id	sid	tid	token	lemma	pos
ap-6786	1	1	acta	acta	PROPN
ap-6786	1	2	polytechnica	polytechnica	PROPN
ap-6786	1	3	https://doi.org/10.14311/ap.2021.61.0242	https://doi.org/10.14311/ap.2021.61.0242	PROPN
ap-6786	1	4	acta	acta	PROPN
ap-6786	1	5	polytechnica	polytechnica	PROPN
ap-6786	1	6	61(1):242–252	61(1):242–252	PROPN
ap-6786	1	7	,	,	PUNCT
ap-6786	1	8	2021	2021	NUM
ap-6786	1	9	©	©	ADP
ap-6786	1	10	2021	2021	NUM
ap-6786	1	11	the	the	DET
ap-6786	1	12	author(s	author(s	NOUN
ap-6786	1	13	)	)	PUNCT
ap-6786	1	14	.	.	PUNCT
ap-6786	2	1	licensed	license	VERB
ap-6786	2	2	under	under	ADP
ap-6786	2	3	a	a	DET
ap-6786	2	4	cc	cc	NOUN
ap-6786	2	5	-	-	PUNCT
ap-6786	2	6	by	by	ADP
ap-6786	2	7	4.0	4.0	NUM
ap-6786	2	8	licence	licence	NOUN
ap-6786	2	9	published	publish	VERB
ap-6786	2	10	by	by	ADP
ap-6786	2	11	the	the	DET
ap-6786	2	12	czech	czech	PROPN
ap-6786	2	13	technical	technical	PROPN
ap-6786	2	14	university	university	PROPN
ap-6786	2	15	in	in	ADP
ap-6786	2	16	prague	prague	PROPN
ap-6786	2	17	application	application	NOUN
ap-6786	2	18	of	of	ADP
ap-6786	2	19	global	global	ADJ
ap-6786	2	20	optimization	optimization	NOUN
ap-6786	2	21	to	to	PART
ap-6786	2	22	predict	predict	VERB
ap-6786	2	23	strains	strain	NOUN
ap-6786	2	24	in	in	ADP
ap-6786	2	25	rc	rc	PROPN
ap-6786	2	26	compressed	compress	VERB
ap-6786	2	27	columns	column	NOUN
ap-6786	2	28	marek	marek	PROPN
ap-6786	2	29	lechmana,∗	lechmana,∗	PROPN
ap-6786	2	30	,	,	PUNCT
ap-6786	2	31	andrzej	andrzej	PROPN
ap-6786	2	32	stachurskib	stachurskib	VERB
ap-6786	2	33	a	a	DET
ap-6786	2	34	building	building	NOUN
ap-6786	2	35	research	research	NOUN
ap-6786	2	36	institute	institute	NOUN
ap-6786	2	37	,	,	PUNCT
ap-6786	2	38	filtrowa	filtrowa	NOUN
ap-6786	2	39	1	1	NUM
ap-6786	2	40	,	,	PUNCT
ap-6786	2	41	00	00	NUM
ap-6786	2	42	-	-	SYM
ap-6786	2	43	611	611	NUM
ap-6786	2	44	,	,	PUNCT
ap-6786	2	45	warsaw	warsaw	PROPN
ap-6786	2	46	,	,	PUNCT
ap-6786	2	47	poland	poland	PROPN
ap-6786	2	48	b	b	PROPN
ap-6786	2	49	warsaw	warsaw	PROPN
ap-6786	2	50	university	university	PROPN
ap-6786	2	51	of	of	ADP
ap-6786	2	52	technology	technology	PROPN
ap-6786	2	53	,	,	PUNCT
ap-6786	2	54	institute	institute	NOUN
ap-6786	2	55	of	of	ADP
ap-6786	2	56	control	control	PROPN
ap-6786	2	57	and	and	CCONJ
ap-6786	2	58	computation	computation	NOUN
ap-6786	2	59	engineering	engineering	NOUN
ap-6786	2	60	,	,	PUNCT
ap-6786	2	61	nowowiejska	nowowiejska	NOUN
ap-6786	2	62	15/19	15/19	NUM
ap-6786	2	63	,	,	PUNCT
ap-6786	2	64	00	00	NUM
ap-6786	2	65	-	-	SYM
ap-6786	2	66	665	665	NUM
ap-6786	2	67	warsaw	warsaw	NOUN
ap-6786	2	68	,	,	PUNCT
ap-6786	2	69	poland	poland	PROPN
ap-6786	2	70	∗	∗	NOUN
ap-6786	2	71	corresponding	correspond	VERB
ap-6786	2	72	author	author	NOUN
ap-6786	2	73	:	:	PUNCT
ap-6786	2	74	m.lechman@itb.pl	m.lechman@itb.pl	PROPN
ap-6786	2	75	abstract	abstract	NOUN
ap-6786	2	76	.	.	PUNCT
ap-6786	3	1	in	in	ADP
ap-6786	3	2	this	this	DET
ap-6786	3	3	paper	paper	NOUN
ap-6786	3	4	,	,	PUNCT
ap-6786	3	5	the	the	DET
ap-6786	3	6	results	result	NOUN
ap-6786	3	7	of	of	ADP
ap-6786	3	8	an	an	DET
ap-6786	3	9	application	application	NOUN
ap-6786	3	10	of	of	ADP
ap-6786	3	11	global	global	ADJ
ap-6786	3	12	and	and	CCONJ
ap-6786	3	13	local	local	ADJ
ap-6786	3	14	optimization	optimization	NOUN
ap-6786	3	15	methods	method	NOUN
ap-6786	3	16	to	to	PART
ap-6786	3	17	solve	solve	VERB
ap-6786	3	18	a	a	DET
ap-6786	3	19	problem	problem	NOUN
ap-6786	3	20	of	of	ADP
ap-6786	3	21	determination	determination	NOUN
ap-6786	3	22	of	of	ADP
ap-6786	3	23	strains	strain	NOUN
ap-6786	3	24	in	in	ADP
ap-6786	3	25	rc	rc	PROPN
ap-6786	3	26	compressed	compress	VERB
ap-6786	3	27	structure	structure	NOUN
ap-6786	3	28	members	member	NOUN
ap-6786	3	29	are	be	AUX
ap-6786	3	30	presented	present	VERB
ap-6786	3	31	.	.	PUNCT
ap-6786	4	1	solutions	solution	NOUN
ap-6786	4	2	of	of	ADP
ap-6786	4	3	appropriate	appropriate	ADJ
ap-6786	4	4	sets	set	NOUN
ap-6786	4	5	of	of	ADP
ap-6786	4	6	nonlinear	nonlinear	ADJ
ap-6786	4	7	equations	equation	NOUN
ap-6786	4	8	in	in	ADP
ap-6786	4	9	the	the	DET
ap-6786	4	10	presence	presence	NOUN
ap-6786	4	11	of	of	ADP
ap-6786	4	12	box	box	NOUN
ap-6786	4	13	constraints	constraint	NOUN
ap-6786	4	14	have	have	VERB
ap-6786	4	15	to	to	PART
ap-6786	4	16	be	be	AUX
ap-6786	4	17	found	find	VERB
ap-6786	4	18	.	.	PUNCT
ap-6786	5	1	the	the	DET
ap-6786	5	2	use	use	NOUN
ap-6786	5	3	of	of	ADP
ap-6786	5	4	the	the	DET
ap-6786	5	5	least	least	ADJ
ap-6786	5	6	squares	square	NOUN
ap-6786	5	7	method	method	NOUN
ap-6786	5	8	leads	lead	VERB
ap-6786	5	9	to	to	ADP
ap-6786	5	10	finding	find	VERB
ap-6786	5	11	global	global	ADJ
ap-6786	5	12	solutions	solution	NOUN
ap-6786	5	13	of	of	ADP
ap-6786	5	14	optimization	optimization	NOUN
ap-6786	5	15	problems	problem	NOUN
ap-6786	5	16	with	with	ADP
ap-6786	5	17	box	box	NOUN
ap-6786	5	18	constraints	constraint	NOUN
ap-6786	5	19	.	.	PUNCT
ap-6786	6	1	numerical	numerical	ADJ
ap-6786	6	2	examples	example	NOUN
ap-6786	6	3	illustrate	illustrate	VERB
ap-6786	6	4	the	the	DET
ap-6786	6	5	effects	effect	NOUN
ap-6786	6	6	of	of	ADP
ap-6786	6	7	the	the	DET
ap-6786	6	8	loading	loading	NOUN
ap-6786	6	9	value	value	NOUN
ap-6786	6	10	and	and	CCONJ
ap-6786	6	11	the	the	DET
ap-6786	6	12	loading	loading	NOUN
ap-6786	6	13	eccentricity	eccentricity	NOUN
ap-6786	6	14	on	on	ADP
ap-6786	6	15	the	the	DET
ap-6786	6	16	strains	strain	NOUN
ap-6786	6	17	in	in	ADP
ap-6786	6	18	concrete	concrete	ADJ
ap-6786	6	19	and	and	CCONJ
ap-6786	6	20	reinforcing	reinforce	VERB
ap-6786	6	21	steel	steel	NOUN
ap-6786	6	22	in	in	ADP
ap-6786	6	23	the	the	DET
ap-6786	6	24	cross	cross	NOUN
ap-6786	6	25	-	-	NOUN
ap-6786	6	26	section	section	NOUN
ap-6786	6	27	.	.	PUNCT
ap-6786	7	1	three	three	NUM
ap-6786	7	2	different	different	ADJ
ap-6786	7	3	minimization	minimization	NOUN
ap-6786	7	4	methods	method	NOUN
ap-6786	7	5	were	be	AUX
ap-6786	7	6	applied	apply	VERB
ap-6786	7	7	to	to	PART
ap-6786	7	8	compute	compute	VERB
ap-6786	7	9	them	they	PRON
ap-6786	7	10	:	:	PUNCT
ap-6786	7	11	trust	trust	NOUN
ap-6786	7	12	region	region	PROPN
ap-6786	7	13	reflective	reflective	ADJ
ap-6786	7	14	,	,	PUNCT
ap-6786	7	15	genetic	genetic	ADJ
ap-6786	7	16	algorithm	algorithm	NOUN
ap-6786	7	17	tailored	tailor	VERB
ap-6786	7	18	to	to	ADP
ap-6786	7	19	problems	problem	NOUN
ap-6786	7	20	with	with	ADP
ap-6786	7	21	real	real	ADJ
ap-6786	7	22	double	double	ADJ
ap-6786	7	23	variables	variable	NOUN
ap-6786	7	24	and	and	CCONJ
ap-6786	7	25	particle	particle	NOUN
ap-6786	7	26	swarm	swarm	NOUN
ap-6786	7	27	method	method	NOUN
ap-6786	7	28	.	.	PUNCT
ap-6786	8	1	numerical	numerical	ADJ
ap-6786	8	2	results	result	NOUN
ap-6786	8	3	on	on	ADP
ap-6786	8	4	practical	practical	ADJ
ap-6786	8	5	data	datum	NOUN
ap-6786	8	6	are	be	AUX
ap-6786	8	7	presented	present	VERB
ap-6786	8	8	.	.	PUNCT
ap-6786	9	1	in	in	ADP
ap-6786	9	2	some	some	DET
ap-6786	9	3	cases	case	NOUN
ap-6786	9	4	,	,	PUNCT
ap-6786	9	5	several	several	ADJ
ap-6786	9	6	solutions	solution	NOUN
ap-6786	9	7	were	be	AUX
ap-6786	9	8	found	find	VERB
ap-6786	9	9	.	.	PUNCT
ap-6786	10	1	their	their	PRON
ap-6786	10	2	existence	existence	NOUN
ap-6786	10	3	has	have	AUX
ap-6786	10	4	been	be	AUX
ap-6786	10	5	detected	detect	VERB
ap-6786	10	6	by	by	ADP
ap-6786	10	7	the	the	DET
ap-6786	10	8	local	local	ADJ
ap-6786	10	9	search	search	NOUN
ap-6786	10	10	with	with	ADP
ap-6786	10	11	multistart	multistart	NOUN
ap-6786	10	12	,	,	PUNCT
ap-6786	10	13	while	while	SCONJ
ap-6786	10	14	the	the	DET
ap-6786	10	15	genetic	genetic	ADJ
ap-6786	10	16	and	and	CCONJ
ap-6786	10	17	particle	particle	NOUN
ap-6786	10	18	swarm	swarm	NOUN
ap-6786	10	19	methods	method	NOUN
ap-6786	10	20	failed	fail	VERB
ap-6786	10	21	to	to	PART
ap-6786	10	22	recognize	recognize	VERB
ap-6786	10	23	their	their	PRON
ap-6786	10	24	presence	presence	NOUN
ap-6786	10	25	.	.	PUNCT
ap-6786	11	1	keywords	keyword	NOUN
ap-6786	11	2	:	:	PUNCT
ap-6786	11	3	global	global	ADJ
ap-6786	11	4	optimization	optimization	NOUN
ap-6786	11	5	,	,	PUNCT
ap-6786	11	6	nonlinear	nonlinear	ADJ
ap-6786	11	7	equations	equation	NOUN
ap-6786	11	8	,	,	PUNCT
ap-6786	11	9	least	least	ADJ
ap-6786	11	10	squares	square	NOUN
ap-6786	11	11	method	method	NOUN
ap-6786	11	12	,	,	PUNCT
ap-6786	11	13	rc	rc	PROPN
ap-6786	11	14	compressed	compress	VERB
ap-6786	11	15	structure	structure	NOUN
ap-6786	11	16	members	member	NOUN
ap-6786	11	17	.	.	PUNCT
ap-6786	12	1	1	1	X
ap-6786	12	2	.	.	X
ap-6786	12	3	introduction	introduction	NOUN
ap-6786	12	4	our	our	PRON
ap-6786	12	5	problem	problem	NOUN
ap-6786	12	6	is	be	AUX
ap-6786	12	7	to	to	PART
ap-6786	12	8	determine	determine	VERB
ap-6786	12	9	the	the	DET
ap-6786	12	10	normal	normal	ADJ
ap-6786	12	11	strains	strain	NOUN
ap-6786	12	12	in	in	ADP
ap-6786	12	13	the	the	DET
ap-6786	12	14	cross	cross	NOUN
ap-6786	12	15	-	-	NOUN
ap-6786	12	16	sections	section	NOUN
ap-6786	12	17	of	of	ADP
ap-6786	12	18	reinforced	reinforce	VERB
ap-6786	12	19	concrete	concrete	ADJ
ap-6786	12	20	structure	structure	NOUN
ap-6786	12	21	members	member	NOUN
ap-6786	12	22	subjected	subject	VERB
ap-6786	12	23	to	to	ADP
ap-6786	12	24	compression	compression	NOUN
ap-6786	12	25	.	.	PUNCT
ap-6786	13	1	mathematically	mathematically	ADV
ap-6786	13	2	,	,	PUNCT
ap-6786	13	3	it	it	PRON
ap-6786	13	4	may	may	AUX
ap-6786	13	5	be	be	AUX
ap-6786	13	6	formulated	formulate	VERB
ap-6786	13	7	as	as	ADP
ap-6786	13	8	a	a	DET
ap-6786	13	9	task	task	NOUN
ap-6786	13	10	of	of	ADP
ap-6786	13	11	solving	solve	VERB
ap-6786	13	12	sets	set	NOUN
ap-6786	13	13	of	of	ADP
ap-6786	13	14	equations	equation	NOUN
ap-6786	13	15	with	with	ADP
ap-6786	13	16	box	box	NOUN
ap-6786	13	17	constraints	constraint	NOUN
ap-6786	13	18	.	.	PUNCT
ap-6786	14	1	the	the	DET
ap-6786	14	2	unknown	unknown	ADJ
ap-6786	14	3	variables	variable	NOUN
ap-6786	14	4	are	be	AUX
ap-6786	14	5	:	:	PUNCT
ap-6786	14	6	ε′	ε′	X
ap-6786	14	7	–	–	PUNCT
ap-6786	14	8	maximum	maximum	ADJ
ap-6786	14	9	strain	strain	NOUN
ap-6786	14	10	in	in	ADP
ap-6786	14	11	the	the	DET
ap-6786	14	12	cross	cross	NOUN
ap-6786	14	13	section	section	NOUN
ap-6786	14	14	and	and	CCONJ
ap-6786	14	15	ξ	ξ	PROPN
ap-6786	14	16	–	–	PUNCT
ap-6786	14	17	coordinate	coordinate	NOUN
ap-6786	14	18	describing	describe	VERB
ap-6786	14	19	the	the	DET
ap-6786	14	20	location	location	NOUN
ap-6786	14	21	of	of	ADP
ap-6786	14	22	the	the	DET
ap-6786	14	23	neutral	neutral	ADJ
ap-6786	14	24	axis	axis	NOUN
ap-6786	14	25	.	.	PUNCT
ap-6786	15	1	the	the	DET
ap-6786	15	2	presence	presence	NOUN
ap-6786	15	3	of	of	ADP
ap-6786	15	4	the	the	DET
ap-6786	15	5	box	box	NOUN
ap-6786	15	6	constraints	constraint	NOUN
ap-6786	15	7	makes	make	VERB
ap-6786	15	8	a	a	DET
ap-6786	15	9	direct	direct	ADJ
ap-6786	15	10	use	use	NOUN
ap-6786	15	11	of	of	ADP
ap-6786	15	12	numerical	numerical	ADJ
ap-6786	15	13	methods	method	NOUN
ap-6786	15	14	for	for	ADP
ap-6786	15	15	solving	solve	VERB
ap-6786	15	16	sets	set	NOUN
ap-6786	15	17	of	of	ADP
ap-6786	15	18	nonlinear	nonlinear	ADJ
ap-6786	15	19	equations	equation	NOUN
ap-6786	15	20	impractical	impractical	ADJ
ap-6786	15	21	.	.	PUNCT
ap-6786	16	1	therefore	therefore	ADV
ap-6786	16	2	,	,	PUNCT
ap-6786	16	3	our	our	PRON
ap-6786	16	4	task	task	NOUN
ap-6786	16	5	is	be	AUX
ap-6786	16	6	reformulated	reformulate	VERB
ap-6786	16	7	by	by	ADP
ap-6786	16	8	means	mean	NOUN
ap-6786	16	9	of	of	ADP
ap-6786	16	10	the	the	DET
ap-6786	16	11	frequently	frequently	ADV
ap-6786	16	12	used	use	VERB
ap-6786	16	13	least	least	ADJ
ap-6786	16	14	squares	square	NOUN
ap-6786	16	15	method	method	NOUN
ap-6786	16	16	.	.	PUNCT
ap-6786	17	1	it	it	PRON
ap-6786	17	2	leads	lead	VERB
ap-6786	17	3	to	to	ADP
ap-6786	17	4	a	a	DET
ap-6786	17	5	nonlinear	nonlinear	ADJ
ap-6786	17	6	,	,	PUNCT
ap-6786	17	7	nonconvex	nonconvex	NOUN
ap-6786	17	8	optimization	optimization	NOUN
ap-6786	17	9	problem	problem	NOUN
ap-6786	17	10	of	of	ADP
ap-6786	17	11	finding	find	VERB
ap-6786	17	12	a	a	DET
ap-6786	17	13	minimum	minimum	NOUN
ap-6786	17	14	of	of	ADP
ap-6786	17	15	a	a	DET
ap-6786	17	16	nonlinear	nonlinear	ADJ
ap-6786	17	17	function	function	NOUN
ap-6786	17	18	with	with	ADP
ap-6786	17	19	the	the	DET
ap-6786	17	20	restricted	restricted	ADJ
ap-6786	17	21	scope	scope	NOUN
ap-6786	17	22	of	of	ADP
ap-6786	17	23	variables	variable	NOUN
ap-6786	17	24	.	.	PUNCT
ap-6786	18	1	1.1	1.1	NUM
ap-6786	18	2	.	.	PUNCT
ap-6786	18	3	motivation	motivation	NOUN
ap-6786	18	4	to	to	PART
ap-6786	18	5	study	study	VERB
ap-6786	18	6	the	the	DET
ap-6786	18	7	strains	strain	NOUN
ap-6786	18	8	in	in	ADP
ap-6786	18	9	rc	rc	PROPN
ap-6786	18	10	compressed	compress	VERB
ap-6786	18	11	structure	structure	NOUN
ap-6786	18	12	members	member	NOUN
ap-6786	18	13	reinforced	reinforce	VERB
ap-6786	18	14	concrete	concrete	ADJ
ap-6786	18	15	structure	structure	NOUN
ap-6786	18	16	members	member	NOUN
ap-6786	18	17	subjected	subject	VERB
ap-6786	18	18	to	to	ADP
ap-6786	18	19	the	the	DET
ap-6786	18	20	compression	compression	NOUN
ap-6786	18	21	are	be	AUX
ap-6786	18	22	frequently	frequently	ADV
ap-6786	18	23	encountered	encounter	VERB
ap-6786	18	24	in	in	ADP
ap-6786	18	25	the	the	DET
ap-6786	18	26	engineering	engineering	NOUN
ap-6786	18	27	practice	practice	NOUN
ap-6786	18	28	(	(	PUNCT
ap-6786	18	29	columns	column	NOUN
ap-6786	18	30	,	,	PUNCT
ap-6786	18	31	pillars	pillar	NOUN
ap-6786	18	32	,	,	PUNCT
ap-6786	18	33	tower	tower	NOUN
ap-6786	18	34	-	-	PUNCT
ap-6786	18	35	like	like	ADJ
ap-6786	18	36	structures	structure	NOUN
ap-6786	18	37	etc	etc	X
ap-6786	18	38	.	.	PUNCT
ap-6786	18	39	)	)	PUNCT
ap-6786	18	40	.	.	PUNCT
ap-6786	19	1	the	the	DET
ap-6786	19	2	determination	determination	NOUN
ap-6786	19	3	of	of	ADP
ap-6786	19	4	strains	strain	NOUN
ap-6786	19	5	is	be	AUX
ap-6786	19	6	very	very	ADV
ap-6786	19	7	important	important	ADJ
ap-6786	19	8	in	in	ADP
ap-6786	19	9	the	the	DET
ap-6786	19	10	safety	safety	NOUN
ap-6786	19	11	assessment	assessment	NOUN
ap-6786	19	12	of	of	ADP
ap-6786	19	13	existing	exist	VERB
ap-6786	19	14	rc	rc	PROPN
ap-6786	19	15	structures	structure	NOUN
ap-6786	19	16	.	.	PUNCT
ap-6786	20	1	in	in	ADP
ap-6786	20	2	order	order	NOUN
ap-6786	20	3	to	to	PART
ap-6786	20	4	solve	solve	VERB
ap-6786	20	5	this	this	DET
ap-6786	20	6	problem	problem	NOUN
ap-6786	20	7	analytically	analytically	ADV
ap-6786	20	8	,	,	PUNCT
ap-6786	20	9	several	several	ADJ
ap-6786	20	10	physical	physical	ADJ
ap-6786	20	11	models	model	NOUN
ap-6786	20	12	of	of	ADP
ap-6786	20	13	materials	material	NOUN
ap-6786	20	14	and	and	CCONJ
ap-6786	20	15	methods	method	NOUN
ap-6786	20	16	were	be	AUX
ap-6786	20	17	proposed	propose	VERB
ap-6786	20	18	.	.	PUNCT
ap-6786	21	1	lechman	lechman	NOUN
ap-6786	21	2	and	and	CCONJ
ap-6786	21	3	lewiński	lewiński	NOUN
ap-6786	21	4	[	[	X
ap-6786	21	5	1	1	X
ap-6786	21	6	]	]	PUNCT
ap-6786	21	7	considered	consider	VERB
ap-6786	21	8	a	a	DET
ap-6786	21	9	generalized	generalized	ADJ
ap-6786	21	10	linear	linear	NOUN
ap-6786	21	11	section	section	NOUN
ap-6786	21	12	model	model	NOUN
ap-6786	21	13	.	.	PUNCT
ap-6786	22	1	a	a	DET
ap-6786	22	2	simplified	simplified	ADJ
ap-6786	22	3	approach	approach	NOUN
ap-6786	22	4	based	base	VERB
ap-6786	22	5	on	on	ADP
ap-6786	22	6	the	the	DET
ap-6786	22	7	rectangular	rectangular	ADJ
ap-6786	22	8	stress	stress	NOUN
ap-6786	22	9	distribution	distribution	NOUN
ap-6786	22	10	for	for	ADP
ap-6786	22	11	concrete	concrete	NOUN
ap-6786	22	12	was	be	AUX
ap-6786	22	13	used	use	VERB
ap-6786	22	14	by	by	ADP
ap-6786	22	15	knauff	knauff	PROPN
ap-6786	23	1	[	[	X
ap-6786	23	2	2	2	NUM
ap-6786	23	3	]	]	PUNCT
ap-6786	23	4	and	and	CCONJ
ap-6786	23	5	knauff	knauff	PROPN
ap-6786	23	6	et	et	PROPN
ap-6786	23	7	al	al	PROPN
ap-6786	23	8	.	.	PUNCT
ap-6786	24	1	[	[	X
ap-6786	24	2	3	3	NUM
ap-6786	24	3	]	]	PUNCT
ap-6786	24	4	.	.	PUNCT
ap-6786	25	1	nieser	nieser	PROPN
ap-6786	25	2	and	and	CCONJ
ap-6786	25	3	engel	engel	PROPN
ap-6786	26	1	[	[	X
ap-6786	26	2	4	4	NUM
ap-6786	26	3	]	]	PUNCT
ap-6786	26	4	and	and	CCONJ
ap-6786	26	5	cicind	cicind	NOUN
ap-6786	26	6	[	[	X
ap-6786	26	7	5	5	NUM
ap-6786	26	8	]	]	PUNCT
ap-6786	26	9	applied	apply	VERB
ap-6786	26	10	the	the	DET
ap-6786	26	11	parabola	parabola	ADJ
ap-6786	26	12	-	-	PUNCT
ap-6786	26	13	rectangle	rectangle	NOUN
ap-6786	26	14	diagram	diagram	NOUN
ap-6786	26	15	for	for	ADP
ap-6786	26	16	the	the	DET
ap-6786	26	17	design	design	NOUN
ap-6786	26	18	of	of	ADP
ap-6786	26	19	cross	cross	NOUN
ap-6786	26	20	-	-	NOUN
ap-6786	26	21	sections	section	NOUN
ap-6786	26	22	.	.	PUNCT
ap-6786	27	1	for	for	ADP
ap-6786	27	2	reinforcing	reinforce	VERB
ap-6786	27	3	steel	steel	NOUN
ap-6786	27	4	itself	itself	PRON
ap-6786	27	5	,	,	PUNCT
ap-6786	27	6	both	both	CCONJ
ap-6786	27	7	linear	linear	ADJ
ap-6786	27	8	and	and	CCONJ
ap-6786	27	9	nonlinear	nonlinear	ADJ
ap-6786	27	10	models	model	NOUN
ap-6786	27	11	are	be	AUX
ap-6786	27	12	used	use	VERB
ap-6786	27	13	,	,	PUNCT
ap-6786	27	14	see	see	VERB
ap-6786	27	15	for	for	ADP
ap-6786	27	16	instance	instance	NOUN
ap-6786	27	17	lechman	lechman	NOUN
ap-6786	27	18	and	and	CCONJ
ap-6786	27	19	stachurski	stachurski	VERB
ap-6786	27	20	[	[	PUNCT
ap-6786	27	21	6	6	NUM
ap-6786	27	22	]	]	PUNCT
ap-6786	27	23	,	,	PUNCT
ap-6786	27	24	lechman	lechman	PROPN
ap-6786	28	1	[	[	X
ap-6786	28	2	7–10	7–10	X
ap-6786	28	3	]	]	X
ap-6786	28	4	,	,	PUNCT
