7684	207	5	−	−	NOUN
ap-7684	207	6	ν	ν	NOUN
ap-7684	207	7	)	)	PUNCT
ap-7684	207	8	)	)	PUNCT
ap-7684	208	1	(	(	PUNCT
ap-7684	208	2	17	17	X
ap-7684	208	3	)	)	PUNCT
ap-7684	208	4	derivatives	derivative	NOUN
ap-7684	208	5	of	of	ADP
ap-7684	208	6	the	the	DET
ap-7684	208	7	nodal	nodal	NOUN
ap-7684	208	8	forces	force	NOUN
ap-7684	208	9	gi	gi	ADP
ap-7684	208	10	,	,	PUNCT
ap-7684	208	11	t	t	PROPN
ap-7684	208	12	/	/	SYM
ap-7684	208	13	b	b	PROPN
ap-7684	208	14	,	,	PUNCT
ap-7684	208	15	x	x	PROPN
ap-7684	208	16	/	/	SYM
ap-7684	208	17	y	y	NOUN
ap-7684	208	18	with	with	ADP
ap-7684	208	19	respect	respect	NOUN
ap-7684	208	20	to	to	ADP
ap-7684	208	21	the	the	DET
ap-7684	208	22	dofs	dof	NOUN
ap-7684	208	23	can	can	AUX
ap-7684	208	24	be	be	AUX
ap-7684	208	25	written	write	VERB
ap-7684	208	26	in	in	ADP
ap-7684	208	27	terms	term	NOUN
ap-7684	208	28	of	of	ADP
ap-7684	208	29	the	the	DET
ap-7684	208	30	st	st	PROPN
ap-7684	208	31	/	/	SYM
ap-7684	208	32	b	b	PROPN
ap-7684	208	33	functions	function	NOUN
ap-7684	208	34	,	,	PUNCT
ap-7684	208	35	for	for	ADP
ap-7684	208	36	instance	instance	NOUN
ap-7684	208	37	∂gi	∂gi	PROPN
ap-7684	208	38	,	,	PUNCT
ap-7684	208	39	t	t	PROPN
ap-7684	208	40	,	,	PUNCT
ap-7684	208	41	x	x	PROPN
ap-7684	208	42	∂uj	∂uj	PROPN
ap-7684	208	43	,	,	PUNCT
ap-7684	208	44	t	t	PROPN
ap-7684	208	45	,	,	PUNCT
ap-7684	208	46	x	x	X
ap-7684	208	47	=	=	SYM
ap-7684	208	48	∂gi	∂gi	PROPN
ap-7684	208	49	,	,	PUNCT
ap-7684	208	50	t	t	PROPN
ap-7684	208	51	,	,	PUNCT
ap-7684	208	52	x	x	SYM
ap-7684	208	53	∂εt	∂εt	NOUN
ap-7684	208	54	,	,	PUNCT
ap-7684	208	55	x	x	PUNCT
ap-7684	208	56	∂εt	∂εt	NOUN
ap-7684	208	57	,	,	PUNCT
ap-7684	208	58	x	x	SYM
ap-7684	208	59	∂uj	∂uj	PROPN
ap-7684	208	60	,	,	PUNCT
ap-7684	208	61	t	t	PROPN
ap-7684	208	62	,	,	PUNCT
ap-7684	208	63	x	x	PUNCT
ap-7684	208	64	+	+	CCONJ
ap-7684	208	65	∂gi	∂gi	PROPN
ap-7684	208	66	,	,	PUNCT
ap-7684	208	67	t	t	PROPN
ap-7684	208	68	,	,	PUNCT
ap-7684	208	69	x	x	SYM
ap-7684	208	70	∂εt	∂εt	NOUN
ap-7684	208	71	,	,	PUNCT
ap-7684	208	72	xy	xy	PROPN
ap-7684	208	73	∂εt	∂εt	PROPN
ap-7684	208	74	,	,	PUNCT
ap-7684	208	75	xy	xy	PROPN
ap-7684	208	76	∂uj	∂uj	PROPN
ap-7684	208	77	,	,	PUNCT
ap-7684	208	78	t	t	PROPN
ap-7684	208	79	,	,	PUNCT
ap-7684	208	80	x	x	X
ap-7684	209	1	=	=	NOUN
ap-7684	209	2	ed	ed	NOUN
ap-7684	209	3	4a	4a	NOUN
ap-7684	209	4	(	(	PUNCT
ap-7684	209	5	bibj	bibj	NOUN
ap-7684	209	6	∂st	∂st	PROPN
ap-7684	209	7	∂εt	∂εt	NOUN
ap-7684	209	8	,	,	PUNCT
ap-7684	209	9	x	x	PUNCT
ap-7684	209	10	+	+	CCONJ
ap-7684	209	11	aiaj	aiaj	VERB
ap-7684	209	12	1	1	NUM
ap-7684	209	13	−	−	NOUN
ap-7684	209	14	ν	ν	NOUN
ap-7684	209	15	2	2	NUM
ap-7684	209	16	1	1	NUM
ap-7684	209	17	3	3	NUM
ap-7684	209	18	)	)	PUNCT
ap-7684	209	19	functions	function	NOUN
ap-7684	209	20	st	st	PROPN
ap-7684	209	21	,	,	PUNCT
ap-7684	209	22	sb	sb	PROPN
ap-7684	209	23	depend	depend	VERB
ap-7684	209	24	on	on	ADP
ap-7684	209	25	x	x	PART
ap-7684	209	26	components	component	NOUN
ap-7684	209	27	of	of	ADP
ap-7684	209	28	εt	εt	PROPN
ap-7684	209	29	,	,	PUNCT
ap-7684	209	30	εb	εb	ADP
ap-7684	209	31	only	only	ADV
ap-7684	209	32	.	.	PUNCT
ap-7684	210	1	the	the	DET
ap-7684	210	2	subscript	subscript	NOUN
ap-7684	210	3	x	x	PUNCT
ap-7684	210	4	can	can	AUX
ap-7684	210	5	thus	thus	ADV
ap-7684	210	6	be	be	AUX
ap-7684	210	7	omitted	omit	VERB
ap-7684	210	8	in	in	ADP
ap-7684	210	9	their	their	PRON
ap-7684	210	10	derivatives	derivative	NOUN
ap-7684	210	11	.	.	PUNCT
ap-7684	211	1	formulas	formula	NOUN
ap-7684	211	2	for	for	ADP
ap-7684	211	3	the	the	DET
ap-7684	211	4	derivatives	derivative	NOUN
ap-7684	211	5	are	be	AUX
ap-7684	211	6	in	in	ADP
ap-7684	211	7	section	section	NOUN
ap-7684	211	8	2.1	2.1	NUM
ap-7684	211	9	.	.	PUNCT
ap-7684	212	1	when	when	SCONJ
ap-7684	212	2	µ	µ	X
ap-7684	212	3	=	=	SYM
ap-7684	212	4	1−ν	1−ν	NUM
ap-7684	212	5	2	2	NUM
ap-7684	212	6	is	be	AUX
ap-7684	212	7	introduced	introduce	VERB
ap-7684	212	8	and	and	CCONJ
ap-7684	212	9	common	common	ADJ
ap-7684	212	10	factor	factor	NOUN
ap-7684	212	11	ed	ed	NOUN
ap-7684	212	12	4a	4a	NOUN
ap-7684	212	13	is	be	AUX
ap-7684	212	14	omitted	omit	VERB
ap-7684	212	15	for	for	ADP
ap-7684	212	16	brevity	brevity	NOUN
ap-7684	212	17	,	,	PUNCT
ap-7684	212	18	submatrices	submatrice	NOUN
ap-7684	213	1	[	[	X
ap-7684	213	2	kbend	kbend	NOUN
ap-7684	213	3	,	,	PUNCT
ap-7684	213	4	i	i	PRON
ap-7684	213	5	,	,	PUNCT
ap-7684	213	6	j	j	PROPN
ap-7684	213	7	]	]	PUNCT
ap-7684	213	8	of	of	ADP
ap-7684	213	9	the	the	DET
ap-7684	213	10	element	element	ADJ
ap-7684	213	11	stiffness	stiffness	NOUN
ap-7684	213	12	matrix	matrix	NOUN
ap-7684	213	13	associated	associate	VERB
ap-7684	213	14	with	with	ADP
ap-7684	213	15	the	the	DET
ap-7684	213	16	inplane	inplane	NOUN
ap-7684	213	17	dofs	dof	NOUN
ap-7684	213	18	{	{	PUNCT
ap-7684	213	19	uplane}t	uplane}t	PROPN
ap-7684	213	20	=	=	SYM
ap-7684	213	21	{	{	PUNCT
ap-7684	213	22	ui	ui	PROPN
ap-7684	213	23	,	,	PUNCT
ap-7684	213	24	t	t	PROPN
ap-7684	213	25	,	,	PUNCT
ap-7684	213	26	x	x	NOUN
ap-7684	213	27	,	,	PUNCT
ap-7684	213	28	ui	ui	PROPN
ap-7684	213	29	,	,	PUNCT
ap-7684	213	30	t	t	PROPN
ap-7684	213	31	,	,	PUNCT
ap-7684	213	32	y	y	PROPN
ap-7684	213	33	,	,	PUNCT
ap-7684	213	34	ui	ui	PROPN
ap-7684	213	35	,	,	PUNCT
ap-7684	213	36	b	b	PROPN
ap-7684	213	37	,	,	PUNCT
ap-7684	213	38	x	x	NOUN
ap-7684	213	39	,	,	PUNCT
ap-7684	213	40	ui	ui	PROPN
ap-7684	213	41	,	,	PUNCT
ap-7684	213	42	b	b	PROPN
ap-7684	213	43	,	,	PUNCT
ap-7684	213	44	y	y	PROPN
ap-7684	213	45	}	}	PUNCT
ap-7684	213	46	are	be	AUX
ap-7684	213	47	:	:	PUNCT
ap-7684	213	48	i	i	PRON
ap-7684	213	49	,	,	PUNCT
ap-7684	213	50	i	i	PRON
ap-7684	213	51	:	:	PUNCT
ap-7684	213	52	[	[	PUNCT
ap-7684	213	53	bibj	bibj	VERB
ap-7684	213	54	∂st	∂st	PROPN
ap-7684	213	55	∂εt	∂εt	NOUN
ap-7684	213	56	+	+	CCONJ
ap-7684	213	57	aiajµ/3	aiajµ/3	ADP
ap-7684	213	58	aibjµ/3	aibjµ/3	PROPN
ap-7684	213	59	ajbiµ/3	ajbiµ/3	PROPN
ap-7684	213	60	bibjµ/3	bibjµ/3	PROPN
ap-7684	213	61	+	+	CCONJ
ap-7684	213	62	aiaj/3	aiaj/3	X
ap-7684	213	63	]	]	PUNCT
ap-7684	214	1	i	i	PRON
ap-7684	214	2	,	,	PUNCT
ap-7684	214	3	j	j	PROPN
ap-7684	214	4	:	:	PUNCT
ap-7684	214	5	[	[	PUNCT
ap-7684	214	6	bibj	bibj	VERB
ap-7684	214	7	∂st	∂st	PROPN
ap-7684	214	8	∂εb	∂εb	PROPN
ap-7684	214	9	+	+	PROPN
ap-7684	214	10	aiajµ/6	aiajµ/6	PROPN
ap-7684	214	11	aibjµ/6	aibjµ/6	PROPN
ap-7684	214	12	ajbiµ/6	ajbiµ/6	PROPN
ap-7684	214	13	bibjµ/6	bibjµ/6	PROPN
ap-7684	214	14	+	+	CCONJ
ap-7684	214	15	aiaj/6	aiaj/6	NUM
ap-7684	214	16	]	]	X
ap-7684	215	1	j	j	X
ap-7684	215	2	,	,	PUNCT
ap-7684	215	3	i	i	PRON
ap-7684	215	4	:	:	PUNCT
ap-7684	215	5	[	[	PUNCT
ap-7684	215	6	bibj	bibj	X
ap-7684	215	7	∂sb	∂sb	PROPN
ap-7684	215	8	∂εb	∂εb	PROPN
ap-7684	215	9	+	+	PROPN
ap-7684	215	10	aiajµ/6	aiajµ/6	PROPN
ap-7684	215	11	aibjµ/6	aibjµ/6	PROPN
ap-7684	215	12	ajbiµ/6	ajbiµ/6	PROPN
ap-7684	215	13	bibj/6µ+	bibj/6µ+	VERB
ap-7684	215	14	aiaj/6	aiaj/6	PROPN
ap-7684	215	15	]	]	X
ap-7684	216	1	j	j	PROPN
ap-7684	216	2	,	,	PUNCT
ap-7684	216	3	j	j	PROPN
ap-7684	216	4	:	:	PUNCT
ap-7684	216	5	[	[	PUNCT
ap-7684	216	6	bibj	bibj	X
ap-7684	216	7	∂sb	∂sb	PROPN
ap-7684	216	8	∂εb	∂εb	NOUN
ap-7684	216	9	+	+	CCONJ
ap-7684	216	10	aiajµ/3	aiajµ/3	PROPN
ap-7684	216	11	aibjµ/3	aibjµ/3	PROPN
ap-7684	216	12	ajbiµ/3	ajbiµ/3	PROPN
ap-7684	216	13	bibjµ/3	bibjµ/3	PROPN
ap-7684	216	14	+	+	CCONJ
ap-7684	216	15	aiaj/3	aiaj/3	PROPN
ap-7684	216	16	]	]	PUNCT
ap-7684	216	17	(	(	PUNCT
ap-7684	216	18	18	18	NUM
ap-7684	216	19	)	)	PUNCT
ap-7684	216	20	for	for	ADP
ap-7684	216	21	a	a	DET
ap-7684	216	22	linear	linear	ADJ
ap-7684	216	23	element	element	NOUN
ap-7684	216	24	(	(	PUNCT
ap-7684	216	25	uncracked	uncracked	ADJ
ap-7684	216	26	bed	bed	NOUN
ap-7684	216	27	joints	joint	NOUN
ap-7684	216	28	)	)	PUNCT
ap-7684	217	1	[	[	X
ap-7684	217	2	ki	ki	PROPN
ap-7684	217	3	,	,	PUNCT
ap-7684	217	4	j	j	PROPN
ap-7684	217	5	]	]	X
ap-7684	217	6	t	t	X
ap-7684	217	7	=	=	PUNCT
ap-7684	218	1	[	[	X
ap-7684	218	2	kj	kj	PROPN
ap-7684	218	3	,	,	PUNCT
ap-7684	218	4	i	i	PRON
ap-7684	218	5	]	]	X
ap-7684	218	6	,	,	PUNCT
ap-7684	218	7	which	which	PRON
ap-7684	218	8	implies	imply	VERB
ap-7684	218	9	symmetry	symmetry	NOUN
ap-7684	218	10	of	of	ADP
ap-7684	218	11	the	the	DET
ap-7684	218	12	whole	whole	ADJ
ap-7684	218	13	matrix	matrix	NOUN
ap-7684	218	14	[	[	X
ap-7684	218	15	k	k	X
ap-7684	218	16	]	]	X
ap-7684	218	17	.	.	PUNCT
ap-7684	219	1	for	for	ADP
ap-7684	219	2	cracked	crack	VERB
ap-7684	219	3	bed	bed	NOUN
ap-7684	219	4	joints	joint	NOUN
ap-7684	219	5	ht	ht	PROPN
ap-7684	219	6	,	,	PUNCT
ap-7684	219	7	b	b	PROPN
ap-7684	219	8	̸=	̸=	PROPN
ap-7684	219	9	hb	hb	PROPN
ap-7684	219	10	,	,	PUNCT
ap-7684	219	11	t	t	PROPN
ap-7684	219	12	,	,	PUNCT
ap-7684	219	13	the	the	DET
ap-7684	219	14	symmetry	symmetry	NOUN
ap-7684	219	15	is	be	AUX
ap-7684	219	16	lost	lose	VERB
ap-7684	219	17	.	.	PUNCT
ap-7684	220	1	298	298	NUM
ap-7684	220	2	vol	vol	NOUN
ap-7684	220	3	.	.	PUNCT
ap-7684	221	1	62	62	NUM
ap-7684	221	2	no	no	INTJ
ap-7684	221	3	.	.	PUNCT
ap-7684	222	1	2/2022	2/2022	PROPN
ap-7684	223	1	a	a	DET
ap-7684	223	2	mindlin	mindlin	PROPN
ap-7684	223	3	shell	shell	PROPN
ap-7684	223	4	finite	finite	PROPN
ap-7684	223	5	element	element	NOUN
ap-7684	223	6	for	for	ADP
ap-7684	223	7	stone	stone	NOUN
ap-7684	223	8	masonry	masonry	NOUN
ap-7684	223	9	bridges	bridge	NOUN
ap-7684	223	10	with	with	ADP
ap-7684	223	11	backfill	backfill	NOUN
ap-7684	223	12	4.2	4.2	NUM
ap-7684	223	13	.	.	PUNCT
ap-7684	224	1	shear	shear	NOUN
ap-7684	224	2	owing	owe	VERB
ap-7684	224	3	to	to	ADP
ap-7684	224	4	the	the	DET
ap-7684	224	5	rotations	rotation	NOUN
ap-7684	224	6	of	of	ADP
ap-7684	224	7	normals	normal	NOUN
ap-7684	224	8	the	the	DET
ap-7684	224	9	rotation	rotation	NOUN
ap-7684	224	10	of	of	ADP
ap-7684	224	11	normals	normal	NOUN
ap-7684	224	12	φ⃗	φ⃗	PROPN
ap-7684	224	13	induces	induce	VERB
ap-7684	224	14	shear	shear	ADJ
ap-7684	224	15	deformation	deformation	NOUN
ap-7684	224	16	,	,	PUNCT
ap-7684	224	17	too	too	ADV
ap-7684	224	18	.	.	PUNCT
ap-7684	225	1	it	it	PRON
ap-7684	225	2	would	would	AUX
ap-7684	225	3	not	not	PART
ap-7684	225	4	induce	induce	VERB
ap-7684	225	5	any	any	DET
ap-7684	225	6	deflection	deflection	NOUN
ap-7684	225	7	in	in	ADP
ap-7684	225	8	a	a	DET
ap-7684	225	9	consistent	consistent	ADJ
ap-7684	225	10	isoparametric	isoparametric	ADJ
ap-7684	225	11	element	element	NOUN
ap-7684	225	12	and	and	CCONJ
ap-7684	225	13	then	then	ADV
ap-7684	225	14	φ⃗	φ⃗	PROPN
ap-7684	225	15	would	would	AUX
ap-7684	225	16	simply	simply	ADV
ap-7684	225	17	be	be	AUX
ap-7684	225	18	added	add	VERB
ap-7684	225	19	to	to	ADP
ap-7684	225	20	γ⃗	γ⃗	NOUN
ap-7684	225	21	to	to	PART
ap-7684	225	22	obtain	obtain	VERB
ap-7684	225	23	the	the	DET
ap-7684	225	24	total	total	ADJ
ap-7684	225	25	shear	shear	NOUN
ap-7684	225	26	deformation	deformation	NOUN
ap-7684	225	27	.	.	PUNCT
ap-7684	226	1	such	such	ADJ
ap-7684	226	2	displacement	displacement	ADJ
ap-7684	226	3	pattern	pattern	NOUN
ap-7684	226	4	is	be	AUX
ap-7684	226	5	known	know	VERB
ap-7684	226	6	to	to	PART
ap-7684	226	7	imply	imply	VERB
ap-7684	226	8	locking	lock	VERB
ap-7684	226	9	in	in	ADP
ap-7684	226	10	thin	thin	ADJ
ap-7684	226	11	elements	element	NOUN
ap-7684	226	12	,	,	PUNCT
ap-7684	226	13	like	like	SCONJ
ap-7684	226	14	it	it	PRON
ap-7684	226	15	does	do	VERB
ap-7684	226	16	in	in	ADP
ap-7684	226	17	the	the	DET
ap-7684	226	18	isoparametric	isoparametric	ADJ
ap-7684	226	19	variant	variant	NOUN
ap-7684	226	20	of	of	ADP
ap-7684	226	21	the	the	DET
ap-7684	226	22	tt	tt	PROPN
ap-7684	226	23	element	element	NOUN
ap-7684	226	24	.	.	PUNCT
ap-7684	227	1	in	in	ADP
ap-7684	227	2	the	the	DET
ap-7684	227	3	tm	tm	PROPN
ap-7684	227	4	element	element	NOUN
ap-7684	227	5	,	,	PUNCT
ap-7684	227	6	φ⃗	φ⃗	PROPN
ap-7684	227	7	induces	induce	VERB
ap-7684	227	8	a	a	DET
ap-7684	227	9	quadratic	quadratic	ADJ
ap-7684	227	10	field	field	NOUN
ap-7684	227	11	of	of	ADP
ap-7684	227	12	deflection	deflection	NOUN
ap-7684	227	13	wφ	wφ	NOUN
ap-7684	227	14	,	,	PUNCT
ap-7684	227	15	which	which	PRON
ap-7684	227	16	must	must	AUX
ap-7684	227	17	have	have	VERB
ap-7684	227	18	zero	zero	NUM
ap-7684	227	19	values	value	NOUN
ap-7684	227	20	at	at	ADP
ap-7684	227	21	all	all	DET
ap-7684	227	22	joints	joint	NOUN
ap-7684	227	23	.	.	PUNCT
ap-7684	228	1	the	the	DET
ap-7684	228	2	deflection	deflection	NOUN
ap-7684	228	3	should	should	AUX
ap-7684	228	4	be	be	AUX
ap-7684	228	5	compatible	compatible	ADJ
ap-7684	228	6	with	with	ADP
ap-7684	228	7	the	the	DET
ap-7684	228	8	neighbouring	neighbouring	ADJ
ap-7684	228	9	elements	element	NOUN
ap-7684	228	10	along	along	ADP
ap-7684	228	11	the	the	DET
ap-7684	228	12	boundaries	boundary	NOUN
ap-7684	228	13	.	.	PUNCT
ap-7684	229	1	the	the	DET
ap-7684	229	2	antisymmetric	antisymmetric	ADJ
ap-7684	229	3	part	part	NOUN
ap-7684	229	4	of	of	ADP
ap-7684	229	5	the	the	DET
ap-7684	229	6	normal	normal	ADJ
ap-7684	229	7	component	component	NOUN
ap-7684	229	8	of	of	ADP
ap-7684	229	9	φ⃗	φ⃗	PROPN
ap-7684	229	10	along	along	ADP
ap-7684	229	11	an	an	DET
ap-7684	229	12	element	element	NOUN
ap-7684	229	13	’s	’s	PART
ap-7684	229	14	side	side	NOUN
ap-7684	229	15	is	be	AUX
ap-7684	229	16	assigned	assign	VERB
ap-7684	229	17	to	to	ADP
ap-7684	229	18	deflection	deflection	NOUN
ap-7684	229	19	,	,	PUNCT
ap-7684	229	20	the	the	DET
ap-7684	229	21	symmetric	symmetric	ADJ
ap-7684	229	22	part	part	NOUN
ap-7684	229	23	to	to	ADP
ap-7684	229	24	shear	shear	ADJ
ap-7684	229	25	deformation	deformation	NOUN
ap-7684	229	26	,	,	PUNCT
ap-7684	229	27	in	in	ADP
ap-7684	229	28	analogue	analogue	NOUN
ap-7684	229	29	,	,	PUNCT
ap-7684	229	30	to	to	ADP
ap-7684	229	31	the	the	DET
ap-7684	229	32	tt	tt	PROPN
ap-7684	229	33	element	element	NOUN
ap-7684	229	34	.	.	PUNCT
ap-7684	230	1	perfect	perfect	ADJ
ap-7684	230	2	compatibility	compatibility	NOUN
ap-7684	230	3	of	of	ADP
ap-7684	230	4	deflections	deflection	NOUN
ap-7684	230	5	along	along	ADP
ap-7684	230	6	boundaries	boundary	NOUN
ap-7684	230	7	with	with	ADP
ap-7684	230	8	neighbouring	neighbouring	ADJ
ap-7684	230	9	elements	element	NOUN
ap-7684	230	10	is	be	AUX
ap-7684	230	11	attained	attain	VERB
ap-7684	230	12	for	for	ADP
ap-7684	230	13	elements	element	NOUN
ap-7684	230	14	lying	lie	VERB
ap-7684	230	15	in	in	ADP
ap-7684	230	16	a	a	DET
ap-7684	230	17	plane	plane	NOUN
ap-7684	230	18	.	.	PUNCT
ap-7684	231	1	the	the	DET
ap-7684	231	2	implementation	implementation	NOUN
ap-7684	231	3	of	of	ADP
ap-7684	231	4	the	the	DET
ap-7684	231	5	outlined	outline	VERB
ap-7684	231	6	displacement	displacement	NOUN
ap-7684	231	7	pattern	pattern	NOUN
ap-7684	231	8	is	be	AUX
ap-7684	231	9	rather	rather	ADV
ap-7684	231	10	lengthy	lengthy	ADJ
ap-7684	231	11	and	and	CCONJ
ap-7684	231	12	it	it	PRON
ap-7684	231	13	is	be	AUX
ap-7684	231	14	skipped	skip	VERB
ap-7684	231	15	here	here	ADV
ap-7684	231	16	.	.	PUNCT
ap-7684	232	1	the	the	DET
ap-7684	232	2	resulting	result	VERB
ap-7684	232	3	constant	constant	ADJ
ap-7684	232	4	transverse	transverse	NOUN
ap-7684	232	5	shear	shear	NOUN
ap-7684	232	6	owing	owe	VERB
ap-7684	232	7	to	to	ADP
ap-7684	232	8	normals	normal	NOUN
ap-7684	232	9	rotation	rotation	NOUN
ap-7684	232	10	is	be	AUX
ap-7684	232	11	γu	γu	ADJ
ap-7684	232	12	=	=	PUNCT
ap-7684	232	13	∑	∑	PUNCT
ap-7684	232	14	i	i	PROPN
ap-7684	232	15	[	[	X
ap-7684	232	16	ψi]({ui	ψi]({ui	PROPN
ap-7684	232	17	,	,	PUNCT
ap-7684	232	18	t	t	PROPN
ap-7684	232	19	}	}	PUNCT