ap-6786	28	5	where	where	SCONJ
ap-6786	28	6	the	the	DET
ap-6786	28	7	ring	ring	NOUN
ap-6786	28	8	sections	section	NOUN
ap-6786	28	9	were	be	AUX
ap-6786	28	10	investigated	investigate	VERB
ap-6786	28	11	.	.	PUNCT
ap-6786	29	1	the	the	DET
ap-6786	29	2	results	result	NOUN
ap-6786	29	3	of	of	ADP
ap-6786	29	4	fe	fe	X
ap-6786	29	5	(	(	PUNCT
ap-6786	29	6	finite	finite	PROPN
ap-6786	29	7	element	element	NOUN
ap-6786	29	8	)	)	PUNCT
ap-6786	29	9	modelling	modelling	NOUN
ap-6786	29	10	of	of	ADP
ap-6786	29	11	failure	failure	NOUN
ap-6786	29	12	behaviour	behaviour	NOUN
ap-6786	29	13	of	of	ADP
ap-6786	29	14	rc	rc	PROPN
ap-6786	29	15	compressed	compress	VERB
ap-6786	29	16	columns	column	NOUN
ap-6786	29	17	were	be	AUX
ap-6786	29	18	presented	present	VERB
ap-6786	29	19	by	by	ADP
ap-6786	29	20	majewski	majewski	PROPN
ap-6786	29	21	et	et	PROPN
ap-6786	29	22	al	al	PROPN
ap-6786	29	23	.	.	PUNCT
ap-6786	30	1	[	[	X
ap-6786	30	2	11	11	NUM
ap-6786	30	3	]	]	PUNCT
ap-6786	30	4	and	and	CCONJ
ap-6786	30	5	rodriguez	rodriguez	PROPN
ap-6786	30	6	et	et	PROPN
ap-6786	30	7	al	al	PROPN
ap-6786	30	8	.	.	PUNCT
ap-6786	31	1	[	[	X
ap-6786	31	2	12	12	NUM
ap-6786	31	3	]	]	PUNCT
ap-6786	31	4	.	.	PUNCT
ap-6786	32	1	in	in	ADP
ap-6786	32	2	kim	kim	PROPN
ap-6786	32	3	and	and	CCONJ
ap-6786	32	4	lee	lee	PROPN
ap-6786	33	1	[	[	X
ap-6786	33	2	13	13	NUM
ap-6786	33	3	]	]	PUNCT
ap-6786	33	4	,	,	PUNCT
ap-6786	33	5	a	a	DET
ap-6786	33	6	numerical	numerical	ADJ
ap-6786	33	7	method	method	NOUN
ap-6786	33	8	for	for	ADP
ap-6786	33	9	predicting	predict	VERB
ap-6786	33	10	the	the	DET
ap-6786	33	11	behaviour	behaviour	NOUN
ap-6786	33	12	of	of	ADP
ap-6786	33	13	rc	rc	PROPN
ap-6786	33	14	columns	column	NOUN
ap-6786	33	15	subjected	subject	VERB
ap-6786	33	16	to	to	ADP
ap-6786	33	17	axial	axial	ADJ
ap-6786	33	18	force	force	NOUN
ap-6786	33	19	and	and	CCONJ
ap-6786	33	20	biaxial	biaxial	ADJ
ap-6786	33	21	bending	bending	NOUN
ap-6786	33	22	is	be	AUX
ap-6786	33	23	proposed	propose	VERB
ap-6786	33	24	and	and	CCONJ
ap-6786	33	25	verified	verify	VERB
ap-6786	33	26	in	in	ADP
ap-6786	33	27	tests	test	NOUN
ap-6786	33	28	.	.	PUNCT
ap-6786	34	1	campione	campione	NOUN
ap-6786	34	2	et	et	PROPN
ap-6786	34	3	al	al	PROPN
ap-6786	34	4	.	.	PUNCT
ap-6786	35	1	[	[	X
ap-6786	35	2	14	14	NUM
ap-6786	35	3	]	]	PUNCT
ap-6786	35	4	experimentally	experimentally	ADV
ap-6786	35	5	investigated	investigate	VERB
ap-6786	35	6	the	the	DET
ap-6786	35	7	behaviour	behaviour	NOUN
ap-6786	35	8	of	of	ADP
ap-6786	35	9	compressed	compressed	ADJ
ap-6786	35	10	concrete	concrete	ADJ
ap-6786	35	11	columns	column	NOUN
ap-6786	35	12	subjected	subject	VERB
ap-6786	35	13	to	to	ADP
ap-6786	35	14	the	the	DET
ap-6786	35	15	overcoring	overcoring	NOUN
ap-6786	35	16	technique	technique	NOUN
ap-6786	35	17	,	,	PUNCT
ap-6786	35	18	see	see	VERB
ap-6786	35	19	also	also	ADV
ap-6786	35	20	campione	campione	VERB
ap-6786	35	21	et	et	PROPN
ap-6786	35	22	al	al	PROPN
ap-6786	35	23	.	.	PUNCT
ap-6786	36	1	[	[	X
ap-6786	36	2	15	15	NUM
ap-6786	36	3	]	]	PUNCT
ap-6786	36	4	.	.	PUNCT
ap-6786	37	1	the	the	DET
ap-6786	37	2	list	list	NOUN
ap-6786	37	3	of	of	ADP
ap-6786	37	4	researchers	researcher	NOUN
ap-6786	37	5	working	work	VERB
ap-6786	37	6	in	in	ADP
ap-6786	37	7	various	various	ADJ
ap-6786	37	8	directions	direction	NOUN
ap-6786	37	9	could	could	AUX
ap-6786	37	10	be	be	AUX
ap-6786	37	11	continued	continue	VERB
ap-6786	37	12	.	.	PUNCT
ap-6786	38	1	let	let	VERB
ap-6786	38	2	’s	’s	NOUN
ap-6786	38	3	mention	mention	VERB
ap-6786	38	4	some	some	PRON
ap-6786	38	5	of	of	ADP
ap-6786	38	6	them	they	PRON
ap-6786	38	7	:	:	PUNCT
ap-6786	39	1	lloyd	lloyd	PROPN
ap-6786	39	2	and	and	CCONJ
ap-6786	39	3	rangan	rangan	VERB
ap-6786	39	4	[	[	X
ap-6786	39	5	16	16	NUM
ap-6786	39	6	]	]	PUNCT
ap-6786	39	7	,	,	PUNCT
ap-6786	39	8	bonet	bonet	PROPN
ap-6786	39	9	et	et	PROPN
ap-6786	39	10	al	al	PROPN
ap-6786	39	11	.	.	PUNCT
ap-6786	40	1	[	[	X
ap-6786	40	2	17	17	NUM
ap-6786	40	3	]	]	PUNCT
ap-6786	40	4	,	,	PUNCT
ap-6786	40	5	ye	ye	PRON
ap-6786	40	6	et	et	NOUN
ap-6786	40	7	al	al	PROPN
ap-6786	40	8	.	.	PUNCT
ap-6786	41	1	[	[	X
ap-6786	41	2	18	18	NUM
ap-6786	41	3	]	]	PUNCT
ap-6786	41	4	,	,	PUNCT
ap-6786	41	5	xu	xu	PROPN
ap-6786	41	6	et	et	PROPN
ap-6786	41	7	al	al	PROPN
ap-6786	41	8	.	.	PUNCT
ap-6786	42	1	[	[	X
ap-6786	42	2	19	19	NUM
ap-6786	42	3	]	]	PUNCT
ap-6786	42	4	,	,	PUNCT
ap-6786	42	5	trapko	trapko	PROPN
ap-6786	42	6	and	and	CCONJ
ap-6786	42	7	musiał	musiał	PROPN
ap-6786	42	8	[	[	X
ap-6786	42	9	20	20	NUM
ap-6786	42	10	]	]	PUNCT
ap-6786	42	11	,	,	PUNCT
ap-6786	42	12	trapko	trapko	PROPN
ap-6786	43	1	[	[	X
ap-6786	43	2	21	21	NUM
ap-6786	43	3	]	]	PUNCT
ap-6786	43	4	,	,	PUNCT
ap-6786	43	5	hadi	hadi	NOUN
ap-6786	43	6	and	and	CCONJ
ap-6786	43	7	le	le	X
ap-6786	44	1	[	[	X
ap-6786	44	2	22	22	NUM
ap-6786	44	3	]	]	PUNCT
ap-6786	44	4	,	,	PUNCT
ap-6786	44	5	el	el	PROPN
ap-6786	44	6	maddawy	maddawy	PROPN
ap-6786	44	7	et	et	PROPN
ap-6786	44	8	al	al	PROPN
ap-6786	44	9	.	.	PUNCT
ap-6786	45	1	[	[	X
ap-6786	45	2	23	23	NUM
ap-6786	45	3	]	]	PUNCT
ap-6786	45	4	,	,	PUNCT
ap-6786	45	5	csuka	csuka	PROPN
ap-6786	45	6	and	and	CCONJ
ap-6786	45	7	kollar	kollar	ADJ
ap-6786	46	1	[	[	X
ap-6786	46	2	24	24	NUM
ap-6786	46	3	]	]	PUNCT
ap-6786	46	4	,	,	PUNCT
ap-6786	46	5	elwan	elwan	PROPN
ap-6786	47	1	and	and	CCONJ
ap-6786	47	2	rashed	rashe	VERB
ap-6786	48	1	[	[	X
ap-6786	48	2	25	25	NUM
ap-6786	48	3	]	]	PUNCT
ap-6786	48	4	,	,	PUNCT
ap-6786	48	5	sadeghian	sadeghian	PROPN
ap-6786	48	6	et	et	PROPN
ap-6786	48	7	al	al	PROPN
ap-6786	48	8	.	.	PUNCT
ap-6786	49	1	[	[	X
ap-6786	49	2	26	26	NUM
ap-6786	49	3	]	]	PUNCT
ap-6786	49	4	,	,	PUNCT
ap-6786	49	5	eid	eid	NOUN
ap-6786	49	6	and	and	CCONJ
ap-6786	49	7	paultre	paultre	NOUN
ap-6786	49	8	[	[	X
ap-6786	49	9	27	27	NUM
ap-6786	49	10	]	]	PUNCT
ap-6786	49	11	,	,	PUNCT
ap-6786	49	12	wu	wu	PROPN
ap-6786	49	13	and	and	CCONJ
ap-6786	49	14	jiang	jiang	PROPN
ap-6786	50	1	[	[	X
ap-6786	50	2	28	28	NUM
ap-6786	50	3	]	]	PUNCT
ap-6786	50	4	,	,	PUNCT
ap-6786	50	5	quiertant	quiertant	NOUN
ap-6786	50	6	and	and	CCONJ
ap-6786	50	7	clement	clement	NOUN
ap-6786	51	1	[	[	X
ap-6786	51	2	29	29	NUM
ap-6786	51	3	]	]	PUNCT
ap-6786	51	4	,	,	PUNCT
ap-6786	51	5	lee	lee	PROPN
ap-6786	51	6	et	et	PROPN
ap-6786	51	7	al	al	PROPN
ap-6786	51	8	.	.	PUNCT
ap-6786	52	1	[	[	X
ap-6786	52	2	30	30	NUM
ap-6786	52	3	]	]	PUNCT
ap-6786	52	4	,	,	PUNCT
ap-6786	52	5	kumar	kumar	PROPN
ap-6786	52	6	and	and	CCONJ
ap-6786	52	7	patel	patel	PROPN
ap-6786	53	1	[	[	X
ap-6786	53	2	31	31	NUM
ap-6786	53	3	]	]	PUNCT
ap-6786	53	4	and	and	CCONJ
ap-6786	53	5	many	many	ADJ
ap-6786	53	6	others	other	NOUN
ap-6786	53	7	.	.	PUNCT
ap-6786	54	1	of	of	ADP
ap-6786	54	2	course	course	ADV
ap-6786	54	3	,	,	PUNCT
ap-6786	54	4	the	the	DET
ap-6786	54	5	list	list	NOUN
ap-6786	54	6	is	be	AUX
ap-6786	54	7	not	not	PART
ap-6786	54	8	complete	complete	ADJ
ap-6786	54	9	.	.	PUNCT
ap-6786	55	1	despite	despite	SCONJ
ap-6786	55	2	the	the	DET
ap-6786	55	3	variety	variety	NOUN
ap-6786	55	4	of	of	ADP
ap-6786	55	5	calculation	calculation	NOUN
ap-6786	55	6	methods	method	NOUN
ap-6786	55	7	and	and	CCONJ
ap-6786	55	8	experimental	experimental	ADJ
ap-6786	55	9	investigations	investigation	NOUN
ap-6786	55	10	concerning	concern	VERB
ap-6786	55	11	this	this	DET
ap-6786	55	12	problem	problem	NOUN
ap-6786	55	13	,	,	PUNCT
ap-6786	55	14	there	there	PRON
ap-6786	55	15	are	be	VERB
ap-6786	55	16	not	not	PART
ap-6786	55	17	any	any	DET
ap-6786	55	18	appropriate	appropriate	ADJ
ap-6786	55	19	analytical	analytical	ADJ
ap-6786	55	20	solutions	solution	NOUN
ap-6786	55	21	based	base	VERB
ap-6786	55	22	on	on	ADP
ap-6786	55	23	the	the	DET
ap-6786	55	24	nonlinear	nonlinear	ADJ
ap-6786	55	25	material	material	NOUN
ap-6786	55	26	laws	law	NOUN
ap-6786	55	27	for	for	ADP
ap-6786	55	28	determining	determine	VERB
ap-6786	55	29	the	the	DET
ap-6786	55	30	strains	strain	NOUN
ap-6786	55	31	in	in	ADP
ap-6786	55	32	rc	rc	PROPN
ap-6786	55	33	externally	externally	ADV
ap-6786	55	34	compressed	compress	VERB
ap-6786	55	35	structure	structure	NOUN
ap-6786	55	36	members	member	NOUN
ap-6786	55	37	that	that	PRON
ap-6786	55	38	considers	consider	VERB
ap-6786	55	39	concrete	concrete	ADJ
ap-6786	55	40	softening	softening	NOUN
ap-6786	55	41	.	.	PUNCT
ap-6786	56	1	the	the	DET
ap-6786	56	2	aim	aim	NOUN
ap-6786	56	3	of	of	ADP
ap-6786	56	4	our	our	PRON
ap-6786	56	5	paper	paper	NOUN
ap-6786	56	6	is	be	AUX
ap-6786	56	7	twofold	twofold	ADV
ap-6786	56	8	.	.	PUNCT
ap-6786	57	1	firstly	firstly	ADV
ap-6786	57	2	,	,	PUNCT
ap-6786	57	3	to	to	PART
ap-6786	57	4	formulate	formulate	VERB
ap-6786	57	5	equilibrium	equilibrium	NOUN
ap-6786	57	6	equations	equation	NOUN
ap-6786	57	7	allowing	allow	VERB
ap-6786	57	8	to	to	PART
ap-6786	57	9	calculate	calculate	VERB
ap-6786	57	10	the	the	DET
ap-6786	57	11	strains	strain	NOUN
ap-6786	57	12	.	.	PUNCT
ap-6786	58	1	secondly	secondly	ADV
ap-6786	58	2	,	,	PUNCT
ap-6786	58	3	to	to	PART
ap-6786	58	4	investigate	investigate	VERB
ap-6786	58	5	the	the	DET
ap-6786	58	6	usefulness	usefulness	NOUN
ap-6786	58	7	of	of	ADP
ap-6786	58	8	some	some	DET
ap-6786	58	9	242	242	NUM
ap-6786	58	10	https://doi.org/10.14311/ap.2021.61.0242	https://doi.org/10.14311/ap.2021.61.0242	PROPN
ap-6786	58	11	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-6786	58	12	https://www.cvut.cz/en	https://www.cvut.cz/en	ADJ
ap-6786	58	13	vol	vol	NOUN
ap-6786	58	14	.	.	PROPN
ap-6786	59	1	61	61	NUM
ap-6786	59	2	no	no	NOUN
ap-6786	59	3	.	.	PUNCT
ap-6786	60	1	1/2021	1/2021	NUM
ap-6786	60	2	global	global	ADJ
ap-6786	60	3	optimization	optimization	NOUN
ap-6786	60	4	to	to	PART
ap-6786	60	5	predict	predict	VERB
ap-6786	60	6	strains	strain	NOUN
ap-6786	60	7	in	in	ADP
ap-6786	60	8	rc	rc	PROPN
ap-6786	60	9	compressed	compress	VERB
ap-6786	60	10	columns	column	NOUN
ap-6786	60	11	figure	figure	VERB
ap-6786	60	12	1	1	NUM
ap-6786	60	13	.	.	PUNCT
ap-6786	60	14	distribution	distribution	NOUN
ap-6786	60	15	of	of	ADP
ap-6786	60	16	strain	strain	NOUN
ap-6786	60	17	ε	ε	PROPN
ap-6786	60	18	,	,	PUNCT
ap-6786	60	19	stresses	stress	VERB
ap-6786	60	20	in	in	ADP
ap-6786	60	21	concrete	concrete	ADJ
ap-6786	60	22	σc	σc	PROPN
ap-6786	60	23	and	and	CCONJ
ap-6786	60	24	stresses	stress	NOUN
ap-6786	60	25	in	in	ADP
ap-6786	60	26	steel	steel	NOUN
ap-6786	60	27	σs	σs	ADP
ap-6786	60	28	across	across	ADP
ap-6786	60	29	the	the	DET
ap-6786	60	30	section	section	NOUN
ap-6786	60	31	global	global	ADJ
ap-6786	60	32	optimization	optimization	NOUN
ap-6786	60	33	methods	method	NOUN
ap-6786	60	34	to	to	PART
ap-6786	60	35	solve	solve	VERB
ap-6786	60	36	the	the	DET
ap-6786	60	37	problem	problem	NOUN
ap-6786	60	38	numerically	numerically	ADV
ap-6786	60	39	.	.	PUNCT
ap-6786	61	1	2	2	X
ap-6786	61	2	.	.	X
ap-6786	61	3	formulation	formulation	NOUN
ap-6786	61	4	of	of	ADP
ap-6786	61	5	the	the	DET
ap-6786	61	6	equilibrium	equilibrium	NOUN
ap-6786	61	7	equations	equation	NOUN
ap-6786	61	8	to	to	PART
ap-6786	61	9	get	get	VERB
ap-6786	61	10	the	the	DET
ap-6786	61	11	required	require	VERB
ap-6786	61	12	equations	equation	NOUN
ap-6786	61	13	,	,	PUNCT
ap-6786	61	14	we	we	PRON
ap-6786	61	15	started	start	VERB
ap-6786	61	16	with	with	ADP
ap-6786	61	17	the	the	DET
ap-6786	61	18	integral	integral	ADJ
ap-6786	61	19	equilibrium	equilibrium	NOUN
ap-6786	61	20	equations	equation	NOUN
ap-6786	61	21	and	and	CCONJ
ap-6786	61	22	integrated	integrate	VERB
ap-6786	61	23	them	they	PRON
ap-6786	61	24	.	.	PUNCT
ap-6786	62	1	the	the	DET
ap-6786	62	2	rectangular	rectangular	PROPN
ap-6786	62	3	rc	rc	PROPN
ap-6786	62	4	cross	cross	NOUN
ap-6786	62	5	-	-	NOUN
ap-6786	62	6	section	section	NOUN
ap-6786	62	7	is	be	AUX
ap-6786	62	8	subjected	subject	VERB
ap-6786	62	9	to	to	ADP
ap-6786	62	10	the	the	DET
ap-6786	62	11	axial	axial	ADJ
ap-6786	62	12	force	force	NOUN
ap-6786	62	13	n	n	CCONJ
ap-6786	62	14	and	and	CCONJ
ap-6786	62	15	the	the	DET
ap-6786	62	16	bending	bend	VERB
ap-6786	62	17	moment	moment	NOUN
ap-6786	62	18	m	m	VERB
ap-6786	62	19	(	(	PUNCT
ap-6786	62	20	see	see	VERB
ap-6786	62	21	fig	fig	NOUN
ap-6786	62	22	.	.	PUNCT
ap-6786	63	1	1	1	NUM
ap-6786	63	2	)	)	PUNCT
ap-6786	63	3	.	.	PUNCT
ap-6786	64	1	the	the	DET
ap-6786	64	2	content	content	NOUN
ap-6786	64	3	of	of	ADP
ap-6786	64	4	the	the	DET
ap-6786	64	5	current	current	ADJ
ap-6786	64	6	section	section	NOUN
ap-6786	64	7	is	be	AUX
ap-6786	64	8	an	an	DET
ap-6786	64	9	extension	extension	NOUN
ap-6786	64	10	of	of	ADP
ap-6786	64	11	that	that	PRON
ap-6786	64	12	presented	present	VERB
ap-6786	64	13	in	in	ADP
ap-6786	64	14	lechman	lechman	NOUN
ap-6786	64	15	and	and	CCONJ
ap-6786	64	16	stachurski	stachurski	VERB
ap-6786	64	17	[	[	X
ap-6786	64	18	32	32	NUM
ap-6786	64	19	]	]	PUNCT
ap-6786	64	20	.	.	PUNCT
ap-6786	65	1	the	the	DET
ap-6786	65	2	detailed	detailed	ADJ
ap-6786	65	3	way	way	NOUN
ap-6786	65	4	of	of	ADP
ap-6786	65	5	deriving	derive	VERB
ap-6786	65	6	the	the	DET
ap-6786	65	7	formulas	formula	NOUN
ap-6786	65	8	for	for	ADP
ap-6786	65	9	the	the	DET
ap-6786	65	10	section	section	NOUN
ap-6786	65	11	wholly	wholly	ADV
ap-6786	65	12	in	in	ADP
ap-6786	65	13	compression	compression	NOUN
ap-6786	65	14	is	be	AUX
ap-6786	65	15	included	include	VERB
ap-6786	65	16	.	.	PUNCT
ap-6786	66	1	in	in	ADP
ap-6786	66	2	the	the	DET
ap-6786	66	3	derivation	derivation	NOUN
ap-6786	66	4	of	of	ADP
ap-6786	66	5	the	the	DET
ap-6786	66	6	governing	govern	VERB
ap-6786	66	7	equations	equation	NOUN
ap-6786	66	8	,	,	PUNCT
ap-6786	66	9	the	the	DET
ap-6786	66	10	following	follow	VERB
ap-6786	66	11	assumptions	assumption	NOUN
ap-6786	66	12	are	be	AUX
ap-6786	66	13	made	make	VERB
ap-6786	66	14	:	:	PUNCT
ap-6786	66	15	•	•	NUM
ap-6786	66	16	plane	plane	NOUN
ap-6786	66	17	cross	cross	NOUN
ap-6786	66	18	-	-	ADJ
ap-6786	66	19	sections	section	NOUN
ap-6786	66	20	remain	remain	VERB
ap-6786	66	21	plane	plane	NOUN
ap-6786	66	22	,	,	PUNCT
ap-6786	66	23	•	•	NUM
ap-6786	66	24	elasto	elasto	NOUN
ap-6786	66	25	-	-	PUNCT
ap-6786	66	26	plastic	plastic	NOUN
ap-6786	66	27	stress	stress	NOUN
ap-6786	66	28	/	/	SYM
ap-6786	66	29	strain	strain	NOUN
ap-6786	66	30	relationships	relationship	NOUN
ap-6786	66	31	for	for	ADP
ap-6786	66	32	concrete	concrete	ADJ
ap-6786	66	33	and	and	CCONJ
ap-6786	66	34	reinforcing	reinforce	VERB
ap-6786	66	35	steel	steel	NOUN
ap-6786	66	36	are	be	AUX
ap-6786	66	37	used	use	VERB
ap-6786	66	38	,	,	PUNCT
ap-6786	66	39	•	•	SCONJ
ap-6786	66	40	the	the	DET
ap-6786	66	41	tensile	tensile	NOUN
ap-6786	66	42	strength	strength	NOUN
ap-6786	66	43	of	of	ADP
ap-6786	66	44	concrete	concrete	NOUN
ap-6786	66	45	is	be	AUX
ap-6786	66	46	ignored	ignore	VERB
ap-6786	66	47	,	,	PUNCT
ap-6786	66	48	•	•	ADP
ap-6786	66	49	the	the	DET
ap-6786	66	50	ultimate	ultimate	ADJ
ap-6786	66	51	strains	strain	NOUN
ap-6786	66	52	for	for	ADP
ap-6786	66	53	concrete	concrete	NOUN
ap-6786	66	54	are	be	AUX
ap-6786	66	55	determined	determine	VERB
ap-6786	66	56	as	as	ADP
ap-6786	66	57	εcu	εcu	NOUN
ap-6786	66	58	and	and	CCONJ
ap-6786	66	59	for	for	ADP
ap-6786	66	60	reinforcing	reinforce	VERB
ap-6786	66	61	steel	steel	NOUN
ap-6786	66	62	as	as	ADP
ap-6786	66	63	εsu	εsu	NOUN
ap-6786	66	64	.	.	PUNCT
ap-6786	67	1	in	in	ADP
ap-6786	67	2	fig	fig	NOUN
ap-6786	67	3	.	.	PUNCT
ap-6786	68	1	1	1	NUM
ap-6786	68	2	,	,	PUNCT
ap-6786	68	3	the	the	DET
ap-6786	68	4	following	follow	VERB
ap-6786	68	5	notation	notation	NOUN
ap-6786	68	6	is	be	AUX
ap-6786	68	7	used	use	VERB
ap-6786	68	8	:	:	PUNCT
ap-6786	68	9	t	t	PROPN
ap-6786	68	10	,	,	PUNCT
ap-6786	68	11	b	b	PROPN
ap-6786	68	12	the	the	DET
ap-6786	68	13	thickness	thickness	NOUN
ap-6786	68	14	and	and	CCONJ
ap-6786	68	15	the	the	DET
ap-6786	68	16	width	width	NOUN
ap-6786	68	17	of	of	ADP
ap-6786	68	18	the	the	DET
ap-6786	68	19	cross	cross	NOUN
ap-6786	68	20	-	-	NOUN
ap-6786	68	21	section	section	NOUN
ap-6786	68	22	,	,	PUNCT
ap-6786	68	23	respectively	respectively	ADV
ap-6786	68	24	,	,	PUNCT
ap-6786	68	25	t1	t1	PROPN
ap-6786	68	26	,	,	PUNCT
ap-6786	68	27	t2	t2	NOUN
ap-6786	68	28	coordinates	coordinate	NOUN
ap-6786	68	29	describing	describe	VERB
ap-6786	68	30	the	the	DET
ap-6786	68	31	locations	location	NOUN
ap-6786	68	32	of	of	ADP
ap-6786	68	33	rebars	rebar	NOUN
ap-6786	68	34	,	,	PUNCT
ap-6786	68	35	x	x	PRON
ap-6786	68	36	,	,	PUNCT
ap-6786	68	37	x′	x′	PROPN
ap-6786	68	38	coordinates	coordinate	NOUN
ap-6786	68	39	describing	describe	VERB
ap-6786	68	40	the	the	DET
ap-6786	68	41	location	location	NOUN
ap-6786	68	42	of	of	ADP
ap-6786	68	43	the	the	DET
ap-6786	68	44	neutral	neutral	ADJ
ap-6786	68	45	axis	axis	NOUN
ap-6786	68	46	and	and	CCONJ
ap-6786	68	47	the	the	DET
ap-6786	68	48	location	location	NOUN
ap-6786	68	49	of	of	ADP
ap-6786	68	50	any	any	DET
ap-6786	68	51	point	point	NOUN
ap-6786	68	52	of	of	ADP
ap-6786	68	53	the	the	DET
ap-6786	68	54	section	section	NOUN
ap-6786	68	55	,	,	PUNCT
ap-6786	68	56	respectively	respectively	ADV
ap-6786	68	57	.	.	PUNCT
ap-6786	69	1	in	in	ADP
ap-6786	69	2	accordance	accordance	NOUN
ap-6786	69	3	with	with	ADP
ap-6786	69	4	the	the	DET
ap-6786	69	5	eurocode	eurocode	NOUN
ap-6786	69	6	2	2	NUM
ap-6786	70	1	[	[	X
ap-6786	70	2	33	33	NUM
ap-6786	70	3	]	]	PUNCT
ap-6786	70	4	,	,	PUNCT
ap-6786	70	5	the	the	DET
ap-6786	70	6	stress	stress	NOUN
ap-6786	70	7	-	-	PUNCT
ap-6786	70	8	strain	strain	NOUN