ap-7684	232	20	−	−	PROPN
ap-7684	232	21	{	{	PUNCT
ap-7684	232	22	ui	ui	PROPN
ap-7684	232	23	,	,	PUNCT
ap-7684	232	24	b	b	NOUN
ap-7684	232	25	}	}	PUNCT
ap-7684	232	26	)	)	PUNCT
ap-7684	233	1	[	[	X
ap-7684	233	2	ψi	ψi	NOUN
ap-7684	233	3	]	]	X
ap-7684	233	4	=	=	SYM
ap-7684	233	5	(	(	PUNCT
ap-7684	233	6	[	[	PUNCT
ap-7684	233	7	0	0	NUM
ap-7684	233	8	−1/3	−1/3	NOUN
ap-7684	233	9	1/3	1/3	NOUN
ap-7684	233	10	0	0	NUM
ap-7684	233	11	]	]	PUNCT
ap-7684	233	12	−	−	PROPN
ap-7684	233	13	1	1	NUM
ap-7684	233	14	12a	12a	NOUN
ap-7684	233	15	[	[	PUNCT
ap-7684	233	16	a2	a2	PROPN
ap-7684	233	17	k	k	PROPN
ap-7684	233	18	−	−	PROPN
ap-7684	233	19	a2	a2	PROPN
ap-7684	233	20	j	j	PROPN
ap-7684	233	21	bjaj	bjaj	PROPN
ap-7684	233	22	−	−	PROPN
ap-7684	233	23	bkak	bkak	PROPN
ap-7684	233	24	−bkak	−bkak	NOUN
ap-7684	233	25	+	+	CCONJ
ap-7684	233	26	bjaj	bjaj	ADJ
ap-7684	233	27	b2	b2	NOUN
ap-7684	233	28	j	j	PROPN
ap-7684	233	29	−	−	PROPN
ap-7684	233	30	b2	b2	NOUN
ap-7684	234	1	k	k	PROPN
ap-7684	235	1	]	]	X
ap-7684	236	1	)	)	PUNCT
ap-7684	237	1	1	1	NUM
ap-7684	237	2	d	d	NOUN
ap-7684	237	3	(	(	PUNCT
ap-7684	237	4	19	19	NUM
ap-7684	237	5	)	)	PUNCT
ap-7684	237	6	the	the	DET
ap-7684	237	7	full	full	ADJ
ap-7684	237	8	transverse	transverse	NOUN
ap-7684	237	9	shear	shear	NOUN
ap-7684	237	10	of	of	ADP
ap-7684	237	11	the	the	DET
ap-7684	237	12	tm	tm	PROPN
ap-7684	237	13	element	element	NOUN
ap-7684	237	14	is	be	AUX
ap-7684	237	15	then	then	ADV
ap-7684	237	16	{	{	PUNCT
ap-7684	237	17	γ	γ	X
ap-7684	237	18	}	}	PUNCT
ap-7684	237	19	=	=	PUNCT
ap-7684	237	20	∑	∑	PUNCT
ap-7684	237	21	i	i	PRON
ap-7684	237	22	(	(	PUNCT
ap-7684	237	23	[	[	X
ap-7684	237	24	ψi	ψi	NOUN
ap-7684	237	25	]	]	X
ap-7684	237	26	,	,	PUNCT
ap-7684	237	27	1	1	NUM
ap-7684	237	28	2a	2a	NUM
ap-7684	237	29	[	[	PUNCT
ap-7684	237	30	−ai	−ai	NOUN
ap-7684	237	31	bi	bi	NOUN
ap-7684	237	32	]	]	PUNCT
ap-7684	237	33	,	,	PUNCT
ap-7684	237	34	−[ψi	−[ψi	ADV
ap-7684	237	35	]	]	PUNCT
ap-7684	237	36	)	)	PUNCT
ap-7684	237	37	{	{	PUNCT
ap-7684	237	38	u}i	u}i	NOUN
ap-7684	237	39	(	(	PUNCT
ap-7684	237	40	20	20	NUM
ap-7684	237	41	)	)	PUNCT
ap-7684	237	42	where	where	SCONJ
ap-7684	237	43	indices	indice	VERB
ap-7684	237	44	i	i	PRON
ap-7684	237	45	,	,	PUNCT
ap-7684	237	46	j	j	PROPN
ap-7684	237	47	,	,	PUNCT
ap-7684	237	48	k	k	PROPN
ap-7684	237	49	are	be	AUX
ap-7684	237	50	subject	subject	ADJ
ap-7684	237	51	to	to	ADP
ap-7684	237	52	cyclic	cyclic	ADJ
ap-7684	237	53	replacement	replacement	NOUN
ap-7684	237	54	.	.	PUNCT
ap-7684	238	1	formula	formula	NOUN
ap-7684	238	2	20	20	NUM
ap-7684	238	3	is	be	AUX
ap-7684	238	4	necessary	necessary	ADJ
ap-7684	238	5	with	with	ADP
ap-7684	238	6	thin	thin	ADJ
ap-7684	238	7	shells	shell	NOUN
ap-7684	238	8	where	where	SCONJ
ap-7684	238	9	shear	shear	NOUN
ap-7684	238	10	locking	locking	NOUN
ap-7684	238	11	can	can	AUX
ap-7684	238	12	occur	occur	VERB
ap-7684	238	13	.	.	PUNCT
ap-7684	239	1	masonry	masonry	NOUN
ap-7684	239	2	arches	arch	NOUN
ap-7684	239	3	and	and	CCONJ
ap-7684	239	4	other	other	ADJ
ap-7684	239	5	burried	burried	ADJ
ap-7684	239	6	shells	shell	NOUN
ap-7684	239	7	are	be	AUX
ap-7684	239	8	mostly	mostly	ADV
ap-7684	239	9	thick	thick	ADJ
ap-7684	239	10	shells	shell	NOUN
ap-7684	239	11	.	.	PUNCT
ap-7684	240	1	matrices	matrix	NOUN
ap-7684	241	1	[	[	X
ap-7684	241	2	ψi	ψi	NOUN
ap-7684	241	3	]	]	PUNCT
ap-7684	241	4	can	can	AUX
ap-7684	241	5	be	be	AUX
ap-7684	241	6	simplified	simplify	VERB
ap-7684	241	7	by	by	ADP
ap-7684	241	8	omitting	omit	VERB
ap-7684	241	9	the	the	DET
ap-7684	241	10	second	second	ADJ
ap-7684	241	11	summand	summand	NOUN
ap-7684	241	12	in	in	ADP
ap-7684	241	13	such	such	ADJ
ap-7684	241	14	applications	application	NOUN
ap-7684	241	15	.	.	PUNCT
ap-7684	242	1	experience	experience	NOUN
ap-7684	242	2	with	with	ADP
ap-7684	242	3	tests	test	NOUN
ap-7684	242	4	and	and	CCONJ
ap-7684	242	5	applications	application	NOUN
ap-7684	242	6	testifies	testify	VERB
ap-7684	242	7	that	that	SCONJ
ap-7684	242	8	keeping	keep	VERB
ap-7684	242	9	the	the	DET
ap-7684	242	10	second	second	ADJ
ap-7684	242	11	summand	summand	NOUN
ap-7684	242	12	improves	improve	VERB
ap-7684	242	13	the	the	DET
ap-7684	242	14	element	element	NOUN
ap-7684	242	15	convergence	convergence	NOUN
ap-7684	242	16	.	.	PUNCT
ap-7684	243	1	4.3	4.3	NUM
ap-7684	243	2	.	.	PUNCT
ap-7684	244	1	tm	tm	PRON
ap-7684	244	2	flat	flat	ADJ
ap-7684	244	3	slab	slab	NOUN
ap-7684	244	4	element	element	NOUN
ap-7684	244	5	simple	simple	ADJ
ap-7684	244	6	linear	linear	PROPN
ap-7684	244	7	constitutive	constitutive	ADJ
ap-7684	244	8	equations	equation	NOUN
ap-7684	244	9	are	be	AUX
ap-7684	244	10	assumed	assume	VERB
ap-7684	244	11	for	for	ADP
ap-7684	244	12	the	the	DET
ap-7684	244	13	transverse	transverse	NOUN
ap-7684	244	14	shear	shear	NOUN
ap-7684	244	15	,	,	PUNCT
ap-7684	244	16	vx	vx	PROPN
ap-7684	244	17	=	=	SYM
ap-7684	244	18	gγx	gγx	PROPN
ap-7684	244	19	,	,	PUNCT
ap-7684	244	20	vy	vy	NOUN
ap-7684	244	21	=	=	SYM
ap-7684	244	22	gγy	gγy	PROPN
ap-7684	244	23	.	.	PUNCT
ap-7684	245	1	(	(	PUNCT
ap-7684	245	2	21	21	NUM
ap-7684	245	3	)	)	PUNCT
ap-7684	245	4	vx	vx	PROPN
ap-7684	245	5	is	be	AUX
ap-7684	245	6	the	the	DET
ap-7684	245	7	standard	standard	ADJ
ap-7684	245	8	shear	shear	NOUN
ap-7684	245	9	force	force	NOUN
ap-7684	245	10	in	in	ADP
ap-7684	245	11	element	element	NOUN
ap-7684	245	12	local	local	ADJ
ap-7684	245	13	y	y	PROPN
ap-7684	245	14	−	−	PROPN
ap-7684	245	15	z	z	NOUN
ap-7684	245	16	plane	plane	NOUN
ap-7684	245	17	when	when	SCONJ
ap-7684	245	18	looking	look	VERB
ap-7684	245	19	along	along	ADP
ap-7684	245	20	x	x	PUNCT
ap-7684	245	21	axis	axis	NOUN
ap-7684	245	22	and	and	CCONJ
ap-7684	245	23	vy	vy	NOUN
ap-7684	245	24	is	be	AUX
ap-7684	245	25	the	the	DET
ap-7684	245	26	standard	standard	ADJ
ap-7684	245	27	shear	shear	NOUN
ap-7684	245	28	force	force	NOUN
ap-7684	245	29	in	in	ADP
ap-7684	245	30	element	element	ADJ
ap-7684	245	31	local	local	ADJ
ap-7684	245	32	x−	x−	PROPN
ap-7684	245	33	z	z	PROPN
ap-7684	245	34	plane	plane	NOUN
ap-7684	245	35	when	when	SCONJ
ap-7684	245	36	looking	look	VERB
ap-7684	245	37	along	along	ADP
ap-7684	245	38	y	y	PROPN
ap-7684	245	39	axis	axis	NOUN
ap-7684	245	40	.	.	PUNCT
ap-7684	246	1	the	the	DET
ap-7684	246	2	contribution	contribution	NOUN
ap-7684	246	3	of	of	ADP
ap-7684	246	4	the	the	DET
ap-7684	246	5	shear	shear	NOUN
ap-7684	246	6	stiffness	stiffness	NOUN
ap-7684	246	7	to	to	ADP
ap-7684	246	8	the	the	DET
ap-7684	246	9	element	element	ADJ
ap-7684	246	10	stiffness	stiffness	NOUN
ap-7684	246	11	matrix	matrix	NOUN
ap-7684	246	12	is	be	AUX
ap-7684	246	13	written	write	VERB
ap-7684	246	14	down	down	ADP
ap-7684	246	15	in	in	ADP
ap-7684	246	16	terms	term	NOUN
ap-7684	246	17	of	of	ADP
ap-7684	246	18	the	the	DET
ap-7684	246	19	5x5	5x5	NUM
ap-7684	246	20	submatrices	submatrice	NOUN
ap-7684	246	21	associated	associate	VERB
ap-7684	246	22	with	with	ADP
ap-7684	246	23	the	the	DET
ap-7684	246	24	two	two	NUM
ap-7684	246	25	top	top	ADJ
ap-7684	246	26	vertex	vertex	NOUN
ap-7684	246	27	,	,	PUNCT
ap-7684	246	28	one	one	NUM
ap-7684	246	29	transverse	transverse	NOUN
ap-7684	246	30	and	and	CCONJ
ap-7684	246	31	two	two	NUM
ap-7684	246	32	bottom	bottom	ADJ
ap-7684	246	33	vertices	vertex	NOUN
ap-7684	246	34	translational	translational	ADJ
ap-7684	246	35	dofs	dof	NOUN
ap-7684	246	36	of	of	ADP
ap-7684	246	37	each	each	DET
ap-7684	246	38	node	node	NOUN
ap-7684	246	39	.	.	PUNCT
ap-7684	247	1	column	column	NOUN
ap-7684	247	2	matrices	matrice	VERB
ap-7684	247	3	[	[	X
ap-7684	247	4	φi	φi	X
ap-7684	247	5	]	]	X
ap-7684	247	6	=	=	SYM
ap-7684	248	1	[	[	X
ap-7684	248	2	−ai	−ai	NOUN
ap-7684	248	3	,	,	PUNCT
ap-7684	248	4	bi]t	bi]t	PROPN
ap-7684	248	5	/2a	/2a	PUNCT
ap-7684	248	6	and	and	CCONJ
ap-7684	248	7	2x2	2x2	NUM
ap-7684	248	8	symmetric	symmetric	ADJ
ap-7684	248	9	matrices	matrix	NOUN
ap-7684	248	10	ψij	ψij	VERB
ap-7684	248	11	=	=	PUNCT
ap-7684	249	1	[	[	X
ap-7684	249	2	ψi]t	ψi]t	PROPN
ap-7684	249	3	[	[	X
ap-7684	249	4	ψj	ψj	ADV
ap-7684	249	5	]	]	PUNCT
ap-7684	249	6	help	help	VERB
ap-7684	249	7	to	to	PART
ap-7684	249	8	write	write	VERB
ap-7684	249	9	down	down	ADP
ap-7684	249	10	the	the	DET
ap-7684	249	11	shear	shear	NOUN
ap-7684	249	12	contribution	contribution	NOUN
ap-7684	249	13	to	to	ADP
ap-7684	249	14	the	the	DET
ap-7684	249	15	submatrices	submatrice	NOUN
ap-7684	249	16	:	:	PUNCT
ap-7684	250	1	[	[	X
ap-7684	250	2	kshear	kshear	X
ap-7684	250	3	,	,	PUNCT
ap-7684	250	4	i	i	PRON
ap-7684	250	5	,	,	PUNCT
ap-7684	250	6	j	j	PROPN
ap-7684	250	7	]	]	X
ap-7684	250	8	=	=	PUNCT
ap-7684	250	9	gad2	gad2	PROPN
ap-7684	250	10			PROPN
ap-7684	250	11	[	[	X
ap-7684	250	12	ψij	ψij	X
ap-7684	250	13	]	]	X
ap-7684	251	1	[	[	X
ap-7684	251	2	ψi]t	ψi]t	PROPN
ap-7684	251	3	[	[	X
ap-7684	251	4	φj	φj	X
ap-7684	251	5	]	]	PUNCT
ap-7684	251	6	−[ψij	−[ψij	X
ap-7684	251	7	]	]	PUNCT
ap-7684	252	1	[	[	X
ap-7684	252	2	φi]t	φi]t	PROPN
ap-7684	252	3	[	[	X
ap-7684	252	4	ψj	ψj	X
ap-7684	252	5	]	]	PUNCT
ap-7684	253	1	[	[	X
ap-7684	253	2	φi]t	φi]t	PROPN
ap-7684	253	3	[	[	X
ap-7684	253	4	φj	φj	X
ap-7684	253	5	]	]	PUNCT
ap-7684	253	6	−[φi]t	−[φi]t	PROPN
ap-7684	254	1	[	[	X
ap-7684	254	2	ψj	ψj	X
ap-7684	254	3	]	]	X
ap-7684	254	4	−[ψij	−[ψij	X
ap-7684	254	5	]	]	X
ap-7684	254	6	−[ψt	−[ψt	X
ap-7684	255	1	i	i	PRON
ap-7684	256	1	[	[	X
ap-7684	256	2	φj	φj	X
ap-7684	256	3	]	]	X
ap-7684	257	1	[	[	X
ap-7684	257	2	ψij	ψij	X
ap-7684	257	3	]	]	PUNCT
ap-7684	257	4			NOUN
ap-7684	257	5	(	(	PUNCT
ap-7684	257	6	22	22	NUM
ap-7684	257	7	)	)	PUNCT
ap-7684	257	8	complete	complete	ADJ
ap-7684	257	9	5×5	5×5	NUM
ap-7684	257	10	stiffness	stiffness	NOUN
ap-7684	257	11	submatrices	submatrice	NOUN
ap-7684	257	12	are	be	AUX
ap-7684	257	13	the	the	DET
ap-7684	257	14	sums	sum	NOUN
ap-7684	257	15	of	of	ADP
ap-7684	257	16	the	the	DET
ap-7684	257	17	bending	bend	VERB
ap-7684	257	18	stiffness	stiffness	NOUN
ap-7684	257	19	submatrices	submatrice	NOUN
ap-7684	257	20	18	18	NUM
ap-7684	257	21	extended	extend	VERB
ap-7684	257	22	by	by	ADP
ap-7684	257	23	an	an	DET
ap-7684	257	24	empty	empty	ADJ
ap-7684	257	25	third	third	ADJ
ap-7684	257	26	column	column	NOUN
ap-7684	257	27	and	and	CCONJ
ap-7684	257	28	row	row	NOUN
ap-7684	257	29	inserted	insert	VERB
ap-7684	257	30	between	between	ADP
ap-7684	257	31	the	the	DET
ap-7684	257	32	2×2	2×2	NUM
ap-7684	257	33	subsubmatrices	subsubmatrice	NOUN
ap-7684	257	34	and	and	CCONJ
ap-7684	257	35	submatrices	submatrice	NOUN
ap-7684	257	36	22	22	NUM
ap-7684	257	37	:	:	PUNCT
ap-7684	258	1	[	[	X
ap-7684	258	2	ki	ki	PROPN
ap-7684	258	3	,	,	PUNCT
ap-7684	258	4	j	j	PROPN
ap-7684	258	5	]	]	PUNCT
ap-7684	258	6	=	=	PUNCT
ap-7684	259	1	[	[	X
ap-7684	259	2	kbend	kbend	NOUN
ap-7684	259	3	,	,	PUNCT
ap-7684	259	4	i	i	PRON
ap-7684	259	5	,	,	PUNCT
ap-7684	259	6	j	j	PROPN
ap-7684	259	7	]	]	X
ap-7684	259	8	extended	extended	ADJ
ap-7684	259	9	+	+	X
ap-7684	260	1	[	[	X
ap-7684	260	2	kshear	kshear	X
ap-7684	260	3	,	,	PUNCT
ap-7684	260	4	i	i	PRON
ap-7684	260	5	,	,	PUNCT
ap-7684	260	6	j	j	PROPN
ap-7684	260	7	]	]	X
ap-7684	260	8	(	(	PUNCT
ap-7684	260	9	23	23	NUM
ap-7684	260	10	)	)	PUNCT
ap-7684	260	11	the	the	DET
ap-7684	260	12	whole	whole	ADJ
ap-7684	260	13	element	element	ADJ
ap-7684	260	14	stiffness	stiffness	NOUN
ap-7684	260	15	matrix	matrix	NOUN
ap-7684	260	16	is	be	AUX
ap-7684	260	17	the	the	DET
ap-7684	260	18	size	size	NOUN
ap-7684	260	19	15×15	15×15	NUM
ap-7684	260	20	composition	composition	NOUN
ap-7684	260	21	of	of	ADP
ap-7684	260	22	submatrices	submatrice	NOUN
ap-7684	261	1	[	[	X
ap-7684	261	2	ki	ki	PROPN
ap-7684	261	3	,	,	PUNCT
ap-7684	261	4	j	j	PROPN
ap-7684	261	5	]	]	X
ap-7684	261	6	,	,	PUNCT
ap-7684	261	7	but	but	CCONJ
ap-7684	261	8	the	the	DET
ap-7684	261	9	submatrices	submatrice	NOUN
ap-7684	261	10	are	be	AUX
ap-7684	261	11	assembled	assemble	VERB
ap-7684	261	12	in	in	ADP
ap-7684	261	13	the	the	DET
ap-7684	261	14	global	global	ADJ
ap-7684	261	15	stiffness	stiffness	NOUN
ap-7684	261	16	matrix	matrix	NOUN
ap-7684	261	17	so	so	SCONJ
ap-7684	261	18	that	that	SCONJ
ap-7684	261	19	the	the	DET
ap-7684	261	20	whole	whole	ADJ
ap-7684	261	21	matrix	matrix	NOUN
ap-7684	261	22	is	be	AUX
ap-7684	261	23	never	never	ADV
ap-7684	261	24	set	set	VERB
ap-7684	261	25	up	up	ADP
ap-7684	261	26	.	.	PUNCT
ap-7684	262	1	cracking	crack	VERB
ap-7684	262	2	in	in	ADP
ap-7684	262	3	the	the	DET
ap-7684	262	4	bed	bed	NOUN
ap-7684	262	5	joints	joint	NOUN
ap-7684	262	6	followed	follow	VERB
ap-7684	262	7	by	by	ADP
ap-7684	262	8	development	development	NOUN
ap-7684	262	9	of	of	ADP
ap-7684	262	10	virtual	virtual	ADJ
ap-7684	262	11	hinges	hinge	NOUN
ap-7684	262	12	in	in	ADP
ap-7684	262	13	the	the	DET
ap-7684	262	14	arch	arch	NOUN
ap-7684	262	15	have	have	AUX
ap-7684	262	16	been	be	AUX
ap-7684	262	17	considered	consider	VERB
ap-7684	262	18	the	the	DET
ap-7684	262	19	dominant	dominant	ADJ
ap-7684	262	20	failure	failure	NOUN
ap-7684	262	21	pattern	pattern	NOUN
ap-7684	262	22	of	of	ADP
ap-7684	262	23	masonry	masonry	NOUN
ap-7684	262	24	bridges	bridge	NOUN
ap-7684	262	25	since	since	SCONJ
ap-7684	262	26	the	the	DET
ap-7684	262	27	early	early	ADJ
ap-7684	262	28	attempts	attempt	NOUN
ap-7684	262	29	[	[	X
ap-7684	262	30	10	10	NUM
ap-7684	262	31	]	]	PUNCT
ap-7684	262	32	,	,	PUNCT
ap-7684	262	33	[	[	X
ap-7684	262	34	11	11	NUM
ap-7684	262	35	]	]	PUNCT
ap-7684	262	36	to	to	PART
ap-7684	262	37	assess	assess	VERB
ap-7684	262	38	the	the	DET
ap-7684	262	39	load	load	NOUN
ap-7684	262	40	capacity	capacity	NOUN
ap-7684	262	41	.	.	PUNCT
ap-7684	263	1	other	other	ADJ
ap-7684	263	2	failure	failure	NOUN
ap-7684	263	3	modes	mode	NOUN
ap-7684	263	4	like	like	ADP
ap-7684	263	5	shear	shear	NOUN
ap-7684	263	6	sliding	slide	VERB
ap-7684	263	7	of	of	ADP
ap-7684	263	8	the	the	DET
ap-7684	263	9	bed	bed	NOUN
ap-7684	263	10	joints	joint	NOUN
ap-7684	263	11	or	or	CCONJ
ap-7684	263	12	transverse	transverse	NOUN
ap-7684	263	13	tension	tension	NOUN
ap-7684	263	14	cracking	cracking	NOUN
ap-7684	263	15	of	of	ADP
ap-7684	263	16	the	the	DET
ap-7684	263	17	arch	arch	ADJ
ap-7684	263	18	require	require	NOUN
ap-7684	263	19	sophisticated	sophisticated	ADJ
ap-7684	263	20	material	material	NOUN
ap-7684	263	21	models	model	NOUN
ap-7684	263	22	and	and	CCONJ
ap-7684	263	23	properties	property	NOUN
ap-7684	263	24	which	which	PRON
ap-7684	263	25	are	be	AUX
ap-7684	263	26	almost	almost	ADV
ap-7684	263	27	impossible	impossible	ADJ
ap-7684	263	28	to	to	PART
ap-7684	263	29	obtain	obtain	VERB
ap-7684	263	30	in	in	ADP
ap-7684	263	31	the	the	DET
ap-7684	263	32	design	design	NOUN
ap-7684	263	33	practice	practice	NOUN
ap-7684	263	34	.	.	PUNCT
ap-7684	264	1	this	this	DET
ap-7684	264	2	stiffness	stiffness	ADJ
ap-7684	264	3	matrix	matrix	NOUN
ap-7684	264	4	can	can	AUX
ap-7684	264	5	be	be	AUX
ap-7684	264	6	used	use	VERB
ap-7684	264	7	for	for	ADP
ap-7684	264	8	the	the	DET
ap-7684	264	9	solution	solution	NOUN
ap-7684	264	10	of	of	ADP
ap-7684	264	11	flat	flat	ADJ
ap-7684	264	12	slabs	slab	NOUN
ap-7684	264	13	loaded	load	VERB
ap-7684	264	14	both	both	CCONJ
ap-7684	264	15	in	in	ADP
ap-7684	264	16	and	and	CCONJ
ap-7684	264	17	out	out	ADP
ap-7684	264	18	of	of	ADP
ap-7684	264	19	plane	plane	NOUN
ap-7684	264	20	but	but	CCONJ
ap-7684	264	21	in	in	ADP
ap-7684	264	22	shells	shell	NOUN
ap-7684	264	23	,	,	PUNCT
ap-7684	264	24	the	the	DET
ap-7684	264	25	bottom	bottom	ADJ
ap-7684	264	26	face	face	NOUN
ap-7684	264	27	dofs	dof	NOUN
ap-7684	264	28	ub	ub	ADP
ap-7684	264	29	,	,	PUNCT
ap-7684	264	30	x	x	X
ap-7684	264	31	,	,	PUNCT
ap-7684	264	32	ub	ub	PROPN
ap-7684	264	33	,	,	PUNCT
ap-7684	264	34	y	y	PRON
ap-7684	264	35	require	require	VERB
ap-7684	264	36	a	a	DET
ap-7684	264	37	special	special	ADJ
ap-7684	264	38	treatment	treatment	NOUN
ap-7684	264	39	since	since	SCONJ
ap-7684	264	40	they	they	PRON
ap-7684	264	41	are	be	AUX
ap-7684	264	42	not	not	PART
ap-7684	264	43	simply	simply	ADV
ap-7684	264	44	shared	share	VERB
ap-7684	264	45	by	by	ADP
ap-7684	264	46	the	the	DET
ap-7684	264	47	elements	element	NOUN
ap-7684	264	48	attached	attach	VERB
ap-7684	264	49	to	to	ADP
ap-7684	264	50	a	a	DET
ap-7684	264	51	node	node	NOUN
ap-7684	264	52	.	.	PUNCT
ap-7684	265	1	4.4	4.4	NUM
ap-7684	265	2	.	.	PUNCT
ap-7684	266	1	tm	tm	PROPN
ap-7684	266	2	shell	shell	PROPN
ap-7684	266	3	element	element	NOUN
ap-7684	266	4	the	the	DET
ap-7684	266	5	dofs	dof	NOUN
ap-7684	266	6	at	at	ADP
ap-7684	266	7	the	the	DET
ap-7684	266	8	bottom	bottom	ADJ
ap-7684	266	9	vertices	vertex	NOUN
ap-7684	266	10	of	of	ADP
ap-7684	266	11	the	the	DET
ap-7684	266	12	elements	element	NOUN
ap-7684	266	13	connecting	connect	VERB
ap-7684	266	14	to	to	ADP
ap-7684	266	15	a	a	DET
ap-7684	266	16	node	node	NOUN
ap-7684	266	17	do	do	AUX
ap-7684	266	18	not	not	PART
ap-7684	266	19	lie	lie	VERB
ap-7684	266	20	in	in	ADP
ap-7684	266	21	the	the	DET
ap-7684	266	22	same	same	ADJ
ap-7684	266	23	plane	plane	NOUN
ap-7684	266	24	and	and	CCONJ
ap-7684	266	25	are	be	AUX
ap-7684	266	26	not	not	PART
ap-7684	266	27	independent	independent	ADJ
ap-7684	266	28	of	of	ADP
ap-7684	266	29	the	the	DET
ap-7684	266	30	dofs	dof	NOUN
ap-7684	266	31	at	at	ADP
ap-7684	266	32	the	the	DET
ap-7684	266	33	top	top	ADJ
ap-7684	266	34	vertices	vertex	NOUN
ap-7684	266	35	.	.	PUNCT
ap-7684	267	1	the	the	DET
ap-7684	267	2	equilibrium	equilibrium	NOUN
ap-7684	267	3	of	of	ADP
ap-7684	267	4	the	the	DET
ap-7684	267	5	nodal	nodal	NOUN
ap-7684	267	6	forces	force	NOUN
ap-7684	267	7	at	at	ADP
ap-7684	267	8	the	the	DET
ap-7684	267	9	top	top	ADJ
ap-7684	267	10	vertices	vertex	NOUN
ap-7684	267	11	is	be	AUX
ap-7684	267	12	affected	affect	VERB
ap-7684	267	13	by	by	ADP
ap-7684	267	14	the	the	DET
ap-7684	267	15	nodal	nodal	NOUN
ap-7684	267	16	forces	force	NOUN
ap-7684	267	17	at	at	ADP
ap-7684	267	18	the	the	DET
ap-7684	267	19	bottom	bottom	ADJ
ap-7684	267	20	vertices	vertex	NOUN
ap-7684	267	21	.	.	PUNCT
ap-7684	268	1	these	these	DET
ap-7684	268	2	two	two	NUM
ap-7684	268	3	conjugate	conjugate	ADJ
ap-7684	268	4	deficiencies	deficiency	NOUN
ap-7684	268	5	must	must	AUX
ap-7684	268	6	be	be	AUX
ap-7684	268	7	removed	remove	VERB
ap-7684	268	8	.	.	PUNCT
ap-7684	269	1	the	the	DET
ap-7684	269	2	normal	normal	ADJ
ap-7684	269	3	to	to	ADP
ap-7684	269	4	the	the	DET
ap-7684	269	5	shell	shell	NOUN
ap-7684	269	6	surface	surface	NOUN
ap-7684	269	7	is	be	AUX
ap-7684	269	8	needed	need	VERB
ap-7684	269	9	for	for	ADP
ap-7684	269	10	a	a	DET
ap-7684	269	11	consistent	consistent	ADJ
ap-7684	269	12	formulation	formulation	NOUN
ap-7684	269	13	of	of	ADP
ap-7684	269	14	the	the	DET
ap-7684	269	15	tm	tm	PROPN
ap-7684	269	16	element	element	NOUN
ap-7684	269	17	.	.	PUNCT
ap-7684	270	1	the	the	DET
ap-7684	270	2	normal	normal	ADJ
ap-7684	270	3	is	be	AUX
ap-7684	270	4	rigid	rigid	ADJ
ap-7684	270	5	in	in	ADP
ap-7684	270	6	the	the	DET
ap-7684	270	7	frame	frame	NOUN
ap-7684	270	8	of	of	ADP
ap-7684	270	9	the	the	DET
ap-7684	270	10	timoshenko	timoshenko	ADJ
ap-7684	270	11	-	-	PUNCT
ap-7684	270	12	mindlin	mindlin	NOUN
ap-7684	270	13	shell	shell	NOUN
ap-7684	270	14	theory	theory	NOUN
ap-7684	270	15	,	,	PUNCT
ap-7684	270	16	which	which	PRON
ap-7684	270	17	implies	imply	VERB
ap-7684	270	18	that	that	SCONJ
ap-7684	270	19	the	the	DET
ap-7684	270	20	displacements	displacement	NOUN
ap-7684	270	21	of	of	ADP
ap-7684	270	22	all	all	DET
ap-7684	270	23	points	point	NOUN
ap-7684	270	24	of	of	ADP
ap-7684	270	25	the	the	DET
ap-7684	270	26	normal	normal	ADJ
ap-7684	270	27	share	share	NOUN
ap-7684	270	28	the	the	DET
ap-7684	270	29	same	same	ADJ
ap-7684	270	30	lateral	lateral	ADJ
ap-7684	270	31	displacement	displacement	ADJ
ap-7684	270	32	component	component	NOUN
ap-7684	270	33	.	.	PUNCT
ap-7684	271	1	the	the	DET
ap-7684	271	2	exact	exact	ADJ
ap-7684	271	3	definition	definition	NOUN
ap-7684	271	4	of	of	ADP
ap-7684	271	5	the	the	DET
ap-7684	271	6	normal	normal	ADJ
ap-7684	271	7	direction	direction	NOUN
ap-7684	271	8	n⃗	n⃗	PROPN
ap-7684	271	9	would	would	AUX
ap-7684	271	10	be	be	AUX
ap-7684	271	11	through	through	ADP
ap-7684	271	12	the	the	DET
ap-7684	271	13	shell	shell	ADJ
ap-7684	271	14	surface	surface	PROPN
ap-7684	271	15	mathematical	mathematical	ADJ
ap-7684	271	16	definition	definition	NOUN
ap-7684	271	17	.	.	PUNCT
ap-7684	272	1	for	for	ADP
ap-7684	272	2	practical	practical	ADJ
ap-7684	272	3	applications	application	NOUN
ap-7684	272	4	of	of	ADP
ap-7684	272	5	the	the	DET
ap-7684	272	6	tm	tm	PROPN
ap-7684	272	7	element	element	NOUN
ap-7684	272	8	,	,	PUNCT
ap-7684	272	9	it	it	PRON
ap-7684	272	10	is	be	AUX
ap-7684	272	11	sufficient	sufficient	ADJ
ap-7684	272	12	to	to	PART
ap-7684	272	13	define	define	VERB
ap-7684	272	14	the	the	DET
ap-7684	272	15	unit	unit	NOUN
ap-7684	272	16	normal	normal	ADJ
ap-7684	272	17	n⃗i	n⃗i	PROPN
ap-7684	272	18	at	at	ADP
ap-7684	272	19	a	a	DET
ap-7684	272	20	node	node	NOUN
ap-7684	272	21	i	i	PRON
ap-7684	272	22	as	as	ADP
ap-7684	272	23	the	the	DET
ap-7684	272	24	normalized	normalized	ADJ
ap-7684	272	25	sum	sum	NOUN
ap-7684	272	26	of	of	ADP
ap-7684	272	27	the	the	DET
ap-7684	272	28	normals	normal	NOUN
ap-7684	272	29	of	of	ADP
ap-7684	272	30	all	all	DET
ap-7684	272	31	elements	element	NOUN
ap-7684	272	32	connecting	connect	VERB
ap-7684	272	33	to	to	ADP
ap-7684	272	34	the	the	DET
ap-7684	272	35	node	node	NOUN
ap-7684	272	36	,	,	PUNCT
ap-7684	272	37	each	each	PRON
ap-7684	272	38	element	element	VERB
ap-7684	272	39	normal	normal	ADJ
ap-7684	272	40	length	length	NOUN
ap-7684	272	41	proportional	proportional	NOUN
ap-7684	272	42	to	to	ADP
ap-7684	272	43	the	the	DET
ap-7684	272	44	sine	sine	NOUN
ap-7684	272	45	of	of	ADP
ap-7684	272	46	the	the	DET
ap-7684	272	47	angle	angle	NOUN
ap-7684	272	48	of	of	ADP
ap-7684	272	49	the	the	DET
ap-7684	272	50	two	two	NUM
ap-7684	272	51	adjacent	adjacent	ADJ
ap-7684	272	52	sides	side	NOUN
ap-7684	272	53	of	of	ADP
ap-7684	272	54	the	the	DET
ap-7684	272	55	respective	respective	ADJ
ap-7684	272	56	element	element	NOUN
ap-7684	272	57	.	.	PUNCT
ap-7684	273	1	position	position	NOUN
ap-7684	273	2	vectors	vector	NOUN
ap-7684	273	3	of	of	ADP
ap-7684	273	4	nodes	node	NOUN
ap-7684	273	5	are	be	AUX
ap-7684	273	6	denoted	denote	VERB
ap-7684	273	7	x⃗i	x⃗i	PROPN
ap-7684	273	8	and	and	CCONJ
ap-7684	273	9	nodes	node	NOUN
ap-7684	273	10	of	of	ADP
ap-7684	273	11	the	the	DET
ap-7684	273	12	connecting	connect	VERB
ap-7684	273	13	elements	element	NOUN
ap-7684	273	14	i	i	PRON
ap-7684	273	15	,	,	PUNCT
ap-7684	273	16	j	j	PROPN
ap-7684	273	17	,	,	PUNCT
ap-7684	273	18	k	k	PROPN
ap-7684	273	19	,	,	PUNCT
ap-7684	273	20	ordered	order	VERB
ap-7684	273	21	counterclockwise	counterclockwise	NOUN
ap-7684	273	22	when	when	SCONJ
ap-7684	273	23	viewed	view	VERB
ap-7684	273	24	from	from	ADP
ap-7684	273	25	the	the	DET
ap-7684	273	26	top	top	ADJ
ap-7684	273	27	side	side	NOUN
ap-7684	273	28	of	of	ADP
ap-7684	273	29	the	the	DET
ap-7684	273	30	shell	shell	NOUN
ap-7684	273	31	.	.	PUNCT
ap-7684	274	1	the	the	DET
ap-7684	274	2	sum	sum	NOUN
ap-7684	274	3	is	be	AUX
ap-7684	274	4	n⃗s	n⃗s	NOUN
ap-7684	274	5	,	,	PUNCT
ap-7684	274	6	i	i	PRON
ap-7684	274	7	=	=	PUNCT
ap-7684	274	8	∑	∑	PUNCT
ap-7684	274	9	e	e	PROPN
ap-7684	274	10	n⃗e	n⃗e	NOUN
ap-7684	274	11	sin(αe	sin(αe	NOUN
ap-7684	274	12	)	)	PUNCT
ap-7684	274	13	=	=	SYM
ap-7684	274	14	299	299	NUM
ap-7684	274	15	petr	petr	PROPN
ap-7684	274	16	řeřicha	řeřicha	PROPN
ap-7684	274	17	acta	acta	PROPN
ap-7684	274	18	polytechnica∑	polytechnica∑	PROPN
ap-7684	274	19	e	e	X
ap-7684	274	20	(	(	PUNCT
ap-7684	274	21	x⃗j	x⃗j	NOUN
ap-7684	274	22	−	−	PROPN
ap-7684	274	23	x⃗i	x⃗i	PROPN
ap-7684	274	24	)	)	PUNCT
ap-7684	274	25	×	×	NOUN
ap-7684	274	26	(	(	PUNCT
ap-7684	274	27	x⃗k	x⃗k	PROPN
ap-7684	274	28	−	−	PROPN
ap-7684	274	29	x⃗i)/(|(x⃗j	x⃗i)/(|(x⃗j	PUNCT
ap-7684	275	1	−	−	PROPN
ap-7684	275	2	x⃗i)||(x⃗k	x⃗i)||(x⃗k	PROPN
ap-7684	276	1	−	−	PROPN
ap-7684	276	2	x⃗i)|)e	x⃗i)|)e	PROPN
ap-7684	276	3	n⃗i	n⃗i	PROPN
ap-7684	276	4	=	=	SYM
ap-7684	276	5	n⃗s	n⃗s	PROPN
ap-7684	276	6	,	,	PUNCT
ap-7684	276	7	i/|n⃗s	i/|n⃗s	PROPN
ap-7684	276	8	,	,	PUNCT
ap-7684	276	9	i|	i|	PROPN
ap-7684	276	10	vector	vector	PROPN
ap-7684	276	11	n⃗i	n⃗i	PROPN
ap-7684	276	12	’s	’s	PART
ap-7684	276	13	positive	positive	ADJ
ap-7684	276	14	direction	direction	NOUN
ap-7684	276	15	is	be	AUX
ap-7684	276	16	outwards	outward	NOUN
ap-7684	276	17	from	from	ADP
ap-7684	276	18	top	top	ADJ
ap-7684	276	19	surface	surface	NOUN
ap-7684	276	20	of	of	ADP
ap-7684	276	21	the	the	DET
ap-7684	276	22	shell	shell	NOUN
ap-7684	276	23	.	.	PUNCT
ap-7684	277	1	the	the	DET
ap-7684	277	2	vector	vector	NOUN
ap-7684	277	3	also	also	ADV
ap-7684	277	4	defines	define	VERB
ap-7684	277	5	the	the	DET
ap-7684	277	6	tangential	tangential	ADJ
ap-7684	277	7	plane	plane	NOUN
ap-7684	277	8	τi	τi	VERB
ap-7684	277	9	at	at	ADP
ap-7684	277	10	node	node	PROPN
ap-7684	277	11	i	i	PRON
ap-7684	277	12	,	,	PUNCT
ap-7684	277	13	τi	τi	PROPN
ap-7684	277	14	⊥	⊥	PROPN
ap-7684	277	15	n⃗i	n⃗i	PROPN
ap-7684	277	16	.	.	PUNCT
ap-7684	278	1	the	the	DET
ap-7684	278	2	top	top	ADJ
ap-7684	278	3	vertices	vertex	NOUN
ap-7684	278	4	of	of	ADP
ap-7684	278	5	the	the	DET
ap-7684	278	6	connecting	connect	VERB
ap-7684	278	7	elements	element	NOUN
ap-7684	278	8	share	share	VERB
ap-7684	278	9	the	the	DET
ap-7684	278	10	displacement	displacement	ADJ
ap-7684	278	11	r⃗t	r⃗t	PROPN
ap-7684	278	12	,	,	PUNCT
ap-7684	278	13	i	i	PRON
ap-7684	278	14	of	of	ADP
ap-7684	278	15	the	the	DET
ap-7684	278	16	top	top	ADJ
ap-7684	278	17	end	end	NOUN
ap-7684	278	18	of	of	ADP
ap-7684	278	19	the	the	DET
ap-7684	278	20	rigid	rigid	ADJ
ap-7684	278	21	normal	normal	NOUN
ap-7684	278	22	.	.	PUNCT
ap-7684	279	1	the	the	DET
ap-7684	279	2	global	global	ADJ
ap-7684	279	3	components	component	NOUN
ap-7684	279	4	of	of	ADP
ap-7684	279	5	vector	vector	PROPN
ap-7684	279	6	r⃗t	r⃗t	PROPN
ap-7684	279	7	,	,	PUNCT
ap-7684	279	8	i	i	PRON
ap-7684	279	9	constitute	constitute	VERB
ap-7684	279	10	the	the	DET
ap-7684	279	11	first	first	ADJ
ap-7684	279	12	three	three	NUM
ap-7684	279	13	dofs	dof	NOUN
ap-7684	279	14	of	of	ADP
ap-7684	279	15	the	the	DET
ap-7684	279	16	node	node	PROPN
ap-7684	279	17	i.	i.	PROPN
ap-7684	279	18	the	the	DET
ap-7684	279	19	index	index	NOUN
ap-7684	279	20	of	of	ADP
ap-7684	279	21	the	the	DET
ap-7684	279	22	node	node	NOUN
ap-7684	279	23	is	be	AUX
ap-7684	279	24	omitted	omit	VERB
ap-7684	279	25	forthwith	forthwith	NOUN
ap-7684	279	26	since	since	SCONJ
ap-7684	279	27	a	a	DET
ap-7684	279	28	single	single	ADJ
ap-7684	279	29	node	node	NOUN
ap-7684	279	30	is	be	AUX
ap-7684	279	31	considered	consider	VERB
ap-7684	279	32	.	.	PUNCT
ap-7684	280	1	the	the	DET
ap-7684	280	2	compatibility	compatibility	NOUN
ap-7684	280	3	of	of	ADP
ap-7684	280	4	displacements	displacement	NOUN
ap-7684	280	5	at	at	ADP
ap-7684	280	6	the	the	DET
ap-7684	280	7	bottom	bottom	ADJ
ap-7684	280	8	facets	facet	NOUN
ap-7684	280	9	of	of	ADP
ap-7684	280	10	the	the	DET
ap-7684	280	11	connecting	connect	VERB
ap-7684	280	12	elements	element	NOUN
ap-7684	280	13	demands	demand	VERB
ap-7684	280	14	that	that	SCONJ
ap-7684	280	15	the	the	DET
ap-7684	280	16	projections	projection	NOUN
ap-7684	280	17	on	on	ADP
ap-7684	280	18	the	the	DET
ap-7684	280	19	τ	τ	PROPN
ap-7684	280	20	plane	plane	NOUN
ap-7684	280	21	of	of	ADP
ap-7684	280	22	the	the	DET
ap-7684	280	23	bottom	bottom	ADJ
ap-7684	280	24	vertices	vertex	NOUN
ap-7684	280	25	displacements	displacement	NOUN
ap-7684	280	26	of	of	ADP
ap-7684	280	27	all	all	DET
ap-7684	280	28	connecting	connect	VERB
ap-7684	280	29	elements	element	NOUN
ap-7684	280	30	share	share	VERB
ap-7684	280	31	the	the	DET
ap-7684	280	32	same	same	ADJ
ap-7684	280	33	displacement	displacement	NOUN
ap-7684	280	34	vector	vector	NOUN
ap-7684	280	35	r⃗b	r⃗b	PROPN
ap-7684	280	36	,	,	PUNCT
ap-7684	280	37	τ	τ	PROPN
ap-7684	280	38	⊂	⊂	PROPN
ap-7684	280	39	τ	τ	PROPN
ap-7684	280	40	.	.	PUNCT
ap-7684	281	1	a	a	DET
ap-7684	281	2	coordinate	coordinate	NOUN
ap-7684	281	3	system	system	NOUN
ap-7684	281	4	is	be	AUX
ap-7684	281	5	established	establish	VERB
ap-7684	281	6	in	in	ADP
ap-7684	281	7	the	the	DET
ap-7684	281	8	τ	τ	PROPN
ap-7684	281	9	plane	plane	NOUN
ap-7684	281	10	such	such	DET
ap-7684	281	11	that	that	DET
ap-7684	281	12	axis	axis	NOUN
ap-7684	281	13	1	1	NUM
ap-7684	281	14	direction	direction	NOUN
ap-7684	281	15	vector	vector	NOUN
ap-7684	281	16	n⃗1	n⃗1	NOUN
ap-7684	281	17	lies	lie	VERB
ap-7684	281	18	in	in	ADP
ap-7684	281	19	the	the	DET
ap-7684	281	20	intersection	intersection	NOUN
ap-7684	281	21	of	of	ADP
ap-7684	281	22	the	the	DET
ap-7684	281	23	global	global	ADJ
ap-7684	281	24	coordinates	coordinate	NOUN
ap-7684	281	25	plane	plane	NOUN
ap-7684	281	26	x−z	x−z	PROPN
ap-7684	281	27	and	and	CCONJ
ap-7684	281	28	the	the	DET
ap-7684	281	29	τ	τ	PROPN
ap-7684	281	30	plane	plane	NOUN
ap-7684	281	31	,	,	PUNCT
ap-7684	281	32	oriented	orient	VERB
ap-7684	281	33	as	as	ADP
ap-7684	281	34	the	the	DET
ap-7684	281	35	global	global	ADJ
ap-7684	281	36	x	x	ADJ
ap-7684	281	37	axis	axis	NOUN
ap-7684	281	38	.	.	PUNCT
ap-7684	282	1	axis	axis	ADJ
ap-7684	282	2	2	2	NUM
ap-7684	282	3	direction	direction	NOUN
ap-7684	282	4	vector	vector	NOUN
ap-7684	282	5	is	be	AUX
ap-7684	282	6	n⃗2	n⃗2	ADJ
ap-7684	282	7	=	=	SYM
ap-7684	282	8	n⃗×	n⃗×	PROPN
ap-7684	282	9	n⃗1	n⃗1	PROPN
ap-7684	282	10	(	(	PUNCT
ap-7684	282	11	vector	vector	NOUN
ap-7684	282	12	product	product	NOUN
ap-7684	282	13	)	)	PUNCT
ap-7684	282	14	.	.	PUNCT
ap-7684	283	1	the	the	DET
ap-7684	283	2	component	component	NOUN
ap-7684	283	3	expansion	expansion	NOUN
ap-7684	283	4	of	of	ADP
ap-7684	283	5	vector	vector	NOUN
ap-7684	283	6	r⃗b	r⃗b	PROPN
ap-7684	283	7	,	,	PUNCT
ap-7684	283	8	τ	τ	PROPN
ap-7684	283	9	is	be	AUX
ap-7684	283	10	defined	define	VERB
ap-7684	283	11	this	this	DET
ap-7684	283	12	way	way	NOUN
ap-7684	283	13	.	.	PUNCT
ap-7684	284	1	the	the	DET
ap-7684	284	2	two	two	NUM
ap-7684	284	3	components	component	NOUN
ap-7684	284	4	in	in	ADP
ap-7684	284	5	the	the	DET
ap-7684	284	6	τ	τ	PROPN
ap-7684	284	7	plane	plane	NOUN
ap-7684	284	8	define	define	VERB
ap-7684	284	9	the	the	DET
ap-7684	284	10	two	two	NUM
ap-7684	284	11	complementary	complementary	ADJ
ap-7684	284	12	dofs	dof	NOUN
ap-7684	284	13	of	of	ADP
ap-7684	284	14	the	the	DET
ap-7684	284	15	node	node	NOUN
ap-7684	284	16	.	.	PUNCT
ap-7684	285	1	note	note	VERB
ap-7684	285	2	that	that	SCONJ
ap-7684	285	3	they	they	PRON
ap-7684	285	4	are	be	AUX
ap-7684	285	5	not	not	PART
ap-7684	285	6	the	the	DET
ap-7684	285	7	displacement	displacement	ADJ
ap-7684	285	8	components	component	NOUN
ap-7684	285	9	in	in	ADP
ap-7684	285	10	the	the	DET
ap-7684	285	11	global	global	ADJ
ap-7684	285	12	coordinate	coordinate	NOUN
ap-7684	285	13	system	system	NOUN
ap-7684	286	1	x−	x−	PROPN
ap-7684	286	2	y	y	PROPN
ap-7684	286	3	−	−	PROPN