ap-6786	70	9	relation	relation	NOUN
ap-6786	70	10	for	for	ADP
ap-6786	70	11	concrete	concrete	ADJ
ap-6786	70	12	σc	σc	PROPN
ap-6786	70	13	–	–	PUNCT
ap-6786	70	14	εc	εc	VERB
ap-6786	70	15	in	in	ADP
ap-6786	70	16	compression	compression	NOUN
ap-6786	70	17	for	for	ADP
ap-6786	70	18	a	a	DET
ap-6786	70	19	short	short	ADJ
ap-6786	70	20	term	term	NOUN
ap-6786	70	21	uniaxial	uniaxial	ADJ
ap-6786	70	22	loading	loading	NOUN
ap-6786	70	23	is	be	AUX
ap-6786	70	24	assumed	assume	VERB
ap-6786	70	25	as	as	ADP
ap-6786	70	26	σc	σc	PROPN
ap-6786	70	27	=	=	PUNCT
ap-6786	70	28	kηc	kηc	PROPN
ap-6786	70	29	−	−	PROPN
ap-6786	70	30	η2	η2	PROPN
ap-6786	70	31	c	c	NOUN
ap-6786	70	32	1	1	NUM
ap-6786	70	33	+	+	CCONJ
ap-6786	70	34	(	(	PUNCT
ap-6786	70	35	k	k	PROPN
ap-6786	70	36	−	−	PROPN
ap-6786	70	37	2)ηc	2)ηc	PROPN
ap-6786	70	38	fcm	fcm	X
ap-6786	70	39	,	,	PUNCT
ap-6786	70	40	(	(	PUNCT
ap-6786	70	41	1	1	NUM
ap-6786	70	42	)	)	PUNCT
ap-6786	71	1	where	where	SCONJ
ap-6786	71	2	:	:	PUNCT
ap-6786	71	3	ηc	ηc	X
ap-6786	71	4	=	=	PUNCT
ap-6786	71	5	εc	εc	PROPN
ap-6786	71	6	/	/	SYM
ap-6786	71	7	εc1	εc1	NOUN
ap-6786	71	8	,	,	PUNCT
ap-6786	71	9	εc1	εc1	NOUN
ap-6786	71	10	–	–	PUNCT
ap-6786	71	11	the	the	DET
ap-6786	71	12	strain	strain	NOUN
ap-6786	71	13	at	at	ADP
ap-6786	71	14	peak	peak	NOUN
ap-6786	71	15	stress	stress	NOUN
ap-6786	71	16	on	on	ADP
ap-6786	71	17	the	the	DET
ap-6786	71	18	σc	σc	PROPN
ap-6786	71	19	–	–	PUNCT
ap-6786	71	20	εc	εc	ADP
ap-6786	71	21	diagram	diagram	NOUN
ap-6786	71	22	,	,	PUNCT
ap-6786	71	23	k	k	X
ap-6786	71	24	=	=	PUNCT
ap-6786	71	25	1.05	1.05	NUM
ap-6786	71	26	ecm|εc1|/fcm	ecm|εc1|/fcm	NUM
ap-6786	71	27	,	,	PUNCT
ap-6786	71	28	fcm	fcm	X
ap-6786	71	29	–	–	PUNCT
ap-6786	71	30	the	the	DET
ap-6786	71	31	mean	mean	ADJ
ap-6786	71	32	compressive	compressive	ADJ
ap-6786	71	33	strength	strength	NOUN
ap-6786	71	34	of	of	ADP
ap-6786	71	35	concrete	concrete	NOUN
ap-6786	71	36	,	,	PUNCT
ap-6786	71	37	ecm	ecm	NOUN
ap-6786	71	38	–	–	PUNCT
ap-6786	71	39	secant	secant	ADJ
ap-6786	71	40	modulus	modulus	NOUN
ap-6786	71	41	of	of	ADP
ap-6786	71	42	elasticity	elasticity	NOUN
ap-6786	71	43	of	of	ADP
ap-6786	71	44	concrete	concrete	NOUN
ap-6786	71	45	,	,	PUNCT
ap-6786	71	46	εcu	εcu	NOUN
ap-6786	71	47	(	(	PUNCT
ap-6786	71	48	εcu1	εcu1	PROPN
ap-6786	71	49	)	)	PUNCT
ap-6786	71	50	–	–	PUNCT
ap-6786	71	51	the	the	DET
ap-6786	71	52	ultimate	ultimate	ADJ
ap-6786	71	53	strain	strain	NOUN
ap-6786	71	54	for	for	ADP
ap-6786	71	55	concrete	concrete	NOUN
ap-6786	71	56	.	.	PUNCT
ap-6786	72	1	the	the	DET
ap-6786	72	2	reinforcing	reinforce	VERB
ap-6786	72	3	steel	steel	NOUN
ap-6786	72	4	is	be	AUX
ap-6786	72	5	characterized	characterize	VERB
ap-6786	72	6	by	by	ADP
ap-6786	72	7	yield	yield	NOUN
ap-6786	72	8	stress	stress	NOUN
ap-6786	72	9	fyk	fyk	PROPN
ap-6786	72	10	,	,	PUNCT
ap-6786	72	11	es	es	NOUN
ap-6786	72	12	–	–	PUNCT
ap-6786	72	13	modulus	modulus	NOUN
ap-6786	72	14	of	of	ADP
ap-6786	72	15	elasticity	elasticity	NOUN
ap-6786	72	16	and	and	CCONJ
ap-6786	72	17	eh	eh	INTJ
ap-6786	72	18	–	–	PUNCT
ap-6786	72	19	coefficient	coefficient	NOUN
ap-6786	72	20	of	of	ADP
ap-6786	72	21	steel	steel	NOUN
ap-6786	72	22	hardening	harden	VERB
ap-6786	72	23	(	(	PUNCT
ap-6786	72	24	linear	linear	ADJ
ap-6786	72	25	elastic	elastic	ADJ
ap-6786	72	26	model	model	NOUN
ap-6786	72	27	with	with	ADP
ap-6786	72	28	hardening	hardening	NOUN
ap-6786	72	29	)	)	PUNCT
ap-6786	72	30	.	.	PUNCT
ap-6786	73	1	2.1	2.1	NUM
ap-6786	73	2	.	.	PUNCT
ap-6786	73	3	equations	equation	NOUN
ap-6786	73	4	for	for	ADP
ap-6786	73	5	strains	strain	NOUN
ap-6786	73	6	in	in	ADP
ap-6786	73	7	the	the	DET
ap-6786	73	8	rectangular	rectangular	ADJ
ap-6786	73	9	sections	section	NOUN
ap-6786	73	10	in	in	ADP
ap-6786	73	11	further	further	ADJ
ap-6786	73	12	considerations	consideration	NOUN
ap-6786	73	13	,	,	PUNCT
ap-6786	73	14	the	the	DET
ap-6786	73	15	corresponding	corresponding	ADJ
ap-6786	73	16	dimensionless	dimensionless	NOUN
ap-6786	73	17	coordinates	coordinate	NOUN
ap-6786	73	18	are	be	AUX
ap-6786	73	19	used	use	VERB
ap-6786	73	20	:	:	PUNCT
ap-6786	73	21	ξ	ξ	X
ap-6786	73	22	=	=	SYM
ap-6786	73	23	x	x	PROPN
ap-6786	73	24	/	/	SYM
ap-6786	73	25	t	t	PROPN
ap-6786	73	26	,	,	PUNCT
ap-6786	73	27	ξ	ξ	X
ap-6786	73	28	′	′	NUM
ap-6786	74	1	=	=	PUNCT
ap-6786	74	2	x	x	SYM
ap-6786	74	3	′	′	NUM
ap-6786	74	4	/t	/t	PUNCT
ap-6786	74	5	,	,	PUNCT
ap-6786	74	6	ξ1	ξ1	PROPN
ap-6786	74	7	=	=	SYM
ap-6786	74	8	t1	t1	PROPN
ap-6786	74	9	/	/	SYM
ap-6786	74	10	t	t	PROPN
ap-6786	74	11	,	,	PUNCT
ap-6786	74	12	ξ2	ξ2	NOUN
ap-6786	74	13	=	=	SYM
ap-6786	74	14	t2	t2	PROPN
ap-6786	74	15	/	/	SYM
ap-6786	74	16	t.	t.	NOUN
ap-6786	74	17	(	(	PUNCT
ap-6786	74	18	2	2	NUM
ap-6786	74	19	)	)	PUNCT
ap-6786	74	20	2.1.1	2.1.1	NUM
ap-6786	74	21	.	.	PUNCT
ap-6786	75	1	equations	equation	NOUN
ap-6786	75	2	for	for	ADP
ap-6786	75	3	sections	section	NOUN
ap-6786	75	4	wholly	wholly	ADV
ap-6786	75	5	in	in	ADP
ap-6786	75	6	compression	compression	NOUN
ap-6786	75	7	let	let	VERB
ap-6786	75	8	us	we	PRON
ap-6786	75	9	consider	consider	VERB
ap-6786	75	10	the	the	DET
ap-6786	75	11	section	section	NOUN
ap-6786	75	12	wholly	wholly	ADV
ap-6786	75	13	in	in	ADP
ap-6786	75	14	compression	compression	NOUN
ap-6786	75	15	.	.	PUNCT
ap-6786	76	1	the	the	DET
ap-6786	76	2	strain	strain	NOUN
ap-6786	76	3	distribution	distribution	NOUN
ap-6786	76	4	can	can	AUX
ap-6786	76	5	be	be	AUX
ap-6786	76	6	expressed	express	VERB
ap-6786	76	7	in	in	ADP
ap-6786	76	8	the	the	DET
ap-6786	76	9	form	form	NOUN
ap-6786	76	10	ε	ε	PROPN
ap-6786	76	11	=	=	SYM
ap-6786	76	12	ε1	ε1	PROPN
ap-6786	76	13	+	+	CCONJ
ap-6786	76	14	(	(	PUNCT
ap-6786	76	15	ε2	ε2	ADJ
ap-6786	76	16	−	−	PROPN
ap-6786	76	17	ε1)ξ	ε1)ξ	ADJ
ap-6786	76	18	′	′	NOUN
ap-6786	76	19	,	,	PUNCT
ap-6786	76	20	(	(	PUNCT
ap-6786	76	21	3	3	X
ap-6786	76	22	)	)	PUNCT
ap-6786	76	23	where	where	SCONJ
ap-6786	76	24	:	:	PUNCT
ap-6786	76	25	ε1	ε1	PROPN
ap-6786	76	26	–	–	PUNCT
ap-6786	76	27	maximum	maximum	ADJ
ap-6786	76	28	compressive	compressive	ADJ
ap-6786	76	29	strain	strain	NOUN
ap-6786	76	30	in	in	ADP
ap-6786	76	31	the	the	DET
ap-6786	76	32	cross	cross	NOUN
ap-6786	76	33	section	section	NOUN
ap-6786	76	34	,	,	PUNCT
ap-6786	76	35	ε2	ε2	ADJ
ap-6786	76	36	–	–	PUNCT
ap-6786	76	37	minimum	minimum	ADJ
ap-6786	76	38	compressive	compressive	ADJ
ap-6786	76	39	strain	strain	NOUN
ap-6786	76	40	in	in	ADP
ap-6786	76	41	the	the	DET
ap-6786	76	42	cross	cross	NOUN
ap-6786	76	43	section	section	NOUN
ap-6786	76	44	.	.	PUNCT
ap-6786	77	1	thus	thus	ADV
ap-6786	77	2	,	,	PUNCT
ap-6786	77	3	ηc	ηc	PRON
ap-6786	77	4	occuring	occur	VERB
ap-6786	77	5	in	in	ADP
ap-6786	77	6	(	(	PUNCT
ap-6786	77	7	1	1	NUM
ap-6786	77	8	)	)	PUNCT
ap-6786	77	9	assumes	assume	VERB
ap-6786	77	10	the	the	DET
ap-6786	77	11	form	form	NOUN
ap-6786	77	12	ηc	ηc	X
ap-6786	77	13	=	=	PUNCT
ap-6786	77	14	k2ξ	k2ξ	NOUN
ap-6786	77	15	′	′	NUM
ap-6786	78	1	+	+	CCONJ
ap-6786	78	2	k1	k1	NOUN
ap-6786	78	3	,	,	PUNCT
ap-6786	78	4	(	(	PUNCT
ap-6786	78	5	4	4	NUM
ap-6786	78	6	)	)	PUNCT
ap-6786	78	7	after	after	ADP
ap-6786	78	8	including	include	VERB
ap-6786	78	9	in	in	ADP
ap-6786	78	10	(	(	PUNCT
ap-6786	78	11	3	3	NUM
ap-6786	78	12	)	)	PUNCT
ap-6786	78	13	the	the	DET
ap-6786	78	14	following	follow	VERB
ap-6786	78	15	assignements	assignement	NOUN
ap-6786	78	16	:	:	PUNCT
ap-6786	78	17	k1	k1	PROPN
ap-6786	78	18	=	=	PUNCT
ap-6786	78	19	ε1	ε1	VERB
ap-6786	78	20	εc1	εc1	NOUN
ap-6786	78	21	and	and	CCONJ
ap-6786	78	22	k2	k2	PROPN
ap-6786	78	23	=	=	PROPN
ap-6786	78	24	ε2	ε2	NOUN
ap-6786	78	25	−	−	PROPN
ap-6786	78	26	ε1	ε1	PROPN
ap-6786	78	27	εc1	εc1	NOUN
ap-6786	78	28	.	.	PUNCT
ap-6786	79	1	the	the	DET
ap-6786	79	2	equilibrium	equilibrium	NOUN
ap-6786	79	3	equation	equation	NOUN
ap-6786	79	4	of	of	ADP
ap-6786	79	5	the	the	DET
ap-6786	79	6	axial	axial	ADJ
ap-6786	79	7	forces	force	NOUN
ap-6786	79	8	in	in	ADP
ap-6786	79	9	the	the	DET
ap-6786	79	10	cross	cross	NOUN
ap-6786	79	11	-	-	NOUN
ap-6786	79	12	section	section	NOUN
ap-6786	79	13	takes	take	VERB
ap-6786	79	14	the	the	DET
ap-6786	79	15	following	follow	VERB
ap-6786	79	16	form∫	form∫	PROPN
ap-6786	79	17	ac	ac	PROPN
ap-6786	79	18	σcdac	σcdac	PROPN
ap-6786	79	19	+	+	CCONJ
ap-6786	79	20	σs1fa1	σs1fa1	NOUN
ap-6786	79	21	+	+	CCONJ
ap-6786	79	22	σs2fa2	σs2fa2	NOUN
ap-6786	79	23	+	+	NOUN
ap-6786	79	24	n	n	NOUN
ap-6786	79	25	=	=	SYM
ap-6786	79	26	0	0	NUM
ap-6786	79	27	,	,	PUNCT
ap-6786	79	28	(	(	PUNCT
ap-6786	79	29	5	5	NUM
ap-6786	79	30	)	)	PUNCT
ap-6786	80	1	where	where	SCONJ
ap-6786	80	2	:	:	PUNCT
ap-6786	80	3	dac	dac	PROPN
ap-6786	80	4	element	element	NOUN
ap-6786	80	5	of	of	ADP
ap-6786	80	6	the	the	DET
ap-6786	80	7	concrete	concrete	ADJ
ap-6786	80	8	area	area	NOUN
ap-6786	80	9	ac	ac	PROPN
ap-6786	80	10	,	,	PUNCT
ap-6786	80	11	fa1	fa1	NOUN
ap-6786	80	12	,	,	PUNCT
ap-6786	80	13	fa2	fa2	NOUN
ap-6786	80	14	areas	area	NOUN
ap-6786	80	15	of	of	ADP
ap-6786	80	16	the	the	DET
ap-6786	80	17	steel	steel	NOUN
ap-6786	80	18	in	in	ADP
ap-6786	80	19	compression	compression	NOUN
ap-6786	80	20	and	and	CCONJ
ap-6786	80	21	in	in	ADP
ap-6786	80	22	tension	tension	NOUN
ap-6786	80	23	,	,	PUNCT
ap-6786	80	24	respectively	respectively	ADV
ap-6786	80	25	.	.	PUNCT
ap-6786	81	1	the	the	DET
ap-6786	81	2	sectional	sectional	ADJ
ap-6786	81	3	equilibrium	equilibrium	NOUN
ap-6786	81	4	of	of	ADP
ap-6786	81	5	the	the	DET
ap-6786	81	6	bending	bend	VERB
ap-6786	81	7	moments	moment	NOUN
ap-6786	81	8	about	about	ADP
ap-6786	81	9	the	the	DET
ap-6786	81	10	symmetry	symmetry	NOUN
ap-6786	81	11	axis	axis	NOUN
ap-6786	81	12	of	of	ADP
ap-6786	81	13	the	the	DET
ap-6786	81	14	rectangle	rectangle	NOUN
ap-6786	81	15	can	can	AUX
ap-6786	81	16	be	be	AUX
ap-6786	81	17	expressed	express	VERB
ap-6786	81	18	in	in	ADP
ap-6786	81	19	the	the	DET
ap-6786	81	20	form∫	form∫	PROPN
ap-6786	81	21	ac	ac	PROPN
ap-6786	81	22	σc(0.5t−	σc(0.5t−	PROPN
ap-6786	81	23	x	x	PROPN
ap-6786	81	24	′	′	X
ap-6786	81	25	)	)	PUNCT
ap-6786	81	26	dac	dac	NOUN
ap-6786	82	1	+	+	CCONJ
ap-6786	82	2	σs1fa1(0.5t−	σs1fa1(0.5t−	PROPN
ap-6786	82	3	t1)+	t1)+	ADJ
ap-6786	82	4	σs2fa2(0.5t−	σs2fa2(0.5t−	NOUN
ap-6786	82	5	t2)−m	t2)−m	NOUN
ap-6786	82	6	=	=	SYM
ap-6786	82	7	0	0	X
ap-6786	82	8	.	.	PUNCT
ap-6786	83	1	(	(	PUNCT
ap-6786	83	2	6	6	NUM
ap-6786	83	3	)	)	PUNCT
ap-6786	83	4	in	in	ADP
ap-6786	83	5	order	order	NOUN
ap-6786	83	6	to	to	PART
ap-6786	83	7	obtain	obtain	VERB
ap-6786	83	8	the	the	DET
ap-6786	83	9	final	final	ADJ
ap-6786	83	10	form	form	NOUN
ap-6786	83	11	of	of	ADP
ap-6786	83	12	the	the	DET
ap-6786	83	13	equilibrium	equilibrium	NOUN
ap-6786	83	14	equations	equation	NOUN
ap-6786	83	15	,	,	PUNCT
ap-6786	83	16	we	we	PRON
ap-6786	83	17	integrated	integrate	VERB
ap-6786	83	18	formulas	formula	NOUN
ap-6786	83	19	in	in	ADP
ap-6786	83	20	(	(	PUNCT
ap-6786	83	21	5	5	NUM
ap-6786	83	22	)	)	PUNCT
ap-6786	83	23	and	and	CCONJ
ap-6786	83	24	(	(	PUNCT
ap-6786	83	25	6	6	NUM
ap-6786	83	26	)	)	PUNCT
ap-6786	83	27	.	.	PUNCT
ap-6786	84	1	the	the	DET
ap-6786	84	2	243	243	NUM
ap-6786	84	3	marek	marek	PROPN
ap-6786	84	4	lechman	lechman	NOUN
ap-6786	84	5	,	,	PUNCT
ap-6786	84	6	andrzej	andrzej	PROPN
ap-6786	84	7	stachurski	stachurski	VERB
ap-6786	84	8	acta	acta	PROPN
ap-6786	84	9	polytechnica	polytechnica	PROPN
ap-6786	84	10	most	most	ADV
ap-6786	84	11	difficult	difficult	ADJ
ap-6786	84	12	part	part	NOUN
ap-6786	84	13	was	be	AUX
ap-6786	84	14	to	to	PART
ap-6786	84	15	find	find	VERB
ap-6786	84	16	the	the	DET
ap-6786	84	17	antiderivatives	antiderivative	NOUN
ap-6786	84	18	of	of	ADP
ap-6786	84	19	the	the	DET
ap-6786	84	20	functions	function	NOUN
ap-6786	84	21	in	in	ADP
ap-6786	84	22	the	the	DET
ap-6786	84	23	integral	integral	ADJ
ap-6786	84	24	expressions	expression	NOUN
ap-6786	84	25	in	in	ADP
ap-6786	84	26	(	(	PUNCT
ap-6786	84	27	5	5	NUM
ap-6786	84	28	)	)	PUNCT
ap-6786	84	29	and	and	CCONJ
ap-6786	84	30	(	(	PUNCT
ap-6786	84	31	6	6	NUM
ap-6786	84	32	)	)	PUNCT
ap-6786	84	33	.	.	PUNCT
ap-6786	85	1	after	after	ADP
ap-6786	85	2	substituting	substitute	VERB
ap-6786	85	3	relations	relation	NOUN
ap-6786	85	4	(	(	PUNCT
ap-6786	85	5	3	3	NUM
ap-6786	85	6	)	)	PUNCT
ap-6786	85	7	and	and	CCONJ
ap-6786	85	8	(	(	PUNCT
ap-6786	85	9	4	4	X
ap-6786	85	10	)	)	PUNCT
ap-6786	85	11	in	in	ADP
ap-6786	85	12	relation	relation	NOUN
ap-6786	85	13	(	(	PUNCT
ap-6786	85	14	1	1	NUM
ap-6786	85	15	)	)	PUNCT
ap-6786	85	16	,	,	PUNCT
ap-6786	85	17	the	the	DET
ap-6786	85	18	function	function	NOUN
ap-6786	85	19	to	to	PART
ap-6786	85	20	be	be	AUX
ap-6786	85	21	integrated	integrate	VERB
ap-6786	85	22	in	in	ADP
ap-6786	85	23	(	(	PUNCT
ap-6786	85	24	5	5	NUM
ap-6786	85	25	)	)	PUNCT
ap-6786	85	26	is	be	AUX
ap-6786	85	27	fn	fn	ADJ
ap-6786	85	28	(	(	PUNCT
ap-6786	85	29	ξ′	ξ′	NOUN
ap-6786	85	30	)	)	PUNCT
ap-6786	85	31	=	=	PUNCT
ap-6786	86	1	k(k2ξ	k(k2ξ	X
ap-6786	86	2	′	′	NOUN
ap-6786	86	3	+	+	CCONJ
ap-6786	86	4	k1)−	k1)−	PROPN
ap-6786	86	5	(	(	PUNCT
ap-6786	86	6	k2ξ	k2ξ	NOUN
ap-6786	86	7	′	′	NUM
ap-6786	87	1	+	+	CCONJ
ap-6786	87	2	k1)2	k1)2	X
ap-6786	87	3	1	1	NUM
ap-6786	88	1	+	+	CCONJ
ap-6786	88	2	(	(	PUNCT
ap-6786	88	3	k	k	NOUN
ap-6786	88	4	−	−	PROPN
ap-6786	88	5	2)(k2ξ	2)(k2ξ	NUM
ap-6786	88	6	′	′	NUM
ap-6786	88	7	+	+	CCONJ
ap-6786	88	8	k1	k1	NOUN
ap-6786	88	9	)	)	PUNCT
ap-6786	88	10	,	,	PUNCT
ap-6786	88	11	(	(	PUNCT
ap-6786	88	12	7	7	X
ap-6786	88	13	)	)	PUNCT
ap-6786	88	14	and	and	CCONJ
ap-6786	88	15	in	in	ADP
ap-6786	88	16	(	(	PUNCT
ap-6786	88	17	6	6	NUM
ap-6786	88	18	)	)	PUNCT
ap-6786	88	19	is	be	AUX
ap-6786	88	20	fm	fm	PROPN
ap-6786	88	21	(	(	PUNCT
ap-6786	88	22	ξ′	ξ′	NOUN
ap-6786	88	23	)	)	PUNCT
ap-6786	88	24	=	=	PUNCT
ap-6786	89	1	k(k2ξ	k(k2ξ	X
ap-6786	89	2	′	′	NOUN
ap-6786	89	3	+	+	CCONJ
ap-6786	89	4	k1)−	k1)−	PROPN
ap-6786	89	5	(	(	PUNCT
ap-6786	89	6	k2ξ	k2ξ	NOUN
ap-6786	89	7	′	′	NUM
ap-6786	90	1	+	+	CCONJ
ap-6786	90	2	k1)2	k1)2	X
ap-6786	90	3	1	1	NUM
ap-6786	91	1	+	+	CCONJ
ap-6786	91	2	(	(	PUNCT
ap-6786	91	3	k	k	NOUN
ap-6786	91	4	−	−	PROPN
ap-6786	91	5	2)(k2ξ	2)(k2ξ	NUM
ap-6786	91	6	′	′	NUM
ap-6786	91	7	+	+	CCONJ
ap-6786	91	8	k1	k1	NOUN
ap-6786	91	9	)	)	PUNCT
ap-6786	91	10	(	(	PUNCT
ap-6786	91	11	0.5−	0.5−	NOUN
ap-6786	91	12	ξ	ξ	NOUN
ap-6786	91	13	′	′	NUM
ap-6786	91	14	)	)	PUNCT
ap-6786	91	15	.	.	PUNCT
ap-6786	92	1	(	(	PUNCT
ap-6786	92	2	8)	8)	NUM
ap-6786	92	3	finally	finally	ADV
ap-6786	92	4	,	,	PUNCT
ap-6786	92	5	the	the	DET
ap-6786	92	6	following	follow	VERB
ap-6786	92	7	equilibrium	equilibrium	NOUN
ap-6786	92	8	equations	equation	NOUN
ap-6786	92	9	for	for	ADP
ap-6786	92	10	strains	strain	NOUN
ap-6786	92	11	in	in	ADP
ap-6786	92	12	the	the	DET
ap-6786	92	13	rectangular	rectangular	ADJ
ap-6786	92	14	sections	section	NOUN
ap-6786	92	15	are	be	AUX
ap-6786	92	16	found	find	VERB
ap-6786	92	17	.	.	PUNCT
ap-6786	93	1	the	the	DET
ap-6786	93	2	first	first	ADJ
ap-6786	93	3	one	one	NUM
ap-6786	93	4	concerns	concern	VERB
ap-6786	93	5	the	the	DET
ap-6786	93	6	equilibrium	equilibrium	NOUN
ap-6786	93	7	equation	equation	NOUN
ap-6786	93	8	of	of	ADP
ap-6786	93	9	the	the	DET
ap-6786	93	10	axial	axial	ADJ
ap-6786	93	11	forces	force	NOUN
ap-6786	93	12	n+	n+	PUNCT
ap-6786	93	13	1	1	NUM
ap-6786	93	14	k−2	k−2	PROPN
ap-6786	93	15	{	{	PUNCT
ap-6786	93	16	w1	w1	NOUN
ap-6786	93	17	+	+	CCONJ
ap-6786	93	18	0.5k2	0.5k2	ADV
ap-6786	93	19	+	+	CCONJ
ap-6786	93	20	w2	w2	NOUN
ap-6786	93	21	w3	w3	PROPN
ap-6786	93	22	(	(	PUNCT
ap-6786	93	23	lnw5	lnw5	PROPN
ap-6786	93	24	−	−	PROPN
ap-6786	93	25	lnw6	lnw6	PROPN
ap-6786	93	26	)	)	PUNCT
ap-6786	93	27	}	}	PUNCT
ap-6786	94	1	+	+	CCONJ
ap-6786	94	2	µ1	µ1	NOUN
ap-6786	94	3	fyk	fyk	NOUN
ap-6786	94	4	fcm	fcm	X
ap-6786	94	5	{	{	PUNCT
ap-6786	94	6	δi1	δi1	ADP
ap-6786	94	7	[	[	PUNCT
ap-6786	94	8	−1	−1	NOUN
ap-6786	94	9	+	+	CCONJ
ap-6786	94	10	eh	eh	INTJ
ap-6786	94	11	fyk	fyk	NOUN
ap-6786	94	12	(	(	PUNCT
ap-6786	94	13	(	(	PUNCT
ap-6786	94	14	(	(	PUNCT
ap-6786	94	15	ε2	ε2	ADJ
ap-6786	94	16	−	−	PROPN
ap-6786	94	17	ε1	ε1	PROPN
ap-6786	94	18	)	)	PUNCT
ap-6786	94	19	ξ1	ξ1	NOUN
ap-6786	94	20	+	+	CCONJ
ap-6786	94	21	ε1	ε1	PROPN
ap-6786	94	22	)	)	PUNCT
ap-6786	95	1	+	+	CCONJ
ap-6786	95	2	εss	εss	ADV
ap-6786	95	3	)	)	PUNCT
ap-6786	95	4	]	]	PUNCT
ap-6786	96	1	+	+	CCONJ
ap-6786	97	1	δi1	δi1	ADJ
ap-6786	97	2	+	+	ADJ
ap-6786	97	3	1	1	NUM
ap-6786	97	4	(	(	PUNCT
ap-6786	97	5	ε2	ε2	ADJ
ap-6786	97	6	−	−	PUNCT
ap-6786	97	7	ε1)ξ1	ε1)ξ1	NOUN
ap-6786	98	1	+	+	CCONJ
ap-6786	98	2	ε1	ε1	VERB
ap-6786	98	3	εss	εss	ADV
ap-6786	98	4	}	}	PUNCT
ap-6786	98	5	+	+	CCONJ
ap-6786	98	6	µ2	µ2	PROPN
ap-6786	98	7	fyk	fyk	PROPN
ap-6786	98	8	fcm	fcm	X
ap-6786	98	9	{	{	PUNCT
ap-6786	98	10	δi2	δi2	X
ap-6786	98	11	[	[	PUNCT
ap-6786	98	12	1	1	NUM
ap-6786	98	13	+	+	CCONJ
ap-6786	98	14	eh	eh	INTJ
ap-6786	98	15	fyk	fyk	NOUN
ap-6786	99	1	[	[	X
ap-6786	99	2	(	(	PUNCT
ap-6786	99	3	(	(	PUNCT
ap-6786	99	4	ε2	ε2	ADJ
ap-6786	99	5	−	−	PROPN
ap-6786	99	6	ε1	ε1	PROPN
ap-6786	99	7	)	)	PUNCT
ap-6786	99	8	(	(	PUNCT
ap-6786	99	9	1−	1−	NUM
ap-6786	99	10	ξ2	ξ2	NOUN
ap-6786	99	11	)	)	PUNCT
ap-6786	100	1	+	+	SYM
ap-6786	100	2	ε1	ε1	PROPN
ap-6786	100	3	)	)	PUNCT
ap-6786	100	4	−	−	ADP
ap-6786	101	1	εss	εss	ADV
ap-6786	101	2	]	]	X
ap-6786	101	3	]	]	PUNCT
ap-6786	102	1	+	+	CCONJ
ap-6786	102	2	δi2	δi2	SYM
ap-6786	102	3	+	+	ADJ
ap-6786	102	4	1	1	NUM
ap-6786	102	5	(	(	PUNCT
ap-6786	102	6	ε2	ε2	ADJ