ap-7684	287	1	z	z	NOUN
ap-7684	288	1	but	but	CCONJ
ap-7684	288	2	in	in	ADP
ap-7684	288	3	the	the	DET
ap-7684	288	4	local	local	ADJ
ap-7684	288	5	‘	'	PUNCT
ap-7684	288	6	tangential	tangential	ADJ
ap-7684	288	7	’	'	PUNCT
ap-7684	288	8	plane	plane	NOUN
ap-7684	288	9	instead	instead	ADV
ap-7684	288	10	.	.	PUNCT
ap-7684	289	1	the	the	DET
ap-7684	289	2	transformation	transformation	NOUN
ap-7684	289	3	matrix	matrix	NOUN
ap-7684	289	4	from	from	ADP
ap-7684	289	5	global	global	ADJ
ap-7684	289	6	to	to	ADP
ap-7684	289	7	these	these	DET
ap-7684	289	8	tangential	tangential	ADJ
ap-7684	289	9	vector	vector	NOUN
ap-7684	289	10	components	component	NOUN
ap-7684	289	11	is	be	AUX
ap-7684	289	12	[	[	X
ap-7684	289	13	t	t	X
ap-7684	289	14	]	]	X
ap-7684	289	15	τ	τ	X
ap-7684	289	16	=	=	SYM
ap-7684	289	17			PROPN
ap-7684	289	18	{	{	PUNCT
ap-7684	289	19	n1}t	n1}t	NOUN
ap-7684	289	20	{	{	PUNCT
ap-7684	289	21	n2}t	n2}t	NOUN
ap-7684	289	22	{	{	PUNCT
ap-7684	289	23	n}t	n}t	NOUN
ap-7684	289	24			NOUN
ap-7684	289	25	(	(	PUNCT
ap-7684	289	26	24	24	NUM
ap-7684	289	27	)	)	PUNCT
ap-7684	289	28	the	the	DET
ap-7684	289	29	whole	whole	ADJ
ap-7684	289	30	bottom	bottom	NOUN
ap-7684	289	31	vertices	vertice	VERB
ap-7684	289	32	displacement	displacement	ADJ
ap-7684	289	33	vector	vector	NOUN
ap-7684	289	34	is	be	AUX
ap-7684	289	35	r⃗b	r⃗b	PROPN
ap-7684	289	36	=	=	SYM
ap-7684	289	37	r⃗b	r⃗b	PROPN
ap-7684	289	38	,	,	PUNCT
ap-7684	289	39	τ	τ	PROPN
ap-7684	289	40	+	+	CCONJ
ap-7684	289	41	n⃗(n⃗·r⃗t	n⃗(n⃗·r⃗t	NOUN
ap-7684	289	42	)	)	PUNCT
ap-7684	289	43	=	=	SYM
ap-7684	289	44	r⃗b	r⃗b	PROPN
ap-7684	289	45	,	,	PUNCT
ap-7684	289	46	τ	τ	PROPN
ap-7684	289	47	+	+	PROPN
ap-7684	289	48	n⃗⊗	n⃗⊗	NUM
ap-7684	289	49	n⃗r⃗t	n⃗r⃗t	NOUN
ap-7684	289	50	,	,	PUNCT
ap-7684	289	51	but	but	CCONJ
ap-7684	289	52	just	just	ADV
ap-7684	289	53	the	the	DET
ap-7684	289	54	two	two	NUM
ap-7684	289	55	components	component	NOUN
ap-7684	289	56	of	of	ADP
ap-7684	289	57	r⃗b	r⃗b	PROPN
ap-7684	289	58	,	,	PUNCT
ap-7684	289	59	τ	τ	PROPN
ap-7684	289	60	⊂	⊂	PROPN
ap-7684	289	61	τ	τ	PROPN
ap-7684	289	62	constitute	constitute	VERB
ap-7684	289	63	the	the	DET
ap-7684	289	64	two	two	NUM
ap-7684	289	65	complementary	complementary	ADJ
ap-7684	289	66	dofs	dof	NOUN
ap-7684	289	67	of	of	ADP
ap-7684	289	68	the	the	DET
ap-7684	289	69	node	node	NOUN
ap-7684	289	70	.	.	PUNCT
ap-7684	290	1	the	the	DET
ap-7684	290	2	out	out	ADV
ap-7684	290	3	-	-	PUNCT
ap-7684	290	4	of	of	ADP
ap-7684	290	5	-	-	PUNCT
ap-7684	290	6	τ	τ	NOUN
ap-7684	290	7	plane	plane	NOUN
ap-7684	290	8	component	component	NOUN
ap-7684	290	9	depends	depend	VERB
ap-7684	290	10	on	on	ADP
ap-7684	290	11	the	the	DET
ap-7684	290	12	basic	basic	ADJ
ap-7684	290	13	three	three	NUM
ap-7684	290	14	dofs	dof	NOUN
ap-7684	290	15	r⃗t	r⃗t	NOUN
ap-7684	290	16	of	of	ADP
ap-7684	290	17	the	the	DET
ap-7684	290	18	node	node	NOUN
ap-7684	290	19	.	.	PUNCT
ap-7684	291	1	several	several	ADJ
ap-7684	291	2	coordinate	coordinate	NOUN
ap-7684	291	3	systems	system	NOUN
ap-7684	291	4	(	(	PUNCT
ap-7684	291	5	all	all	PRON
ap-7684	291	6	cartesian	cartesian	ADJ
ap-7684	291	7	)	)	PUNCT
ap-7684	291	8	are	be	AUX
ap-7684	291	9	employed	employ	VERB
ap-7684	291	10	.	.	PUNCT
ap-7684	292	1	the	the	DET
ap-7684	292	2	global	global	ADJ
ap-7684	292	3	one	one	NOUN
ap-7684	292	4	,	,	PUNCT
ap-7684	292	5	common	common	ADJ
ap-7684	292	6	for	for	ADP
ap-7684	292	7	all	all	PRON
ap-7684	292	8	,	,	PUNCT
ap-7684	292	9	the	the	DET
ap-7684	292	10	τ	τ	PROPN
ap-7684	292	11	system	system	NOUN
ap-7684	292	12	,	,	PUNCT
ap-7684	292	13	common	common	ADJ
ap-7684	292	14	for	for	ADP
ap-7684	292	15	a	a	DET
ap-7684	292	16	node	node	NOUN
ap-7684	292	17	and	and	CCONJ
ap-7684	292	18	the	the	DET
ap-7684	292	19	local	local	ADJ
ap-7684	292	20	e	e	NOUN
ap-7684	292	21	systems	system	NOUN
ap-7684	292	22	of	of	ADP
ap-7684	292	23	individual	individual	ADJ
ap-7684	292	24	elements	element	NOUN
ap-7684	292	25	.	.	PUNCT
ap-7684	293	1	the	the	DET
ap-7684	293	2	convention	convention	NOUN
ap-7684	293	3	is	be	AUX
ap-7684	293	4	adopted	adopt	VERB
ap-7684	293	5	for	for	ADP
ap-7684	293	6	component	component	NOUN
ap-7684	293	7	matrices	matrix	NOUN
ap-7684	293	8	that	that	PRON
ap-7684	293	9	the	the	DET
ap-7684	293	10	matrix	matrix	NOUN
ap-7684	293	11	with	with	ADP
ap-7684	293	12	components	component	NOUN
ap-7684	293	13	in	in	ADP
ap-7684	293	14	the	the	DET
ap-7684	293	15	global	global	ADJ
ap-7684	293	16	system	system	NOUN
ap-7684	293	17	has	have	VERB
ap-7684	293	18	no	no	DET
ap-7684	293	19	subscript	subscript	NOUN
ap-7684	293	20	τ	τ	X
ap-7684	293	21	,	,	PUNCT
ap-7684	293	22	in	in	ADP
ap-7684	293	23	the	the	DET
ap-7684	293	24	τ	τ	PROPN
ap-7684	293	25	system	system	NOUN
ap-7684	293	26	,	,	PUNCT
ap-7684	293	27	and	and	CCONJ
ap-7684	293	28	subscripts	subscript	NOUN
ap-7684	293	29	e	e	NOUN
ap-7684	293	30	in	in	ADP
ap-7684	293	31	the	the	DET
ap-7684	293	32	element	element	NOUN
ap-7684	293	33	systems	system	NOUN
ap-7684	293	34	.	.	PUNCT
ap-7684	294	1	furthermore	furthermore	ADV
ap-7684	294	2	,	,	PUNCT
ap-7684	294	3	the	the	DET
ap-7684	294	4	transformation	transformation	NOUN
ap-7684	294	5	matrix	matrix	NOUN
ap-7684	294	6	[	[	X
ap-7684	294	7	t	t	X
ap-7684	294	8	]	]	X
ap-7684	294	9	e	e	NOUN
ap-7684	294	10	from	from	ADP
ap-7684	294	11	the	the	DET
ap-7684	294	12	global	global	ADJ
ap-7684	294	13	to	to	ADP
ap-7684	294	14	the	the	DET
ap-7684	294	15	element	element	NOUN
ap-7684	294	16	system	system	NOUN
ap-7684	294	17	has	have	AUX
ap-7684	294	18	subscript	subscript	VERB
ap-7684	294	19	e.	e.	PROPN
ap-7684	294	20	the	the	DET
ap-7684	294	21	matrix	matrix	NOUN
ap-7684	294	22	form	form	NOUN
ap-7684	294	23	of	of	ADP
ap-7684	294	24	the	the	DET
ap-7684	294	25	expression	expression	NOUN
ap-7684	294	26	for	for	ADP
ap-7684	294	27	the	the	DET
ap-7684	294	28	element	element	NOUN
ap-7684	294	29	dofs	dof	NOUN
ap-7684	294	30	is	be	AUX
ap-7684	294	31	{	{	PUNCT
ap-7684	294	32	{	{	PUNCT
ap-7684	294	33	rt}e	rt}e	INTJ
ap-7684	294	34	{	{	PUNCT
ap-7684	294	35	rb}e	rb}e	PROPN
ap-7684	294	36	}	}	PUNCT
ap-7684	294	37	=	=	PUNCT
ap-7684	295	1	[	[	PUNCT
ap-7684	295	2	[	[	X
ap-7684	295	3	t	t	X
ap-7684	295	4	]	]	X
ap-7684	295	5	e	e	X
ap-7684	295	6	0	0	PUNCT
ap-7684	296	1	[	[	X
ap-7684	296	2	t	t	X
ap-7684	296	3	]	]	X
ap-7684	296	4	e{n}{n}t	e{n}{n}t	PROPN
ap-7684	297	1	[	[	X
ap-7684	297	2	t	t	X
ap-7684	297	3	]	]	PUNCT
ap-7684	297	4	e[t	e[t	X
ap-7684	297	5	]	]	X
ap-7684	297	6	tτ	tτ	X
ap-7684	297	7	]	]	X
ap-7684	297	8	{	{	PUNCT
ap-7684	297	9	{	{	PUNCT
ap-7684	297	10	rt	rt	INTJ
ap-7684	297	11	}	}	PUNCT
ap-7684	297	12	{	{	PUNCT
ap-7684	297	13	rb}τ	rb}τ	PROPN
ap-7684	297	14	}	}	PUNCT
ap-7684	297	15	(	(	PUNCT
ap-7684	297	16	25	25	NUM
ap-7684	297	17	)	)	PUNCT
ap-7684	297	18	recall	recall	VERB
ap-7684	297	19	that	that	SCONJ
ap-7684	297	20	both	both	CCONJ
ap-7684	297	21	the	the	DET
ap-7684	297	22	displacement	displacement	ADJ
ap-7684	297	23	component	component	NOUN
ap-7684	297	24	matrices	matrix	NOUN
ap-7684	297	25	{	{	PUNCT
ap-7684	297	26	rb}e	rb}e	PROPN
ap-7684	297	27	and	and	CCONJ
ap-7684	297	28	{	{	PUNCT
ap-7684	297	29	rb}τ	rb}τ	PROPN
ap-7684	297	30	have	have	VERB
ap-7684	297	31	zero	zero	NUM
ap-7684	297	32	third	third	ADJ
ap-7684	297	33	components	component	NOUN
ap-7684	297	34	so	so	SCONJ
ap-7684	297	35	that	that	SCONJ
ap-7684	297	36	the	the	DET
ap-7684	297	37	third	third	ADJ
ap-7684	297	38	column	column	NOUN
ap-7684	297	39	and	and	CCONJ
ap-7684	297	40	row	row	NOUN
ap-7684	297	41	of	of	ADP
ap-7684	297	42	the	the	DET
ap-7684	297	43	transformation	transformation	NOUN
ap-7684	297	44	matrix	matrix	NOUN
ap-7684	297	45	in	in	ADP
ap-7684	297	46	25	25	NUM
ap-7684	297	47	can	can	AUX
ap-7684	297	48	be	be	AUX
ap-7684	297	49	omitted	omit	VERB
ap-7684	297	50	.	.	PUNCT
ap-7684	298	1	the	the	DET
ap-7684	298	2	nodal	nodal	NOUN
ap-7684	298	3	forces	force	NOUN
ap-7684	298	4	conjugate	conjugate	VERB
ap-7684	298	5	to	to	ADP
ap-7684	298	6	{	{	PUNCT
ap-7684	298	7	rt}e	rt}e	ADJ
ap-7684	298	8	and	and	CCONJ
ap-7684	298	9	{	{	PUNCT
ap-7684	298	10	rb}e	rb}e	PROPN
ap-7684	298	11	are	be	AUX
ap-7684	298	12	denoted	denote	VERB
ap-7684	298	13	{	{	PUNCT
ap-7684	298	14	gt}e	gt}e	ADJ
ap-7684	298	15	and	and	CCONJ
ap-7684	298	16	{	{	PUNCT
ap-7684	298	17	gb}e	gb}e	PROPN
ap-7684	298	18	.	.	PUNCT
ap-7684	299	1	rigid	rigid	ADJ
ap-7684	299	2	normals	normal	NOUN
ap-7684	299	3	to	to	ADP
ap-7684	299	4	the	the	DET
ap-7684	299	5	shell	shell	NOUN
ap-7684	299	6	surface	surface	NOUN
ap-7684	299	7	imply	imply	VERB
ap-7684	299	8	that	that	SCONJ
ap-7684	299	9	the	the	DET
ap-7684	299	10	equilibrium	equilibrium	NOUN
ap-7684	299	11	equations	equation	NOUN
ap-7684	299	12	of	of	ADP
ap-7684	299	13	the	the	DET
ap-7684	299	14	top	top	ADJ
ap-7684	299	15	and	and	CCONJ
ap-7684	299	16	bottom	bottom	ADJ
ap-7684	299	17	joints	joint	NOUN
ap-7684	299	18	of	of	ADP
ap-7684	299	19	a	a	DET
ap-7684	299	20	node	node	NOUN
ap-7684	299	21	are	be	AUX
ap-7684	299	22	not	not	PART
ap-7684	299	23	independent	independent	ADJ
ap-7684	299	24	.	.	PUNCT
ap-7684	300	1	just	just	ADV
ap-7684	300	2	a	a	DET
ap-7684	300	3	single	single	ADJ
ap-7684	300	4	equilibrium	equilibrium	NOUN
ap-7684	300	5	equation	equation	NOUN
ap-7684	300	6	can	can	AUX
ap-7684	300	7	be	be	AUX
ap-7684	300	8	written	write	VERB
ap-7684	300	9	in	in	ADP
ap-7684	300	10	the	the	DET
ap-7684	300	11	direction	direction	NOUN
ap-7684	300	12	n⃗	n⃗	PROPN
ap-7684	300	13	and	and	CCONJ
ap-7684	300	14	it	it	PRON
ap-7684	300	15	is	be	AUX
ap-7684	300	16	assigned	assign	VERB
ap-7684	300	17	to	to	ADP
ap-7684	300	18	the	the	DET
ap-7684	300	19	top	top	ADJ
ap-7684	300	20	end	end	NOUN
ap-7684	300	21	of	of	ADP
ap-7684	300	22	the	the	DET
ap-7684	300	23	rigid	rigid	ADJ
ap-7684	300	24	normal	normal	ADJ
ap-7684	300	25	–	–	PUNCT
ap-7684	300	26	the	the	DET
ap-7684	300	27	top	top	ADJ
ap-7684	300	28	joint	joint	NOUN
ap-7684	300	29	of	of	ADP
ap-7684	300	30	the	the	DET
ap-7684	300	31	node	node	NOUN
ap-7684	300	32	.	.	PUNCT
ap-7684	301	1	the	the	DET
ap-7684	301	2	two	two	NUM
ap-7684	301	3	remaining	remain	VERB
ap-7684	301	4	equations	equation	NOUN
ap-7684	301	5	at	at	ADP
ap-7684	301	6	the	the	DET
ap-7684	301	7	bottom	bottom	ADJ
ap-7684	301	8	joint	joint	NOUN
ap-7684	301	9	of	of	ADP
ap-7684	301	10	the	the	DET
ap-7684	301	11	node	node	NOUN
ap-7684	301	12	include	include	VERB
ap-7684	301	13	components	component	NOUN
ap-7684	301	14	acting	act	VERB
ap-7684	301	15	in	in	ADP
ap-7684	301	16	the	the	DET
ap-7684	301	17	τ	τ	PROPN
ap-7684	301	18	plane	plane	NOUN
ap-7684	301	19	.	.	PUNCT
ap-7684	302	1	component	component	NOUN
ap-7684	302	2	decompositions	decomposition	NOUN
ap-7684	302	3	of	of	ADP
ap-7684	302	4	the	the	DET
ap-7684	302	5	element	element	NOUN
ap-7684	302	6	nodal	nodal	NOUN
ap-7684	302	7	forces	force	NOUN
ap-7684	302	8	in	in	ADP
ap-7684	302	9	the	the	DET
ap-7684	302	10	coordinate	coordinate	NOUN
ap-7684	302	11	axes	axis	NOUN
ap-7684	302	12	tripod	tripod	NOUN
ap-7684	302	13	n⃗1	n⃗1	NOUN
ap-7684	302	14	,	,	PUNCT
ap-7684	302	15	n⃗2	n⃗2	PROPN
ap-7684	302	16	,	,	PUNCT
ap-7684	302	17	n⃗	n⃗	PROPN
ap-7684	302	18	–	–	PUNCT
ap-7684	302	19	the	the	DET
ap-7684	302	20	node	node	ADJ
ap-7684	302	21	local	local	ADJ
ap-7684	302	22	τ	τ	PROPN
ap-7684	302	23	system	system	NOUN
ap-7684	302	24	,	,	PUNCT
ap-7684	302	25	are	be	AUX
ap-7684	302	26	added	add	VERB
ap-7684	302	27	in	in	ADP
ap-7684	302	28	the	the	DET
ap-7684	302	29	matrix	matrix	NOUN
ap-7684	302	30	equilibrium	equilibrium	NOUN
ap-7684	302	31	equation	equation	NOUN
ap-7684	302	32	of	of	ADP
ap-7684	302	33	the	the	DET
ap-7684	302	34	bottom	bottom	ADJ
ap-7684	302	35	joint	joint	NOUN
ap-7684	302	36	of	of	ADP
ap-7684	302	37	the	the	DET
ap-7684	302	38	node	node	NOUN
ap-7684	302	39	:	:	PUNCT
ap-7684	302	40	∑	∑	PUNCT
ap-7684	302	41	e	e	X
ap-7684	302	42	{	{	PUNCT
ap-7684	302	43	gb}τ	gb}τ	PROPN
ap-7684	302	44	,	,	PUNCT
ap-7684	302	45	e	e	X
ap-7684	302	46	=	=	SYM
ap-7684	302	47	∑	∑	PUNCT
ap-7684	302	48	e	e	PROPN
ap-7684	303	1	[	[	X
ap-7684	303	2	t	t	X
ap-7684	303	3	]	]	PUNCT
ap-7684	303	4	τ	τ	PROPN
ap-7684	304	1	[	[	X
ap-7684	304	2	t	t	X
ap-7684	304	3	]	]	X
ap-7684	304	4	te	te	PROPN
ap-7684	304	5	{	{	PUNCT
ap-7684	304	6	gb}e	gb}e	PROPN
ap-7684	304	7	=	=	PUNCT
ap-7684	304	8			PROPN
ap-7684	304	9	0	0	NUM
ap-7684	304	10	0	0	NUM
ap-7684	304	11	{	{	PUNCT
ap-7684	304	12	n}{n}t	n}{n}t	NOUN
ap-7684	304	13	{	{	PUNCT
ap-7684	304	14	gb}e	gb}e	ADJ
ap-7684	304	15			NOUN
ap-7684	304	16	the	the	DET
ap-7684	304	17	sum	sum	NOUN
ap-7684	304	18	includes	include	VERB
ap-7684	304	19	all	all	DET
ap-7684	304	20	elements	element	NOUN
ap-7684	304	21	connecting	connect	VERB
ap-7684	304	22	at	at	ADP
ap-7684	304	23	the	the	DET
ap-7684	304	24	node	node	NOUN
ap-7684	304	25	.	.	PUNCT
ap-7684	305	1	the	the	DET
ap-7684	305	2	third	third	ADJ
ap-7684	305	3	(	(	PUNCT
ap-7684	305	4	tranverse	tranverse	ADJ
ap-7684	305	5	)	)	PUNCT
ap-7684	305	6	components	component	NOUN
ap-7684	305	7	are	be	AUX
ap-7684	305	8	added	add	VERB
ap-7684	305	9	to	to	ADP
ap-7684	305	10	forces	force	NOUN
ap-7684	305	11	acting	act	VERB
ap-7684	305	12	at	at	ADP
ap-7684	305	13	the	the	DET
ap-7684	305	14	top	top	ADJ
ap-7684	305	15	vertex	vertex	NOUN
ap-7684	305	16	of	of	ADP
ap-7684	305	17	the	the	DET
ap-7684	305	18	node	node	NOUN
ap-7684	305	19	to	to	PART
ap-7684	305	20	obtain	obtain	VERB
ap-7684	305	21	the	the	DET
ap-7684	305	22	final	final	ADJ
ap-7684	305	23	nodal	nodal	NOUN
ap-7684	305	24	forces	force	NOUN
ap-7684	305	25	of	of	ADP
ap-7684	305	26	the	the	DET
ap-7684	305	27	element	element	NOUN
ap-7684	305	28	:	:	PUNCT
ap-7684	305	29	{	{	PUNCT
ap-7684	305	30	{	{	PUNCT
ap-7684	305	31	gt	gt	INTJ
ap-7684	305	32	}	}	PUNCT
ap-7684	305	33	{	{	PUNCT
ap-7684	305	34	gb}τ	gb}τ	NOUN
ap-7684	305	35	}	}	PUNCT
ap-7684	305	36	=	=	PUNCT
ap-7684	305	37	∑	∑	PUNCT
ap-7684	305	38	e	e	X
ap-7684	305	39	[	[	PUNCT
ap-7684	305	40	[	[	X
ap-7684	305	41	t	t	X
ap-7684	305	42	]	]	X
ap-7684	305	43	te	te	PROPN
ap-7684	305	44	{	{	PUNCT
ap-7684	305	45	n}{n}t	n}{n}t	PROPN
ap-7684	305	46	[	[	X
ap-7684	305	47	t	t	X
ap-7684	305	48	]	]	X
ap-7684	305	49	te	te	PROPN
ap-7684	305	50	0	0	NUM
ap-7684	306	1	[	[	X
ap-7684	306	2	t	t	X
ap-7684	306	3	]	]	X
ap-7684	306	4	τ	τ	PROPN
ap-7684	307	1	[	[	X
ap-7684	307	2	t	t	X
ap-7684	307	3	]	]	X
ap-7684	307	4	te	te	X
ap-7684	307	5	]	]	PUNCT
ap-7684	307	6	{	{	PUNCT
ap-7684	307	7	{	{	PUNCT
ap-7684	307	8	gt}e	gt}e	X
ap-7684	307	9	{	{	PUNCT
ap-7684	307	10	gb}e	gb}e	NOUN
ap-7684	307	11	}	}	PUNCT
ap-7684	307	12	(	(	PUNCT
ap-7684	307	13	26	26	NUM
ap-7684	307	14	)	)	PUNCT
ap-7684	307	15	the	the	DET
ap-7684	307	16	transformation	transformation	NOUN
ap-7684	307	17	matrices	matrix	NOUN
ap-7684	307	18	of	of	ADP
ap-7684	307	19	the	the	DET
ap-7684	307	20	nodal	nodal	NOUN
ap-7684	307	21	displacements	displacement	NOUN
ap-7684	307	22	and	and	CCONJ
ap-7684	307	23	forces	force	NOUN
ap-7684	307	24	are	be	AUX
ap-7684	307	25	transpose	transpose	NOUN
ap-7684	307	26	of	of	ADP
ap-7684	307	27	each	each	DET
ap-7684	307	28	other	other	ADJ
ap-7684	307	29	,	,	PUNCT
ap-7684	307	30	which	which	PRON
ap-7684	307	31	testifies	testify	VERB
ap-7684	307	32	to	to	ADP
ap-7684	307	33	their	their	PRON
ap-7684	307	34	correctness	correctness	NOUN
ap-7684	307	35	.	.	PUNCT
ap-7684	308	1	note	note	VERB
ap-7684	308	2	that	that	SCONJ
ap-7684	308	3	the	the	DET
ap-7684	308	4	last	last	ADJ