ap-6786	102	7	−	−	PROPN
ap-6786	102	8	ε1)(1−	ε1)(1−	NOUN
ap-6786	102	9	ξ2	ξ2	NOUN
ap-6786	102	10	)	)	PUNCT
ap-6786	103	1	+	+	CCONJ
ap-6786	103	2	ε1	ε1	VERB
ap-6786	103	3	εss	εss	ADV
ap-6786	103	4	}	}	PUNCT
ap-6786	103	5	=	=	SYM
ap-6786	103	6	0	0	NUM
ap-6786	103	7	(	(	PUNCT
ap-6786	103	8	9	9	NUM
ap-6786	103	9	)	)	PUNCT
ap-6786	103	10	and	and	CCONJ
ap-6786	103	11	the	the	DET
ap-6786	103	12	second	second	ADJ
ap-6786	103	13	one	one	NOUN
ap-6786	103	14	represents	represent	VERB
ap-6786	103	15	the	the	DET
ap-6786	103	16	sectional	sectional	ADJ
ap-6786	103	17	equilibrium	equilibrium	NOUN
ap-6786	103	18	of	of	ADP
ap-6786	103	19	the	the	DET
ap-6786	103	20	bending	bend	VERB
ap-6786	103	21	moments	moment	NOUN
ap-6786	103	22	−m+	−m+	PROPN
ap-6786	103	23	1	1	NUM
ap-6786	103	24	k−2	k−2	PROPN
ap-6786	103	25	{	{	PUNCT
ap-6786	103	26	−k2	−k2	PROPN
ap-6786	103	27	12	12	NUM
ap-6786	103	28	+	+	CCONJ
ap-6786	103	29	0.5w2	0.5w2	PRON
ap-6786	103	30	w6	w6	PROPN
ap-6786	103	31	(	(	PUNCT
ap-6786	103	32	lnw5	lnw5	PROPN
ap-6786	103	33	−	−	PROPN
ap-6786	103	34	lnw6	lnw6	PROPN
ap-6786	103	35	)	)	PUNCT
ap-6786	103	36	−	−	PROPN
ap-6786	103	37	w2	w2	PROPN
ap-6786	103	38	w3	w3	PROPN
ap-6786	103	39	[	[	PUNCT
ap-6786	103	40	1−	1−	NUM
ap-6786	103	41	w6	w6	PROPN
ap-6786	103	42	w4	w4	PROPN
ap-6786	103	43	(	(	PUNCT
ap-6786	103	44	lnw5	lnw5	PROPN
ap-6786	103	45	−	−	PROPN
ap-6786	103	46	lnw6	lnw6	PROPN
ap-6786	103	47	)	)	PUNCT
ap-6786	103	48	]	]	PUNCT
ap-6786	103	49	}	}	PUNCT
ap-6786	103	50	+	+	CCONJ
ap-6786	103	51	µ1	µ1	NOUN
ap-6786	103	52	fyk	fyk	NOUN
ap-6786	103	53	fcm	fcm	X
ap-6786	103	54	(	(	PUNCT
ap-6786	103	55	0.5−	0.5−	NUM
ap-6786	103	56	ξ1	ξ1	NOUN
ap-6786	103	57	)	)	PUNCT
ap-6786	103	58	{	{	PUNCT
ap-6786	103	59	δi1	δi1	ADP
ap-6786	103	60	[	[	PUNCT
ap-6786	103	61	1	1	NUM
ap-6786	103	62	+	+	CCONJ
ap-6786	103	63	eh	eh	INTJ
ap-6786	103	64	fyk	fyk	NOUN
ap-6786	103	65	(	(	PUNCT
ap-6786	103	66	(	(	PUNCT
ap-6786	103	67	(	(	PUNCT
ap-6786	103	68	ε2	ε2	ADJ
ap-6786	103	69	−	−	PROPN
ap-6786	103	70	ε1	ε1	PROPN
ap-6786	103	71	)	)	PUNCT
ap-6786	103	72	ξ1	ξ1	NOUN
ap-6786	103	73	+	+	CCONJ
ap-6786	103	74	ε1	ε1	PROPN
ap-6786	103	75	)	)	PUNCT
ap-6786	104	1	+	+	CCONJ
ap-6786	104	2	εss	εss	ADV
ap-6786	104	3	)	)	PUNCT
ap-6786	104	4	]	]	PUNCT
ap-6786	105	1	+	+	CCONJ
ap-6786	106	1	δi1	δi1	ADJ
ap-6786	106	2	+	+	ADJ
ap-6786	106	3	1	1	NUM
ap-6786	106	4	(	(	PUNCT
ap-6786	106	5	ε2	ε2	ADJ
ap-6786	106	6	−	−	PUNCT
ap-6786	106	7	ε1)ξ1	ε1)ξ1	NOUN
ap-6786	107	1	+	+	CCONJ
ap-6786	107	2	ε1	ε1	VERB
ap-6786	107	3	εss	εss	ADV
ap-6786	107	4	}	}	PUNCT
ap-6786	107	5	+	+	CCONJ
ap-6786	107	6	µ2	µ2	PROPN
ap-6786	107	7	fyk	fyk	PROPN
ap-6786	107	8	fcm	fcm	X
ap-6786	107	9	(	(	PUNCT
ap-6786	107	10	0.5−	0.5−	NUM
ap-6786	107	11	ξ2	ξ2	NOUN
ap-6786	107	12	)	)	PUNCT
ap-6786	107	13	{	{	PUNCT
ap-6786	107	14	δi2	δi2	X
ap-6786	108	1	[	[	PUNCT
ap-6786	108	2	1	1	NUM
ap-6786	108	3	+	+	CCONJ
ap-6786	108	4	eh	eh	INTJ
ap-6786	108	5	fyk	fyk	NOUN
ap-6786	108	6	(	(	PUNCT
ap-6786	108	7	(	(	PUNCT
ap-6786	108	8	(	(	PUNCT
ap-6786	108	9	ε2	ε2	ADJ
ap-6786	108	10	−	−	PROPN
ap-6786	108	11	ε1	ε1	PROPN
ap-6786	108	12	)	)	PUNCT
ap-6786	108	13	(	(	PUNCT
ap-6786	108	14	1−	1−	NUM
ap-6786	108	15	ξ2	ξ2	NOUN
ap-6786	108	16	)	)	PUNCT
ap-6786	108	17	+	+	CCONJ
ap-6786	108	18	ε1)−	ε1)−	ADJ
ap-6786	108	19	εss	εss	ADJ
ap-6786	108	20	)	)	PUNCT
ap-6786	108	21	]	]	PUNCT
ap-6786	109	1	+	+	CCONJ
ap-6786	109	2	δi2	δi2	VERB
ap-6786	109	3	+	+	ADJ
ap-6786	109	4	1	1	NUM
ap-6786	109	5	(	(	PUNCT
ap-6786	109	6	ε2	ε2	ADJ
ap-6786	109	7	−	−	PROPN
ap-6786	109	8	ε1)(1−	ε1)(1−	NOUN
ap-6786	109	9	ξ2	ξ2	NOUN
ap-6786	109	10	)	)	PUNCT
ap-6786	110	1	+	+	CCONJ
ap-6786	110	2	ε1	ε1	VERB
ap-6786	110	3	εss	εss	ADV
ap-6786	110	4	}	}	PUNCT
ap-6786	110	5	=	=	SYM
ap-6786	110	6	0	0	NUM
ap-6786	110	7	(	(	PUNCT
ap-6786	110	8	10	10	NUM
ap-6786	110	9	)	)	PUNCT
ap-6786	111	1	where	where	SCONJ
ap-6786	111	2	:	:	PUNCT
ap-6786	111	3	w1	w1	NOUN
ap-6786	111	4	=	=	SYM
ap-6786	111	5	k1	k1	PROPN
ap-6786	111	6	−	−	PROPN
ap-6786	112	1	k	k	NOUN
ap-6786	113	1	−	−	PROPN
ap-6786	113	2	1	1	NUM
ap-6786	113	3	k	k	NOUN
ap-6786	113	4	−	−	PROPN
ap-6786	113	5	2	2	NUM
ap-6786	113	6	w2	w2	NOUN
ap-6786	113	7	=	=	PROPN
ap-6786	113	8	k(k	k(k	PROPN
ap-6786	113	9	−	−	NOUN
ap-6786	113	10	2	2	NUM
ap-6786	113	11	)	)	PUNCT
ap-6786	113	12	+	+	CCONJ
ap-6786	113	13	1	1	NUM
ap-6786	113	14	w3	w3	NOUN
ap-6786	113	15	=	=	SYM
ap-6786	113	16	(	(	PUNCT
ap-6786	113	17	k	k	PROPN
ap-6786	113	18	−	−	PROPN
ap-6786	113	19	2)(k	2)(k	NUM
ap-6786	114	1	−	−	PROPN
ap-6786	114	2	2)k2	2)k2	NUM
ap-6786	114	3	w4	w4	NOUN
ap-6786	114	4	=	=	SYM
ap-6786	114	5	(	(	PUNCT
ap-6786	114	6	k	k	NOUN
ap-6786	114	7	−	−	PROPN
ap-6786	114	8	2)k2	2)k2	NUM
ap-6786	114	9	w5	w5	PROPN
ap-6786	114	10	=	=	PUNCT
ap-6786	114	11	1	1	NUM
ap-6786	114	12	+	+	CCONJ
ap-6786	114	13	k	k	PROPN
ap-6786	114	14	−	−	PROPN
ap-6786	114	15	2	2	NUM
ap-6786	114	16	k2	k2	NOUN
ap-6786	114	17	+	+	CCONJ
ap-6786	114	18	k1	k1	PROPN
ap-6786	114	19	n	n	NOUN
ap-6786	114	20	=	=	SYM
ap-6786	114	21	n	n	NUM
ap-6786	114	22	btfcm	btfcm	NOUN
ap-6786	114	23	w6	w6	PROPN
ap-6786	114	24	=	=	PROPN
ap-6786	114	25	1	1	NUM
ap-6786	114	26	+	+	CCONJ
ap-6786	114	27	(	(	PUNCT
ap-6786	114	28	k	k	NOUN
ap-6786	114	29	−	−	PROPN
ap-6786	114	30	2)(k2	2)(k2	NUM
ap-6786	114	31	+	+	NUM
ap-6786	114	32	k1	k1	NOUN
ap-6786	114	33	)	)	PUNCT
ap-6786	114	34	m	m	PROPN
ap-6786	115	1	=	=	NOUN
ap-6786	115	2	m	m	VERB
ap-6786	115	3	bt2fcm	bt2fcm	VERB
ap-6786	115	4	δi	δi	ADP
ap-6786	115	5	=	=	PUNCT
ap-6786	115	6	0.5((−1i	0.5((−1i	NOUN
ap-6786	115	7	)	)	PUNCT
ap-6786	116	1	+	+	CCONJ
ap-6786	116	2	1	1	NUM
ap-6786	116	3	)	)	PUNCT
ap-6786	116	4	,	,	PUNCT
ap-6786	116	5	i	i	PRON
ap-6786	116	6	=	=	NOUN
ap-6786	116	7	1	1	NUM
ap-6786	116	8	,	,	PUNCT
ap-6786	116	9	2	2	NUM
ap-6786	116	10	and	and	CCONJ
ap-6786	116	11	:	:	PUNCT
ap-6786	116	12	µ1	µ1	PROPN
ap-6786	116	13	–	–	PUNCT
ap-6786	116	14	the	the	DET
ap-6786	116	15	reinforcement	reinforcement	NOUN
ap-6786	116	16	ratio	ratio	NOUN
ap-6786	116	17	of	of	ADP
ap-6786	116	18	steel	steel	NOUN
ap-6786	116	19	in	in	ADP
ap-6786	116	20	compression	compression	NOUN
ap-6786	116	21	,	,	PUNCT
ap-6786	116	22	µ2	µ2	PROPN
ap-6786	116	23	–	–	PUNCT
ap-6786	116	24	the	the	DET
ap-6786	116	25	reinforcement	reinforcement	NOUN
ap-6786	116	26	ratio	ratio	NOUN
ap-6786	116	27	of	of	ADP
ap-6786	116	28	steel	steel	NOUN
ap-6786	116	29	in	in	ADP
ap-6786	116	30	tension	tension	NOUN
ap-6786	116	31	.	.	PUNCT
ap-6786	117	1	the	the	DET
ap-6786	117	2	unknown	unknown	ADJ
ap-6786	117	3	variables	variable	NOUN
ap-6786	117	4	are	be	AUX
ap-6786	117	5	:	:	PUNCT
ap-6786	117	6	ε1	ε1	NOUN
ap-6786	117	7	,	,	PUNCT
ap-6786	117	8	ε2	ε2	PROPN
ap-6786	117	9	.	.	PUNCT
ap-6786	118	1	2.1.2	2.1.2	NUM
ap-6786	118	2	.	.	PUNCT
ap-6786	118	3	section	section	NOUN
ap-6786	118	4	under	under	ADP
ap-6786	118	5	combined	combined	ADJ
ap-6786	118	6	compression	compression	NOUN
ap-6786	118	7	with	with	ADP
ap-6786	118	8	bending	bend	VERB
ap-6786	118	9	let	let	VERB
ap-6786	118	10	us	we	PRON
ap-6786	118	11	consider	consider	VERB
ap-6786	118	12	the	the	DET
ap-6786	118	13	section	section	NOUN
ap-6786	118	14	under	under	ADP
ap-6786	118	15	combined	combine	VERB
ap-6786	118	16	compression	compression	NOUN
ap-6786	118	17	and	and	CCONJ
ap-6786	118	18	bending	bending	NOUN
ap-6786	118	19	.	.	PUNCT
ap-6786	119	1	due	due	ADP
ap-6786	119	2	to	to	ADP
ap-6786	119	3	the	the	DET
ap-6786	119	4	bernoulli	bernoulli	PROPN
ap-6786	119	5	assumption	assumption	NOUN
ap-6786	119	6	,	,	PUNCT
ap-6786	119	7	one	one	NUM
ap-6786	119	8	obtains	obtain	VERB
ap-6786	119	9	(	(	PUNCT
ap-6786	119	10	see	see	VERB
ap-6786	119	11	fig	fig	NOUN
ap-6786	119	12	.	.	PUNCT
ap-6786	120	1	1	1	NUM
ap-6786	120	2	)	)	PUNCT
ap-6786	120	3	ε	ε	PROPN
ap-6786	120	4	=	=	PUNCT
ap-6786	120	5	(	(	PUNCT
ap-6786	120	6	1−	1−	NUM
ap-6786	120	7	ξ	ξ	NOUN
ap-6786	120	8	′	′	NUM
ap-6786	120	9	ξ	ξ	X
ap-6786	120	10	)	)	PUNCT
ap-6786	120	11	ε	ε	PROPN
ap-6786	120	12	′	′	NUM
ap-6786	120	13	,	,	PUNCT
ap-6786	120	14	(	(	PUNCT
ap-6786	120	15	11	11	NUM
ap-6786	120	16	)	)	PUNCT
ap-6786	120	17	where	where	SCONJ
ap-6786	120	18	:	:	PUNCT
ap-6786	120	19	ε′	ε′	NOUN
ap-6786	120	20	–	–	PUNCT
ap-6786	120	21	the	the	DET
ap-6786	120	22	maximum	maximum	ADJ
ap-6786	120	23	compressive	compressive	ADJ
ap-6786	120	24	strain	strain	NOUN
ap-6786	120	25	in	in	ADP
ap-6786	120	26	concrete	concrete	NOUN
ap-6786	120	27	.	.	PUNCT
ap-6786	121	1	the	the	DET
ap-6786	121	2	resulting	result	VERB
ap-6786	121	3	formulas	formula	NOUN
ap-6786	121	4	are	be	AUX
ap-6786	121	5	given	give	VERB
ap-6786	121	6	below	below	ADP
ap-6786	121	7	.	.	PUNCT
ap-6786	122	1	equation	equation	NOUN
ap-6786	122	2	(	(	PUNCT
ap-6786	122	3	12	12	NUM
ap-6786	122	4	)	)	PUNCT
ap-6786	122	5	(	(	PUNCT
ap-6786	122	6	for	for	ADP
ap-6786	122	7	axial	axial	ADJ
ap-6786	122	8	forces	force	NOUN
ap-6786	122	9	)	)	PUNCT
ap-6786	122	10	n+	n+	PUNCT
ap-6786	122	11	1	1	NUM
ap-6786	122	12	k−2	k−2	NOUN
ap-6786	122	13	{	{	PUNCT
ap-6786	122	14	w1ξ	w1ξ	VERB
ap-6786	122	15	+	+	NUM
ap-6786	122	16	0.5k2ξ	0.5k2ξ	NUM
ap-6786	122	17	2	2	NUM
ap-6786	122	18	−	−	NOUN
ap-6786	122	19	1	1	NUM
ap-6786	122	20	k−2	k−2	PROPN
ap-6786	122	21	[	[	PUNCT
ap-6786	122	22	w2	w2	NOUN
ap-6786	122	23	w3	w3	PROPN
ap-6786	122	24	lnw	lnw	VERB
ap-6786	122	25	−	−	PROPN
ap-6786	122	26	ξ	ξ	X
ap-6786	122	27	]	]	PUNCT
ap-6786	122	28	}	}	PUNCT
ap-6786	122	29	+	+	CCONJ
ap-6786	122	30	µ1	µ1	NOUN
ap-6786	122	31	fyk	fyk	NOUN
ap-6786	122	32	fcm	fcm	X
ap-6786	122	33	{	{	PUNCT
ap-6786	122	34	δi1	δi1	ADP
ap-6786	122	35	[	[	PUNCT
ap-6786	122	36	−1	−1	NOUN
ap-6786	122	37	+	+	CCONJ
ap-6786	122	38	eh	eh	INTJ
ap-6786	122	39	fyk	fyk	NOUN
ap-6786	123	1	(	(	PUNCT
ap-6786	123	2	(	(	PUNCT
ap-6786	123	3	1−	1−	NUM
ap-6786	123	4	ξ1	ξ1	PROPN
ap-6786	123	5	ξ	ξ	X
ap-6786	123	6	)	)	PUNCT
ap-6786	123	7	ε	ε	PROPN
ap-6786	123	8	′	′	NOUN
ap-6786	124	1	+	+	CCONJ
ap-6786	124	2	εss	εss	NOUN
ap-6786	124	3	)	)	PUNCT
ap-6786	124	4	]	]	PUNCT
ap-6786	125	1	+	+	CCONJ
ap-6786	125	2	δi1	δi1	ADJ
ap-6786	125	3	+	+	ADJ
ap-6786	125	4	1	1	NUM
ap-6786	125	5	ε	ε	NOUN
ap-6786	125	6	′	′	NUM
ap-6786	125	7	εss	εss	INTJ
ap-6786	125	8	(	(	PUNCT
ap-6786	125	9	1−	1−	NUM
ap-6786	125	10	ξ1	ξ1	PROPN
ap-6786	125	11	ξ	ξ	PROPN
ap-6786	125	12	)	)	PUNCT
ap-6786	125	13	}	}	PUNCT
ap-6786	126	1	+	+	CCONJ
ap-6786	126	2	µ2	µ2	PROPN
ap-6786	126	3	fyk	fyk	PROPN
ap-6786	126	4	fcm	fcm	X
ap-6786	126	5	{	{	PUNCT
ap-6786	126	6	δi2	δi2	PROPN
ap-6786	126	7	[	[	PUNCT
ap-6786	126	8	+1	+1	NOUN
ap-6786	126	9	+	+	CCONJ
ap-6786	126	10	eh	eh	INTJ
ap-6786	126	11	fyk	fyk	NOUN
ap-6786	126	12	(	(	PUNCT
ap-6786	126	13	(	(	PUNCT
ap-6786	126	14	1−	1−	NUM
ap-6786	127	1	1−	1−	NUM
ap-6786	127	2	ξ2	ξ2	NOUN
ap-6786	127	3	ξ	ξ	PROPN
ap-6786	127	4	)	)	PUNCT
ap-6786	127	5	ε	ε	PROPN
ap-6786	127	6	′	′	NUM
ap-6786	127	7	−	−	NUM
ap-6786	127	8	εss	εss	NOUN
ap-6786	127	9	)	)	PUNCT
ap-6786	127	10	]	]	PUNCT
ap-6786	128	1	+	+	CCONJ
ap-6786	128	2	δi2	δi2	VERB
ap-6786	128	3	+	+	ADJ
ap-6786	128	4	1	1	NUM
ap-6786	128	5	ε	ε	NOUN
ap-6786	128	6	′	′	NUM
ap-6786	128	7	εss	εss	INTJ
ap-6786	128	8	(	(	PUNCT
ap-6786	128	9	1−	1−	NUM
ap-6786	128	10	1−	1−	NUM
ap-6786	128	11	ξ2	ξ2	NOUN
ap-6786	128	12	ξ	ξ	PROPN
ap-6786	128	13	)	)	PUNCT
ap-6786	128	14	}	}	PUNCT
ap-6786	129	1	=	=	SYM
ap-6786	129	2	0	0	PUNCT
ap-6786	129	3	(	(	PUNCT
ap-6786	129	4	12	12	NUM
ap-6786	129	5	)	)	PUNCT
ap-6786	129	6	and	and	CCONJ
ap-6786	129	7	equation	equation	NOUN
ap-6786	129	8	(	(	PUNCT
ap-6786	129	9	13	13	NUM
ap-6786	129	10	)	)	PUNCT
ap-6786	129	11	,	,	PUNCT
ap-6786	129	12	representing	represent	VERB
ap-6786	129	13	the	the	DET
ap-6786	129	14	sectional	sectional	ADJ
ap-6786	129	15	equilibrium	equilibrium	NOUN
ap-6786	129	16	of	of	ADP
ap-6786	129	17	the	the	DET
ap-6786	129	18	bending	bend	VERB
ap-6786	129	19	moments	moment	NOUN
ap-6786	129	20	−m+	−m+	PROPN
ap-6786	129	21	1	1	NUM
ap-6786	129	22	k−2	k−2	PROPN
ap-6786	129	23	{	{	PUNCT
ap-6786	129	24	0.5	0.5	NUM
ap-6786	129	25	(	(	PUNCT
ap-6786	129	26	w1	w1	NOUN
ap-6786	129	27	+	+	CCONJ
ap-6786	129	28	1	1	NUM
ap-6786	129	29	k−2	k−2	PROPN
ap-6786	129	30	)	)	PUNCT
ap-6786	130	1	ξ	ξ	PROPN
ap-6786	131	1	+	+	NUM
ap-6786	131	2	0.5	0.5	NUM
ap-6786	131	3	[	[	PUNCT
ap-6786	131	4	−w1	−w1	PROPN
ap-6786	131	5	+	+	CCONJ
ap-6786	131	6	0.5k2	0.5k2	NUM
ap-6786	131	7	−	−	NUM
ap-6786	131	8	1	1	NUM
ap-6786	131	9	k−2	k−2	NOUN
ap-6786	131	10	]	]	PUNCT
ap-6786	131	11	ξ2−	ξ2−	NOUN
ap-6786	131	12	1	1	NUM
ap-6786	131	13	3k2ξ	3k2ξ	NUM
ap-6786	131	14	3	3	NUM
ap-6786	131	15	−	−	PROPN
ap-6786	131	16	w2	w2	NOUN
ap-6786	131	17	(	(	PUNCT
ap-6786	131	18	k−2)w3	k−2)w3	PROPN
ap-6786	131	19	[	[	PUNCT
ap-6786	131	20	0.5	0.5	NUM
ap-6786	131	21	lnw	lnw	VERB
ap-6786	131	22	+	+	X
ap-6786	131	23	ξ	ξ	X
ap-6786	131	24	−	−	PROPN
ap-6786	131	25	w	w	PROPN
ap-6786	131	26	w3	w3	PROPN
ap-6786	131	27	lnw	lnw	VERB
ap-6786	131	28	]	]	PUNCT
ap-6786	131	29	}	}	PUNCT
ap-6786	131	30	+	+	CCONJ
ap-6786	131	31	µ1	µ1	NOUN
ap-6786	131	32	fyk	fyk	NOUN
ap-6786	131	33	fcm	fcm	X
ap-6786	131	34	(	(	PUNCT
ap-6786	131	35	0.5−	0.5−	NUM
ap-6786	131	36	ξ1	ξ1	NOUN
ap-6786	131	37	)	)	PUNCT
ap-6786	131	38	{	{	PUNCT
ap-6786	132	1	δi1	δi1	ADP
ap-6786	132	2	[	[	PUNCT
ap-6786	132	3	1	1	NUM
ap-6786	132	4	+	+	CCONJ
ap-6786	132	5	eh	eh	INTJ
ap-6786	132	6	fyk	fyk	NOUN
ap-6786	132	7	(	(	PUNCT
ap-6786	132	8	(	(	PUNCT
ap-6786	132	9	1−	1−	NUM
ap-6786	132	10	ξ1	ξ1	PROPN
ap-6786	132	11	ξ	ξ	X
ap-6786	132	12	)	)	PUNCT
ap-6786	132	13	ε	ε	PROPN
ap-6786	132	14	′	′	NOUN
ap-6786	133	1	+	+	CCONJ
ap-6786	133	2	εss	εss	NOUN
ap-6786	133	3	)	)	PUNCT
ap-6786	133	4	]	]	PUNCT
ap-6786	134	1	+	+	CCONJ
ap-6786	134	2	δi1	δi1	ADJ
ap-6786	134	3	+	+	ADJ
ap-6786	134	4	1	1	NUM
ap-6786	134	5	ε	ε	NOUN
ap-6786	134	6	′	′	NUM
ap-6786	134	7	εss	εss	INTJ
ap-6786	134	8	(	(	PUNCT
ap-6786	134	9	1−	1−	NUM
ap-6786	134	10	ξ1	ξ1	PROPN
ap-6786	134	11	ξ	ξ	PROPN
ap-6786	134	12	)	)	PUNCT
ap-6786	134	13	}	}	PUNCT
ap-6786	135	1	+	+	CCONJ
ap-6786	135	2	µ2	µ2	PROPN
ap-6786	135	3	fyk	fyk	PROPN
ap-6786	135	4	fcm	fcm	X
ap-6786	135	5	(	(	PUNCT
ap-6786	135	6	0.5−	0.5−	NUM
ap-6786	135	7	ξ2	ξ2	NOUN
ap-6786	135	8	)	)	PUNCT
ap-6786	135	9	{	{	PUNCT
ap-6786	135	10	δi2	δi2	X
ap-6786	136	1	[	[	PUNCT
ap-6786	136	2	+1	+1	NOUN
ap-6786	136	3	+	+	CCONJ
ap-6786	136	4	eh	eh	INTJ
ap-6786	136	5	fyk	fyk	NOUN
ap-6786	136	6	(	(	PUNCT
ap-6786	136	7	(	(	PUNCT
ap-6786	136	8	1−	1−	NUM
ap-6786	136	9	1−ξ2	1−ξ2	NUM
ap-6786	136	10	ξ	ξ	X
ap-6786	136	11	)	)	PUNCT
ap-6786	136	12	ε	ε	PROPN
ap-6786	136	13	′	′	NUM
ap-6786	137	1	−	−	ADV
ap-6786	138	1	εss	εss	NOUN
ap-6786	138	2	)	)	PUNCT
ap-6786	138	3	]	]	PUNCT
ap-6786	139	1	+	+	CCONJ
ap-6786	139	2	δi2	δi2	VERB
ap-6786	139	3	+	+	ADJ
ap-6786	139	4	1	1	NUM
ap-6786	139	5	ε	ε	NOUN
ap-6786	139	6	′	′	NUM
ap-6786	139	7	εss	εss	INTJ
ap-6786	139	8	(	(	PUNCT
ap-6786	139	9	1−	1−	NUM
ap-6786	139	10	1−	1−	NUM
ap-6786	139	11	ξ2	ξ2	NOUN
ap-6786	139	12	ξ	ξ	PROPN
ap-6786	139	13	)	)	PUNCT
ap-6786	139	14	}	}	PUNCT
ap-6786	139	15	=	=	SYM
ap-6786	139	16	0	0	NUM
ap-6786	139	17	,	,	PUNCT
ap-6786	139	18	(	(	PUNCT
ap-6786	139	19	13	13	NUM
ap-6786	139	20	)	)	PUNCT
ap-6786	139	21	where	where	SCONJ
ap-6786	139	22	:	:	PUNCT
ap-6786	139	23	w1	w1	NOUN
ap-6786	139	24	=	=	SYM
ap-6786	139	25	k	k	PROPN
ap-6786	140	1	−	−	PROPN
ap-6786	140	2	k2ξ	k2ξ	PROPN
ap-6786	140	3	w2	w2	NOUN
ap-6786	140	4	=	=	PROPN
ap-6786	140	5	k(k	k(k	PROPN
ap-6786	140	6	−	−	NOUN
ap-6786	140	7	2	2	NUM
ap-6786	140	8	)	)	PUNCT
ap-6786	140	9	+	+	CCONJ
ap-6786	140	10	1	1	NUM
ap-6786	140	11	w3	w3	NOUN
ap-6786	140	12	=	=	SYM
ap-6786	140	13	(	(	PUNCT
ap-6786	140	14	k	k	NOUN
ap-6786	140	15	−	−	PROPN
ap-6786	141	1	2)k2	2)k2	NUM
ap-6786	141	2	w	w	NOUN
ap-6786	141	3	=	=	SYM
ap-6786	141	4	1	1	NUM
ap-6786	141	5	+	+	CCONJ
ap-6786	141	6	(	(	PUNCT
ap-6786	141	7	k	k	PART
ap-6786	141	8	−	−	PROPN
ap-6786	141	9	2)k2ξ	2)k2ξ	NOUN
ap-6786	141	10	δi	δi	NOUN
ap-6786	141	11	=	=	PUNCT
ap-6786	141	12	0.5((−1)i	0.5((−1)i	NUM
ap-6786	141	13	+	+	NOUN
ap-6786	141	14	1	1	NUM
ap-6786	141	15	)	)	PUNCT
ap-6786	141	16	,	,	PUNCT
ap-6786	141	17	i	i	PRON
ap-6786	141	18	=	=	NOUN
ap-6786	141	19	1	1	NUM
ap-6786	141	20	,	,	PUNCT
ap-6786	141	21	2	2	NUM
ap-6786	141	22	k2	k2	NOUN
ap-6786	141	23	=	=	SYM
ap-6786	141	24	ε	ε	PROPN
ap-6786	141	25	′	′	NUM
ap-6786	142	1	εc1ξ	εc1ξ	PROPN
ap-6786	142	2	the	the	DET
ap-6786	142	3	unknown	unknown	ADJ
ap-6786	142	4	variables	variable	NOUN
ap-6786	142	5	are	be	AUX
ap-6786	142	6	:	:	PUNCT
ap-6786	142	7	•	•	NUM
ap-6786	142	8	ε	ε	PROPN
ap-6786	142	9	′	′	VERB
ap-6786	142	10	–	–	PUNCT
ap-6786	142	11	maximum	maximum	ADJ
ap-6786	142	12	strain	strain	NOUN
ap-6786	142	13	in	in	ADP
ap-6786	142	14	the	the	DET
ap-6786	142	15	cross	cross	NOUN
ap-6786	142	16	section	section	NOUN
ap-6786	142	17	,	,	PUNCT
ap-6786	142	18	•	•	NUM
ap-6786	142	19	ξ	ξ	X
ap-6786	142	20	–	–	PUNCT
ap-6786	142	21	coordinate	coordinate	NOUN
ap-6786	142	22	describing	describe	VERB
ap-6786	142	23	the	the	DET
ap-6786	142	24	location	location	NOUN
ap-6786	142	25	of	of	ADP
ap-6786	142	26	the	the	DET
ap-6786	142	27	neutral	neutral	ADJ
ap-6786	142	28	axis	axis	NOUN
ap-6786	142	29	.	.	PUNCT
ap-6786	143	1	3	3	X
ap-6786	143	2	.	.	PUNCT
ap-6786	143	3	computational	computational	ADJ
ap-6786	143	4	solution	solution	NOUN
ap-6786	143	5	and	and	CCONJ