ap-7684	308	5	scalar	scalar	ADJ
ap-7684	308	6	equations	equation	NOUN
ap-7684	308	7	in	in	ADP
ap-7684	308	8	25	25	NUM
ap-7684	308	9	and	and	CCONJ
ap-7684	308	10	26	26	NUM
ap-7684	308	11	can	can	AUX
ap-7684	308	12	be	be	AUX
ap-7684	308	13	omitted	omit	VERB
ap-7684	308	14	and	and	CCONJ
ap-7684	308	15	so	so	ADV
ap-7684	308	16	can	can	AUX
ap-7684	308	17	be	be	AUX
ap-7684	308	18	the	the	DET
ap-7684	308	19	last	last	ADJ
ap-7684	308	20	columns	column	NOUN
ap-7684	308	21	of	of	ADP
ap-7684	308	22	the	the	DET
ap-7684	308	23	tranformation	tranformation	NOUN
ap-7684	308	24	matrices	matrix	NOUN
ap-7684	308	25	.	.	PUNCT
ap-7684	309	1	the	the	DET
ap-7684	309	2	transformation	transformation	NOUN
ap-7684	309	3	matrices	matrix	NOUN
ap-7684	309	4	are	be	AUX
ap-7684	309	5	then	then	ADV
ap-7684	309	6	5×5	5×5	NUM
ap-7684	309	7	in	in	ADP
ap-7684	309	8	size	size	NOUN
ap-7684	309	9	.	.	PUNCT
ap-7684	310	1	they	they	PRON
ap-7684	310	2	are	be	AUX
ap-7684	310	3	specific	specific	ADJ
ap-7684	310	4	for	for	ADP
ap-7684	310	5	each	each	DET
ap-7684	310	6	node	node	NOUN
ap-7684	310	7	of	of	ADP
ap-7684	310	8	an	an	DET
ap-7684	310	9	element	element	NOUN
ap-7684	310	10	since	since	SCONJ
ap-7684	310	11	the	the	DET
ap-7684	310	12	{	{	PUNCT
ap-7684	310	13	n	n	CCONJ
ap-7684	310	14	}	}	PUNCT
ap-7684	310	15	and	and	CCONJ
ap-7684	310	16	[	[	X
ap-7684	310	17	t	t	X
ap-7684	310	18	]	]	PUNCT
ap-7684	310	19	τ	τ	X
ap-7684	310	20	matrices	matrix	NOUN
ap-7684	310	21	are	be	AUX
ap-7684	310	22	different	different	ADJ
ap-7684	310	23	at	at	ADP
ap-7684	310	24	each	each	DET
ap-7684	310	25	node	node	NOUN
ap-7684	310	26	.	.	PUNCT
ap-7684	311	1	for	for	ADP
ap-7684	311	2	an	an	DET
ap-7684	311	3	easy	easy	ADJ
ap-7684	311	4	reference	reference	NOUN
ap-7684	311	5	,	,	PUNCT
ap-7684	311	6	they	they	PRON
ap-7684	311	7	are	be	AUX
ap-7684	311	8	denoted	denote	VERB
ap-7684	311	9	[	[	X
ap-7684	311	10	ti	ti	X
ap-7684	311	11	]	]	X
ap-7684	311	12	for	for	ADP
ap-7684	311	13	node	node	PROPN
ap-7684	311	14	i	i	PROPN
ap-7684	311	15	forthwith	forthwith	NOUN
ap-7684	311	16	.	.	PUNCT
ap-7684	312	1	the	the	DET
ap-7684	312	2	submatrices	submatrice	NOUN
ap-7684	312	3	[	[	X
ap-7684	312	4	ki	ki	PROPN
ap-7684	312	5	,	,	PUNCT
ap-7684	312	6	j	j	PROPN
ap-7684	312	7	]	]	PUNCT
ap-7684	312	8	are	be	AUX
ap-7684	312	9	transformed	transform	VERB
ap-7684	312	10	to	to	ADP
ap-7684	312	11	the	the	DET
ap-7684	312	12	global	global	ADJ
ap-7684	312	13	coordinate	coordinate	NOUN
ap-7684	312	14	system	system	NOUN
ap-7684	313	1	[	[	X
ap-7684	313	2	ki	ki	PROPN
ap-7684	313	3	,	,	PUNCT
ap-7684	313	4	j	j	PROPN
ap-7684	313	5	]	]	X
ap-7684	313	6	g	g	X
ap-7684	313	7	=	=	PUNCT
ap-7684	314	1	[	[	X
ap-7684	314	2	ti]t	ti]t	PROPN
ap-7684	314	3	[	[	X
ap-7684	314	4	ki	ki	PROPN
ap-7684	314	5	,	,	PUNCT
ap-7684	314	6	j	j	PROPN
ap-7684	314	7	]	]	X
ap-7684	315	1	[	[	X
ap-7684	315	2	tj	tj	X
ap-7684	315	3	]	]	X
ap-7684	315	4	(	(	PUNCT
ap-7684	315	5	27	27	NUM
ap-7684	315	6	)	)	PUNCT
ap-7684	315	7	and	and	CCONJ
ap-7684	315	8	assembled	assemble	VERB
ap-7684	315	9	in	in	ADP
ap-7684	315	10	the	the	DET
ap-7684	315	11	system	system	NOUN
ap-7684	315	12	matrix	matrix	NOUN
ap-7684	315	13	.	.	PUNCT
ap-7684	316	1	4.5	4.5	NUM
ap-7684	316	2	.	.	PUNCT
ap-7684	317	1	tm	tm	PROPN
ap-7684	317	2	element	element	PROPN
ap-7684	317	3	code	code	PROPN
ap-7684	317	4	and	and	CCONJ
ap-7684	317	5	test	test	VERB
ap-7684	317	6	the	the	DET
ap-7684	317	7	tm	tm	PROPN
ap-7684	317	8	element	element	NOUN
ap-7684	317	9	has	have	AUX
ap-7684	317	10	been	be	AUX
ap-7684	317	11	implemented	implement	VERB
ap-7684	317	12	in	in	ADP
ap-7684	317	13	a	a	DET
ap-7684	317	14	dedicated	dedicated	ADJ
ap-7684	317	15	matlab	matlab	NOUN
ap-7684	317	16	/	/	SYM
ap-7684	317	17	octave	octave	NOUN
ap-7684	317	18	code	code	NOUN
ap-7684	317	19	including	include	VERB
ap-7684	317	20	a	a	DET
ap-7684	317	21	simple	simple	ADJ
ap-7684	317	22	graphic	graphic	ADJ
ap-7684	317	23	output	output	NOUN
ap-7684	317	24	.	.	PUNCT
ap-7684	318	1	just	just	ADV
ap-7684	318	2	the	the	DET
ap-7684	318	3	shell	shell	ADJ
ap-7684	318	4	reference	reference	NOUN
ap-7684	318	5	surface	surface	NOUN
ap-7684	318	6	is	be	AUX
ap-7684	318	7	drawn	draw	VERB
ap-7684	318	8	to	to	PART
ap-7684	318	9	keep	keep	VERB
ap-7684	318	10	the	the	DET
ap-7684	318	11	view	view	NOUN
ap-7684	318	12	readable	readable	ADJ
ap-7684	318	13	.	.	PUNCT
ap-7684	319	1	the	the	DET
ap-7684	319	2	maximum	maximum	ADJ
ap-7684	319	3	compression	compression	NOUN
ap-7684	319	4	stresses	stress	NOUN
ap-7684	319	5	in	in	ADP
ap-7684	319	6	the	the	DET
ap-7684	319	7	bed	bed	NOUN
ap-7684	319	8	joints	joint	NOUN
ap-7684	319	9	and	and	CCONJ
ap-7684	319	10	the	the	DET
ap-7684	319	11	relative	relative	ADJ
ap-7684	319	12	depth	depth	NOUN
ap-7684	319	13	of	of	ADP
ap-7684	319	14	the	the	DET
ap-7684	319	15	cracks	crack	NOUN
ap-7684	319	16	are	be	AUX
ap-7684	319	17	inserted	insert	VERB
ap-7684	319	18	in	in	ADP
ap-7684	319	19	each	each	DET
ap-7684	319	20	element	element	NOUN
ap-7684	319	21	.	.	PUNCT
ap-7684	320	1	these	these	DET
ap-7684	320	2	values	value	NOUN
ap-7684	320	3	are	be	AUX
ap-7684	320	4	sufficient	sufficient	ADJ
ap-7684	320	5	to	to	PART
ap-7684	320	6	decide	decide	VERB
ap-7684	320	7	on	on	ADP
ap-7684	320	8	the	the	DET
ap-7684	320	9	arch	arch	ADJ
ap-7684	320	10	load	load	NOUN
ap-7684	320	11	capacity	capacity	NOUN
ap-7684	320	12	in	in	ADP
ap-7684	320	13	the	the	DET
ap-7684	320	14	context	context	NOUN
ap-7684	320	15	of	of	ADP
ap-7684	320	16	the	the	DET
ap-7684	320	17	present	present	ADJ
ap-7684	320	18	model	model	NOUN
ap-7684	320	19	.	.	PUNCT
ap-7684	321	1	the	the	DET
ap-7684	321	2	graphic	graphic	ADJ
ap-7684	321	3	output	output	NOUN
ap-7684	321	4	uses	use	VERB
ap-7684	321	5	vector	vector	NOUN
ap-7684	321	6	graphics	graphic	NOUN
ap-7684	321	7	so	so	SCONJ
ap-7684	321	8	that	that	SCONJ
ap-7684	321	9	pictures	picture	NOUN
ap-7684	321	10	can	can	AUX
ap-7684	321	11	be	be	AUX
ap-7684	321	12	zoomed	zoom	VERB
ap-7684	321	13	in	in	ADP
ap-7684	321	14	with	with	ADP
ap-7684	321	15	a	a	DET
ap-7684	321	16	stable	stable	ADJ
ap-7684	321	17	resolution	resolution	NOUN
ap-7684	321	18	.	.	PUNCT
ap-7684	322	1	the	the	DET
ap-7684	322	2	mesh	mesh	NOUN
ap-7684	322	3	generator	generator	NOUN
ap-7684	322	4	[	[	X
ap-7684	322	5	8	8	NUM
ap-7684	322	6	]	]	PUNCT
ap-7684	322	7	is	be	AUX
ap-7684	322	8	used	use	VERB
ap-7684	322	9	for	for	ADP
ap-7684	322	10	the	the	DET
ap-7684	322	11	shell	shell	ADJ
ap-7684	322	12	surface	surface	NOUN
ap-7684	322	13	meshing	meshing	NOUN
ap-7684	322	14	.	.	PUNCT
ap-7684	323	1	the	the	DET
ap-7684	323	2	code	code	NOUN
ap-7684	323	3	is	be	AUX
ap-7684	323	4	entirely	entirely	ADV
ap-7684	323	5	self	self	NOUN
ap-7684	323	6	-	-	PUNCT
ap-7684	323	7	contained	contain	VERB
ap-7684	323	8	,	,	PUNCT
ap-7684	323	9	no	no	DET
ap-7684	323	10	input	input	NOUN
ap-7684	323	11	data	data	NOUN
ap-7684	323	12	file	file	NOUN
ap-7684	323	13	and	and	CCONJ
ap-7684	323	14	preor	preor	NOUN
ap-7684	323	15	postprocessing	postprocessing	NOUN
ap-7684	323	16	is	be	AUX
ap-7684	323	17	necessary	necessary	ADJ
ap-7684	323	18	.	.	PUNCT
ap-7684	324	1	it	it	PRON
ap-7684	324	2	contains	contain	VERB
ap-7684	324	3	just	just	ADV
ap-7684	324	4	about	about	ADV
ap-7684	324	5	660	660	NUM
ap-7684	324	6	octave	octave	ADJ
ap-7684	324	7	command	command	NOUN
ap-7684	324	8	lines	line	NOUN
ap-7684	324	9	,	,	PUNCT
ap-7684	324	10	not	not	PART
ap-7684	324	11	including	include	VERB
ap-7684	324	12	the	the	DET
ap-7684	324	13	mesh	mesh	NOUN
ap-7684	324	14	generator	generator	NOUN
ap-7684	324	15	.	.	PUNCT
ap-7684	325	1	the	the	DET
ap-7684	325	2	pinched	pinch	VERB
ap-7684	325	3	cylinder	cylinder	NOUN
ap-7684	325	4	with	with	ADP
ap-7684	325	5	rigid	rigid	ADJ
ap-7684	325	6	end	end	NOUN
ap-7684	325	7	diaphragms	diaphragm	NOUN
ap-7684	325	8	in	in	ADP
ap-7684	325	9	figure	figure	NOUN
ap-7684	325	10	8	8	NUM
ap-7684	325	11	is	be	AUX
ap-7684	325	12	a	a	DET
ap-7684	325	13	popular	popular	ADJ
ap-7684	325	14	benchmark	benchmark	NOUN
ap-7684	325	15	to	to	PART
ap-7684	325	16	test	test	VERB
ap-7684	325	17	shell	shell	NOUN
ap-7684	325	18	elements	element	NOUN
ap-7684	325	19	.	.	PUNCT
ap-7684	326	1	the	the	DET
ap-7684	326	2	shell	shell	NOUN
ap-7684	326	3	is	be	AUX
ap-7684	326	4	thin	thin	ADJ
ap-7684	326	5	,	,	PUNCT
ap-7684	326	6	d	d	NOUN
ap-7684	326	7	/	/	SYM
ap-7684	326	8	r	r	NOUN
ap-7684	326	9	=	=	NOUN
ap-7684	326	10	0.01	0.01	NUM
ap-7684	326	11	so	so	SCONJ
ap-7684	326	12	that	that	SCONJ
ap-7684	326	13	the	the	DET
ap-7684	326	14	test	test	NOUN
ap-7684	326	15	is	be	AUX
ap-7684	326	16	a	a	DET
ap-7684	326	17	severe	severe	ADJ
ap-7684	326	18	one	one	NOUN
ap-7684	326	19	for	for	ADP
ap-7684	326	20	a	a	DET
ap-7684	326	21	thick	thick	ADJ
ap-7684	326	22	shell	shell	NOUN
ap-7684	326	23	element	element	NOUN
ap-7684	326	24	.	.	PUNCT
ap-7684	327	1	the	the	DET
ap-7684	327	2	benchmark	benchmark	NOUN
ap-7684	327	3	solution	solution	NOUN
ap-7684	327	4	by	by	ADP
ap-7684	327	5	double	double	ADJ
ap-7684	327	6	fourier	fourier	NOUN
ap-7684	327	7	series	series	NOUN
ap-7684	327	8	with	with	ADP
ap-7684	327	9	80	80	NUM
ap-7684	327	10	terms	term	NOUN
ap-7684	327	11	in	in	ADP
ap-7684	327	12	both	both	DET
ap-7684	327	13	directions	direction	NOUN
ap-7684	327	14	was	be	AUX
ap-7684	327	15	first	first	ADV
ap-7684	327	16	presented	present	VERB
ap-7684	327	17	in	in	ADP
ap-7684	327	18	[	[	X
ap-7684	327	19	12	12	NUM
ap-7684	327	20	]	]	PUNCT
ap-7684	327	21	based	base	VERB
ap-7684	327	22	on	on	ADP
ap-7684	327	23	300	300	NUM
ap-7684	327	24	vol	vol	NOUN
ap-7684	327	25	.	.	PUNCT
ap-7684	328	1	62	62	NUM
ap-7684	328	2	no	no	INTJ
ap-7684	328	3	.	.	PUNCT
ap-7684	329	1	2/2022	2/2022	PROPN
ap-7684	330	1	a	a	DET
ap-7684	330	2	mindlin	mindlin	PROPN
ap-7684	330	3	shell	shell	PROPN
ap-7684	330	4	finite	finite	PROPN
ap-7684	330	5	element	element	NOUN
ap-7684	330	6	for	for	ADP
ap-7684	330	7	stone	stone	NOUN
ap-7684	330	8	masonry	masonry	NOUN
ap-7684	330	9	bridges	bridge	NOUN
ap-7684	330	10	with	with	ADP
ap-7684	330	11	backfill	backfill	NOUN
ap-7684	330	12	600	600	NUM
ap-7684	330	13	6	6	NUM
ap-7684	330	14	0	0	NUM
ap-7684	330	15	0	0	NUM
ap-7684	330	16	1	1	NUM
ap-7684	330	17	1	1	NUM
ap-7684	330	18	sym	sym	NOUN
ap-7684	330	19	.	.	PROPN
ap-7684	330	20	3	3	NUM
ap-7684	330	21	ri	ri	NOUN
ap-7684	331	1	gi	gi	NOUN
ap-7684	331	2	d	d	NOUN
ap-7684	331	3	sy	sy	INTJ
ap-7684	331	4	m	m	NOUN
ap-7684	331	5	.	.	PUNCT
ap-7684	332	1	sym.x	sym.x	PROPN
ap-7684	332	2	,	,	PUNCT
ap-7684	332	3	y	y	PROPN
ap-7684	332	4	z	z	NOUN
ap-7684	332	5	figure	figure	NOUN
ap-7684	332	6	8	8	NUM
ap-7684	332	7	.	.	PUNCT
ap-7684	332	8	benchmark	benchmark	NOUN
ap-7684	332	9	shell	shell	NOUN
ap-7684	332	10	0.2	0.2	NUM
ap-7684	332	11	0.4	0.4	NUM
ap-7684	332	12	0.6	0.6	NUM
ap-7684	332	13	0.8	0.8	NUM
ap-7684	332	14	1.0	1.0	NUM
ap-7684	332	15	0	0	NUM
ap-7684	332	16	16	16	NUM
ap-7684	332	17	32	32	NUM
ap-7684	332	18	488	488	NUM
ap-7684	332	19	elements	element	NOUN
ap-7684	332	20	along	along	ADP
ap-7684	332	21	directrixra	directrixra	NOUN
ap-7684	332	22	ti	ti	NOUN
ap-7684	332	23	o	o	NOUN
ap-7684	332	24	f	f	PROPN
ap-7684	332	25	e	e	X
ap-7684	332	26	m	m	PROPN
ap-7684	332	27	d	d	X
ap-7684	332	28	ef	ef	X
ap-7684	332	29	le	le	X
ap-7684	332	30	ct	ct	PROPN
ap-7684	332	31	io	io	PROPN
ap-7684	332	32	n	n	PROPN
ap-7684	332	33	/b	/b	PUNCT
ap-7684	332	34	en	en	PROPN
ap-7684	332	35	ch	ch	PROPN
ap-7684	332	36	m	m	PROPN
ap-7684	332	37	ar	ar	PROPN
ap-7684	332	38	k	k	PROPN
ap-7684	332	39	figure	figure	NOUN
ap-7684	332	40	9	9	NUM
ap-7684	332	41	.	.	PUNCT
ap-7684	333	1	convergence	convergence	NOUN
ap-7684	333	2	of	of	ADP
ap-7684	333	3	the	the	DET
ap-7684	333	4	fem	fem	NOUN
ap-7684	333	5	deflections	deflection	NOUN
ap-7684	333	6	,	,	PUNCT
ap-7684	333	7	ratio	ratio	NOUN
ap-7684	333	8	to	to	ADP
ap-7684	333	9	the	the	DET
ap-7684	333	10	benchmark	benchmark	NOUN
ap-7684	333	11	deflection	deflection	NOUN
ap-7684	333	12	the	the	DET
ap-7684	333	13	work	work	NOUN
ap-7684	333	14	[	[	X
ap-7684	333	15	13	13	NUM
ap-7684	333	16	]	]	PUNCT
ap-7684	333	17	.	.	PUNCT
ap-7684	334	1	the	the	DET
ap-7684	334	2	kirchhoff	kirchhoff	NOUN
ap-7684	334	3	-	-	PUNCT
ap-7684	334	4	love	love	NOUN
ap-7684	334	5	kinematic	kinematic	ADJ
ap-7684	334	6	assumptions	assumption	NOUN
ap-7684	334	7	are	be	AUX
ap-7684	334	8	used	use	VERB
ap-7684	334	9	in	in	ADP
ap-7684	334	10	the	the	DET
ap-7684	334	11	benchmark	benchmark	NOUN
ap-7684	334	12	so	so	SCONJ
ap-7684	334	13	that	that	SCONJ
ap-7684	334	14	a	a	DET
ap-7684	334	15	definite	definite	ADJ
ap-7684	334	16	deflection	deflection	NOUN
ap-7684	334	17	is	be	AUX
ap-7684	334	18	obtained	obtain	VERB
ap-7684	334	19	.	.	PUNCT
ap-7684	335	1	differences	difference	NOUN
ap-7684	335	2	can	can	AUX
ap-7684	335	3	be	be	AUX
ap-7684	335	4	expected	expect	VERB
ap-7684	335	5	between	between	ADP
ap-7684	335	6	the	the	DET
ap-7684	335	7	present	present	ADJ
ap-7684	335	8	and	and	CCONJ
ap-7684	335	9	benchmark	benchmark	ADJ
ap-7684	335	10	solutions	solution	NOUN
ap-7684	335	11	in	in	ADP
ap-7684	335	12	the	the	DET
ap-7684	335	13	vicinity	vicinity	NOUN
ap-7684	335	14	of	of	ADP
ap-7684	335	15	the	the	DET
ap-7684	335	16	pin	pin	NOUN
ap-7684	335	17	force	force	NOUN
ap-7684	335	18	,	,	PUNCT
ap-7684	335	19	in	in	ADP
ap-7684	335	20	particular	particular	ADJ
ap-7684	335	21	for	for	ADP
ap-7684	335	22	fine	fine	ADJ
ap-7684	335	23	meshes	mesh	NOUN
ap-7684	335	24	.	.	PUNCT
ap-7684	336	1	the	the	DET
ap-7684	336	2	mindlin	mindlin	PROPN
ap-7684	336	3	assumptions	assumption	NOUN
ap-7684	336	4	imply	imply	VERB
ap-7684	336	5	infinite	infinite	VERB
ap-7684	336	6	deflection	deflection	NOUN
ap-7684	336	7	beneath	beneath	ADP
ap-7684	336	8	the	the	DET
ap-7684	336	9	force	force	NOUN
ap-7684	336	10	in	in	ADP
ap-7684	336	11	the	the	DET
ap-7684	336	12	continuum	continuum	ADJ
ap-7684	336	13	model	model	NOUN
ap-7684	336	14	,	,	PUNCT
ap-7684	336	15	thus	thus	ADV
ap-7684	336	16	making	make	VERB
ap-7684	336	17	the	the	DET
ap-7684	336	18	discretized	discretized	ADJ
ap-7684	336	19	models	model	NOUN
ap-7684	336	20	mesh	mesh	VERB
ap-7684	336	21	dependent	dependent	ADJ
ap-7684	336	22	and	and	CCONJ
ap-7684	336	23	inherently	inherently	ADV
ap-7684	336	24	non	non	ADJ
ap-7684	336	25	-	-	NOUN
ap-7684	336	26	convergent	convergent	ADJ
ap-7684	336	27	.	.	PUNCT
ap-7684	337	1	owing	owe	VERB
ap-7684	337	2	to	to	ADP
ap-7684	337	3	the	the	DET
ap-7684	337	4	three	three	NUM
ap-7684	337	5	symmetry	symmetry	NOUN
ap-7684	337	6	planes	plane	NOUN
ap-7684	337	7	just	just	ADV
ap-7684	337	8	shaded	shade	VERB
ap-7684	337	9	,	,	PUNCT
ap-7684	337	10	1/8	1/8	NUM
ap-7684	337	11	of	of	ADP
ap-7684	337	12	the	the	DET
ap-7684	337	13	cylinder	cylinder	NOUN
ap-7684	337	14	can	can	AUX
ap-7684	337	15	be	be	AUX
ap-7684	337	16	considered	consider	VERB
ap-7684	337	17	.	.	PUNCT
ap-7684	338	1	four	four	NUM
ap-7684	338	2	mesh	mesh	NOUN
ap-7684	338	3	densities	density	NOUN
ap-7684	338	4	were	be	AUX
ap-7684	338	5	considered	consider	VERB
ap-7684	338	6	with	with	ADP
ap-7684	338	7	8	8	NUM
ap-7684	338	8	,	,	PUNCT
ap-7684	338	9	16	16	NUM
ap-7684	338	10	,	,	PUNCT
ap-7684	338	11	32	32	NUM
ap-7684	338	12	and	and	CCONJ
ap-7684	338	13	48	48	NUM
ap-7684	338	14	elements	element	NOUN
ap-7684	338	15	along	along	ADP
ap-7684	338	16	the	the	DET
ap-7684	338	17	directrix	directrix	NOUN
ap-7684	338	18	.	.	PUNCT
ap-7684	339	1	the	the	DET
ap-7684	339	2	ratio	ratio	NOUN