ap-6786	143	6	numerical	numerical	ADJ
ap-6786	143	7	results	result	NOUN
ap-6786	143	8	it	it	PRON
ap-6786	143	9	is	be	AUX
ap-6786	143	10	not	not	PART
ap-6786	143	11	our	our	PRON
ap-6786	143	12	first	first	ADJ
ap-6786	143	13	work	work	NOUN
ap-6786	143	14	with	with	ADP
ap-6786	143	15	models	model	NOUN
ap-6786	143	16	of	of	ADP
ap-6786	143	17	the	the	DET
ap-6786	143	18	processes	process	NOUN
ap-6786	143	19	in	in	ADP
ap-6786	143	20	the	the	DET
ap-6786	143	21	rc	rc	PROPN
ap-6786	143	22	structure	structure	NOUN
ap-6786	143	23	members	member	NOUN
ap-6786	143	24	.	.	PUNCT
ap-6786	144	1	we	we	PRON
ap-6786	144	2	have	have	AUX
ap-6786	144	3	already	already	ADV
ap-6786	144	4	got	get	VERB
ap-6786	144	5	some	some	DET
ap-6786	144	6	experience	experience	NOUN
ap-6786	144	7	with	with	ADP
ap-6786	144	8	the	the	DET
ap-6786	144	9	circular	circular	ADJ
ap-6786	144	10	rc	rc	PROPN
ap-6786	144	11	structure	structure	NOUN
ap-6786	144	12	members	member	NOUN
ap-6786	144	13	[	[	X
ap-6786	144	14	6	6	NUM
ap-6786	144	15	]	]	PUNCT
ap-6786	144	16	.	.	PUNCT
ap-6786	145	1	this	this	DET
ap-6786	145	2	experience	experience	NOUN
ap-6786	145	3	suggests	suggest	VERB
ap-6786	145	4	that	that	SCONJ
ap-6786	145	5	we	we	PRON
ap-6786	145	6	have	have	VERB
ap-6786	145	7	to	to	ADP
ap-6786	145	8	244	244	NUM
ap-6786	145	9	vol	vol	NOUN
ap-6786	145	10	.	.	PUNCT
ap-6786	146	1	61	61	NUM
ap-6786	146	2	no	no	NOUN
ap-6786	146	3	.	.	PUNCT
ap-6786	147	1	1/2021	1/2021	NUM
ap-6786	147	2	global	global	ADJ
ap-6786	147	3	optimization	optimization	NOUN
ap-6786	147	4	to	to	PART
ap-6786	147	5	predict	predict	VERB
ap-6786	147	6	strains	strain	NOUN
ap-6786	147	7	in	in	ADP
ap-6786	147	8	rc	rc	PROPN
ap-6786	147	9	compressed	compress	VERB
ap-6786	147	10	columns	column	NOUN
ap-6786	147	11	expect	expect	VERB
ap-6786	147	12	many	many	ADJ
ap-6786	147	13	global	global	ADJ
ap-6786	147	14	and	and	CCONJ
ap-6786	147	15	local	local	ADJ
ap-6786	147	16	solutions	solution	NOUN
ap-6786	147	17	of	of	ADP
ap-6786	147	18	the	the	DET
ap-6786	147	19	least	least	ADJ
ap-6786	147	20	squares	square	NOUN
ap-6786	147	21	problem	problem	NOUN
ap-6786	147	22	.	.	PUNCT
ap-6786	148	1	therefore	therefore	ADV
ap-6786	148	2	,	,	PUNCT
ap-6786	148	3	we	we	PRON
ap-6786	148	4	decided	decide	VERB
ap-6786	148	5	to	to	PART
ap-6786	148	6	compare	compare	VERB
ap-6786	148	7	three	three	NUM
ap-6786	148	8	different	different	ADJ
ap-6786	148	9	algorithms	algorithm	NOUN
ap-6786	148	10	:	:	PUNCT
ap-6786	148	11	local	local	ADJ
ap-6786	148	12	search	search	NOUN
ap-6786	148	13	method	method	NOUN
ap-6786	148	14	(	(	PUNCT
ap-6786	148	15	trust	trust	NOUN
ap-6786	148	16	region	region	NOUN
ap-6786	148	17	reflective	reflective	NOUN
ap-6786	148	18	)	)	PUNCT
ap-6786	148	19	started	start	VERB
ap-6786	148	20	many	many	ADJ
ap-6786	148	21	times	time	NOUN
ap-6786	148	22	from	from	ADP
ap-6786	148	23	all	all	DET
ap-6786	148	24	points	point	NOUN
ap-6786	148	25	from	from	ADP
ap-6786	148	26	a	a	DET
ap-6786	148	27	net	net	NOUN
ap-6786	148	28	of	of	ADP
ap-6786	148	29	points	point	NOUN
ap-6786	148	30	equally	equally	ADV
ap-6786	148	31	distributed	distribute	VERB
ap-6786	148	32	on	on	ADP
ap-6786	148	33	the	the	DET
ap-6786	148	34	feasible	feasible	ADJ
ap-6786	148	35	box	box	NOUN
ap-6786	148	36	and	and	CCONJ
ap-6786	148	37	genetic	genetic	ADJ
ap-6786	148	38	and	and	CCONJ
ap-6786	148	39	particle	particle	NOUN
ap-6786	148	40	swarm	swarm	NOUN
ap-6786	148	41	algorithms	algorithm	NOUN
ap-6786	148	42	designed	design	VERB
ap-6786	148	43	for	for	ADP
ap-6786	148	44	searching	search	VERB
ap-6786	148	45	a	a	DET
ap-6786	148	46	global	global	ADJ
ap-6786	148	47	optimum	optimum	NOUN
ap-6786	148	48	.	.	PUNCT
ap-6786	149	1	for	for	ADP
ap-6786	149	2	the	the	DET
ap-6786	149	3	verification	verification	NOUN
ap-6786	149	4	of	of	ADP
ap-6786	149	5	the	the	DET
ap-6786	149	6	obtained	obtain	VERB
ap-6786	149	7	formulae	formulae	NOUN
ap-6786	149	8	,	,	PUNCT
ap-6786	149	9	two	two	NUM
ap-6786	149	10	rectangular	rectangular	ADJ
ap-6786	149	11	cross	cross	NOUN
ap-6786	149	12	-	-	NOUN
ap-6786	149	13	sections	section	NOUN
ap-6786	149	14	0.3	0.3	NUM
ap-6786	149	15	m	m	NOUN
ap-6786	149	16	×	×	NOUN
ap-6786	149	17	0.3	0.3	NUM
ap-6786	149	18	m	m	NOUN
ap-6786	149	19	under	under	ADP
ap-6786	149	20	the	the	DET
ap-6786	149	21	compression	compression	NOUN
ap-6786	149	22	have	have	AUX
ap-6786	149	23	been	be	AUX
ap-6786	149	24	considered	consider	VERB
ap-6786	149	25	:	:	PUNCT
ap-6786	149	26	the	the	DET
ap-6786	149	27	unreinforced	unreinforced	ADJ
ap-6786	149	28	one	one	NOUN
ap-6786	149	29	and	and	CCONJ
ap-6786	149	30	that	that	PRON
ap-6786	149	31	of	of	ADP
ap-6786	149	32	reinforced	reinforce	VERB
ap-6786	149	33	(	(	PUNCT
ap-6786	149	34	µfyk	µfyk	PROPN
ap-6786	149	35	/	/	SYM
ap-6786	149	36	fcm	fcm	X
ap-6786	149	37	=	=	NOUN
ap-6786	149	38	0.1	0.1	NUM
ap-6786	149	39	)	)	PUNCT
ap-6786	149	40	.	.	PUNCT
ap-6786	150	1	both	both	DET
ap-6786	150	2	sections	section	NOUN
ap-6786	150	3	had	have	VERB
ap-6786	150	4	the	the	DET
ap-6786	150	5	following	following	ADJ
ap-6786	150	6	characteristics	characteristic	NOUN
ap-6786	150	7	:	:	PUNCT
ap-6786	150	8	the	the	DET
ap-6786	150	9	concrete	concrete	ADJ
ap-6786	150	10	grade	grade	NOUN
ap-6786	150	11	c20/25	c20/25	PROPN
ap-6786	150	12	,	,	PUNCT
ap-6786	150	13	the	the	DET
ap-6786	150	14	yield	yield	NOUN
ap-6786	150	15	stress	stress	NOUN
ap-6786	150	16	of	of	ADP
ap-6786	150	17	steel	steel	NOUN
ap-6786	150	18	fyk	fyk	NOUN
ap-6786	150	19	=	=	SYM
ap-6786	150	20	500mpa	500mpa	NUM
ap-6786	150	21	(	(	PUNCT
ap-6786	150	22	reinforced	reinforce	VERB
ap-6786	150	23	)	)	PUNCT
ap-6786	150	24	,	,	PUNCT
ap-6786	150	25	reinforcement	reinforcement	NOUN
ap-6786	150	26	ratios	ratio	NOUN
ap-6786	150	27	of	of	ADP
ap-6786	150	28	the	the	DET
ap-6786	150	29	steel	steel	NOUN
ap-6786	150	30	in	in	ADP
ap-6786	150	31	compression	compression	NOUN
ap-6786	150	32	and	and	CCONJ
ap-6786	150	33	in	in	ADP
ap-6786	150	34	tension	tension	NOUN
ap-6786	150	35	µ1	µ1	NOUN
ap-6786	150	36	=	=	SYM
ap-6786	150	37	µ2	µ2	PROPN
ap-6786	150	38	=	=	PROPN
ap-6786	150	39	µ	µ	PROPN
ap-6786	150	40	,	,	PUNCT
ap-6786	150	41	t1	t1	PROPN
ap-6786	150	42	/	/	SYM
ap-6786	150	43	t	t	PROPN
ap-6786	150	44	=	=	SYM
ap-6786	150	45	t2	t2	PROPN
ap-6786	150	46	/	/	SYM
ap-6786	150	47	t	t	NOUN
ap-6786	150	48	=	=	SYM
ap-6786	150	49	0.1	0.1	NUM
ap-6786	150	50	,	,	PUNCT
ap-6786	150	51	eh	eh	INTJ
ap-6786	150	52	=	=	NOUN
ap-6786	150	53	0	0	PROPN
ap-6786	150	54	.	.	PUNCT
ap-6786	151	1	it	it	PRON
ap-6786	151	2	is	be	AUX
ap-6786	151	3	assumed	assume	VERB
ap-6786	151	4	that	that	SCONJ
ap-6786	151	5	the	the	DET
ap-6786	151	6	resistance	resistance	NOUN
ap-6786	151	7	of	of	ADP
ap-6786	151	8	the	the	DET
ap-6786	151	9	cross	cross	NOUN
ap-6786	151	10	-	-	NOUN
ap-6786	151	11	section	section	NOUN
ap-6786	151	12	is	be	AUX
ap-6786	151	13	reached	reach	VERB
ap-6786	151	14	when	when	SCONJ
ap-6786	151	15	the	the	DET
ap-6786	151	16	compressive	compressive	ADJ
ap-6786	151	17	strain	strain	NOUN
ap-6786	151	18	in	in	ADP
ap-6786	151	19	concrete	concrete	ADJ
ap-6786	151	20	εcu	εcu	NOUN
ap-6786	151	21	=	=	SYM
ap-6786	151	22	−3.5‰	−3.5‰	NOUN
ap-6786	151	23	or	or	CCONJ
ap-6786	151	24	the	the	DET
ap-6786	151	25	ultimate	ultimate	ADJ
ap-6786	151	26	strain	strain	NOUN
ap-6786	151	27	in	in	ADP
ap-6786	151	28	the	the	DET
ap-6786	151	29	reinforcing	reinforce	VERB
ap-6786	151	30	steel	steel	NOUN
ap-6786	151	31	equals	equal	VERB
ap-6786	151	32	εsu	εsu	NOUN
ap-6786	151	33	=	=	NOUN
ap-6786	151	34	10‰.	10‰.	NUM
ap-6786	151	35	after	after	ADP
ap-6786	151	36	some	some	DET
ap-6786	151	37	rearrangements	rearrangement	NOUN
ap-6786	151	38	and	and	CCONJ
ap-6786	151	39	substituting	substitute	VERB
ap-6786	151	40	ε′	ε′	NOUN
ap-6786	151	41	=	=	PUNCT
ap-6786	151	42	x	x	X
ap-6786	151	43	and	and	CCONJ
ap-6786	151	44	ξ	ξ	X
ap-6786	151	45	=	=	SYM
ap-6786	151	46	y	y	PROPN
ap-6786	151	47	,	,	PUNCT
ap-6786	151	48	the	the	DET
ap-6786	151	49	set	set	NOUN
ap-6786	151	50	of	of	ADP
ap-6786	151	51	equations	equation	NOUN
ap-6786	151	52	(	(	PUNCT
ap-6786	151	53	12–13	12–13	NUM
ap-6786	151	54	)	)	PUNCT
ap-6786	151	55	takes	take	VERB
ap-6786	151	56	the	the	DET
ap-6786	151	57	forms	form	NOUN
ap-6786	151	58	(	(	PUNCT
ap-6786	151	59	14–15	14–15	NUM
ap-6786	151	60	)	)	PUNCT
ap-6786	151	61	for	for	ADP
ap-6786	151	62	the	the	DET
ap-6786	151	63	unreinforced	unreinforced	ADJ
ap-6786	151	64	and	and	CCONJ
ap-6786	151	65	(	(	PUNCT
ap-6786	151	66	16–17	16–17	NUM
ap-6786	151	67	)	)	PUNCT
ap-6786	151	68	for	for	ADP
ap-6786	151	69	the	the	DET
ap-6786	151	70	reinforced	reinforce	VERB
ap-6786	151	71	cross	cross	NOUN
ap-6786	151	72	-	-	NOUN
ap-6786	151	73	sections	section	NOUN
ap-6786	151	74	,	,	PUNCT
ap-6786	151	75	respectively	respectively	ADV
ap-6786	151	76	.	.	PUNCT
ap-6786	152	1	due	due	ADP
ap-6786	152	2	to	to	ADP
ap-6786	152	3	the	the	DET
ap-6786	152	4	appearance	appearance	NOUN
ap-6786	152	5	of	of	ADP
ap-6786	152	6	the	the	DET
ap-6786	152	7	term	term	NOUN
ap-6786	152	8	y	y	PROPN
ap-6786	152	9	−	−	PROPN
ap-6786	152	10	x	x	PUNCT
ap-6786	152	11	in	in	ADP
ap-6786	152	12	the	the	DET
ap-6786	152	13	denominator	denominator	NOUN
ap-6786	152	14	in	in	ADP
ap-6786	152	15	some	some	DET
ap-6786	152	16	sets	set	NOUN
ap-6786	152	17	of	of	ADP
ap-6786	152	18	equations	equation	NOUN
ap-6786	152	19	,	,	PUNCT
ap-6786	152	20	a	a	DET
ap-6786	152	21	danger	danger	NOUN
ap-6786	152	22	of	of	ADP
ap-6786	152	23	the	the	DET
ap-6786	152	24	division	division	NOUN
ap-6786	152	25	by	by	ADP
ap-6786	152	26	0	0	NUM
ap-6786	152	27	occurs	occur	NOUN
ap-6786	152	28	.	.	PUNCT
ap-6786	153	1	for	for	ADP
ap-6786	153	2	this	this	DET
ap-6786	153	3	reason	reason	NOUN
ap-6786	153	4	,	,	PUNCT
ap-6786	153	5	fmincon	fmincon	PROPN
ap-6786	153	6	has	have	AUX
ap-6786	153	7	been	be	AUX
ap-6786	153	8	finally	finally	ADV
ap-6786	153	9	applied	apply	VERB
ap-6786	153	10	with	with	ADP
ap-6786	153	11	the	the	DET
ap-6786	153	12	algorithm	algorithm	NOUN
ap-6786	153	13	option	option	NOUN
ap-6786	153	14	set	set	VERB
ap-6786	153	15	to	to	ADP
ap-6786	153	16	”	"	PUNCT
ap-6786	153	17	interior	interior	ADJ
ap-6786	153	18	point	point	NOUN
ap-6786	153	19	method	method	NOUN
ap-6786	153	20	”	"	PUNCT
ap-6786	153	21	,	,	PUNCT
ap-6786	153	22	that	that	PRON
ap-6786	153	23	allowed	allow	VERB
ap-6786	153	24	to	to	PART
ap-6786	153	25	include	include	VERB
ap-6786	153	26	special	special	ADJ
ap-6786	153	27	constraints	constraint	NOUN
ap-6786	153	28	eliminating	eliminate	VERB
ap-6786	153	29	this	this	DET
ap-6786	153	30	danger	danger	NOUN
ap-6786	153	31	.	.	PUNCT
ap-6786	154	1	moreover	moreover	ADV
ap-6786	154	2	,	,	PUNCT
ap-6786	154	3	the	the	DET
ap-6786	154	4	existence	existence	NOUN
ap-6786	154	5	of	of	ADP
ap-6786	154	6	multiple	multiple	ADJ
ap-6786	154	7	minima	minima	NOUN
ap-6786	154	8	may	may	AUX
ap-6786	154	9	not	not	PART
ap-6786	154	10	be	be	AUX
ap-6786	154	11	avoided	avoid	VERB
ap-6786	154	12	.	.	PUNCT
ap-6786	155	1	however	however	ADV
ap-6786	155	2	,	,	PUNCT
ap-6786	155	3	the	the	DET
ap-6786	155	4	least	least	ADJ
ap-6786	155	5	squares	square	NOUN
ap-6786	155	6	formulation	formulation	NOUN
ap-6786	155	7	of	of	ADP
ap-6786	155	8	the	the	DET
ap-6786	155	9	problem	problem	NOUN
ap-6786	155	10	itself	itself	PRON
ap-6786	155	11	may	may	AUX
ap-6786	155	12	,	,	PUNCT
ap-6786	155	13	in	in	ADP
ap-6786	155	14	general	general	ADJ
ap-6786	155	15	,	,	PUNCT
ap-6786	155	16	involve	involve	VERB
ap-6786	155	17	extra	extra	ADJ
ap-6786	155	18	local	local	ADJ
ap-6786	155	19	solutions	solution	NOUN
ap-6786	155	20	(	(	PUNCT
ap-6786	155	21	such	such	DET
ap-6786	155	22	a	a	DET
ap-6786	155	23	counterexample	counterexample	NOUN
ap-6786	155	24	may	may	AUX
ap-6786	155	25	be	be	AUX
ap-6786	155	26	found	find	VERB
ap-6786	155	27	in	in	ADP
ap-6786	155	28	stachurski	stachurski	NOUN
ap-6786	155	29	[	[	X
ap-6786	155	30	34	34	NUM
ap-6786	155	31	]	]	PUNCT
ap-6786	155	32	)	)	PUNCT
ap-6786	155	33	.	.	PUNCT
ap-6786	156	1	this	this	PRON
ap-6786	156	2	has	have	AUX
ap-6786	156	3	been	be	AUX
ap-6786	156	4	confirmed	confirm	VERB
ap-6786	156	5	through	through	ADP
ap-6786	156	6	computational	computational	ADJ
ap-6786	156	7	results	result	NOUN
ap-6786	156	8	.	.	PUNCT
ap-6786	157	1	many	many	ADJ
ap-6786	157	2	local	local	ADJ
ap-6786	157	3	minima	minima	NOUN
ap-6786	157	4	and	and	CCONJ
ap-6786	157	5	sometimes	sometimes	ADV
ap-6786	157	6	several	several	ADJ
ap-6786	157	7	global	global	ADJ
ap-6786	157	8	minima	minima	NOUN
ap-6786	157	9	that	that	PRON
ap-6786	157	10	resulted	result	VERB
ap-6786	157	11	from	from	ADP
ap-6786	157	12	the	the	DET
ap-6786	157	13	numerical	numerical	ADJ
ap-6786	157	14	properties	property	NOUN
ap-6786	157	15	of	of	ADP
ap-6786	157	16	the	the	DET
ap-6786	157	17	optimization	optimization	NOUN
ap-6786	157	18	problem	problem	NOUN
ap-6786	157	19	were	be	AUX
ap-6786	157	20	encountered	encounter	VERB
ap-6786	157	21	.	.	PUNCT
ap-6786	158	1	therefore	therefore	ADV
ap-6786	158	2	,	,	PUNCT
ap-6786	158	3	the	the	DET
ap-6786	158	4	clusterization	clusterization	NOUN
ap-6786	158	5	idea	idea	NOUN
ap-6786	158	6	imported	import	VERB
ap-6786	158	7	from	from	ADP
ap-6786	158	8	clusterization	clusterization	NOUN
ap-6786	158	9	the	the	DET
ap-6786	158	10	methods	method	NOUN
ap-6786	158	11	of	of	ADP
ap-6786	158	12	the	the	DET
ap-6786	158	13	global	global	ADJ
ap-6786	158	14	optimization	optimization	NOUN
ap-6786	158	15	was	be	AUX
ap-6786	158	16	incorporated	incorporate	VERB
ap-6786	158	17	(	(	PUNCT
ap-6786	158	18	see	see	VERB
ap-6786	158	19	,	,	PUNCT
ap-6786	158	20	for	for	ADP
ap-6786	158	21	instance	instance	NOUN
ap-6786	158	22	,	,	PUNCT
ap-6786	158	23	thorn	thorn	NOUN
ap-6786	158	24	and	and	CCONJ
ap-6786	158	25	żilinstas	żilinsta	NOUN
ap-6786	158	26	[	[	X
ap-6786	158	27	35	35	NUM
ap-6786	158	28	]	]	SYM
ap-6786	158	29	)	)	PUNCT
ap-6786	158	30	.	.	PUNCT
ap-6786	159	1	the	the	DET
ap-6786	159	2	size	size	NOUN
ap-6786	159	3	of	of	ADP
ap-6786	159	4	the	the	DET
ap-6786	159	5	problem	problem	NOUN
ap-6786	159	6	and	and	CCONJ
ap-6786	159	7	computation	computation	NOUN
ap-6786	159	8	time	time	NOUN
ap-6786	159	9	were	be	AUX
ap-6786	159	10	of	of	ADP
ap-6786	159	11	secondary	secondary	ADJ
ap-6786	159	12	importance	importance	NOUN
ap-6786	159	13	.	.	PUNCT
ap-6786	160	1	we	we	PRON
ap-6786	160	2	have	have	AUX
ap-6786	160	3	also	also	ADV
ap-6786	160	4	tested	test	VERB
ap-6786	160	5	the	the	DET
ap-6786	160	6	genetic	genetic	ADJ
ap-6786	160	7	and	and	CCONJ
ap-6786	160	8	particle	particle	NOUN
ap-6786	160	9	swarm	swarm	NOUN
ap-6786	160	10	algorithms	algorithms	NOUN
ap-6786	160	11	from	from	ADP
ap-6786	160	12	the	the	DET
ap-6786	160	13	global	global	ADJ
ap-6786	160	14	optimization	optimization	NOUN
ap-6786	160	15	matlab	matlab	PROPN
ap-6786	160	16	’s	’s	PART
ap-6786	160	17	toolbox	toolbox	NOUN
ap-6786	160	18	,	,	PUNCT
ap-6786	160	19	comparing	compare	VERB
ap-6786	160	20	them	they	PRON
ap-6786	160	21	with	with	ADP
ap-6786	160	22	a	a	DET
ap-6786	160	23	local	local	ADJ
ap-6786	160	24	search	search	NOUN
ap-6786	160	25	method	method	NOUN
ap-6786	160	26	started	start	VERB
ap-6786	160	27	from	from	ADP
ap-6786	160	28	all	all	DET
ap-6786	160	29	points	point	NOUN
ap-6786	160	30	of	of	ADP
ap-6786	160	31	the	the	DET
ap-6786	160	32	net	net	NOUN
ap-6786	160	33	covering	cover	VERB
ap-6786	160	34	the	the	DET
ap-6786	160	35	whole	whole	ADJ
ap-6786	160	36	set	set	NOUN
ap-6786	160	37	ω	ω	PROPN
ap-6786	160	38	of	of	ADP
ap-6786	160	39	feasible	feasible	ADJ
ap-6786	160	40	points	point	NOUN
ap-6786	160	41	.	.	PUNCT
ap-6786	161	1	for	for	ADP
ap-6786	161	2	testing	testing	NOUN
ap-6786	161	3	purposes	purpose	NOUN
ap-6786	161	4	,	,	PUNCT
ap-6786	161	5	the	the	DET
ap-6786	161	6	sets	set	NOUN
ap-6786	161	7	of	of	ADP
ap-6786	161	8	equations	equation	NOUN
ap-6786	161	9	were	be	AUX
ap-6786	161	10	used	use	VERB
ap-6786	161	11	that	that	PRON
ap-6786	161	12	described	describe	VERB
ap-6786	161	13	the	the	DET
ap-6786	161	14	reinforced	reinforce	VERB
ap-6786	161	15	or	or	CCONJ
ap-6786	161	16	unreinforced	unreinforced	ADJ
ap-6786	161	17	concrete	concrete	ADJ
ap-6786	161	18	sections	section	NOUN
ap-6786	161	19	subjected	subject	VERB
ap-6786	161	20	to	to	ADP
ap-6786	161	21	the	the	DET
ap-6786	161	22	compression	compression	NOUN
ap-6786	161	23	.	.	PUNCT
ap-6786	162	1	the	the	DET
ap-6786	162	2	equations	equation	NOUN
ap-6786	162	3	for	for	ADP
ap-6786	162	4	the	the	DET
ap-6786	162	5	concrete	concrete	NOUN
ap-6786	162	6	without	without	ADP
ap-6786	162	7	the	the	DET
ap-6786	162	8	reinforcement	reinforcement	NOUN
ap-6786	162	9	–	–	PUNCT
ap-6786	162	10	the	the	DET
ap-6786	162	11	subject	subject	NOUN
ap-6786	162	12	to	to	ADP
ap-6786	162	13	the	the	DET
ap-6786	162	14	compression	compression	NOUN
ap-6786	162	15	with	with	ADP
ap-6786	162	16	bending	bending	NOUN
ap-6786	162	17	are	be	AUX
ap-6786	162	18	r1(x	r1(x	PRON
ap-6786	162	19	,	,	PUNCT
ap-6786	162	20	y	y	NOUN
ap-6786	162	21	)	)	PUNCT
ap-6786	163	1	=	=	PUNCT
ap-6786	163	2	−a1	−a1	VERB
ap-6786	163	3	+	+	X
ap-6786	163	4	(	(	PUNCT
ap-6786	163	5	2.25	2.25	NUM
ap-6786	163	6	+	+	NOUN
ap-6786	163	7	0.5x)y−	0.5x)y−	NUM
ap-6786	163	8	0.25xy−	0.25xy−	VERB
ap-6786	163	9	4	4	NUM
ap-6786	163	10	[	[	PUNCT
ap-6786	163	11	−12.5y	−12.5y	ADV
ap-6786	163	12	x	x	SYM