ap-7684	339	3	of	of	ADP
ap-7684	339	4	the	the	DET
ap-7684	339	5	loaded	load	VERB
ap-7684	339	6	node	node	NOUN
ap-7684	339	7	deflection	deflection	NOUN
ap-7684	339	8	of	of	ADP
ap-7684	339	9	the	the	DET
ap-7684	339	10	tm	tm	PROPN
ap-7684	339	11	finite	finite	PROPN
ap-7684	339	12	element	element	NOUN
ap-7684	339	13	solutions	solution	NOUN
ap-7684	339	14	to	to	ADP
ap-7684	339	15	the	the	DET
ap-7684	339	16	benchmark	benchmark	NOUN
ap-7684	339	17	deflection	deflection	NOUN
ap-7684	339	18	1.825	1.825	NUM
ap-7684	339	19	·	·	PUNCT
ap-7684	339	20	10−5	10−5	NUM
ap-7684	339	21	is	be	AUX
ap-7684	339	22	shown	show	VERB
ap-7684	339	23	in	in	ADP
ap-7684	339	24	figure	figure	NOUN
ap-7684	339	25	9	9	NUM
ap-7684	339	26	.	.	PUNCT
ap-7684	340	1	in	in	ADP
ap-7684	340	2	spite	spite	NOUN
ap-7684	340	3	of	of	ADP
ap-7684	340	4	the	the	DET
ap-7684	340	5	correction	correction	NOUN
ap-7684	340	6	of	of	ADP
ap-7684	340	7	the	the	DET
ap-7684	340	8	transverse	transverse	ADJ
ap-7684	340	9	shear	shear	NOUN
ap-7684	340	10	strain	strain	NOUN
ap-7684	340	11	in	in	ADP
ap-7684	340	12	equation	equation	NOUN
ap-7684	340	13	20	20	NUM
ap-7684	340	14	,	,	PUNCT
ap-7684	340	15	the	the	DET
ap-7684	340	16	residual	residual	ADJ
ap-7684	340	17	shear	shear	NOUN
ap-7684	340	18	locking	locking	NOUN
ap-7684	340	19	still	still	ADV
ap-7684	340	20	persisted	persist	VERB
ap-7684	340	21	and	and	CCONJ
ap-7684	340	22	affected	affect	VERB
ap-7684	340	23	the	the	DET
ap-7684	340	24	results	result	NOUN
ap-7684	340	25	in	in	ADP
ap-7684	340	26	this	this	DET
ap-7684	340	27	thin	thin	ADJ
ap-7684	340	28	shell	shell	NOUN
ap-7684	340	29	,	,	PUNCT
ap-7684	340	30	in	in	ADP
ap-7684	340	31	particular	particular	ADJ
ap-7684	340	32	,	,	PUNCT
ap-7684	340	33	for	for	ADP
ap-7684	340	34	low	low	ADJ
ap-7684	340	35	densiiy	densiiy	PROPN
ap-7684	340	36	meshes	mesh	NOUN
ap-7684	340	37	.	.	PUNCT
ap-7684	341	1	in	in	ADP
ap-7684	341	2	order	order	NOUN
ap-7684	341	3	to	to	PART
ap-7684	341	4	reduce	reduce	VERB
ap-7684	341	5	it	it	PRON
ap-7684	341	6	further	far	ADV
ap-7684	341	7	,	,	PUNCT
ap-7684	341	8	the	the	DET
ap-7684	341	9	material	material	ADJ
ap-7684	341	10	shear	shear	NOUN
ap-7684	341	11	stiffness	stiffness	NOUN
ap-7684	341	12	in	in	ADP
ap-7684	341	13	the	the	DET
ap-7684	341	14	transverse	transverse	NOUN
ap-7684	341	15	direction	direction	NOUN
ap-7684	341	16	(	(	PUNCT
ap-7684	341	17	element	element	NOUN
ap-7684	341	18	local	local	ADJ
ap-7684	341	19	x	x	SYM
ap-7684	341	20	−	−	PROPN
ap-7684	341	21	z	z	NOUN
ap-7684	341	22	and	and	CCONJ
ap-7684	341	23	y−	y−	NOUN
ap-7684	341	24	z	z	NOUN
ap-7684	341	25	planes	plane	NOUN
ap-7684	341	26	)	)	PUNCT
ap-7684	341	27	was	be	AUX
ap-7684	341	28	selectively	selectively	ADV
ap-7684	341	29	lowered	lower	VERB
ap-7684	341	30	eight	eight	NUM
ap-7684	341	31	times	time	NOUN
ap-7684	341	32	.	.	PUNCT
ap-7684	342	1	this	this	PRON
ap-7684	342	2	has	have	VERB
ap-7684	342	3	a	a	DET
ap-7684	342	4	negligible	negligible	ADJ
ap-7684	342	5	effect	effect	NOUN
ap-7684	342	6	on	on	ADP
ap-7684	342	7	the	the	DET
ap-7684	342	8	overall	overall	ADJ
ap-7684	342	9	response	response	NOUN
ap-7684	342	10	of	of	ADP
ap-7684	342	11	the	the	DET
ap-7684	342	12	fem	fem	NOUN
ap-7684	342	13	model	model	NOUN
ap-7684	342	14	since	since	SCONJ
ap-7684	342	15	the	the	DET
ap-7684	342	16	contribution	contribution	NOUN
ap-7684	342	17	of	of	ADP
ap-7684	342	18	the	the	DET
ap-7684	342	19	transverse	transverse	ADJ
ap-7684	342	20	shear	shear	NOUN
ap-7684	342	21	compliance	compliance	NOUN
ap-7684	342	22	to	to	ADP
ap-7684	342	23	it	it	PRON
ap-7684	342	24	is	be	AUX
ap-7684	342	25	small	small	ADJ
ap-7684	342	26	.	.	PUNCT
ap-7684	343	1	at	at	ADP
ap-7684	343	2	the	the	DET
ap-7684	343	3	denser	dense	ADJ
ap-7684	343	4	mesh	mesh	NOUN
ap-7684	343	5	side	side	NOUN
ap-7684	343	6	of	of	ADP
ap-7684	343	7	the	the	DET
ap-7684	343	8	figure	figure	NOUN
ap-7684	343	9	9	9	NUM
ap-7684	343	10	,	,	PUNCT
ap-7684	343	11	the	the	DET
ap-7684	343	12	curve	curve	NOUN
ap-7684	343	13	already	already	ADV
ap-7684	343	14	tends	tend	VERB
ap-7684	343	15	to	to	PART
ap-7684	343	16	adopt	adopt	VERB
ap-7684	343	17	to	to	ADP
ap-7684	343	18	the	the	DET
ap-7684	343	19	infinite	infinite	ADJ
ap-7684	343	20	deflection	deflection	NOUN
ap-7684	343	21	of	of	ADP
ap-7684	343	22	the	the	DET
ap-7684	343	23	continuum	continuum	ADJ
ap-7684	343	24	mindlin	mindlin	PROPN
ap-7684	343	25	shell	shell	NOUN
ap-7684	343	26	and	and	CCONJ
ap-7684	343	27	break	break	VERB
ap-7684	343	28	the	the	DET
ap-7684	343	29	kirchhoff	kirchhoff	NOUN
ap-7684	343	30	-	-	PUNCT
ap-7684	343	31	love	love	NOUN
ap-7684	343	32	benchmark	benchmark	NOUN
ap-7684	343	33	limit	limit	NOUN
ap-7684	343	34	.	.	PUNCT
ap-7684	344	1	the	the	DET
ap-7684	344	2	deformed	deform	VERB
ap-7684	344	3	mesh	mesh	NOUN
ap-7684	344	4	is	be	AUX
ap-7684	344	5	shown	show	VERB
ap-7684	344	6	in	in	ADP
ap-7684	344	7	figure	figure	NOUN
ap-7684	344	8	10	10	NUM
ap-7684	344	9	.	.	PUNCT
ap-7684	345	1	the	the	DET
ap-7684	345	2	radial	radial	ADJ
ap-7684	345	3	component	component	NOUN
ap-7684	345	4	of	of	ADP
ap-7684	345	5	the	the	DET
ap-7684	345	6	deflection	deflection	NOUN
ap-7684	345	7	along	along	ADP
ap-7684	345	8	the	the	DET
ap-7684	345	9	directrix	directrix	NOUN
ap-7684	345	10	from	from	ADP
ap-7684	345	11	the	the	DET
ap-7684	345	12	benchmark	benchmark	NOUN
ap-7684	345	13	solution	solution	NOUN
ap-7684	345	14	[	[	X
ap-7684	345	15	12	12	NUM
ap-7684	345	16	]	]	PUNCT
ap-7684	345	17	in	in	ADP
ap-7684	345	18	figure	figure	NOUN
ap-7684	345	19	11	11	NUM
ap-7684	345	20	compares	compare	NOUN
ap-7684	345	21	well	well	ADV
ap-7684	345	22	to	to	ADP
ap-7684	345	23	the	the	DET
ap-7684	345	24	deformed	deform	VERB
ap-7684	345	25	mesh	mesh	NOUN
ap-7684	345	26	in	in	ADP
ap-7684	345	27	figure	figure	NOUN
ap-7684	345	28	10	10	NUM
ap-7684	345	29	,	,	PUNCT
ap-7684	345	30	note	note	VERB
ap-7684	345	31	50	50	NUM
ap-7684	345	32	100	100	NUM
ap-7684	345	33	150	150	NUM
ap-7684	345	34	200	200	NUM
ap-7684	345	35	250	250	NUM
ap-7684	345	36	300	300	NUM
ap-7684	346	1	-300	-300	NUM
ap-7684	346	2	-250	-250	NUM
ap-7684	347	1	-200	-200	NUM
ap-7684	347	2	-150	-150	PROPN
ap-7684	347	3	-100	-100	PROPN
ap-7684	347	4	-50	-50	PUNCT
ap-7684	347	5	0	0	NUM
ap-7684	347	6	0	0	NUM
ap-7684	347	7	100	100	NUM
ap-7684	347	8	200	200	NUM
ap-7684	347	9	300	300	NUM
ap-7684	347	10	figure	figure	NOUN
ap-7684	347	11	10	10	NUM
ap-7684	347	12	.	.	PUNCT
ap-7684	348	1	deformed	deform	VERB
ap-7684	348	2	mesh	mesh	NOUN
ap-7684	348	3	,	,	PUNCT
ap-7684	348	4	48	48	NUM
ap-7684	348	5	elements	element	NOUN
ap-7684	348	6	along	along	ADP
ap-7684	348	7	the	the	DET
ap-7684	348	8	directrix	directrix	NOUN
ap-7684	348	9	figure	figure	NOUN
ap-7684	348	10	11	11	NUM
ap-7684	348	11	.	.	PUNCT
ap-7684	349	1	radial	radial	ADJ
ap-7684	349	2	component	component	NOUN
ap-7684	349	3	of	of	ADP
ap-7684	349	4	deflection	deflection	NOUN
ap-7684	349	5	along	along	ADP
ap-7684	349	6	the	the	DET
ap-7684	349	7	directrix	directrix	NOUN
ap-7684	349	8	,	,	PUNCT
ap-7684	349	9	benchmark	benchmark	NOUN
ap-7684	349	10	by	by	ADP
ap-7684	349	11	the	the	DET
ap-7684	349	12	solid	solid	ADJ
ap-7684	349	13	line	line	NOUN
ap-7684	349	14	,	,	PUNCT
ap-7684	349	15	[	[	X
ap-7684	349	16	12	12	NUM
ap-7684	349	17	]	]	PUNCT
ap-7684	349	18	the	the	DET
ap-7684	349	19	shalow	shalow	NOUN
ap-7684	349	20	inward	inward	ADJ
ap-7684	349	21	deflection	deflection	NOUN
ap-7684	349	22	in	in	ADP
ap-7684	349	23	the	the	DET
ap-7684	349	24	lower	low	ADJ
ap-7684	349	25	part	part	NOUN
ap-7684	349	26	of	of	ADP
ap-7684	349	27	the	the	DET
ap-7684	349	28	front	front	ADJ
ap-7684	349	29	directrix	directrix	NOUN
ap-7684	349	30	.	.	PUNCT
ap-7684	350	1	the	the	DET
ap-7684	350	2	precision	precision	NOUN
ap-7684	350	3	and	and	CCONJ
ap-7684	350	4	convergence	convergence	NOUN
ap-7684	350	5	of	of	ADP
ap-7684	350	6	the	the	DET
ap-7684	350	7	deflection	deflection	NOUN
ap-7684	350	8	beneath	beneath	ADP
ap-7684	350	9	the	the	DET
ap-7684	350	10	pin	pin	NOUN
ap-7684	350	11	force	force	NOUN
ap-7684	350	12	is	be	AUX
ap-7684	350	13	,	,	PUNCT
ap-7684	350	14	as	as	SCONJ
ap-7684	350	15	expected	expect	VERB
ap-7684	350	16	,	,	PUNCT
ap-7684	350	17	worse	bad	ADJ
ap-7684	350	18	than	than	ADP
ap-7684	350	19	for	for	ADP
ap-7684	350	20	elements	element	NOUN
ap-7684	350	21	based	base	VERB
ap-7684	350	22	on	on	ADP
ap-7684	350	23	the	the	DET
ap-7684	350	24	kirchhoff	kirchhoff	NOUN
ap-7684	350	25	-	-	PUNCT
ap-7684	350	26	love	love	NOUN
ap-7684	350	27	assumptions	assumption	NOUN
ap-7684	350	28	.	.	PUNCT
ap-7684	351	1	a	a	DET
ap-7684	351	2	solution	solution	NOUN
ap-7684	351	3	of	of	ADP
ap-7684	351	4	the	the	DET
ap-7684	351	5	ponikla	ponikla	NOUN
ap-7684	351	6	bridge	bridge	NOUN
ap-7684	351	7	arch	arch	NOUN
ap-7684	351	8	loaded	load	VERB
ap-7684	351	9	by	by	ADP
ap-7684	351	10	characteristic	characteristic	ADJ
ap-7684	351	11	arch	arch	ADJ
ap-7684	351	12	selfweight	selfweight	NOUN
ap-7684	351	13	and	and	CCONJ
ap-7684	351	14	standard	standard	ADJ
ap-7684	351	15	lm1	lm1	NOUN
ap-7684	351	16	tandem	tandem	NOUN
ap-7684	351	17	axle	axle	NOUN
ap-7684	351	18	with	with	ADP
ap-7684	351	19	wheel	wheel	NOUN
ap-7684	351	20	forces	force	NOUN
ap-7684	351	21	of	of	ADP
ap-7684	351	22	250	250	NUM
ap-7684	351	23	kn	kn	PROPN
ap-7684	351	24	is	be	AUX
ap-7684	351	25	provided	provide	VERB
ap-7684	351	26	for	for	ADP
ap-7684	351	27	the	the	DET
ap-7684	351	28	illustration	illustration	NOUN
ap-7684	351	29	of	of	ADP
ap-7684	351	30	the	the	DET
ap-7684	351	31	code	code	NOUN
ap-7684	351	32	output	output	NOUN
ap-7684	351	33	in	in	ADP
ap-7684	351	34	figure	figure	NOUN
ap-7684	351	35	12	12	NUM
ap-7684	351	36	.	.	PUNCT
ap-7684	352	1	displacements	displacement	NOUN
ap-7684	352	2	are	be	AUX
ap-7684	352	3	2000	2000	NUM
ap-7684	352	4	times	time	NOUN
ap-7684	352	5	scaled	scale	VERB
ap-7684	352	6	up	up	ADP
ap-7684	352	7	.	.	PUNCT
ap-7684	353	1	in	in	ADP
ap-7684	353	2	comparison	comparison	NOUN
ap-7684	353	3	to	to	ADP
ap-7684	353	4	the	the	DET
ap-7684	353	5	2d	2d	NOUN
ap-7684	353	6	solution	solution	NOUN
ap-7684	353	7	of	of	ADP
ap-7684	353	8	the	the	DET
ap-7684	353	9	same	same	ADJ
ap-7684	353	10	bridge	bridge	NOUN
ap-7684	353	11	arch	arch	NOUN
ap-7684	353	12	in	in	ADP
ap-7684	353	13	section	section	NOUN
ap-7684	353	14	3	3	NUM
ap-7684	353	15	,	,	PUNCT
ap-7684	353	16	the	the	DET
ap-7684	353	17	interaction	interaction	NOUN
ap-7684	353	18	and	and	CCONJ
ap-7684	353	19	selfweight	selfweight	NOUN
ap-7684	353	20	of	of	ADP
ap-7684	353	21	the	the	DET
ap-7684	353	22	fill	fill	NOUN
ap-7684	353	23	and	and	CCONJ
ap-7684	353	24	pavement	pavement	NOUN
ap-7684	353	25	are	be	AUX
ap-7684	353	26	not	not	PART
ap-7684	353	27	accounted	account	VERB
ap-7684	353	28	for	for	ADP
ap-7684	353	29	,	,	PUNCT
ap-7684	353	30	the	the	DET
ap-7684	353	31	tandem	tandem	NOUN
ap-7684	353	32	axle	axle	NOUN
ap-7684	353	33	load	load	NOUN
ap-7684	353	34	and	and	CCONJ
ap-7684	353	35	mesh	mesh	NOUN
ap-7684	353	36	density	density	NOUN
ap-7684	353	37	are	be	AUX
ap-7684	353	38	slightly	slightly	ADV
ap-7684	353	39	different	different	ADJ
ap-7684	353	40	,	,	PUNCT
ap-7684	353	41	too	too	ADV
ap-7684	353	42	.	.	PUNCT
ap-7684	354	1	the	the	DET
ap-7684	354	2	tandem	tandem	PROPN
ap-7684	354	3	axle	axle	NOUN
ap-7684	354	4	position	position	NOUN
ap-7684	354	5	in	in	ADP
ap-7684	354	6	the	the	DET
ap-7684	354	7	transverse	transverse	NOUN
ap-7684	354	8	direction	direction	NOUN
ap-7684	354	9	is	be	AUX
ap-7684	354	10	the	the	DET
ap-7684	354	11	extreme	extreme	ADJ
ap-7684	354	12	eccentric	eccentric	ADJ
ap-7684	354	13	one	one	NOUN
ap-7684	354	14	within	within	ADP
ap-7684	354	15	the	the	DET
ap-7684	354	16	bounds	bound	NOUN
ap-7684	354	17	defined	define	VERB
ap-7684	354	18	by	by	ADP
ap-7684	354	19	the	the	DET
ap-7684	354	20	en	en	PROPN
ap-7684	354	21	1991	1991	NUM
ap-7684	354	22	-	-	SYM
ap-7684	354	23	2	2	NUM
ap-7684	354	24	.	.	PUNCT
ap-7684	355	1	the	the	DET
ap-7684	355	2	differences	difference	NOUN
ap-7684	355	3	between	between	ADP
ap-7684	355	4	the	the	DET
ap-7684	355	5	loaded	load	VERB
ap-7684	355	6	/	/	SYM
ap-7684	355	7	unloaded	unload	VERB
ap-7684	355	8	sides	side	NOUN
ap-7684	355	9	of	of	ADP
ap-7684	355	10	the	the	DET
ap-7684	355	11	arch	arch	ADJ
ap-7684	355	12	barrel	barrel	NOUN
ap-7684	355	13	are	be	AUX
ap-7684	355	14	1261/405	1261/405	PROPN
ap-7684	355	15	kpa	kpa	NOUN
ap-7684	355	16	in	in	ADP
ap-7684	355	17	extreme	extreme	ADJ
ap-7684	355	18	normal	normal	ADJ
ap-7684	355	19	stresses	stress	NOUN
ap-7684	355	20	in	in	ADP
ap-7684	355	21	the	the	DET
ap-7684	355	22	bed	bed	NOUN
ap-7684	355	23	joints	joint	NOUN
ap-7684	355	24	and	and	CCONJ
ap-7684	355	25	0.41/0.25	0.41/0.25	NOUN
ap-7684	355	26	in	in	ADP
ap-7684	355	27	relative	relative	ADJ
ap-7684	355	28	crack	crack	NOUN
ap-7684	355	29	depths	depth	NOUN
ap-7684	355	30	.	.	PUNCT
ap-7684	356	1	the	the	DET
ap-7684	356	2	backfill	backfill	NOUN
ap-7684	356	3	and	and	CCONJ
ap-7684	356	4	pavement	pavement	VERB
ap-7684	356	5	stiffness	stiffness	NOUN
ap-7684	356	6	and	and	CCONJ
ap-7684	356	7	selfweight	selfweight	VERB
ap-7684	356	8	reduce	reduce	VERB
ap-7684	356	9	the	the	DET
ap-7684	356	10	differences	difference	NOUN
ap-7684	356	11	in	in	ADP
ap-7684	356	12	the	the	DET
ap-7684	356	13	real	real	ADJ
ap-7684	356	14	bridge	bridge	NOUN
ap-7684	356	15	,	,	PUNCT
ap-7684	356	16	but	but	CCONJ
ap-7684	356	17	the	the	DET
ap-7684	356	18	example	example	NOUN
ap-7684	356	19	testifies	testify	VERB
ap-7684	356	20	that	that	SCONJ
ap-7684	356	21	the	the	DET
ap-7684	356	22	2d	2d	NOUN
ap-7684	356	23	models	model	NOUN
ap-7684	356	24	need	need	VERB
ap-7684	356	25	corrections	correction	NOUN
ap-7684	356	26	.	.	PUNCT
ap-7684	357	1	the	the	DET
ap-7684	357	2	3d	3d	PROPN
ap-7684	357	3	bridge	bridge	PROPN
ap-7684	357	4	model	model	NOUN
ap-7684	357	5	analogue	analogue	NOUN
ap-7684	357	6	to	to	ADP
ap-7684	357	7	the	the	DET
ap-7684	357	8	one	one	NUM
ap-7684	357	9	in	in	ADP
ap-7684	357	10	section	section	NOUN
ap-7684	357	11	3	3	NUM
ap-7684	357	12	is	be	AUX
ap-7684	357	13	currently	currently	ADV
ap-7684	357	14	being	be	AUX
ap-7684	357	15	worked	work	VERB
ap-7684	357	16	on	on	ADP
ap-7684	357	17	.	.	PUNCT
ap-7684	358	1	the	the	DET
ap-7684	358	2	absence	absence	NOUN
ap-7684	358	3	of	of	ADP
ap-7684	358	4	rotational	rotational	ADJ
ap-7684	358	5	dofs	dof	NOUN
ap-7684	358	6	improves	improve	VERB
ap-7684	358	7	the	the	DET
ap-7684	358	8	convergence	convergence	NOUN
ap-7684	358	9	of	of	ADP
ap-7684	358	10	the	the	DET
ap-7684	358	11	iterations	iteration	NOUN
ap-7684	358	12	.	.	PUNCT
ap-7684	359	1	the	the	DET
ap-7684	359	2	no	no	DET
ap-7684	359	3	-	-	PUNCT
ap-7684	359	4	tension	tension	NOUN
ap-7684	359	5	,	,	PUNCT
ap-7684	359	6	history	history	NOUN
ap-7684	359	7	independent	independent	ADJ
ap-7684	359	8	material	material	NOUN
ap-7684	359	9	model	model	NOUN
ap-7684	359	10	admits	admit	VERB
ap-7684	359	11	a	a	DET
ap-7684	359	12	single	single	ADJ
ap-7684	359	13	load	load	NOUN
ap-7684	359	14	increment	increment	NOUN
ap-7684	359	15	strategy	strategy	NOUN
ap-7684	359	16	.	.	PUNCT
ap-7684	360	1	in	in	ADP
ap-7684	360	2	the	the	DET
ap-7684	360	3	illustration	illustration	NOUN
ap-7684	360	4	example	example	NOUN
ap-7684	360	5	,	,	PUNCT
ap-7684	360	6	the	the	DET
ap-7684	360	7	301	301	NUM
ap-7684	360	8	petr	petr	PROPN
ap-7684	360	9	řeřicha	řeřicha	PROPN
ap-7684	360	10	acta	acta	PROPN
ap-7684	360	11	polytechnica	polytechnica	PROPN
ap-7684	360	12	0	0	NUM
ap-7684	360	13	2	2	NUM
ap-7684	360	14	4	4	NUM
ap-7684	360	15	6	6	NUM
ap-7684	360	16	8	8	NUM
ap-7684	360	17	0	0	NUM
ap-7684	360	18	-10.5	-10.5	NUM
ap-7684	360	19	-10	-10	PUNCT
ap-7684	360	20	-9.5	-9.5	NOUN
ap-7684	360	21	2	2	NUM
ap-7684	360	22	4	4	NUM
ap-7684	360	23	6	6	NUM
ap-7684	360	24	8	8	NUM
ap-7684	360	25	10	10	NUM
ap-7684	360	26	-1758||0.34	-1758||0.34	PROPN
ap-7684	360	27	-	-	PUNCT
ap-7684	360	28	1647||0.3	1647||0.3	NUM
ap-7684	360	29	-963.8||0	-963.8||0	X
ap-7684	361	1	-1222||0.36	-1222||0.36	INTJ
ap-7684	361	2	-1493||0.36	-1493||0.36	PROPN
ap-7684	361	3	-1368||0.36	-1368||0.36	PUNCT
ap-7684	361	4	-795.9||0	-795.9||0	PRON
ap-7684	361	5	-1594||0.35	-1594||0.35	PROPN
ap-7684	361	6	-862.4||0.35	-862.4||0.35	NOUN
ap-7684	361	7	-	-	PUNCT
ap-7684	361	8	1046||0.36	1046||0.36	NUM
ap-7684	361	9	-593.7||0	-593.7||0	NUM
ap-7684	361	10	-680.6||0	-680.6||0	NUM
ap-7684	361	11	368.1||0	368.1||0	NUM
ap-7684	361	12	-1663||0.35	-1663||0.35	NOUN
ap-7684	361	13	-	-	PUNCT
ap-7684	361	14	1727||0.35	1727||0.35	PROPN
ap-7684	361	15	-921.3||0	-921.3||0	NUM
ap-7684	361	16	-899.1||0	-899.1||0	NUM
ap-7684	361	17	-884.5||0	-884.5||0	NUM
ap-7684	361	18	-832.6||0	-832.6||0	NUM
ap-7684	361	19	-891.1||0	-891.1||0	NUM
ap-7684	361	20	893.6||0	893.6||0	NUM
ap-7684	361	21	924||0	924||0	NUM
ap-7684	362	1	1036||0.21	1036||0.21	NUM
ap-7684	362	2	1139||0.27637.6||0	1139||0.27637.6||0	NUM
ap-7684	362	3	740.3||0	740.3||0	NUM
ap-7684	362	4	678.6||0	678.6||0	NUM
ap-7684	362	5	726.5||0.16	726.5||0.16	NUM
ap-7684	362	6	693.5||0	693.5||0	NUM
ap-7684	362	7	993.4||0.2	993.4||0.2	NOUN
ap-7684	362	8	952.8||0.26	952.8||0.26	NUM
ap-7684	362	9	952.8||0.26	952.8||0.26	NUM
ap-7684	362	10	875.1||0	875.1||0	NUM
ap-7684	362	11	1071||0.221139||0.27	1071||0.221139||0.27	NUM
ap-7684	362	12	1087||0.2	1087||0.2	NUM
ap-7684	362	13	1141||0.35	1141||0.35	NUM
ap-7684	362	14	1141||0.33	1141||0.33	PROPN
ap-7684	362	15	1186||0.33	1186||0.33	PROPN
ap-7684	362	16	-499.6||0	-499.6||0	NUM
ap-7684	362	17	333.4||0	333.4||0	NUM
ap-7684	362	18	370.9||0	370.9||0	NUM
ap-7684	362	19	727.8||0.15	727.8||0.15	NUM
ap-7684	362	20	891.2||0.3	891.2||0.3	NUM
ap-7684	362	21	849.8||0.33	849.8||0.33	NUM
ap-7684	362	22	599||0.24847.9||0.33	599||0.24847.9||0.33	NUM
ap-7684	362	23	889.3||0.31	889.3||0.31	NUM
ap-7684	362	24	594.3||0.23	594.3||0.23	NUM
ap-7684	362	25	605.2||0.099	605.2||0.099	NUM
ap-7684	362	26	608||0.27	608||0.27	NUM
ap-7684	362	27	495.5||0.27608.1||0.27	495.5||0.27608.1||0.27	NUM
ap-7684	362	28	610||0.1	610||0.1	NUM
ap-7684	362	29	-622.6||0.33	-622.6||0.33	ADJ
ap-7684	362	30	-466.7||0.36	-466.7||0.36	NOUN
ap-7684	362	31	-346.7||0.4	-346.7||0.4	PUNCT
ap-7684	362	32	-527.3||0.35	-527.3||0.35	ADJ
ap-7684	363	1	-331.1||0.087	-331.1||0.087	NOUN
ap-7684	363	2	-719.4||0.34	-719.4||0.34	NOUN
ap-7684	364	1	-459.8||0	-459.8||0	PRON
ap-7684	364	2	-301.5||0	-301.5||0	NUM
ap-7684	364	3	-301.1||0	-301.1||0	NUM
ap-7684	364	4	349.1||0	349.1||0	NUM
ap-7684	364	5	342.1||0	342.1||0	NUM
ap-7684	365	1	159||0	159||0	NUM
ap-7684	365	2	336.4||0	336.4||0	NUM
ap-7684	365	3	-342||0.13	-342||0.13	VERB
ap-7684	365	4	-218.1||0	-218.1||0	NUM
ap-7684	365	5	162.3||0	162.3||0	NUM
ap-7684	365	6	189.8||0	189.8||0	NUM
ap-7684	365	7	329.3||0.096	329.3||0.096	NUM
ap-7684	366	1	324.7||0.09	324.7||0.09	NUM
ap-7684	366	2	495.6||0.27	495.6||0.27	NUM
ap-7684	366	3	459.9||0.2	459.9||0.2	NOUN
ap-7684	366	4	405.9||0.25	405.9||0.25	NOUN
ap-7684	366	5	329.8||0.17405.8||0.25	329.8||0.17405.8||0.25	NUM
ap-7684	366	6	459.9||0.2	459.9||0.2	NOUN
ap-7684	366	7	459.3||0.015	459.3||0.015	NUM
ap-7684	367	1	461.2||0.021	461.2||0.021	NUM
ap-7684	368	1	351.8||0.21	351.8||0.21	NUM
ap-7684	368	2	358.1||0.11	358.1||0.11	NUM
ap-7684	368	3	362||0	362||0	NUM
ap-7684	369	1	362.5||0	362.5||0	NUM
ap-7684	369	2	358.1||0.11	358.1||0.11	NUM
ap-7684	369	3	291.1||0.039	291.1||0.039	NUM
ap-7684	369	4	286.7||0	286.7||0	NUM
ap-7684	369	5	287||0	287||0	NUM
ap-7684	369	6	220.9||0	220.9||0	NUM
ap-7684	369	7	1261||0.41	1261||0.41	NUM
ap-7684	369	8	1066||0.34732||0.048	1066||0.34732||0.048	NUM
ap-7684	369	9	607||0	607||0	NUM
ap-7684	370	1	1068||0.34	1068||0.34	NUM
ap-7684	370	2	773.3||0.096607.5||0	773.3||0.096607.5||0	NUM
ap-7684	370	3	781.3||0.1	781.3||0.1	NOUN
ap-7684	370	4	471.9||0	471.9||0	NUM
ap-7684	370	5	529.7||0	529.7||0	NUM
ap-7684	370	6	529.4||0	529.4||0	NUM
ap-7684	370	7	413||0	413||0	NUM
ap-7684	370	8	413.8||0	413.8||0	NUM
ap-7684	370	9	326.9||0	326.9||0	NUM
ap-7684	370	10	467||0	467||0	NUM
ap-7684	370	11	467.6||0	467.6||0	NUM
ap-7684	370	12	364.7||0	364.7||0	VERB
ap-7684	370	13	364.7||0	364.7||0	NUM
ap-7684	370	14	-426.6||0	-426.6||0	NUM
ap-7684	370	15	-497.2||0	-497.2||0	INTJ
ap-7684	370	16	-557.2||0	-557.2||0	INTJ
ap-7684	370	17	-585||0	-585||0	PUNCT
ap-7684	370	18	-625||0	-625||0	PUNCT
ap-7684	370	19	-609||0	-609||0	PROPN
ap-7684	370	20	-	-	PUNCT
ap-7684	370	21	409.8||0	409.8||0	NUM
ap-7684	370	22	336.9||0	336.9||0	NUM
ap-7684	370	23	-409.8||0	-409.8||0	NUM
ap-7684	371	1	337||0	337||0	NUM
ap-7684	371	2	-497.2||0	-497.2||0	NUM
ap-7684	371	3	-290.2||0	-290.2||0	NUM
ap-7684	371	4	-420.3||0	-420.3||0	PUNCT
ap-7684	371	5	-420.3||0	-420.3||0	PUNCT
ap-7684	372	1	-520.3||0	-520.3||0	NUM
ap-7684	372	2	-585||0	-585||0	NOUN
ap-7684	373	1	-520.3||0	-520.3||0	NUM
ap-7684	373	2	-573||0	-573||0	PUNCT
ap-7684	374	1	-499||0	-499||0	PROPN
ap-7684	374	2	-399.5||0	-399.5||0	PROPN
ap-7684	375	1	-498.9||0	-498.9||0	NUM
ap-7684	375	2	-462.6||0	-462.6||0	INTJ
ap-7684	375	3	-573.2||0	-573.2||0	NUM
ap-7684	375	4	-528.8||0	-528.8||0	NUM
ap-7684	375	5	-529.8||0	-529.8||0	NUM
ap-7684	376	1	-462.6||0	-462.6||0	NUM
ap-7684	376	2	-290.1||0	-290.1||0	NUM
ap-7684	376	3	-272.1||0	-272.1||0	PROPN
ap-7684	376	4	-399.5||0	-399.5||0	NUM
ap-7684	376	5	-367.1||0	-367.1||0	NUM
ap-7684	376	6	-609||0	-609||0	PUNCT
ap-7684	376	7	-560.4||0	-560.4||0	NUM
ap-7684	376	8	-560.5||0	-560.5||0	NUM
ap-7684	376	9	-492.6||0	-492.6||0	INTJ
ap-7684	376	10	-415.9||0	-415.9||0	INTJ
ap-7684	376	11	-481||0	-481||0	PUNCT
ap-7684	377	1	-493.3||0	-493.3||0	PRON
ap-7684	377	2	-480.3||0	-480.3||0	INTJ
ap-7684	378	1	-415.9||0	-415.9||0	INTJ
ap-7684	378	2	-412.4||0	-412.4||0	PUNCT
ap-7684	378	3	-373.3||0	-373.3||0	NUM
ap-7684	379	1	-416.4||0	-416.4||0	NUM
ap-7684	379	2	-416||0	-416||0	INTJ
ap-7684	379	3	-411.6||0	-411.6||0	INTJ
ap-7684	379	4	-371.7||0	-371.7||0	INTJ
ap-7684	379	5	-391.1||0	-391.1||0	INTJ
ap-7684	380	1	327.4||0	327.4||0	NUM
ap-7684	380	2	264.6||0	264.6||0	NUM
ap-7684	380	3	-271.6||0	-271.6||0	NUM
ap-7684	380	4	-252.6||0	-252.6||0	PROPN
ap-7684	380	5	-366.9||0	-366.9||0	NUM
ap-7684	380	6	264.8||0	264.8||0	NUM
ap-7684	380	7	209.4||0	209.4||0	NUM
ap-7684	380	8	209.4||0	209.4||0	NOUN
ap-7684	380	9	-252.2||0	-252.2||0	NUM
ap-7684	380	10	-331.3||0	-331.3||0	NUM
ap-7684	380	11	-157.2||0	-157.2||0	NUM
ap-7684	380	12	-243.2||0	-243.2||0	NUM
ap-7684	380	13	-331.3||0	-331.3||0	NUM
ap-7684	380	14	-242.7||0	-242.7||0	NUM
ap-7684	380	15	-237||0	-237||0	NOUN
ap-7684	381	1	-305.4||0	-305.4||0	ADP
ap-7684	381	2	-308.9||0	-308.9||0	VERB
ap-7684	381	3	-373||0	-373||0	PRON
ap-7684	382	1	-283.4||0	-283.4||0	PRON
ap-7684	382	2	-356.3||0	-356.3||0	NUM
ap-7684	382	3	-344.6||0	-344.6||0	NUM
ap-7684	382	4	-329.8||0	-329.8||0	NUM
ap-7684	382	5	-369.7||0	-369.7||0	NUM
ap-7684	382	6	-	-	PUNCT
ap-7684	382	7	339.5||0	339.5||0	NUM
ap-7684	382	8	-325.6||0	-325.6||0	NOUN
ap-7684	382	9	-	-	PROPN
ap-7684	382	10	312.6||0	312.6||0	NUM
ap-7684	382	11	-321.4||0	-321.4||0	NUM
ap-7684	382	12	-316.1||0	-316.1||0	NUM
ap-7684	382	13	-277.8||0	-277.8||0	NUM
ap-7684	382	14	-283.5||0	-283.5||0	NUM
ap-7684	382	15	322.6||0	322.6||0	NUM
ap-7684	382	16	301||0	301||0	NUM
ap-7684	382	17	277.8||0	277.8||0	NUM
ap-7684	382	18	-275.3||0	-275.3||0	NUM
ap-7684	382	19	-279.3||0	-279.3||0	NUM
ap-7684	382	20	-630.6||0	-630.6||0	NUM
ap-7684	383	1	-566.2||0	-566.2||0	NUM
ap-7684	383	2	-566.2||0	-566.2||0	NUM
ap-7684	383	3	-	-	SYM
ap-7684	383	4	469.2||0	469.2||0	NUM
ap-7684	383	5	-470.3||0	-470.3||0	NUM
ap-7684	383	6	-569.9||0	-569.9||0	NUM
ap-7684	383	7	-	-	SYM
ap-7684	383	8	451.3||0	451.3||0	NUM
ap-7684	383	9	-452.3||0	-452.3||0	NUM
ap-7684	383	10	-428.4||0	-428.4||0	NUM
ap-7684	383	11	425.4||0	425.4||0	NUM
ap-7684	383	12	456.5||0	456.5||0	VERB
ap-7684	383	13	447.1||0	447.1||0	PROPN
ap-7684	383	14	420.9||0	420.9||0	NUM
ap-7684	383	15	-395.3||0	-395.3||0	NOUN
ap-7684	384	1	-398.2||0	-398.2||0	NUM
ap-7684	384	2	411.7||0	411.7||0	NUM
ap-7684	384	3	393.8||0	393.8||0	NUM
ap-7684	384	4	366.5||0	366.5||0	NUM
ap-7684	384	5	345.6||0	345.6||0	NUM
ap-7684	384	6	figure	figure	NOUN
ap-7684	384	7	12	12	NUM
ap-7684	384	8	.	.	PUNCT
ap-7684	385	1	bridge	bridge	NOUN
ap-7684	385	2	at	at	ADP
ap-7684	385	3	ponikla	ponikla	NOUN
ap-7684	385	4	,	,	PUNCT
ap-7684	385	5	3d	3d	PROPN
ap-7684	385	6	shell	shell	NOUN
ap-7684	385	7	,	,	PUNCT
ap-7684	385	8	compression	compression	NOUN
ap-7684	385	9	stresses	stress	NOUN
ap-7684	386	1	[	[	X
ap-7684	386	2	kpa	kpa	X
ap-7684	386	3	]	]	X
ap-7684	386	4	and	and	CCONJ
ap-7684	386	5	relative	relative	ADJ
ap-7684	386	6	depths	depth	NOUN
ap-7684	386	7	of	of	ADP
ap-7684	386	8	the	the	DET
ap-7684	386	9	cracks	crack	NOUN
ap-7684	386	10	in	in	ADP
ap-7684	386	11	the	the	DET
ap-7684	386	12	bed	bed	NOUN
ap-7684	386	13	joints	joint	NOUN
ap-7684	386	14	ratio	ratio	NOUN
ap-7684	386	15	0.005	0.005	NUM
ap-7684	386	16	of	of	ADP
ap-7684	386	17	the	the	DET
ap-7684	386	18	rms	rm	NOUN
ap-7684	386	19	norms	norm	NOUN
ap-7684	386	20	of	of	ADP
ap-7684	386	21	the	the	DET
ap-7684	386	22	imbalance	imbalance	NOUN
ap-7684	386	23	and	and	CCONJ
ap-7684	386	24	load	load	NOUN
ap-7684	386	25	was	be	AUX
ap-7684	386	26	reached	reach	VERB
ap-7684	386	27	in	in	ADP
ap-7684	386	28	3	3	NUM
ap-7684	386	29	iterations	iteration	NOUN
ap-7684	386	30	.	.	PUNCT
ap-7684	387	1	5	5	X
ap-7684	387	2	.	.	X
ap-7684	387	3	conclusions	conclusion	NOUN
ap-7684	387	4	the	the	DET
ap-7684	387	5	simplest	simple	ADJ
ap-7684	387	6	finite	finite	ADJ
ap-7684	387	7	elements	element	NOUN
ap-7684	387	8	for	for	ADP
ap-7684	387	9	2d	2d	NUM
ap-7684	387	10	and	and	CCONJ
ap-7684	387	11	3d	3d	NUM
ap-7684	387	12	thick	thick	ADJ
ap-7684	387	13	shells	shell	NOUN
ap-7684	387	14	have	have	AUX
ap-7684	387	15	been	be	AUX
ap-7684	387	16	developed	develop	VERB
ap-7684	387	17	for	for	ADP
ap-7684	387	18	applications	application	NOUN
ap-7684	387	19	in	in	ADP
ap-7684	387	20	masonry	masonry	NOUN
ap-7684	387	21	arch	arch	ADJ
ap-7684	387	22	bridges	bridge	NOUN
ap-7684	387	23	limit	limit	VERB
ap-7684	387	24	load	load	NOUN
ap-7684	387	25	analysis	analysis	NOUN
ap-7684	387	26	.	.	PUNCT
ap-7684	388	1	they	they	PRON
ap-7684	388	2	feature	feature	VERB
ap-7684	388	3	seamless	seamless	ADJ
ap-7684	388	4	combination	combination	NOUN
ap-7684	388	5	with	with	ADP
ap-7684	388	6	2d	2d	PROPN
ap-7684	388	7	cst	cst	PROPN
ap-7684	388	8	and	and	CCONJ
ap-7684	388	9	3d	3d	NUM
ap-7684	388	10	tetrahedron	tetrahedron	NOUN
ap-7684	388	11	elements	element	NOUN
ap-7684	388	12	for	for	ADP
ap-7684	388	13	the	the	DET
ap-7684	388	14	bridge	bridge	NOUN
ap-7684	388	15	’s	’s	PART
ap-7684	388	16	backfill	backfill	NOUN
ap-7684	388	17	.	.	PUNCT
ap-7684	389	1	exclusively	exclusively	ADV
ap-7684	389	2	translational	translational	ADJ
ap-7684	389	3	dofs	dof	NOUN
ap-7684	389	4	are	be	AUX
ap-7684	389	5	used	use	VERB
ap-7684	389	6	,	,	PUNCT
ap-7684	389	7	which	which	PRON
ap-7684	389	8	improves	improve	VERB
ap-7684	389	9	the	the	DET
ap-7684	389	10	convergence	convergence	NOUN
ap-7684	389	11	of	of	ADP
ap-7684	389	12	iterations	iteration	NOUN
ap-7684	389	13	.	.	PUNCT
ap-7684	390	1	the	the	DET
ap-7684	390	2	no	no	DET
ap-7684	390	3	-	-	PUNCT
ap-7684	390	4	tension	tension	NOUN
ap-7684	390	5	condition	condition	NOUN
ap-7684	390	6	is	be	AUX
ap-7684	390	7	applied	apply	VERB
ap-7684	390	8	to	to	ADP
ap-7684	390	9	the	the	DET
ap-7684	390	10	normal	normal	ADJ
ap-7684	390	11	stress	stress	NOUN
ap-7684	390	12	in	in	ADP
ap-7684	390	13	the	the	DET
ap-7684	390	14	bed	bed	NOUN
ap-7684	390	15	joints	joint	NOUN
ap-7684	390	16	planes	plane	NOUN
ap-7684	390	17	.	.	PUNCT
ap-7684	391	1	the	the	DET
ap-7684	391	2	output	output	NOUN
ap-7684	391	3	minimum	minimum	NOUN
ap-7684	391	4	normal	normal	ADJ
ap-7684	391	5	stresses	stress	NOUN
ap-7684	391	6	and	and	CCONJ
ap-7684	391	7	cracks	crack	NOUN
ap-7684	391	8	depths	depth	NOUN
ap-7684	391	9	in	in	ADP
ap-7684	391	10	these	these	DET
ap-7684	391	11	planes	plane	NOUN
ap-7684	391	12	can	can	AUX
ap-7684	391	13	be	be	AUX
ap-7684	391	14	used	use	VERB
ap-7684	391	15	to	to	PART
ap-7684	391	16	assess	assess	VERB
ap-7684	391	17	the	the	DET
ap-7684	391	18	ultimate	ultimate	ADJ
ap-7684	391	19	limit	limit	NOUN
ap-7684	391	20	loads	load	NOUN
ap-7684	391	21	of	of	ADP
ap-7684	391	22	a	a	DET
ap-7684	391	23	bridge	bridge	NOUN
ap-7684	391	24	.	.	PUNCT
ap-7684	392	1	a	a	DET
ap-7684	392	2	sample	sample	NOUN
ap-7684	392	3	analysis	analysis	NOUN
ap-7684	392	4	of	of	ADP
ap-7684	392	5	an	an	DET
ap-7684	392	6	arch	arch	NOUN
ap-7684	392	7	of	of	ADP
ap-7684	392	8	the	the	DET
ap-7684	392	9	bridge	bridge	NOUN
ap-7684	392	10	at	at	ADP
ap-7684	392	11	poniklá	poniklá	NOUN
ap-7684	392	12	testifies	testify	VERB
ap-7684	392	13	that	that	SCONJ
ap-7684	392	14	this	this	DET
ap-7684	392	15	material	material	ADJ
ap-7684	392	16	law	law	NOUN
ap-7684	392	17	and	and	CCONJ
ap-7684	392	18	shell	shell	ADJ
ap-7684	392	19	elements	element	NOUN
ap-7684	392	20	develop	develop	VERB
ap-7684	392	21	a	a	DET
ap-7684	392	22	characteristic	characteristic	ADJ
ap-7684	392	23	failure	failure	NOUN
ap-7684	392	24	mode	mode	NOUN
ap-7684	392	25	of	of	ADP
ap-7684	392	26	the	the	DET
ap-7684	392	27	stone	stone	NOUN
ap-7684	392	28	masonry	masonry	PROPN
ap-7684	392	29	arch	arch	NOUN
ap-7684	392	30	bridges	bridge	NOUN
ap-7684	392	31	,	,	PUNCT
ap-7684	392	32	the	the	DET
ap-7684	392	33	gradual	gradual	ADJ
ap-7684	392	34	creation	creation	NOUN
ap-7684	392	35	of	of	ADP
ap-7684	392	36	the	the	DET
ap-7684	392	37	virtual	virtual	ADJ
ap-7684	392	38	hinges	hinge	NOUN
ap-7684	392	39	.	.	PUNCT
ap-7684	393	1	acknowledgements	acknowledgement	NOUN
ap-7684	393	2	the	the	DET
ap-7684	393	3	author	author	NOUN
ap-7684	393	4	was	be	AUX
ap-7684	393	5	supported	support	VERB
ap-7684	393	6	by	by	ADP
ap-7684	393	7	the	the	DET
ap-7684	393	8	grant	grant	PROPN
ap-7684	393	9	naki	naki	PROPN
ap-7684	393	10	dg20p02ovv001	dg20p02ovv001	PROPN
ap-7684	393	11	,	,	PUNCT
ap-7684	393	12	‘	'	PUNCT
ap-7684	393	13	tools	tool	NOUN
ap-7684	393	14	for	for	ADP
ap-7684	393	15	the	the	DET
ap-7684	393	16	preservation	preservation	NOUN
ap-7684	393	17	of	of	ADP
ap-7684	393	18	historical	historical	ADJ
ap-7684	393	19	values	value	NOUN
ap-7684	393	20	and	and	CCONJ
ap-7684	393	21	functions	function	NOUN
ap-7684	393	22	of	of	ADP
ap-7684	393	23	arch	arch	NOUN
ap-7684	393	24	and	and	CCONJ
ap-7684	393	25	vaulted	vaulted	ADJ
ap-7684	393	26	bridges	bridge	NOUN
ap-7684	393	27	’	'	PUNCT
ap-7684	393	28	provided	provide	VERB
ap-7684	393	29	by	by	ADP
ap-7684	393	30	the	the	DET
ap-7684	393	31	ministry	ministry	PROPN
ap-7684	393	32	of	of	ADP
ap-7684	393	33	culture	culture	NOUN
ap-7684	393	34	of	of	ADP
ap-7684	393	35	the	the	DET
ap-7684	393	36	czech	czech	PROPN