ap-6786	164	1	ln(1−	ln(1−	ADJ
ap-6786	164	2	0.125x)−	0.125x)−	NUM
ap-6786	164	3	y	y	NOUN
ap-6786	164	4	]	]	PUNCT
ap-6786	164	5	=	=	PUNCT
ap-6786	164	6	0	0	NUM
ap-6786	164	7	,	,	PUNCT
ap-6786	164	8	(	(	PUNCT
ap-6786	164	9	14	14	NUM
ap-6786	164	10	)	)	PUNCT
ap-6786	164	11	r2(x	r2(x	PROPN
ap-6786	164	12	,	,	PUNCT
ap-6786	164	13	y	y	NOUN
ap-6786	164	14	)	)	PUNCT
ap-6786	164	15	=	=	SYM
ap-6786	164	16	−a2	−a2	NOUN
ap-6786	164	17	+	+	CCONJ
ap-6786	164	18	(	(	PUNCT
ap-6786	164	19	3.125	3.125	NUM
ap-6786	164	20	+	+	NOUN
ap-6786	164	21	0.25x)y+	0.25x)y+	NOUN
ap-6786	164	22	[	[	PUNCT
ap-6786	164	23	−3.125	−3.125	NOUN
ap-6786	165	1	+	+	X
ap-6786	165	2	0.25x−	0.25x−	NUM
ap-6786	166	1	0.125x	0.125x	NUM
ap-6786	166	2	y	y	X
ap-6786	166	3	]	]	PUNCT
ap-6786	166	4	y2	y2	PROPN
ap-6786	166	5	+	+	NUM
ap-6786	166	6	0.16667xy2	0.16667xy2	NOUN
ap-6786	166	7	+	+	SYM
ap-6786	166	8	50y	50y	NOUN
ap-6786	166	9	x	x	PUNCT
ap-6786	167	1	[	[	X
ap-6786	167	2	0.5	0.5	NUM
ap-6786	167	3	ln(1−	ln(1−	PROPN
ap-6786	167	4	0.125x	0.125x	PROPN
ap-6786	167	5	)	)	PUNCT
ap-6786	168	1	+	+	CCONJ
ap-6786	168	2	y	y	PROPN
ap-6786	168	3	+	+	NOUN
ap-6786	168	4	8(1−	8(1−	NUM
ap-6786	168	5	0.125x)y	0.125x)y	NUM
ap-6786	168	6	x	x	SYM
ap-6786	169	1	ln(1−	ln(1−	PROPN
ap-6786	169	2	0.125x	0.125x	PROPN
ap-6786	169	3	)	)	PUNCT
ap-6786	169	4	]	]	PUNCT
ap-6786	170	1	=	=	PUNCT
ap-6786	170	2	0	0	NUM
ap-6786	170	3	,	,	PUNCT
ap-6786	170	4	(	(	PUNCT
ap-6786	170	5	15	15	NUM
ap-6786	170	6	)	)	PUNCT
ap-6786	170	7	where	where	SCONJ
ap-6786	170	8	:	:	PUNCT
ap-6786	170	9	x	x	X
ap-6786	170	10	–	–	PUNCT
ap-6786	170	11	maximum	maximum	ADJ
ap-6786	170	12	compressive	compressive	ADJ
ap-6786	170	13	x	x	X
ap-6786	170	14	∈	∈	PROPN
ap-6786	170	15	[	[	X
ap-6786	170	16	−5,−10−10	−5,−10−10	PUNCT
ap-6786	170	17	]	]	X
ap-6786	170	18	strain	strain	NOUN
ap-6786	170	19	in	in	ADP
ap-6786	170	20	concrete	concrete	ADJ
ap-6786	170	21	y	y	NOUN
ap-6786	170	22	–	–	PUNCT
ap-6786	170	23	coordinate	coordinate	NOUN
ap-6786	170	24	specifying	specify	VERB
ap-6786	170	25	y	y	PROPN
ap-6786	170	26	∈	∈	PROPN
ap-6786	171	1	[	[	X
ap-6786	171	2	10−10	10−10	NUM
ap-6786	171	3	,	,	PUNCT
ap-6786	171	4	1	1	NUM
ap-6786	171	5	]	]	X
ap-6786	171	6	location	location	NOUN
ap-6786	171	7	of	of	ADP
ap-6786	171	8	the	the	DET
ap-6786	171	9	neutral	neutral	ADJ
ap-6786	171	10	axis	axis	NOUN
ap-6786	171	11	of	of	ADP
ap-6786	171	12	the	the	DET
ap-6786	171	13	cross	cross	NOUN
ap-6786	171	14	-	-	ADJ
ap-6786	171	15	section	section	ADJ
ap-6786	171	16	different	different	ADJ
ap-6786	171	17	values	value	NOUN
ap-6786	171	18	of	of	ADP
ap-6786	171	19	constants	constant	NOUN
ap-6786	171	20	a1	a1	NOUN
ap-6786	171	21	and	and	CCONJ
ap-6786	171	22	a2	a2	PROPN
ap-6786	171	23	correspond	correspond	VERB
ap-6786	171	24	to	to	ADP
ap-6786	171	25	different	different	ADJ
ap-6786	171	26	axial	axial	ADJ
ap-6786	171	27	forces	force	NOUN
ap-6786	171	28	n	n	VERB
ap-6786	171	29	and	and	CCONJ
ap-6786	171	30	bending	bend	VERB
ap-6786	171	31	moments	moment	NOUN
ap-6786	171	32	m	m	VERB
ap-6786	171	33	.	.	PUNCT
ap-6786	172	1	parameters	parameter	NOUN
ap-6786	172	2	a	a	PRON
ap-6786	172	3	are	be	AUX
ap-6786	172	4	collected	collect	VERB
ap-6786	172	5	in	in	ADP
ap-6786	172	6	table	table	NOUN
ap-6786	172	7	1	1	NUM
ap-6786	172	8	the	the	DET
ap-6786	172	9	corresponding	corresponding	ADJ
ap-6786	172	10	equations	equation	NOUN
ap-6786	172	11	for	for	ADP
ap-6786	172	12	the	the	DET
ap-6786	172	13	reinforced	reinforce	VERB
ap-6786	172	14	concrete	concrete	ADJ
ap-6786	172	15	section	section	NOUN
ap-6786	172	16	subjected	subject	VERB
ap-6786	172	17	to	to	ADP
ap-6786	172	18	the	the	DET
ap-6786	172	19	compression	compression	NOUN
ap-6786	172	20	with	with	ADP
ap-6786	172	21	bending	bending	NOUN
ap-6786	172	22	are	be	AUX
ap-6786	172	23	given	give	VERB
ap-6786	172	24	below	below	ADP
ap-6786	172	25	r1(x	r1(x	PROPN
ap-6786	172	26	,	,	PUNCT
ap-6786	172	27	y	y	NOUN
ap-6786	172	28	)	)	PUNCT
ap-6786	172	29	=	=	PUNCT
ap-6786	173	1	(	(	PUNCT
ap-6786	173	2	2.25	2.25	NUM
ap-6786	173	3	+	+	NOUN
ap-6786	173	4	0.5x)y	0.5x)y	NUM
ap-6786	173	5	−	−	NOUN
ap-6786	173	6	0.25xy−	0.25xy−	VERB
ap-6786	173	7	4	4	NUM
ap-6786	173	8	[	[	PUNCT
ap-6786	173	9	−12.5y	−12.5y	ADV
ap-6786	173	10	x	x	SYM
ap-6786	174	1	ln(1−	ln(1−	ADJ
ap-6786	174	2	0.125x)−	0.125x)−	NUM
ap-6786	174	3	y	y	NOUN
ap-6786	174	4	]	]	PUNCT
ap-6786	175	1	+	+	CCONJ
ap-6786	175	2	0.01x	0.01x	NUM
ap-6786	175	3	(	(	PUNCT
ap-6786	175	4	1−	1−	NUM
ap-6786	175	5	0.9	0.9	NUM
ap-6786	175	6	y	y	PROPN
ap-6786	175	7	)	)	PUNCT
ap-6786	175	8	−	−	PROPN
ap-6786	175	9	a1	a1	NOUN
ap-6786	175	10	=	=	NOUN
ap-6786	175	11	0	0	PROPN
ap-6786	175	12	,	,	PUNCT
ap-6786	175	13	(	(	PUNCT
ap-6786	175	14	16	16	NUM
ap-6786	175	15	)	)	PUNCT
ap-6786	175	16	r2(x	r2(x	PROPN
ap-6786	175	17	,	,	PUNCT
ap-6786	175	18	y	y	NOUN
ap-6786	175	19	)	)	PUNCT
ap-6786	175	20	=	=	PUNCT
ap-6786	175	21	(	(	PUNCT
ap-6786	175	22	3.125	3.125	NUM
ap-6786	175	23	+	+	CCONJ
ap-6786	175	24	0.25x)y−	0.25x)y−	NOUN
ap-6786	175	25	[	[	PUNCT
ap-6786	175	26	3.125	3.125	NUM
ap-6786	175	27	+	+	CCONJ
ap-6786	175	28	0.25x+	0.25x+	NOUN
ap-6786	175	29	0.125x	0.125x	NUM
ap-6786	175	30	y	y	PROPN
ap-6786	175	31	]	]	PUNCT
ap-6786	175	32	y2	y2	PROPN
ap-6786	175	33	+	+	NUM
ap-6786	175	34	0.16667xy2	0.16667xy2	NOUN
ap-6786	175	35	+	+	SYM
ap-6786	175	36	50y	50y	NOUN
ap-6786	175	37	x	x	PUNCT
ap-6786	176	1	[	[	X
ap-6786	176	2	0.5	0.5	NUM
ap-6786	176	3	ln(1−	ln(1−	PROPN
ap-6786	176	4	0.125x	0.125x	PROPN
ap-6786	176	5	)	)	PUNCT
ap-6786	177	1	+	+	CCONJ
ap-6786	177	2	y	y	PROPN
ap-6786	177	3	+	+	NOUN
ap-6786	177	4	8(1−	8(1−	NUM
ap-6786	177	5	0.125x)y	0.125x)y	NUM
ap-6786	177	6	x	x	SYM
ap-6786	178	1	ln(1−	ln(1−	PROPN
ap-6786	178	2	0.125x	0.125x	PROPN
ap-6786	178	3	)	)	PUNCT
ap-6786	178	4	]	]	PUNCT
ap-6786	179	1	+	+	CCONJ
ap-6786	179	2	0.004x(1−	0.004x(1−	NUM
ap-6786	179	3	0.9	0.9	NUM
ap-6786	179	4	y	y	NOUN
ap-6786	179	5	)	)	PUNCT
ap-6786	179	6	−	−	PROPN
ap-6786	179	7	a2	a2	PROPN
ap-6786	179	8	=	=	SYM
ap-6786	179	9	0	0	NUM
ap-6786	179	10	,	,	PUNCT
ap-6786	179	11	(	(	PUNCT
ap-6786	179	12	17	17	NUM
ap-6786	179	13	)	)	PUNCT
ap-6786	179	14	where	where	SCONJ
ap-6786	179	15	x	x	PRON
ap-6786	179	16	and	and	CCONJ
ap-6786	179	17	y	y	PROPN
ap-6786	179	18	have	have	VERB
ap-6786	179	19	the	the	DET
ap-6786	179	20	same	same	ADJ
ap-6786	179	21	meaning	meaning	NOUN
ap-6786	179	22	and	and	CCONJ
ap-6786	179	23	scope	scope	NOUN
ap-6786	179	24	as	as	ADP
ap-6786	179	25	in	in	ADP
ap-6786	179	26	equations	equation	NOUN
ap-6786	179	27	(	(	PUNCT
ap-6786	179	28	14	14	NUM
ap-6786	179	29	)	)	PUNCT
ap-6786	179	30	and	and	CCONJ
ap-6786	179	31	(	(	PUNCT
ap-6786	179	32	15	15	NUM
ap-6786	179	33	)	)	PUNCT
ap-6786	179	34	.	.	PUNCT
ap-6786	180	1	we	we	PRON
ap-6786	180	2	used	use	VERB
ap-6786	180	3	two	two	NUM
ap-6786	180	4	sets	set	NOUN
ap-6786	180	5	of	of	ADP
ap-6786	180	6	constant	constant	ADJ
ap-6786	180	7	parameters	parameter	NOUN
ap-6786	180	8	a1	a1	NOUN
ap-6786	180	9	and	and	CCONJ
ap-6786	180	10	a2	a2	PROPN
ap-6786	180	11	for	for	ADP
ap-6786	180	12	that	that	DET
ap-6786	180	13	case	case	NOUN
ap-6786	180	14	specified	specify	VERB
ap-6786	180	15	below	below	ADV
ap-6786	180	16	.	.	PUNCT
ap-6786	181	1	set	set	VERB
ap-6786	181	2	no	no	INTJ
ap-6786	181	3	.	.	PUNCT
ap-6786	182	1	a1	a1	NOUN
ap-6786	182	2	a2	a2	PROPN
ap-6786	182	3	1	1	NUM
ap-6786	182	4	0.143445	0.143445	NUM
ap-6786	182	5	0.0292155	0.0292155	NUM
ap-6786	182	6	2	2	NUM
ap-6786	182	7	0.129182	0.129182	NUM
ap-6786	182	8	0.0348055	0.0348055	NUM
ap-6786	182	9	we	we	PRON
ap-6786	182	10	have	have	VERB
ap-6786	182	11	to	to	PART
ap-6786	182	12	solve	solve	VERB
ap-6786	182	13	sets	set	NOUN
ap-6786	182	14	of	of	ADP
ap-6786	182	15	two	two	NUM
ap-6786	182	16	nonlinear	nonlinear	ADJ
ap-6786	182	17	equations	equation	NOUN
ap-6786	182	18	with	with	ADP
ap-6786	182	19	two	two	NUM
ap-6786	182	20	unknowns	unknown	NOUN
ap-6786	182	21	x	x	X
ap-6786	182	22	and	and	CCONJ
ap-6786	182	23	y	y	PROPN
ap-6786	182	24	specified	specify	VERB
ap-6786	182	25	above	above	ADV
ap-6786	182	26	{	{	PUNCT
ap-6786	182	27	r1(x	r1(x	NOUN
ap-6786	182	28	,	,	PUNCT
ap-6786	182	29	y	y	NOUN
ap-6786	182	30	)	)	PUNCT
ap-6786	182	31	=	=	SYM
ap-6786	182	32	0	0	PUNCT
ap-6786	183	1	r2(x	r2(x	PROPN
ap-6786	183	2	,	,	PUNCT
ap-6786	183	3	y	y	NOUN
ap-6786	183	4	)	)	PUNCT
ap-6786	183	5	=	=	SYM
ap-6786	183	6	0	0	NUM
ap-6786	184	1	where	where	SCONJ
ap-6786	184	2	[	[	PUNCT
ap-6786	184	3	x	x	X
ap-6786	184	4	y	y	NOUN
ap-6786	184	5	]	]	PUNCT
ap-6786	184	6	∈	∈	PROPN
ap-6786	184	7	ω	ω	X
ap-6786	184	8	ω	ω	PROPN
ap-6786	184	9	=	=	SYM
ap-6786	184	10	{	{	PUNCT
ap-6786	184	11	[	[	PUNCT
ap-6786	184	12	x	x	X
ap-6786	184	13	y	y	NOUN
ap-6786	184	14	]	]	PUNCT
ap-6786	184	15	∈	∈	PROPN
ap-6786	184	16	r2	r2	PROPN
ap-6786	184	17	∣∣∣∣	∣∣∣∣	PROPN
ap-6786	184	18	xl	xl	PROPN
ap-6786	184	19	≤	≤	PROPN
ap-6786	184	20	x	x	X
ap-6786	184	21	≤	≤	NUM
ap-6786	184	22	xu	xu	NUM
ap-6786	184	23	yl	yl	NOUN
ap-6786	184	24	≤	≤	NUM
ap-6786	184	25	y	y	PROPN
ap-6786	184	26	≤	≤	PROPN
ap-6786	184	27	yu	yu	PROPN
ap-6786	184	28	}	}	PUNCT
ap-6786	184	29	(	(	PUNCT
ap-6786	184	30	18	18	NUM
ap-6786	184	31	)	)	PUNCT
ap-6786	184	32	xl	xl	PROPN
ap-6786	184	33	,	,	PUNCT
ap-6786	184	34	xu	xu	PROPN
ap-6786	184	35	are	be	AUX
ap-6786	184	36	the	the	DET
ap-6786	184	37	lower	lower	ADV
ap-6786	184	38	bound	bind	VERB
ap-6786	184	39	and	and	CCONJ
ap-6786	184	40	upper	upper	ADJ
ap-6786	184	41	bound	bind	VERB
ap-6786	184	42	on	on	ADP
ap-6786	184	43	variable	variable	ADJ
ap-6786	184	44	x	x	PUNCT
ap-6786	184	45	and	and	CCONJ
ap-6786	184	46	similarly	similarly	ADV
ap-6786	184	47	yl	yl	NOUN
ap-6786	184	48	,	,	PUNCT
ap-6786	184	49	yu	yu	PROPN
ap-6786	184	50	are	be	AUX
ap-6786	184	51	the	the	DET
ap-6786	184	52	lower	lower	ADV
ap-6786	184	53	bound	bind	VERB
ap-6786	184	54	and	and	CCONJ
ap-6786	184	55	upper	upper	ADJ
ap-6786	184	56	bound	bind	VERB
ap-6786	184	57	on	on	ADP
ap-6786	184	58	variable	variable	ADJ
ap-6786	184	59	y.	y.	NOUN
ap-6786	184	60	due	due	ADP
ap-6786	184	61	to	to	ADP
ap-6786	184	62	their	their	PRON
ap-6786	184	63	presence	presence	NOUN
ap-6786	184	64	,	,	PUNCT
ap-6786	184	65	a	a	DET
ap-6786	184	66	direct	direct	ADJ
ap-6786	184	67	use	use	NOUN
ap-6786	184	68	of	of	ADP
ap-6786	184	69	numerical	numerical	ADJ
ap-6786	184	70	methods	method	NOUN
ap-6786	184	71	for	for	ADP
ap-6786	184	72	solving	solve	VERB
ap-6786	184	73	sets	set	NOUN
ap-6786	184	74	of	of	ADP
ap-6786	184	75	nonlinear	nonlinear	ADJ
ap-6786	184	76	equations	equation	NOUN
ap-6786	184	77	seems	seem	VERB
ap-6786	184	78	to	to	PART
ap-6786	184	79	be	be	AUX
ap-6786	184	80	impractical	impractical	ADJ
ap-6786	184	81	.	.	PUNCT
ap-6786	185	1	therefore	therefore	ADV
ap-6786	185	2	,	,	PUNCT
ap-6786	185	3	our	our	PRON
ap-6786	185	4	task	task	NOUN
ap-6786	185	5	was	be	AUX
ap-6786	185	6	reformulated	reformulate	VERB
ap-6786	185	7	by	by	ADP
ap-6786	185	8	means	mean	NOUN
ap-6786	185	9	of	of	ADP
ap-6786	185	10	the	the	DET
ap-6786	185	11	frequently	frequently	ADV
ap-6786	185	12	used	use	VERB
ap-6786	185	13	the	the	DET
ap-6786	185	14	least	least	ADJ
ap-6786	185	15	squares	square	NOUN
ap-6786	185	16	method	method	NOUN
ap-6786	185	17	.	.	PUNCT
ap-6786	186	1	it	it	PRON
ap-6786	186	2	has	have	VERB
ap-6786	186	3	245	245	NUM
ap-6786	186	4	marek	marek	PROPN
ap-6786	186	5	lechman	lechman	NOUN
ap-6786	186	6	,	,	PUNCT
ap-6786	186	7	andrzej	andrzej	PROPN
ap-6786	186	8	stachurski	stachurski	PROPN
ap-6786	186	9	acta	acta	PROPN
ap-6786	186	10	polytechnica	polytechnica	PROPN
ap-6786	186	11	set	set	VERB
ap-6786	186	12	no	no	INTJ
ap-6786	186	13	.	.	PUNCT
ap-6786	187	1	a1	a1	NOUN
ap-6786	187	2	a2	a2	PROPN
ap-6786	187	3	1	1	NUM
ap-6786	187	4	0.17157	0.17157	NUM
ap-6786	187	5	0.01717	0.01717	NUM
ap-6786	187	6	2	2	NUM
ap-6786	187	7	0.13345	0.13345	NUM
ap-6786	187	8	0.02522	0.02522	NUM
ap-6786	187	9	3	3	NUM
ap-6786	187	10	0.10918	0.10918	NUM
ap-6786	187	11	0.026805	0.026805	NUM
ap-6786	187	12	4	4	NUM
ap-6786	187	13	0.08579	0.08579	NUM
ap-6786	187	14	0.02574	0.02574	NUM
ap-6786	187	15	5	5	NUM
ap-6786	187	16	0.07065	0.07065	NUM
ap-6786	187	17	0.02369	0.02369	NUM
ap-6786	187	18	6	6	NUM
ap-6786	187	19	0.04448	0.04448	NUM
ap-6786	187	20	0.01763	0.01763	NUM
ap-6786	187	21	7	7	NUM
ap-6786	187	22	0.02571	0.02571	NUM
ap-6786	187	23	0.01138	0.01138	NUM
ap-6786	187	24	table	table	NOUN
ap-6786	187	25	1	1	NUM
ap-6786	187	26	.	.	PUNCT
ap-6786	187	27	sets	set	NOUN
ap-6786	187	28	of	of	ADP
ap-6786	187	29	parameters	parameter	NOUN
ap-6786	187	30	for	for	ADP
ap-6786	187	31	unreinforced	unreinforced	ADJ
ap-6786	187	32	concrete	concrete	NOUN
ap-6786	187	33	subjected	subject	VERB
ap-6786	187	34	to	to	PART
ap-6786	187	35	compression	compression	VERB
ap-6786	187	36	with	with	ADP
ap-6786	187	37	bending	bend	VERB
ap-6786	187	38	lead	lead	NOUN
ap-6786	187	39	to	to	ADP
ap-6786	187	40	a	a	DET
ap-6786	187	41	nonlinear	nonlinear	ADJ
ap-6786	187	42	,	,	PUNCT
ap-6786	187	43	nonconvex	nonconvex	NOUN
ap-6786	187	44	optimization	optimization	NOUN
ap-6786	187	45	problem	problem	NOUN
ap-6786	187	46	min	min	PROPN
ap-6786	187	47	(	(	PUNCT
ap-6786	187	48	x	x	NOUN
ap-6786	187	49	,	,	PUNCT
ap-6786	187	50	y	y	PROPN
ap-6786	187	51	)	)	PUNCT
ap-6786	187	52	f(x	f(x	PROPN
ap-6786	187	53	,	,	PUNCT
ap-6786	187	54	y	y	NOUN
ap-6786	187	55	)	)	PUNCT
ap-6786	187	56	=	=	SYM
ap-6786	187	57	1	1	NUM
ap-6786	187	58	2	2	NUM
ap-6786	187	59	(	(	PUNCT
ap-6786	187	60	r2	r2	PROPN
ap-6786	187	61	1(x	1(x	NUM
ap-6786	187	62	,	,	PUNCT
ap-6786	187	63	y	y	NOUN
ap-6786	187	64	)	)	PUNCT
ap-6786	187	65	+	+	CCONJ
ap-6786	187	66	r2	r2	PROPN
ap-6786	187	67	2(x	2(x	NUM
ap-6786	187	68	,	,	PUNCT
ap-6786	187	69	y	y	NOUN
ap-6786	187	70	)	)	PUNCT
ap-6786	187	71	)	)	PUNCT
ap-6786	188	1	s.t	s.t	PROPN
ap-6786	188	2	.	.	PROPN
ap-6786	188	3	xl	xl	PROPN
ap-6786	188	4	≤	≤	PROPN
ap-6786	188	5	x	x	PUNCT
ap-6786	188	6	≤	≤	NUM
ap-6786	188	7	xu	xu	NUM
ap-6786	188	8	yl	yl	NOUN
ap-6786	188	9	≤	≤	NUM
ap-6786	188	10	y	y	PROPN
ap-6786	188	11	≤	≤	PROPN
ap-6786	188	12	yu	yu	PROPN
ap-6786	188	13	(	(	PUNCT
ap-6786	188	14	19	19	NUM
ap-6786	188	15	)	)	PUNCT
ap-6786	188	16	below	below	ADV
ap-6786	188	17	are	be	AUX
ap-6786	188	18	given	give	VERB
ap-6786	188	19	the	the	DET
ap-6786	188	20	results	result	NOUN
ap-6786	188	21	of	of	ADP
ap-6786	188	22	the	the	DET
ap-6786	188	23	local	local	ADJ
ap-6786	188	24	search	search	NOUN
ap-6786	188	25	with	with	ADP
ap-6786	188	26	multiple	multiple	ADJ
ap-6786	188	27	starting	starting	NOUN
ap-6786	188	28	points	point	NOUN
ap-6786	188	29	,	,	PUNCT
ap-6786	188	30	genetic	genetic	ADJ
ap-6786	188	31	algorithm	algorithm	NOUN
ap-6786	188	32	and	and	CCONJ
ap-6786	188	33	the	the	DET
ap-6786	188	34	particle	particle	NOUN
ap-6786	188	35	swarm	swarm	NOUN
ap-6786	188	36	optimization	optimization	NOUN
ap-6786	188	37	method	method	NOUN
ap-6786	188	38	.	.	PUNCT
ap-6786	189	1	in	in	ADP
ap-6786	189	2	the	the	DET
ap-6786	189	3	first	first	ADJ
ap-6786	189	4	approach	approach	NOUN
ap-6786	189	5	,	,	PUNCT
ap-6786	189	6	we	we	PRON
ap-6786	189	7	selected	select	VERB
ap-6786	189	8	the	the	DET
ap-6786	189	9	fmincon	fmincon	NOUN
ap-6786	189	10	function	function	NOUN
ap-6786	189	11	from	from	ADP
ap-6786	189	12	the	the	DET
ap-6786	189	13	matlab	matlab	PROPN
ap-6786	189	14	optimization	optimization	NOUN
ap-6786	189	15	toolbox	toolbox	NOUN
ap-6786	189	16	as	as	ADP
ap-6786	189	17	a	a	DET
ap-6786	189	18	tool	tool	NOUN
ap-6786	189	19	to	to	PART
ap-6786	189	20	solve	solve	VERB
ap-6786	189	21	the	the	DET
ap-6786	189	22	least	least	ADJ
ap-6786	189	23	squares	square	NOUN
ap-6786	189	24	problem	problem	NOUN
ap-6786	189	25	(	(	PUNCT
ap-6786	189	26	19	19	NUM
ap-6786	189	27	)	)	PUNCT
ap-6786	189	28	,	,	PUNCT
ap-6786	189	29	because	because	SCONJ
ap-6786	189	30	it	it	PRON
ap-6786	189	31	allows	allow	VERB
ap-6786	189	32	the	the	DET
ap-6786	189	33	introduction	introduction	NOUN
ap-6786	189	34	of	of	ADP
ap-6786	189	35	of	of	ADP
ap-6786	189	36	the	the	DET
ap-6786	189	37	box	box	NOUN
ap-6786	189	38	constraints	constraint	NOUN
ap-6786	189	39	.	.	PUNCT
ap-6786	190	1	the	the	DET
ap-6786	190	2	steps	step	NOUN
ap-6786	190	3	of	of	ADP
ap-6786	190	4	the	the	DET
ap-6786	190	5	procedure	procedure	NOUN
ap-6786	190	6	may	may	AUX
ap-6786	190	7	be	be	AUX
ap-6786	190	8	summarized	summarize	VERB
ap-6786	190	9	as	as	SCONJ
ap-6786	190	10	follows	follow	VERB
ap-6786	190	11	:	:	PUNCT
ap-6786	190	12	set	set	PROPN
ap-6786	190	13	s	s	PRON
ap-6786	190	14	–	–	PUNCT
ap-6786	190	15	set	set	NOUN
ap-6786	190	16	of	of	ADP
ap-6786	190	17	solution	solution	NOUN
ap-6786	190	18	clusters	cluster	NOUN
ap-6786	190	19	to	to	PART
ap-6786	190	20	be	be	AUX
ap-6786	190	21	an	an	DET
ap-6786	190	22	empty	empty	ADJ
ap-6786	190	23	set	set	NOUN
ap-6786	190	24	.	.	PUNCT
ap-6786	191	1	while	while	SCONJ
ap-6786	191	2	(	(	PUNCT
ap-6786	191	3	there	there	PRON
ap-6786	191	4	are	be	VERB
ap-6786	191	5	non	non	X
ap-6786	191	6	used	use	VERB
ap-6786	191	7	points	point	NOUN
ap-6786	191	8	in	in	ADP
ap-6786	191	9	the	the	DET
ap-6786	191	10	net	net	NOUN
ap-6786	191	11	covering	covering	NOUN
ap-6786	191	12	ω	ω	NOUN
ap-6786	191	13	)	)	PUNCT
ap-6786	191	14	•	•	NOUN
ap-6786	191	15	take	take	VERB
ap-6786	191	16	a	a	DET
ap-6786	191	17	new	new	ADJ
ap-6786	191	18	point	point	NOUN
ap-6786	191	19	x0	x0	PROPN
ap-6786	191	20	∈	∈	PROPN
ap-6786	191	21	ω	ω	PROPN
ap-6786	191	22	,	,	PUNCT
ap-6786	191	23	•	•	NOUN
ap-6786	191	24	solve	solve	VERB
ap-6786	191	25	the	the	DET
ap-6786	191	26	least	least	ADJ
ap-6786	191	27	squares	square	NOUN
ap-6786	191	28	problem	problem	NOUN
ap-6786	191	29	by	by	ADP
ap-6786	191	30	means	mean	NOUN
ap-6786	191	31	of	of	ADP
ap-6786	191	32	the	the	DET
ap-6786	191	33	fmincon	fmincon	NOUN
ap-6786	191	34	function	function	NOUN
ap-6786	191	35	from	from	ADP
ap-6786	191	36	the	the	DET
ap-6786	191	37	matlab	matlab	PROPN
ap-6786	191	38	’s	’s	PART
ap-6786	191	39	toolbox	toolbox	NOUN
ap-6786	191	40	optimization	optimization	NOUN
ap-6786	191	41	starting	start	VERB
ap-6786	191	42	from	from	ADP
ap-6786	191	43	the	the	DET
ap-6786	191	44	point	point	NOUN
ap-6786	191	45	x0	x0	PROPN
ap-6786	191	46	,	,	PUNCT
ap-6786	191	47	•	•	NUM
ap-6786	191	48	denote	denote	VERB
ap-6786	191	49	the	the	DET
ap-6786	191	50	found	find	VERB
ap-6786	191	51	solution	solution	NOUN
ap-6786	191	52	by	by	ADP
ap-6786	191	53	x	x	NOUN
ap-6786	191	54	,	,	PUNCT
ap-6786	191	55	•	•	ADP
ap-6786	191	56	if	if	SCONJ
ap-6786	191	57	f(x	f(x	PROPN
ap-6786	191	58	)	)	PUNCT
ap-6786	191	59	<	<	X
ap-6786	191	60	restol	restol	NOUN
ap-6786	191	61	if	if	SCONJ
ap-6786	191	62	x	x	PRON
ap-6786	191	63	belongs	belong	VERB
ap-6786	191	64	to	to	ADP
ap-6786	191	65	some	some	DET
ap-6786	191	66	cluster	cluster	NOUN
ap-6786	191	67	in	in	ADP
ap-6786	191	68	s	s	NOUN
ap-6786	191	69	compare	compare	NOUN
ap-6786	191	70	function	function	NOUN
ap-6786	191	71	value	value	NOUN
ap-6786	191	72	f(x	f(x	PROPN
ap-6786	191	73	)	)	PUNCT
ap-6786	191	74	with	with	ADP
ap-6786	191	75	the	the	DET
ap-6786	191	76	best	good	ADJ
ap-6786	191	77	in	in	ADP
ap-6786	191	78	the	the	DET
ap-6786	191	79	cluster	cluster	NOUN
ap-6786	191	80	and	and	CCONJ
ap-6786	191	81	save	save	VERB
ap-6786	191	82	the	the	DET
ap-6786	191	83	better	well	ADJ
ap-6786	191	84	of	of	ADP
ap-6786	191	85	the	the	DET
ap-6786	191	86	two	two	NUM
ap-6786	191	87	points	point	NOUN
ap-6786	191	88	as	as	ADP
ap-6786	191	89	the	the	DET
ap-6786	191	90	seed	seed	NOUN
ap-6786	191	91	of	of	ADP
ap-6786	191	92	the	the	DET
ap-6786	191	93	cluster	cluster	NOUN
ap-6786	191	94	else	else	ADV
ap-6786	191	95	save	save	VERB
ap-6786	191	96	the	the	DET
ap-6786	191	97	current	current	ADJ
ap-6786	191	98	point	point	NOUN
ap-6786	191	99	as	as	ADP
ap-6786	191	100	the	the	DET
ap-6786	191	101	seed	seed	NOUN
ap-6786	191	102	of	of	ADP
ap-6786	191	103	a	a	DET
ap-6786	191	104	new	new	ADJ
ap-6786	191	105	cluster	cluster	NOUN
ap-6786	191	106	endif	endif	NOUN
ap-6786	191	107	endif	endif	NOUN
ap-6786	191	108	we	we	PRON
ap-6786	191	109	assumed	assume	VERB
ap-6786	191	110	the	the	DET
ap-6786	191	111	threshold	threshold	NOUN
ap-6786	191	112	value	value	NOUN
ap-6786	191	113	restol	restol	NOUN
ap-6786	191	114	=	=	PUNCT
ap-6786	191	115	1.0e−	1.0e−	NUM
ap-6786	191	116	20	20	NUM
ap-6786	191	117	.	.	PUNCT
ap-6786	192	1	the	the	DET
ap-6786	192	2	only	only	ADJ
ap-6786	192	3	exception	exception	NOUN
ap-6786	192	4	was	be	AUX
ap-6786	192	5	the	the	DET
ap-6786	192	6	set	set	NOUN
ap-6786	192	7	of	of	ADP
ap-6786	192	8	sample	sample	NOUN
ap-6786	192	9	problems	problem	NOUN
ap-6786	192	10	for	for	ADP
ap-6786	192	11	the	the	DET
ap-6786	192	12	reinforced	reinforce	VERB
ap-6786	192	13	concrete	concrete	ADJ
ap-6786	192	14	section	section	NOUN
ap-6786	192	15	subjected	subject	VERB
ap-6786	192	16	to	to	ADP
ap-6786	192	17	the	the	DET
ap-6786	192	18	compression	compression	NOUN
ap-6786	192	19	with	with	ADP
ap-6786	192	20	bending	bend	VERB
ap-6786	192	21	where	where	SCONJ
ap-6786	192	22	restol	restol	NOUN
ap-6786	192	23	=	=	SYM
ap-6786	192	24	1.0e	1.0e	PROPN
ap-6786	192	25	−	−	PROPN
ap-6786	192	26	10	10	NUM
ap-6786	192	27	.	.	PUNCT
ap-6786	193	1	in	in	ADP
ap-6786	193	2	the	the	DET
ap-6786	193	3	clusterization	clusterization	NOUN
ap-6786	193	4	,	,	PUNCT
ap-6786	193	5	we	we	PRON
ap-6786	193	6	treated	treat	VERB
ap-6786	193	7	a	a	DET
ap-6786	193	8	new	new	ADJ
ap-6786	193	9	point	point	NOUN
ap-6786	193	10	as	as	ADP
ap-6786	193	11	a	a	DET
ap-6786	193	12	structure	structure	NOUN
ap-6786	193	13	member	member	NOUN
ap-6786	193	14	of	of	ADP
ap-6786	193	15	the	the	DET
ap-6786	193	16	cluster	cluster	NOUN
ap-6786	193	17	if	if	SCONJ
ap-6786	193	18	the	the	DET
ap-6786	193	19	following	follow	VERB
ap-6786	193	20	inequality	inequality	NOUN
ap-6786	193	21	was	be	AUX
ap-6786	193	22	verified	verify	VERB
ap-6786	193	23	‖x̂−	‖x̂−	X
ap-6786	193	24	xseed‖	xseed‖	PROPN
ap-6786	193	25	≤	≤	ADJ
ap-6786	193	26	disttol	disttol	NOUN
ap-6786	193	27	where	where	SCONJ
ap-6786	193	28	xseed	xseed	PROPN
ap-6786	193	29	is	be	AUX
ap-6786	193	30	the	the	DET
ap-6786	193	31	seed	seed	NOUN
ap-6786	193	32	point	point	NOUN
ap-6786	193	33	of	of	ADP
ap-6786	193	34	the	the	DET
ap-6786	193	35	current	current	ADJ
ap-6786	193	36	cluster	cluster	NOUN
ap-6786	193	37	.	.	PUNCT
ap-6786	194	1	we	we	PRON
ap-6786	194	2	assumed	assume	VERB
ap-6786	194	3	disttol	disttol	NOUN
ap-6786	194	4	=	=	SYM
ap-6786	194	5	1.0e−10	1.0e−10	NUM
ap-6786	194	6	.	.	PUNCT
ap-6786	195	1	the	the	DET
ap-6786	195	2	need	need	NOUN
ap-6786	195	3	of	of	ADP
ap-6786	195	4	the	the	DET
ap-6786	195	5	clusterization	clusterization	NOUN
ap-6786	195	6	is	be	AUX
ap-6786	195	7	fully	fully	ADV
ap-6786	195	8	justified	justify	VERB
ap-6786	195	9	by	by	ADP
ap-6786	195	10	the	the	DET
ap-6786	195	11	table	table	NOUN
ap-6786	195	12	2	2	NUM
ap-6786	195	13	presented	present	VERB
ap-6786	195	14	below	below	ADV
ap-6786	195	15	.	.	PUNCT
ap-6786	196	1	we	we	PRON
ap-6786	196	2	can	can	AUX
ap-6786	196	3	evidently	evidently	ADV
ap-6786	196	4	observe	observe	VERB
ap-6786	196	5	four	four	NUM
ap-6786	196	6	different	different	ADJ
ap-6786	196	7	clusters	cluster	NOUN
ap-6786	196	8	in	in	ADP
ap-6786	196	9	the	the	DET
ap-6786	196	10	table	table	NOUN
ap-6786	196	11	.	.	PUNCT
ap-6786	197	1	first	first	ADJ
ap-6786	197	2	seven	seven	NUM
ap-6786	197	3	examples	example	NOUN
ap-6786	197	4	are	be	AUX
ap-6786	197	5	connected	connect	VERB
ap-6786	197	6	with	with	ADP
ap-6786	197	7	the	the	DET
ap-6786	197	8	concrete	concrete	ADJ
ap-6786	197	9	sections	section	NOUN
ap-6786	197	10	without	without	ADP
ap-6786	197	11	reinforcement	reinforcement	NOUN
ap-6786	197	12	.	.	PUNCT
ap-6786	198	1	they	they	PRON
ap-6786	198	2	are	be	AUX
ap-6786	198	3	subjected	subject	VERB
ap-6786	198	4	to	to	PART
ap-6786	198	5	compression	compression	VERB
ap-6786	198	6	and	and	CCONJ
ap-6786	198	7	bending	bending	NOUN
ap-6786	198	8	.	.	PUNCT
ap-6786	199	1	parameters	parameter	NOUN
ap-6786	199	2	a	a	PRON
ap-6786	199	3	are	be	AUX
ap-6786	199	4	collected	collect	VERB
ap-6786	199	5	in	in	ADP
ap-6786	199	6	table	table	NOUN
ap-6786	199	7	1	1	NUM
ap-6786	199	8	and	and	CCONJ
ap-6786	199	9	the	the	DET
ap-6786	199	10	calculated	calculate	VERB
ap-6786	199	11	solutions	solution	NOUN
ap-6786	199	12	are	be	AUX
ap-6786	199	13	put	put	VERB
ap-6786	199	14	to	to	ADP
ap-6786	199	15	table	table	NOUN
ap-6786	199	16	3	3	NUM
ap-6786	199	17	.	.	NOUN
ap-6786	199	18	consecutive	consecutive	ADJ
ap-6786	199	19	table	table	NOUN
ap-6786	199	20	4	4	NUM
ap-6786	199	21	contains	contain	VERB
ap-6786	199	22	the	the	DET
ap-6786	199	23	solutions	solution	NOUN
ap-6786	199	24	for	for	ADP
ap-6786	199	25	two	two	NUM
ap-6786	199	26	sets	set	NOUN
ap-6786	199	27	associated	associate	VERB
ap-6786	199	28	with	with	ADP
ap-6786	199	29	the	the	DET
ap-6786	199	30	situation	situation	NOUN
ap-6786	199	31	,	,	PUNCT
ap-6786	199	32	when	when	SCONJ
ap-6786	199	33	the	the	DET
ap-6786	199	34	sections	section	NOUN
ap-6786	199	35	are	be	AUX
ap-6786	199	36	reinforced	reinforce	VERB
ap-6786	199	37	.	.	PUNCT
ap-6786	200	1	the	the	DET
ap-6786	200	2	results	result	NOUN
ap-6786	200	3	of	of	ADP
ap-6786	200	4	calculations	calculation	NOUN
ap-6786	200	5	with	with	ADP
ap-6786	200	6	the	the	DET
ap-6786	200	7	genetic	genetic	ADJ
ap-6786	200	8	algorithm	algorithm	NOUN
ap-6786	200	9	are	be	AUX
ap-6786	200	10	summarized	summarize	VERB
ap-6786	200	11	in	in	ADP
ap-6786	200	12	table	table	NOUN
ap-6786	200	13	5	5	NUM
ap-6786	200	14	(	(	PUNCT
ap-6786	200	15	for	for	ADP
ap-6786	200	16	the	the	DET
ap-6786	200	17	sections	section	NOUN
ap-6786	200	18	without	without	ADP
ap-6786	200	19	reinforcement	reinforcement	NOUN
ap-6786	200	20	)	)	PUNCT
ap-6786	200	21	and	and	CCONJ
ap-6786	200	22	in	in	ADP
ap-6786	200	23	table	table	NOUN
ap-6786	200	24	6	6	NUM
ap-6786	200	25	(	(	PUNCT
ap-6786	200	26	for	for	ADP
ap-6786	200	27	sections	section	NOUN
ap-6786	200	28	with	with	ADP
ap-6786	200	29	reinforcement	reinforcement	NOUN
ap-6786	200	30	)	)	PUNCT
ap-6786	200	31	.	.	PUNCT
ap-6786	201	1	unfortunately	unfortunately	ADV
ap-6786	201	2	,	,	PUNCT
ap-6786	201	3	the	the	DET
ap-6786	201	4	implementation	implementation	NOUN
ap-6786	201	5	of	of	ADP
ap-6786	201	6	the	the	DET
ap-6786	201	7	genetic	genetic	ADJ
ap-6786	201	8	algorithm	algorithm	NOUN
ap-6786	201	9	from	from	ADP
ap-6786	201	10	the	the	DET
ap-6786	201	11	matlab	matlab	PROPN
ap-6786	201	12	’s	’s	PART
ap-6786	201	13	global	global	ADJ
ap-6786	201	14	optimization	optimization	NOUN
ap-6786	201	15	toolbox	toolbox	NOUN
ap-6786	201	16	has	have	AUX
ap-6786	201	17	found	find	VERB
ap-6786	201	18	only	only	ADV
ap-6786	201	19	one	one	NUM
ap-6786	201	20	global	global	ADJ
ap-6786	201	21	solution	solution	NOUN
ap-6786	201	22	,	,	PUNCT
ap-6786	201	23	even	even	ADV
ap-6786	201	24	for	for	ADP
ap-6786	201	25	sets	set	NOUN
ap-6786	201	26	where	where	SCONJ
ap-6786	201	27	the	the	DET
ap-6786	201	28	local	local	ADJ
ap-6786	201	29	minimizer	minimizer	NOUN
ap-6786	201	30	detected	detect	VERB
ap-6786	201	31	more	more	ADJ
ap-6786	201	32	global	global	ADJ
ap-6786	201	33	solutions	solution	NOUN
ap-6786	201	34	.	.	PUNCT
ap-6786	202	1	furthermore	furthermore	ADV
ap-6786	202	2	,	,	PUNCT
ap-6786	202	3	the	the	DET
ap-6786	202	4	accuracy	accuracy	NOUN
ap-6786	202	5	of	of	ADP
ap-6786	202	6	the	the	DET
ap-6786	202	7	ga	ga	NOUN
ap-6786	202	8	solution	solution	NOUN
ap-6786	202	9	is	be	AUX
ap-6786	202	10	definitely	definitely	ADV
ap-6786	202	11	poorer	poor	ADJ
ap-6786	202	12	compared	compare	VERB
ap-6786	202	13	with	with	ADP
ap-6786	202	14	that	that	PRON
ap-6786	202	15	found	find	VERB
ap-6786	202	16	by	by	ADP
ap-6786	202	17	the	the	DET
ap-6786	202	18	local	local	ADJ
ap-6786	202	19	minimizer	minimizer	NOUN
ap-6786	202	20	.	.	PUNCT
ap-6786	203	1	tables	table	NOUN
ap-6786	203	2	7	7	NUM
ap-6786	203	3	and	and	CCONJ
ap-6786	203	4	8	8	NUM
ap-6786	203	5	summarize	summarize	VERB
ap-6786	203	6	the	the	DET
ap-6786	203	7	results	result	NOUN
ap-6786	203	8	obtained	obtain	VERB
ap-6786	203	9	by	by	ADP
ap-6786	203	10	means	mean	NOUN
ap-6786	203	11	of	of	ADP
ap-6786	203	12	the	the	DET
ap-6786	203	13	particle	particle	NOUN
ap-6786	203	14	swarm	swarm	NOUN
ap-6786	203	15	algorithm	algorithm	NOUN
ap-6786	203	16	implementation	implementation	NOUN
ap-6786	203	17	in	in	ADP
ap-6786	203	18	the	the	DET
ap-6786	203	19	matlab	matlab	PROPN
ap-6786	203	20	’s	’s	PART
ap-6786	203	21	global	global	ADJ
ap-6786	203	22	optimization	optimization	NOUN
ap-6786	203	23	toolbox	toolbox	NOUN
ap-6786	203	24	.	.	PUNCT
ap-6786	204	1	the	the	DET
ap-6786	204	2	same	same	ADJ
ap-6786	204	3	comment	comment	NOUN
ap-6786	204	4	as	as	ADP
ap-6786	204	5	for	for	ADP
ap-6786	204	6	the	the	DET
ap-6786	204	7	ga	ga	PROPN
ap-6786	204	8	matlab	matlab	PROPN
ap-6786	204	9	function	function	NOUN
ap-6786	204	10	is	be	AUX
ap-6786	204	11	valid	valid	ADJ
ap-6786	204	12	for	for	ADP
ap-6786	204	13	the	the	DET
ap-6786	204	14	particle	particle	NOUN
ap-6786	204	15	swarm	swarm	NOUN
ap-6786	204	16	one	one	NUM
ap-6786	204	17	.	.	PUNCT
ap-6786	205	1	4	4	NUM
ap-6786	205	2	.	.	X
ap-6786	205	3	comparison	comparison	NOUN
ap-6786	205	4	of	of	ADP
ap-6786	205	5	experimental	experimental	ADJ
ap-6786	205	6	and	and	CCONJ
ap-6786	205	7	numerical	numerical	ADJ
ap-6786	205	8	results	result	NOUN
ap-6786	205	9	in	in	ADP
ap-6786	205	10	order	order	NOUN
ap-6786	205	11	to	to	PART
ap-6786	205	12	verify	verify	VERB
ap-6786	205	13	the	the	DET
ap-6786	205	14	calculated	calculate	VERB
ap-6786	205	15	results	result	NOUN
ap-6786	205	16	,	,	PUNCT
ap-6786	205	17	175	175	NUM
ap-6786	205	18	mm	mm	NOUN
ap-6786	205	19	×	×	NOUN
ap-6786	205	20	175	175	NUM
ap-6786	205	21	mm	mm	INTJ
ap-6786	205	22	×	×	NOUN
ap-6786	205	23	1680	1680	NUM
ap-6786	205	24	mm	mm	NOUN
ap-6786	205	25	(	(	PUNCT
ap-6786	205	26	the	the	DET
ap-6786	205	27	height	height	NOUN
ap-6786	205	28	)	)	PUNCT
ap-6786	205	29	column	column	NOUN
ap-6786	205	30	specimens	specimen	VERB
ap-6786	205	31	under	under	ADP
ap-6786	205	32	eccentric	eccentric	ADJ
ap-6786	205	33	compression	compression	NOUN
ap-6786	205	34	were	be	AUX
ap-6786	205	35	considered	consider	VERB
ap-6786	205	36	,	,	PUNCT
ap-6786	205	37	the	the	DET
ap-6786	205	38	results	result	NOUN
ap-6786	205	39	of	of	ADP
ap-6786	205	40	which	which	PRON
ap-6786	205	41	were	be	AUX
ap-6786	205	42	presented	present	VERB
ap-6786	205	43	in	in	ADP
ap-6786	205	44	detail	detail	NOUN
ap-6786	205	45	by	by	ADP
ap-6786	205	46	lloyd	lloyd	PROPN
ap-6786	205	47	at	at	ADP
ap-6786	205	48	al	al	PROPN
ap-6786	205	49	.	.	PUNCT
ap-6786	206	1	[	[	X
ap-6786	206	2	16	16	NUM
ap-6786	206	3	]	]	PUNCT
ap-6786	206	4	.	.	PUNCT
ap-6786	207	1	the	the	DET
ap-6786	207	2	longitudinal	longitudinal	ADJ
ap-6786	207	3	steel	steel	NOUN
ap-6786	207	4	reinforcement	reinforcement	NOUN
ap-6786	207	5	of	of	ADP
ap-6786	207	6	the	the	DET
ap-6786	207	7	columns	column	NOUN
ap-6786	207	8	consisted	consist	VERB
ap-6786	207	9	of	of	ADP
ap-6786	207	10	three	three	NUM
ap-6786	207	11	rebars	rebar	NOUN
ap-6786	207	12	φ12	φ12	X
ap-6786	207	13	mm	mm	NOUN
ap-6786	207	14	,	,	PUNCT
ap-6786	207	15	fyk	fyk	X
ap-6786	207	16	=	=	NOUN
ap-6786	207	17	430	430	NUM
ap-6786	207	18	mpa	mpa	NOUN
ap-6786	207	19	,	,	PUNCT
ap-6786	207	20	es	es	ADP
ap-6786	207	21	=	=	SYM
ap-6786	207	22	200	200	NUM
ap-6786	207	23	gpa	gpa	NOUN
ap-6786	207	24	and	and	CCONJ
ap-6786	207	25	they	they	PRON
ap-6786	207	26	were	be	AUX
ap-6786	207	27	made	make	VERB
ap-6786	207	28	of	of	ADP
ap-6786	207	29	concrete	concrete	ADJ
ap-6786	207	30	fcm	fcm	X
ap-6786	207	31	=	=	SYM
ap-6786	207	32	44.78	44.78	NUM
ap-6786	207	33	mpa	mpa	PROPN
ap-6786	207	34	,	,	PUNCT
ap-6786	207	35	ecm	ecm	NOUN
ap-6786	207	36	=	=	SYM
ap-6786	207	37	32	32	NUM
ap-6786	207	38	gpa	gpa	PROPN
ap-6786	207	39	.	.	PUNCT
ap-6786	208	1	the	the	DET
ap-6786	208	2	static	static	ADJ
ap-6786	208	3	diagram	diagram	NOUN
ap-6786	208	4	and	and	CCONJ
ap-6786	208	5	test	test	NOUN
ap-6786	208	6	specimen	speciman	NOUN
ap-6786	208	7	are	be	AUX
ap-6786	208	8	shown	show	VERB
ap-6786	208	9	in	in	ADP
ap-6786	208	10	fig	fig	NOUN
ap-6786	208	11	.	.	PUNCT
ap-6786	209	1	2	2	X
ap-6786	209	2	.	.	X
ap-6786	209	3	in	in	ADP
ap-6786	209	4	the	the	DET
ap-6786	209	5	above	above	ADJ
ap-6786	209	6	mentioned	mention	VERB
ap-6786	209	7	tests	test	NOUN
ap-6786	209	8	,	,	PUNCT
ap-6786	209	9	the	the	DET
ap-6786	209	10	following	follow	VERB
ap-6786	209	11	failure	failure	NOUN
ap-6786	209	12	loads	load	NOUN
ap-6786	209	13	and	and	CCONJ
ap-6786	209	14	corresponding	corresponding	ADJ
ap-6786	209	15	eccentricities	eccentricity	NOUN
ap-6786	209	16	were	be	AUX
ap-6786	209	17	measured	measure	VERB
ap-6786	209	18	:	:	PUNCT
ap-6786	209	19	p1	p1	PROPN
ap-6786	209	20	=	=	SYM
ap-6786	209	21	1476	1476	NUM
ap-6786	209	22	kn	kn	PROPN
ap-6786	209	23	,	,	PUNCT
ap-6786	209	24	e1	e1	PROPN
ap-6786	209	25	=	=	SYM
ap-6786	209	26	15	15	NUM
ap-6786	209	27	mm	mm	NOUN
ap-6786	209	28	;	;	PUNCT
ap-6786	209	29	p2	p2	PROPN
ap-6786	209	30	=	=	SYM
ap-6786	209	31	830	830	NUM
ap-6786	209	32	kn	kn	PROPN
ap-6786	209	33	,	,	PUNCT
ap-6786	209	34	e2	e2	PROPN
ap-6786	209	35	=	=	PROPN
ap-6786	209	36	50	50	NUM
ap-6786	209	37	mm	mm	NOUN
ap-6786	209	38	;	;	PUNCT
ap-6786	209	39	p3	p3	PROPN
ap-6786	209	40	=	=	SYM
ap-6786	209	41	660	660	NUM
ap-6786	209	42	kn	kn	PROPN
ap-6786	209	43	,	,	PUNCT
ap-6786	209	44	e3	e3	VERB
ap-6786	209	45	=	=	SYM
ap-6786	209	46	65	65	NUM
ap-6786	209	47	mm	mm	NOUN
ap-6786	209	48	.	.	PUNCT
ap-6786	210	1	the	the	DET
ap-6786	210	2	ultimate	ultimate	ADJ
ap-6786	210	3	strain	strain	NOUN
ap-6786	210	4	in	in	ADP
ap-6786	210	5	concrete	concrete	NOUN
ap-6786	210	6	at	at	ADP
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ap-6786	256	26	x(1	x(1	PROPN
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ap-6786	258	5	=	=	SYM
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ap-6786	285	4	steel	steel	NOUN
ap-6786	285	5	εs	εs	ADP
ap-6786	286	1	[	[	X
ap-6786	286	2	‰	‰	X
ap-6786	286	3	]	]	X
ap-6786	286	4	p1	p1	NOUN
ap-6786	286	5	=	=	PUNCT
ap-6786	286	6	1476	1476	NUM
ap-6786	286	7	;	;	PUNCT
ap-6786	286	8	e1	e1	NOUN
ap-6786	286	9	=	=	SYM
ap-6786	286	10	15	15	NUM
ap-6786	286	11	-2.4	-2.4	NOUN
ap-6786	286	12	-2.20	-2.20	NUM
ap-6786	286	13	-2.20	-2.20	NUM
ap-6786	286	14	/	/	SYM
ap-6786	286	15	-0.35	-0.35	NOUN
ap-6786	286	16	p2	p2	NOUN
ap-6786	286	17	=	=	SYM
ap-6786	286	18	830	830	NUM
ap-6786	286	19	;	;	PUNCT
ap-6786	286	20	e2	e2	PROPN
ap-6786	286	21	=	=	SYM
ap-6786	286	22	50	50	NUM
ap-6786	286	23	-2.4	-2.4	NOUN
ap-6786	286	24	-2.20	-2.20	NUM
ap-6786	286	25	0.63	0.63	NUM
ap-6786	286	26	0.92	0.92	NUM