ap-7684	393	37	republic	republic	NOUN
ap-7684	393	38	.	.	PUNCT
ap-7684	394	1	references	reference	NOUN
ap-7684	394	2	[	[	X
ap-7684	394	3	1	1	X
ap-7684	394	4	]	]	PUNCT
ap-7684	394	5	the	the	DET
ap-7684	394	6	highways	highway	NOUN
ap-7684	394	7	agency	agency	PROPN
ap-7684	394	8	,	,	PUNCT
ap-7684	394	9	london	london	PROPN
ap-7684	394	10	.	.	PUNCT
ap-7684	395	1	design	design	NOUN
ap-7684	395	2	manual	manual	NOUN
ap-7684	395	3	for	for	ADP
ap-7684	395	4	roads	road	NOUN
ap-7684	395	5	and	and	CCONJ
ap-7684	395	6	bridges	bridge	NOUN
ap-7684	395	7	,	,	PUNCT
ap-7684	395	8	vol	vol	NOUN
ap-7684	395	9	.	.	PROPN
ap-7684	396	1	3	3	NUM
ap-7684	396	2	,	,	PUNCT
ap-7684	396	3	highway	highway	NOUN
ap-7684	396	4	structures	structure	NOUN
ap-7684	396	5	:	:	PUNCT
ap-7684	396	6	inspection	inspection	NOUN
ap-7684	396	7	and	and	CCONJ
ap-7684	396	8	maintenance	maintenance	NOUN
ap-7684	396	9	,	,	PUNCT
ap-7684	396	10	section	section	NOUN
ap-7684	396	11	4	4	NUM
ap-7684	396	12	,	,	PUNCT
ap-7684	396	13	assessment	assessment	NOUN
ap-7684	396	14	,	,	PUNCT
ap-7684	396	15	part	part	NOUN
ap-7684	396	16	3	3	NUM
ap-7684	396	17	,	,	PUNCT
ap-7684	396	18	the	the	DET
ap-7684	396	19	assessment	assessment	NOUN
ap-7684	396	20	of	of	ADP
ap-7684	396	21	highway	highway	NOUN
ap-7684	396	22	bridges	bridge	NOUN
ap-7684	396	23	and	and	CCONJ
ap-7684	396	24	structures	structure	NOUN
ap-7684	396	25	,	,	PUNCT
ap-7684	396	26	2001	2001	NUM
ap-7684	396	27	.	.	PUNCT
ap-7684	397	1	[	[	X
ap-7684	397	2	2	2	NUM
ap-7684	397	3	]	]	X
ap-7684	397	4	ministry	ministry	NOUN
ap-7684	397	5	of	of	ADP
ap-7684	397	6	transport	transport	NOUN
ap-7684	397	7	of	of	ADP
ap-7684	397	8	the	the	DET
ap-7684	397	9	czech	czech	PROPN
ap-7684	397	10	republic	republic	NOUN
ap-7684	397	11	.	.	PUNCT
ap-7684	398	1	zatížitelnost	zatížitelnost	PROPN
ap-7684	398	2	zděných	zděných	PROPN
ap-7684	398	3	klenbových	klenbových	PROPN
ap-7684	398	4	mostů	mostů	PROPN
ap-7684	398	5	load	load	NOUN
ap-7684	398	6	rating	rating	NOUN
ap-7684	398	7	of	of	ADP
ap-7684	398	8	masonry	masonry	NOUN
ap-7684	398	9	arch	arch	ADJ
ap-7684	398	10	bridges	bridge	NOUN
ap-7684	398	11	,	,	PUNCT
ap-7684	398	12	2008	2008	NUM
ap-7684	398	13	.	.	PUNCT
ap-7684	399	1	[	[	X
ap-7684	399	2	3	3	X
ap-7684	399	3	]	]	PUNCT
ap-7684	399	4	t.	t.	PROPN
ap-7684	399	5	e.	e.	PROPN
ap-7684	399	6	ford	ford	PROPN
ap-7684	399	7	,	,	PUNCT
ap-7684	399	8	c.	c.	PROPN
ap-7684	399	9	e.	e.	PROPN
ap-7684	399	10	augarde	augarde	PROPN
ap-7684	399	11	,	,	PUNCT
ap-7684	399	12	s.	s.	PROPN
ap-7684	399	13	s.	s.	PROPN
ap-7684	399	14	tuxford	tuxford	PROPN
ap-7684	399	15	.	.	PUNCT
ap-7684	400	1	modelling	model	VERB
ap-7684	400	2	masonry	masonry	NOUN
ap-7684	400	3	arch	arch	ADJ
ap-7684	400	4	bridges	bridge	NOUN
ap-7684	400	5	using	use	VERB
ap-7684	400	6	commercial	commercial	ADJ
ap-7684	400	7	finite	finite	ADJ
ap-7684	400	8	element	element	NOUN
ap-7684	400	9	software	software	NOUN
ap-7684	400	10	.	.	PUNCT
ap-7684	401	1	in	in	ADP
ap-7684	401	2	proceeding	proceeding	NOUN
ap-7684	401	3	of	of	ADP
ap-7684	401	4	the	the	DET
ap-7684	401	5	9th	9th	ADJ
ap-7684	401	6	international	international	ADJ
ap-7684	401	7	conference	conference	NOUN
ap-7684	401	8	on	on	ADP
ap-7684	401	9	civil	civil	ADJ
ap-7684	401	10	and	and	CCONJ
ap-7684	401	11	structural	structural	ADJ
ap-7684	401	12	engineering	engineering	NOUN
ap-7684	401	13	computing	computing	NOUN
ap-7684	401	14	.	.	PUNCT
ap-7684	402	1	civil	civil	ADJ
ap-7684	402	2	-	-	PUNCT
ap-7684	402	3	comp	comp	NOUN
ap-7684	402	4	press	press	NOUN
ap-7684	402	5	,	,	PUNCT
ap-7684	402	6	stirling	stirling	NOUN
ap-7684	402	7	,	,	PUNCT
ap-7684	402	8	2001	2001	NUM
ap-7684	402	9	.	.	PUNCT
ap-7684	403	1	[	[	X
ap-7684	403	2	4	4	NUM
ap-7684	403	3	]	]	X
ap-7684	403	4	mott	mott	PROPN
ap-7684	403	5	-	-	PUNCT
ap-7684	403	6	macdonald	macdonald	PROPN
ap-7684	403	7	,	,	PUNCT
ap-7684	403	8	20	20	NUM
ap-7684	403	9	-	-	SYM
ap-7684	403	10	26	26	NUM
ap-7684	403	11	wellesley	wellesley	PROPN
ap-7684	403	12	road	road	PROPN
ap-7684	403	13	,	,	PUNCT
ap-7684	403	14	croydon	croydon	PROPN
ap-7684	403	15	,	,	PUNCT
ap-7684	403	16	cr9	cr9	PROPN
ap-7684	403	17	2ul	2ul	NOUN
ap-7684	403	18	,	,	PUNCT
ap-7684	403	19	uk	uk	PROPN
ap-7684	403	20	.	.	PROPN
ap-7684	403	21	ctap	ctap	ADJ
ap-7684	403	22	manual	manual	NOUN
ap-7684	403	23	for	for	ADP
ap-7684	403	24	the	the	DET
ap-7684	403	25	assessment	assessment	NOUN
ap-7684	403	26	of	of	ADP
ap-7684	403	27	masonry	masonry	NOUN
ap-7684	403	28	arch	arch	ADJ
ap-7684	403	29	bridges	bridge	NOUN
ap-7684	403	30	,	,	PUNCT
ap-7684	403	31	1990	1990	NUM
ap-7684	403	32	.	.	PUNCT
ap-7684	404	1	[	[	X
ap-7684	404	2	5	5	NUM
ap-7684	404	3	]	]	X
ap-7684	404	4	r.	r.	PROPN
ap-7684	404	5	bridle	bridle	PROPN
ap-7684	404	6	,	,	PUNCT
ap-7684	404	7	t.	t.	PROPN
ap-7684	404	8	hughes	hughes	PROPN
ap-7684	404	9	.	.	PUNCT
ap-7684	405	1	an	an	DET
ap-7684	405	2	energy	energy	NOUN
ap-7684	405	3	method	method	NOUN
ap-7684	405	4	for	for	ADP
ap-7684	405	5	arch	arch	ADJ
ap-7684	405	6	bridge	bridge	NOUN
ap-7684	405	7	analysis	analysis	NOUN
ap-7684	405	8	.	.	PUNCT
ap-7684	406	1	proceedings	proceeding	NOUN
ap-7684	406	2	of	of	ADP
ap-7684	406	3	the	the	DET
ap-7684	406	4	institution	institution	NOUN
ap-7684	406	5	of	of	ADP
ap-7684	406	6	civil	civil	ADJ
ap-7684	406	7	engineers	engineer	NOUN
ap-7684	406	8	89:375–385	89:375–385	NUM
ap-7684	406	9	,	,	PUNCT
ap-7684	406	10	1990	1990	NUM
ap-7684	406	11	.	.	PUNCT
ap-7684	407	1	https://doi.org/10.1680/iicep.1990.9397	https://doi.org/10.1680/iicep.1990.9397	X
ap-7684	407	2	.	.	PUNCT
ap-7684	408	1	[	[	X
ap-7684	408	2	6	6	NUM
ap-7684	408	3	]	]	PUNCT
ap-7684	408	4	m.	m.	PROPN
ap-7684	408	5	gilbert	gilbert	PROPN
ap-7684	408	6	.	.	PUNCT
ap-7684	409	1	ring	ring	NOUN
ap-7684	409	2	:	:	PUNCT
ap-7684	409	3	a	a	DET
ap-7684	409	4	2d	2d	NUM
ap-7684	409	5	rigid	rigid	ADJ
ap-7684	409	6	block	block	NOUN
ap-7684	409	7	analysis	analysis	NOUN
ap-7684	409	8	program	program	NOUN
ap-7684	409	9	for	for	ADP
ap-7684	409	10	masonry	masonry	NOUN
ap-7684	409	11	arch	arch	ADJ
ap-7684	409	12	bridges	bridge	NOUN
ap-7684	409	13	.	.	PUNCT
ap-7684	410	1	in	in	ADP
ap-7684	410	2	proceedings	proceeding	NOUN
ap-7684	410	3	of	of	ADP
ap-7684	410	4	the	the	DET
ap-7684	410	5	3rd	3rd	ADJ
ap-7684	410	6	international	international	ADJ
ap-7684	410	7	arch	arch	ADJ
ap-7684	410	8	bridges	bridge	NOUN
ap-7684	410	9	conference	conference	NOUN
ap-7684	410	10	,	,	PUNCT
ap-7684	410	11	pp	pp	ADJ
ap-7684	410	12	.	.	PUNCT
ap-7684	411	1	459–464	459–464	NUM
ap-7684	411	2	.	.	PUNCT
ap-7684	412	1	2001	2001	NUM
ap-7684	412	2	.	.	PUNCT
ap-7684	413	1	[	[	X
ap-7684	413	2	7	7	X
ap-7684	413	3	]	]	X
ap-7684	413	4	w.	w.	PROPN
ap-7684	413	5	harvey	harvey	PROPN
ap-7684	413	6	.	.	PUNCT
ap-7684	414	1	application	application	NOUN
ap-7684	414	2	of	of	ADP
ap-7684	414	3	the	the	DET
ap-7684	414	4	mechanism	mechanism	NOUN
ap-7684	414	5	analysis	analysis	NOUN
ap-7684	414	6	to	to	ADP
ap-7684	414	7	masonry	masonry	NOUN
ap-7684	414	8	arches	arch	NOUN
ap-7684	414	9	.	.	PUNCT
ap-7684	415	1	structural	structural	ADJ
ap-7684	415	2	engineer	engineer	NOUN
ap-7684	415	3	66:77–84	66:77–84	NOUN
ap-7684	415	4	,	,	PUNCT
ap-7684	415	5	1988	1988	NUM
ap-7684	415	6	.	.	PUNCT
ap-7684	416	1	[	[	X
ap-7684	416	2	8	8	NUM
ap-7684	416	3	]	]	PUNCT
ap-7684	416	4	p.-o	p.-o	NOUN
ap-7684	416	5	.	.	PUNCT
ap-7684	417	1	persson	persson	PROPN
ap-7684	417	2	,	,	PUNCT
ap-7684	417	3	g.	g.	PROPN
ap-7684	417	4	strang	strang	PROPN
ap-7684	417	5	.	.	PUNCT
ap-7684	418	1	simple	simple	ADJ
ap-7684	418	2	mesh	mesh	NOUN
ap-7684	418	3	generator	generator	NOUN
ap-7684	418	4	in	in	ADP
ap-7684	418	5	matlab	matlab	PROPN
ap-7684	418	6	.	.	PUNCT
ap-7684	419	1	siam	siam	PROPN
ap-7684	419	2	review	review	PROPN
ap-7684	419	3	46(2):329–345	46(2):329–345	PROPN
ap-7684	419	4	.	.	PUNCT
ap-7684	420	1	https://doi.org/10.1137/s0036144503429121	https://doi.org/10.1137/s0036144503429121	X
ap-7684	420	2	.	.	PUNCT
ap-7684	421	1	[	[	X
ap-7684	421	2	9	9	NUM
ap-7684	421	3	]	]	PUNCT
ap-7684	421	4	r.	r.	PROPN
ap-7684	421	5	d.	d.	PROPN
ap-7684	421	6	mindlin	mindlin	PROPN
ap-7684	421	7	.	.	PUNCT
ap-7684	422	1	influence	influence	NOUN
ap-7684	422	2	of	of	ADP
ap-7684	422	3	rotatory	rotatory	ADJ
ap-7684	422	4	inertia	inertia	NOUN
ap-7684	422	5	and	and	CCONJ
ap-7684	422	6	shear	shear	NOUN
ap-7684	422	7	on	on	ADP
ap-7684	422	8	flexural	flexural	ADJ
ap-7684	422	9	motions	motion	NOUN
ap-7684	422	10	of	of	ADP
ap-7684	422	11	isotropic	isotropic	NOUN
ap-7684	422	12	,	,	PUNCT
ap-7684	422	13	elastic	elastic	ADJ
ap-7684	422	14	plates	plate	NOUN
ap-7684	422	15	.	.	PUNCT
ap-7684	423	1	asme	asme	PROPN
ap-7684	423	2	journal	journal	PROPN
ap-7684	423	3	of	of	ADP
ap-7684	423	4	applied	apply	VERB
ap-7684	423	5	mechanics	mechanic	NOUN
ap-7684	423	6	18(1):31–38	18(1):31–38	NUM
ap-7684	423	7	,	,	PUNCT
ap-7684	423	8	1951	1951	NUM
ap-7684	423	9	.	.	PUNCT
ap-7684	424	1	https://doi.org/10.1115/1.4010217	https://doi.org/10.1115/1.4010217	X
ap-7684	424	2	.	.	PUNCT
ap-7684	425	1	[	[	X
ap-7684	425	2	10	10	NUM
ap-7684	425	3	]	]	PUNCT
ap-7684	425	4	a.	a.	NOUN
ap-7684	425	5	pipard	pipard	PROPN
ap-7684	425	6	,	,	PUNCT
ap-7684	425	7	r.	r.	PROPN
ap-7684	425	8	ashby	ashby	PROPN
ap-7684	425	9	.	.	PUNCT
ap-7684	426	1	an	an	DET
ap-7684	426	2	experimental	experimental	ADJ
ap-7684	426	3	study	study	NOUN
ap-7684	426	4	of	of	ADP
ap-7684	426	5	a	a	DET
ap-7684	426	6	voussoir	voussoir	NOUN
ap-7684	426	7	arch	arch	NOUN
ap-7684	426	8	.	.	PUNCT
ap-7684	427	1	proceedings	proceeding	NOUN
ap-7684	427	2	of	of	ADP
ap-7684	427	3	the	the	DET
ap-7684	427	4	institution	institution	NOUN
ap-7684	427	5	of	of	ADP
ap-7684	427	6	civil	civil	ADJ
ap-7684	427	7	engineers	engineer	NOUN
ap-7684	427	8	10:383	10:383	NUM
ap-7684	427	9	,	,	PUNCT
ap-7684	427	10	1938	1938	NUM
ap-7684	427	11	.	.	PUNCT
ap-7684	428	1	[	[	X
ap-7684	428	2	11	11	NUM
ap-7684	428	3	]	]	PUNCT
ap-7684	428	4	a.	a.	NOUN
ap-7684	428	5	j.	j.	PROPN
ap-7684	428	6	s.	s.	PROPN
ap-7684	428	7	pippard	pippard	PROPN
ap-7684	428	8	.	.	PUNCT
ap-7684	429	1	the	the	DET
ap-7684	429	2	civil	civil	ADJ
ap-7684	429	3	engineer	engineer	NOUN
ap-7684	429	4	in	in	ADP
ap-7684	429	5	war	war	NOUN
ap-7684	429	6	,	,	PUNCT
ap-7684	429	7	vol	vol	NOUN
ap-7684	429	8	.	.	PROPN
ap-7684	429	9	1	1	NUM
ap-7684	429	10	,	,	PUNCT
ap-7684	429	11	chap	chap	NOUN
ap-7684	429	12	.	.	PUNCT
ap-7684	430	1	the	the	DET
ap-7684	430	2	approximate	approximate	ADJ
ap-7684	430	3	estimation	estimation	NOUN
ap-7684	430	4	of	of	ADP
ap-7684	430	5	safe	safe	ADJ
ap-7684	430	6	loads	load	NOUN
ap-7684	430	7	on	on	ADP
ap-7684	430	8	masonry	masonry	NOUN
ap-7684	430	9	bridges	bridge	NOUN
ap-7684	430	10	.	.	PUNCT
ap-7684	430	11	,	,	PUNCT
ap-7684	430	12	pp	pp	ADP
ap-7684	430	13	.	.	PUNCT
ap-7684	431	1	365–372	365–372	NUM
ap-7684	431	2	.	.	NOUN
ap-7684	431	3	1948	1948	NUM
ap-7684	431	4	.	.	PUNCT
ap-7684	432	1	https://doi.org/10.1680/ciwv1.45170.0021	https://doi.org/10.1680/ciwv1.45170.0021	NOUN
ap-7684	432	2	.	.	PUNCT
ap-7684	433	1	[	[	X
ap-7684	433	2	12	12	NUM
ap-7684	433	3	]	]	X
ap-7684	433	4	g.	g.	PROPN
ap-7684	433	5	lindberg	lindberg	PROPN
ap-7684	433	6	,	,	PUNCT
ap-7684	433	7	m.	m.	PROPN
ap-7684	433	8	d.	d.	PROPN
ap-7684	433	9	olson	olson	PROPN
ap-7684	433	10	,	,	PUNCT
ap-7684	433	11	g.	g.	PROPN
ap-7684	433	12	r.	r.	PROPN
ap-7684	433	13	cowper	cowper	PROPN
ap-7684	433	14	.	.	PUNCT
ap-7684	434	1	new	new	ADJ
ap-7684	434	2	developments	development	NOUN
ap-7684	434	3	in	in	ADP
ap-7684	434	4	the	the	DET
ap-7684	434	5	finite	finite	ADJ
ap-7684	434	6	element	element	NOUN
ap-7684	434	7	analysis	analysis	NOUN
ap-7684	434	8	of	of	ADP
ap-7684	434	9	shells	shell	NOUN
ap-7684	434	10	,	,	PUNCT
ap-7684	434	11	1969	1969	NUM
ap-7684	434	12	.	.	PUNCT
ap-7684	435	1	https://apps.dtic.mil/sti/pdfs/ad0707780.pdf	https://apps.dtic.mil/sti/pdfs/ad0707780.pdf	ADJ
ap-7684	435	2	.	.	PUNCT
ap-7684	436	1	[	[	X
ap-7684	436	2	13	13	NUM
ap-7684	436	3	]	]	X
ap-7684	436	4	w.	w.	PROPN
ap-7684	436	5	flugge	flugge	PROPN
ap-7684	436	6	.	.	PUNCT
ap-7684	437	1	stresses	stress	NOUN
ap-7684	437	2	in	in	ADP
ap-7684	437	3	shells	shell	NOUN
ap-7684	437	4	.	.	PUNCT
ap-7684	438	1	springer	springer	NOUN
ap-7684	438	2	verlag	verlag	PROPN
ap-7684	438	3	,	,	PUNCT
ap-7684	438	4	1962	1962	NUM
ap-7684	438	5	.	.	PUNCT
ap-7684	439	1	302	302	NUM
ap-7684	439	2	https://doi.org/10.1680/iicep.1990.9397	https://doi.org/10.1680/iicep.1990.9397	PROPN
ap-7684	439	3	https://doi.org/10.1137/s0036144503429121	https://doi.org/10.1137/s0036144503429121	NUM
ap-7684	439	4	https://doi.org/10.1115/1.4010217	https://doi.org/10.1115/1.4010217	NOUN
ap-7684	439	5	https://doi.org/10.1680/ciwv1.45170.0021	https://doi.org/10.1680/ciwv1.45170.0021	NOUN
ap-7684	439	6	https://apps.dtic.mil/sti/pdfs/ad0707780.pdf	https://apps.dtic.mil/sti/pdfs/ad0707780.pdf	PROPN
ap-7684	439	7	acta	acta	PROPN
ap-7684	439	8	polytechnica	polytechnica	PROPN
ap-7684	439	9	62(2):293–302	62(2):293–302	PROPN
ap-7684	439	10	,	,	PUNCT
ap-7684	439	11	2022	2022	NUM
ap-7684	439	12	1	1	NUM
ap-7684	439	13	introduction	introduction	NOUN
ap-7684	439	14	2	2	NUM
ap-7684	439	15	the	the	DET
ap-7684	439	16	tt	tt	PROPN
ap-7684	439	17	element	element	NOUN
ap-7684	439	18	,	,	PUNCT
ap-7684	439	19	timoshenko	timoshenko	NOUN
ap-7684	439	20	beam	beam	NOUN
ap-7684	439	21	with	with	ADP
ap-7684	439	22	translational	translational	ADJ
ap-7684	439	23	dofs	dof	NOUN
ap-7684	439	24	2.1	2.1	NUM
ap-7684	439	25	constitutive	constitutive	ADJ
ap-7684	439	26	equations	equation	NOUN
ap-7684	439	27	for	for	ADP
ap-7684	439	28	bending	bend	VERB
ap-7684	439	29	2.2	2.2	NUM
ap-7684	439	30	full	full	ADJ
ap-7684	439	31	cross	cross	ADJ
ap-7684	439	32	-	-	ADJ
ap-7684	439	33	section	section	ADJ
ap-7684	439	34	stiffness	stiffness	NOUN
ap-7684	439	35	matrix	matrix	NOUN
ap-7684	439	36	2.3	2.3	NUM
ap-7684	439	37	arch	arch	ADJ
ap-7684	439	38	nodes	node	NOUN
ap-7684	439	39	equilibrium	equilibrium	NOUN
ap-7684	439	40	3	3	NUM
ap-7684	439	41	application	application	NOUN
ap-7684	439	42	to	to	ADP
ap-7684	439	43	an	an	DET
ap-7684	439	44	arch	arch	ADJ
ap-7684	439	45	bridge	bridge	NOUN
ap-7684	439	46	4	4	NUM
ap-7684	439	47	3d	3d	NUM
ap-7684	439	48	mindlin	mindlin	PROPN
ap-7684	439	49	shell	shell	PROPN
ap-7684	439	50	element	element	NOUN
ap-7684	439	51	tm	tm	ADP
ap-7684	439	52	4.1	4.1	NUM
ap-7684	439	53	bending	bending	NOUN
ap-7684	439	54	and	and	CCONJ
ap-7684	439	55	in	in	ADP
ap-7684	439	56	-	-	PUNCT
ap-7684	439	57	plane	plane	NOUN
ap-7684	439	58	deformation	deformation	NOUN
ap-7684	439	59	4.2	4.2	NUM
ap-7684	439	60	shear	shear	NOUN
ap-7684	439	61	owing	owe	VERB
ap-7684	439	62	to	to	ADP
ap-7684	439	63	the	the	DET
ap-7684	439	64	rotations	rotation	NOUN
ap-7684	439	65	of	of	ADP
ap-7684	439	66	normals	normal	NOUN
ap-7684	439	67	4.3	4.3	NUM
ap-7684	439	68	tm	tm	DET
ap-7684	439	69	flat	flat	ADJ
ap-7684	439	70	slab	slab	NOUN
ap-7684	439	71	element	element	NOUN
ap-7684	439	72	4.4	4.4	NUM
ap-7684	439	73	tm	tm	PROPN
ap-7684	439	74	shell	shell	PROPN
ap-7684	439	75	element	element	NOUN
ap-7684	439	76	4.5	4.5	NUM
ap-7684	439	77	tm	tm	PROPN
ap-7684	439	78	element	element	NOUN
ap-7684	439	79	code	code	NOUN
ap-7684	439	80	and	and	CCONJ
ap-7684	439	81	test	test	NOUN
ap-7684	439	82	5	5	NUM
ap-7684	439	83	conclusions	conclusion	NOUN
ap-7684	439	84	acknowledgements	acknowledgement	NOUN
ap-7684	439	85	references	reference	NOUN