ap-6786	286	27	p3	p3	NOUN
ap-6786	286	28	=	=	PUNCT
ap-6786	286	29	660	660	NUM
ap-6786	286	30	;	;	PUNCT
ap-6786	286	31	e3	e3	NOUN
ap-6786	286	32	=	=	SYM
ap-6786	286	33	65	65	NUM
ap-6786	286	34	-2.4	-2.4	NOUN
ap-6786	286	35	-2.20	-2.20	NUM
ap-6786	286	36	0.49	0.49	NUM
ap-6786	286	37	1.85	1.85	NUM
ap-6786	286	38	table	table	NOUN
ap-6786	286	39	9	9	NUM
ap-6786	286	40	.	.	PUNCT
ap-6786	286	41	comparison	comparison	NOUN
ap-6786	286	42	of	of	ADP
ap-6786	286	43	the	the	DET
ap-6786	286	44	experimental	experimental	ADJ
ap-6786	286	45	and	and	CCONJ
ap-6786	286	46	numerical	numerical	ADJ
ap-6786	286	47	results	result	NOUN
ap-6786	286	48	–	–	PUNCT
ap-6786	286	49	1	1	NUM
ap-6786	286	50	249	249	NUM
ap-6786	286	51	marek	marek	PROPN
ap-6786	286	52	lechman	lechman	PROPN
ap-6786	286	53	,	,	PUNCT
ap-6786	286	54	andrzej	andrzej	PROPN
ap-6786	286	55	stachurski	stachurski	VERB
ap-6786	286	56	acta	acta	PROPN
ap-6786	286	57	polytechnica	polytechnica	PROPN
ap-6786	286	58	experimental	experimental	PROPN
ap-6786	286	59	numerical	numerical	ADJ
ap-6786	286	60	failure	failure	NOUN
ap-6786	286	61	load	load	NOUN
ap-6786	287	1	pi	pi	NOUN
ap-6786	288	1	[	[	X
ap-6786	288	2	kn	kn	X
ap-6786	288	3	]	]	X
ap-6786	288	4	εcu	εcu	NOUN
ap-6786	288	5	=	=	PUNCT
ap-6786	288	6	εc1	εc1	NOUN
ap-6786	288	7	ε1	ε1	VERB
ap-6786	288	8	ε2	ε2	ADJ
ap-6786	288	9	eccentricity	eccentricity	NOUN
ap-6786	288	10	ei	ei	ADP
ap-6786	289	1	[	[	X
ap-6786	289	2	mm	mm	X
ap-6786	289	3	]	]	X
ap-6786	290	1	[	[	X
ap-6786	290	2	‰	‰	X
ap-6786	290	3	]	]	X
ap-6786	291	1	[	[	X
ap-6786	291	2	‰	‰	X
ap-6786	291	3	]	]	X
ap-6786	292	1	[	[	X
ap-6786	292	2	‰	‰	X
ap-6786	292	3	]	]	X
ap-6786	292	4	p1	p1	NOUN
ap-6786	292	5	=	=	SYM
ap-6786	292	6	1548	1548	NUM
ap-6786	292	7	;	;	PUNCT
ap-6786	292	8	e1	e1	NOUN
ap-6786	292	9	=	=	SYM
ap-6786	292	10	0	0	NUM
ap-6786	292	11	-2.1	-2.1	NOUN
ap-6786	292	12	-2.1	-2.1	NOUN
ap-6786	292	13	-2.1	-2.1	NOUN
ap-6786	292	14	p2	p2	PROPN
ap-6786	292	15	=	=	SYM
ap-6786	292	16	1386	1386	NUM
ap-6786	292	17	;	;	PUNCT
ap-6786	292	18	e2	e2	PROPN
ap-6786	292	19	=	=	SYM
ap-6786	292	20	16	16	NUM
ap-6786	292	21	-2.1	-2.1	NOUN
ap-6786	292	22	-1.95	-1.95	NOUN
ap-6786	292	23	-0.31	-0.31	NUM
ap-6786	292	24	p3	p3	NOUN
ap-6786	292	25	=	=	SYM
ap-6786	292	26	1098	1098	NUM
ap-6786	292	27	;	;	PUNCT
ap-6786	292	28	e3	e3	NOUN
ap-6786	292	29	=	=	SYM
ap-6786	292	30	32	32	NUM
ap-6786	292	31	-2.1	-2.1	NOUN
ap-6786	292	32	-1.95	-1.95	NUM
ap-6786	292	33	-0.12	-0.12	NUM
ap-6786	292	34	table	table	NOUN
ap-6786	292	35	10	10	NUM
ap-6786	292	36	.	.	PUNCT
ap-6786	292	37	comparison	comparison	NOUN
ap-6786	292	38	of	of	ADP
ap-6786	292	39	the	the	DET
ap-6786	292	40	experimental	experimental	ADJ
ap-6786	292	41	and	and	CCONJ
ap-6786	292	42	numerical	numerical	ADJ
ap-6786	292	43	results	result	NOUN
ap-6786	292	44	figure	figure	VERB
ap-6786	292	45	2	2	NUM
ap-6786	292	46	.	.	PUNCT
ap-6786	292	47	static	static	ADJ
ap-6786	292	48	diagram	diagram	NOUN
ap-6786	292	49	and	and	CCONJ
ap-6786	292	50	test	test	NOUN
ap-6786	292	51	specimen	speciman	NOUN
ap-6786	292	52	conformity	conformity	NOUN
ap-6786	292	53	between	between	ADP
ap-6786	292	54	the	the	DET
ap-6786	292	55	numerical	numerical	ADJ
ap-6786	292	56	solution	solution	NOUN
ap-6786	292	57	and	and	CCONJ
ap-6786	292	58	the	the	DET
ap-6786	292	59	experimental	experimental	ADJ
ap-6786	292	60	data	datum	NOUN
ap-6786	292	61	given	give	VERB
ap-6786	292	62	by	by	ADP
ap-6786	292	63	lloyd	lloyd	PROPN
ap-6786	292	64	and	and	CCONJ
ap-6786	292	65	rangan	rangan	VERB
ap-6786	292	66	[	[	X
ap-6786	292	67	16	16	NUM
ap-6786	292	68	]	]	PUNCT
ap-6786	292	69	.	.	PUNCT
ap-6786	293	1	it	it	PRON
ap-6786	293	2	is	be	AUX
ap-6786	293	3	worth	worth	ADJ
ap-6786	293	4	noting	note	VERB
ap-6786	293	5	that	that	SCONJ
ap-6786	293	6	the	the	DET
ap-6786	293	7	theoretical	theoretical	ADJ
ap-6786	293	8	values	value	NOUN
ap-6786	293	9	are	be	AUX
ap-6786	293	10	lower	low	ADJ
ap-6786	293	11	than	than	ADP
ap-6786	293	12	those	those	PRON
ap-6786	293	13	obtained	obtain	VERB
ap-6786	293	14	from	from	ADP
ap-6786	293	15	the	the	DET
ap-6786	293	16	experiment	experiment	NOUN
ap-6786	293	17	due	due	ADP
ap-6786	293	18	to	to	ADP
ap-6786	293	19	neglecting	neglect	VERB
ap-6786	293	20	the	the	DET
ap-6786	293	21	effect	effect	NOUN
ap-6786	293	22	of	of	ADP
ap-6786	293	23	confinement	confinement	NOUN
ap-6786	293	24	of	of	ADP
ap-6786	293	25	the	the	DET
ap-6786	293	26	column	column	NOUN
ap-6786	293	27	.	.	PUNCT
ap-6786	294	1	as	as	ADP
ap-6786	294	2	the	the	DET
ap-6786	294	3	next	next	ADJ
ap-6786	294	4	example	example	NOUN
ap-6786	294	5	,	,	PUNCT
ap-6786	294	6	the	the	DET
ap-6786	294	7	results	result	NOUN
ap-6786	294	8	of	of	ADP
ap-6786	294	9	tests	test	NOUN
ap-6786	294	10	conducted	conduct	VERB
ap-6786	294	11	by	by	ADP
ap-6786	294	12	trapko	trapko	PROPN
ap-6786	294	13	at	at	ADP
ap-6786	294	14	al	al	PROPN
ap-6786	294	15	.	.	PUNCT
ap-6786	295	1	[	[	X
ap-6786	295	2	20	20	NUM
ap-6786	295	3	]	]	PUNCT
ap-6786	295	4	on	on	ADP
ap-6786	295	5	unstrenghtened	unstrenghtene	VERB
ap-6786	295	6	column	column	NOUN
ap-6786	295	7	specimens	specimen	VERB
ap-6786	295	8	200	200	NUM
ap-6786	295	9	mm	mm	NOUN
ap-6786	295	10	×	×	NOUN
ap-6786	295	11	200	200	NUM
ap-6786	295	12	mm	mm	NOUN
ap-6786	295	13	×	×	NOUN
ap-6786	295	14	1500	1500	NUM
ap-6786	295	15	mm	mm	INTJ
ap-6786	295	16	(	(	PUNCT
ap-6786	295	17	the	the	DET
ap-6786	295	18	height	height	NOUN
ap-6786	295	19	)	)	PUNCT
ap-6786	295	20	under	under	ADP
ap-6786	295	21	eccentric	eccentric	ADJ
ap-6786	295	22	compression	compression	NOUN
ap-6786	295	23	were	be	AUX
ap-6786	295	24	analyzed	analyze	VERB
ap-6786	295	25	.	.	PUNCT
ap-6786	296	1	the	the	DET
ap-6786	296	2	longitudinal	longitudinal	ADJ
ap-6786	296	3	reinforcement	reinforcement	NOUN
ap-6786	296	4	of	of	ADP
ap-6786	296	5	the	the	DET
ap-6786	296	6	column	column	NOUN
ap-6786	296	7	consisted	consist	VERB
ap-6786	296	8	of	of	ADP
ap-6786	296	9	two	two	NUM
ap-6786	296	10	rebars	rebar	NOUN
ap-6786	296	11	φ12	φ12	X
ap-6786	296	12	mm	mm	PROPN
ap-6786	296	13	,	,	PUNCT
ap-6786	296	14	steel	steel	NOUN
ap-6786	296	15	grade	grade	NOUN
ap-6786	296	16	a	a	NOUN
ap-6786	296	17	-	-	PUNCT
ap-6786	296	18	iiin	iiin	NOUN
ap-6786	296	19	,	,	PUNCT
ap-6786	296	20	fyk	fyk	PROPN
ap-6786	296	21	=	=	NOUN
ap-6786	296	22	608	608	NUM
ap-6786	296	23	mpa	mpa	NOUN
ap-6786	296	24	,	,	PUNCT
ap-6786	296	25	es	es	X
ap-6786	296	26	=	=	PROPN
ap-6786	296	27	224	224	NUM
ap-6786	296	28	gpa	gpa	NOUN
ap-6786	296	29	and	and	CCONJ
ap-6786	296	30	the	the	DET
ap-6786	296	31	transverse	transverse	NOUN
ap-6786	296	32	reinforcement	reinforcement	NOUN
ap-6786	296	33	consisted	consist	VERB
ap-6786	296	34	of	of	ADP
ap-6786	296	35	stirrups	stirrup	NOUN
ap-6786	296	36	φ6	φ6	NOUN
ap-6786	296	37	mm	mm	PROPN
ap-6786	296	38	,	,	PUNCT
ap-6786	296	39	steel	steel	NOUN
ap-6786	296	40	grade	grade	NOUN
ap-6786	296	41	a	a	DET
ap-6786	296	42	-	-	PUNCT
ap-6786	296	43	i.	i.	NOUN
ap-6786	296	44	the	the	DET
ap-6786	296	45	columns	column	NOUN
ap-6786	296	46	were	be	AUX
ap-6786	296	47	made	make	VERB
ap-6786	296	48	of	of	ADP
ap-6786	296	49	concrete	concrete	ADJ
ap-6786	296	50	fcm	fcm	X
ap-6786	296	51	=	=	SYM
ap-6786	296	52	31.9	31.9	NUM
ap-6786	296	53	mpa	mpa	NOUN
ap-6786	296	54	.	.	PUNCT
ap-6786	297	1	ecm	ecm	PROPN
ap-6786	297	2	=	=	SYM
ap-6786	297	3	31	31	NUM
ap-6786	297	4	gpa	gpa	PROPN
ap-6786	297	5	.	.	PUNCT
ap-6786	298	1	the	the	DET
ap-6786	298	2	failure	failure	NOUN
ap-6786	298	3	loads	load	VERB
ap-6786	298	4	and	and	CCONJ
ap-6786	298	5	the	the	DET
ap-6786	298	6	corresponding	corresponding	ADJ
ap-6786	298	7	eccentricities	eccentricity	NOUN
ap-6786	298	8	were	be	AUX
ap-6786	298	9	determined	determine	VERB
ap-6786	298	10	in	in	ADP
ap-6786	298	11	these	these	DET
ap-6786	298	12	tests	test	NOUN
ap-6786	298	13	as	as	ADP
ap-6786	298	14	:	:	PUNCT
ap-6786	298	15	p1	p1	NOUN
ap-6786	298	16	=	=	SYM
ap-6786	298	17	1548	1548	NUM
ap-6786	298	18	kn	kn	PROPN
ap-6786	298	19	,	,	PUNCT
ap-6786	298	20	e1	e1	PROPN
ap-6786	298	21	=	=	SYM
ap-6786	298	22	0	0	NUM
ap-6786	298	23	mm	mm	NOUN
ap-6786	298	24	;	;	PUNCT
ap-6786	298	25	p2	p2	PROPN
ap-6786	298	26	=	=	SYM
ap-6786	298	27	1386	1386	NUM
ap-6786	298	28	kn	kn	PROPN
ap-6786	298	29	,	,	PUNCT
ap-6786	298	30	e2	e2	PROPN
ap-6786	298	31	=	=	PROPN
ap-6786	298	32	16	16	NUM
ap-6786	298	33	mm	mm	NOUN
ap-6786	298	34	;	;	PUNCT
ap-6786	298	35	p3	p3	PROPN
ap-6786	298	36	=	=	SYM
ap-6786	298	37	1098	1098	NUM
ap-6786	298	38	kn	kn	PROPN
ap-6786	298	39	,	,	PUNCT
ap-6786	298	40	e3	e3	PROPN
ap-6786	298	41	=	=	SYM
ap-6786	298	42	32	32	NUM
ap-6786	298	43	mm	mm	NOUN
ap-6786	298	44	.	.	PUNCT
ap-6786	299	1	the	the	DET
ap-6786	299	2	ultimate	ultimate	ADJ
ap-6786	299	3	strain	strain	NOUN
ap-6786	299	4	in	in	ADP
ap-6786	299	5	concrete	concrete	NOUN
ap-6786	299	6	at	at	ADP
ap-6786	299	7	failure	failure	NOUN
ap-6786	299	8	was	be	AUX
ap-6786	299	9	assumed	assume	VERB
ap-6786	299	10	in	in	ADP
ap-6786	299	11	calculations	calculation	NOUN
ap-6786	299	12	as	as	SCONJ
ap-6786	299	13	−2.1	−2.1	PROPN
ap-6786	299	14	‰.	‰.	PROPN
ap-6786	299	15	the	the	DET
ap-6786	299	16	characteristic	characteristic	ADJ
ap-6786	299	17	failure	failure	NOUN
ap-6786	299	18	mechanisms	mechanism	NOUN
ap-6786	299	19	of	of	ADP
ap-6786	299	20	the	the	DET
ap-6786	299	21	tested	test	VERB
ap-6786	299	22	specimens	specimen	NOUN
ap-6786	299	23	occurred	occur	VERB
ap-6786	299	24	in	in	ADP
ap-6786	299	25	the	the	DET
ap-6786	299	26	form	form	NOUN
ap-6786	299	27	of	of	ADP
ap-6786	299	28	crushing	crush	VERB
ap-6786	299	29	the	the	DET
ap-6786	299	30	concrete	concrete	NOUN
ap-6786	299	31	in	in	ADP
ap-6786	299	32	the	the	DET
ap-6786	299	33	upper	upper	ADJ
ap-6786	299	34	part	part	NOUN
ap-6786	299	35	of	of	ADP
ap-6786	299	36	the	the	DET
ap-6786	299	37	structure	structure	NOUN
ap-6786	299	38	members	member	NOUN
ap-6786	299	39	and	and	CCONJ
ap-6786	299	40	yielding	yield	VERB
ap-6786	299	41	the	the	DET
ap-6786	299	42	longitudinal	longitudinal	ADJ
ap-6786	299	43	reinforcing	reinforce	VERB
ap-6786	299	44	steel	steel	NOUN
ap-6786	299	45	.	.	PUNCT
ap-6786	300	1	a	a	DET
ap-6786	300	2	good	good	ADJ
ap-6786	300	3	conformity	conformity	NOUN
ap-6786	300	4	between	between	ADP
ap-6786	300	5	the	the	DET
ap-6786	300	6	calculated	calculate	VERB
ap-6786	300	7	and	and	CCONJ
ap-6786	300	8	experimental	experimental	ADJ
ap-6786	300	9	results	result	NOUN
ap-6786	300	10	are	be	AUX
ap-6786	300	11	confirmed	confirm	VERB
ap-6786	300	12	by	by	ADP
ap-6786	300	13	the	the	DET
ap-6786	300	14	values	value	NOUN
ap-6786	300	15	collected	collect	VERB
ap-6786	300	16	in	in	ADP
ap-6786	300	17	table	table	NOUN
ap-6786	300	18	10	10	NUM
ap-6786	300	19	.	.	PUNCT
ap-6786	301	1	in	in	ADP
ap-6786	301	2	author	author	NOUN
ap-6786	301	3	’s	’s	PART
ap-6786	301	4	opinion	opinion	NOUN
ap-6786	301	5	,	,	PUNCT
ap-6786	301	6	further	far	ADV
ap-6786	301	7	experimental	experimental	ADJ
ap-6786	301	8	work	work	NOUN
ap-6786	301	9	is	be	AUX
ap-6786	301	10	needed	need	VERB
ap-6786	301	11	concerning	concern	VERB
ap-6786	301	12	the	the	DET
ap-6786	301	13	post	post	ADJ
ap-6786	301	14	-	-	ADJ
ap-6786	301	15	critical	critical	ADJ
ap-6786	301	16	behaviour	behaviour	NOUN
ap-6786	301	17	of	of	ADP
ap-6786	301	18	rc	rc	PROPN
ap-6786	301	19	columns	column	NOUN
ap-6786	301	20	under	under	ADP
ap-6786	301	21	eccentric	eccentric	ADJ
ap-6786	301	22	compression	compression	NOUN
ap-6786	301	23	.	.	PUNCT
ap-6786	302	1	5	5	X
ap-6786	302	2	.	.	X
ap-6786	302	3	conclusions	conclusion	NOUN
ap-6786	302	4	and	and	CCONJ
ap-6786	302	5	comments	comment	NOUN
ap-6786	302	6	our	our	PRON
ap-6786	302	7	numerical	numerical	ADJ
ap-6786	302	8	results	result	NOUN
ap-6786	302	9	have	have	AUX
ap-6786	302	10	confirmed	confirm	VERB
ap-6786	302	11	that	that	SCONJ
ap-6786	302	12	the	the	DET
ap-6786	302	13	elaborated	elaborate	VERB
ap-6786	302	14	analytical	analytical	ADJ
ap-6786	302	15	deformation	deformation	NOUN
ap-6786	302	16	model	model	NOUN
ap-6786	302	17	(	(	PUNCT
ap-6786	302	18	taking	take	VERB
ap-6786	302	19	into	into	ADP
ap-6786	302	20	account	account	NOUN
ap-6786	302	21	the	the	DET
ap-6786	302	22	effect	effect	NOUN
ap-6786	302	23	of	of	ADP
ap-6786	302	24	concrete	concrete	ADJ
ap-6786	302	25	softening	softening	NOUN
ap-6786	302	26	)	)	PUNCT
ap-6786	302	27	may	may	AUX
ap-6786	302	28	be	be	AUX
ap-6786	302	29	used	use	VERB
ap-6786	302	30	to	to	PART
ap-6786	302	31	determine	determine	VERB
ap-6786	302	32	the	the	DET
ap-6786	302	33	strains	strain	NOUN
ap-6786	302	34	in	in	ADP
ap-6786	302	35	rectangular	rectangular	ADJ
ap-6786	302	36	cross	cross	NOUN
ap-6786	302	37	-	-	NOUN
ap-6786	302	38	sections	section	NOUN
ap-6786	302	39	of	of	ADP
ap-6786	302	40	rc	rc	PROPN
ap-6786	302	41	compressed	compress	VERB
ap-6786	302	42	structure	structure	NOUN
ap-6786	302	43	members	member	NOUN
ap-6786	302	44	.	.	PUNCT
ap-6786	303	1	it	it	PRON
ap-6786	303	2	can	can	AUX
ap-6786	303	3	be	be	AUX
ap-6786	303	4	applied	apply	VERB
ap-6786	303	5	to	to	PART
ap-6786	303	6	predict	predict	VERB
ap-6786	303	7	the	the	DET
ap-6786	303	8	behaviour	behaviour	NOUN
ap-6786	303	9	of	of	ADP
ap-6786	303	10	such	such	ADJ
ap-6786	303	11	structure	structure	NOUN
ap-6786	303	12	members	member	NOUN
ap-6786	303	13	.	.	PUNCT
ap-6786	304	1	the	the	DET
ap-6786	304	2	current	current	ADJ
ap-6786	304	3	matlab	matlab	PROPN
ap-6786	304	4	’s	’s	PART
ap-6786	304	5	implementations	implementation	NOUN
ap-6786	304	6	of	of	ADP
ap-6786	304	7	the	the	DET
ap-6786	304	8	global	global	ADJ
ap-6786	304	9	optimization	optimization	NOUN
ap-6786	304	10	algorithms	algorithm	NOUN
ap-6786	304	11	(	(	PUNCT
ap-6786	304	12	ga	ga	NOUN
ap-6786	304	13	and	and	CCONJ
ap-6786	304	14	particle	particle	NOUN
ap-6786	304	15	swarm	swarm	NOUN
ap-6786	304	16	)	)	PUNCT
ap-6786	304	17	do	do	AUX
ap-6786	304	18	not	not	PART
ap-6786	304	19	seem	seem	VERB
ap-6786	304	20	to	to	PART
ap-6786	304	21	be	be	AUX
ap-6786	304	22	suitable	suitable	ADJ
ap-6786	304	23	for	for	ADP
ap-6786	304	24	our	our	PRON
ap-6786	304	25	application	application	NOUN
ap-6786	304	26	.	.	PUNCT
ap-6786	305	1	in	in	ADP
ap-6786	305	2	genetic	genetic	ADJ
ap-6786	305	3	algorithm	algorithm	NOUN
ap-6786	305	4	(	(	PUNCT
ap-6786	305	5	ga	ga	PROPN
ap-6786	305	6	)	)	PUNCT
ap-6786	305	7	,	,	PUNCT
ap-6786	305	8	elitism	elitism	NOUN
ap-6786	305	9	is	be	AUX
ap-6786	305	10	used	use	VERB
ap-6786	305	11	(	(	PUNCT
ap-6786	305	12	part	part	NOUN
ap-6786	305	13	of	of	ADP
ap-6786	305	14	the	the	DET
ap-6786	305	15	previous	previous	ADJ
ap-6786	305	16	population	population	NOUN
ap-6786	305	17	survives	survive	VERB
ap-6786	305	18	to	to	ADP
ap-6786	305	19	the	the	DET
ap-6786	305	20	next	next	ADJ
ap-6786	305	21	one	one	NUM
ap-6786	305	22	)	)	PUNCT
ap-6786	305	23	.	.	PUNCT
ap-6786	306	1	but	but	CCONJ
ap-6786	306	2	it	it	PRON
ap-6786	306	3	does	do	AUX
ap-6786	306	4	not	not	PART
ap-6786	306	5	ensure	ensure	VERB
ap-6786	306	6	finding	find	VERB
ap-6786	306	7	the	the	DET
ap-6786	306	8	correct	correct	ADJ
ap-6786	306	9	solution	solution	NOUN
ap-6786	306	10	.	.	PUNCT
ap-6786	307	1	the	the	DET
ap-6786	307	2	particle	particle	NOUN
ap-6786	307	3	swarm	swarm	NOUN
ap-6786	307	4	procedure	procedure	NOUN
ap-6786	307	5	also	also	ADV
ap-6786	307	6	does	do	AUX
ap-6786	307	7	not	not	PART
ap-6786	307	8	guarantee	guarantee	VERB
ap-6786	307	9	the	the	DET
ap-6786	307	10	computation	computation	NOUN
ap-6786	307	11	of	of	ADP
ap-6786	307	12	the	the	DET
ap-6786	307	13	correct	correct	ADJ
ap-6786	307	14	solution	solution	NOUN
ap-6786	307	15	.	.	PUNCT
ap-6786	308	1	of	of	ADP
ap-6786	308	2	course	course	NOUN
ap-6786	308	3	,	,	PUNCT
ap-6786	308	4	we	we	PRON
ap-6786	308	5	may	may	AUX
ap-6786	308	6	tune	tune	VERB
ap-6786	308	7	some	some	PRON
ap-6786	308	8	of	of	ADP
ap-6786	308	9	their	their	PRON
ap-6786	308	10	parameters	parameter	NOUN
ap-6786	308	11	,	,	PUNCT
ap-6786	308	12	but	but	CCONJ
ap-6786	308	13	we	we	PRON
ap-6786	308	14	do	do	AUX
ap-6786	308	15	not	not	PART
ap-6786	308	16	expect	expect	VERB
ap-6786	308	17	to	to	PART
ap-6786	308	18	gain	gain	VERB
ap-6786	308	19	much	much	ADV
ap-6786	308	20	from	from	ADP
ap-6786	308	21	that	that	PRON
ap-6786	308	22	.	.	PUNCT
ap-6786	309	1	our	our	PRON
ap-6786	309	2	experiments	experiment	NOUN
ap-6786	309	3	with	with	ADP
ap-6786	309	4	the	the	DET
ap-6786	309	5	local	local	ADJ
ap-6786	309	6	search	search	NOUN
ap-6786	309	7	method	method	NOUN
ap-6786	309	8	have	have	AUX
ap-6786	309	9	frequently	frequently	ADV
ap-6786	309	10	shown	show	VERB
ap-6786	309	11	the	the	DET
ap-6786	309	12	existence	existence	NOUN
ap-6786	309	13	of	of	ADP
ap-6786	309	14	several	several	ADJ
ap-6786	309	15	global	global	ADJ
ap-6786	309	16	minima	minima	PROPN
ap-6786	309	17	.	.	PUNCT
ap-6786	310	1	all	all	PRON
ap-6786	310	2	of	of	ADP
ap-6786	310	3	them	they	PRON
ap-6786	310	4	are	be	AUX
ap-6786	310	5	almost	almost	ADV
ap-6786	310	6	equally	equally	ADV
ap-6786	310	7	good	good	ADJ
ap-6786	310	8	from	from	ADP
ap-6786	310	9	the	the	DET
ap-6786	310	10	point	point	NOUN
ap-6786	310	11	of	of	ADP
ap-6786	310	12	view	view	NOUN
ap-6786	310	13	of	of	ADP
ap-6786	310	14	a	a	DET
ap-6786	310	15	numerical	numerical	ADJ
ap-6786	310	16	calculations	calculation	NOUN
ap-6786	310	17	specialist	specialist	NOUN
ap-6786	310	18	.	.	PUNCT
ap-6786	311	1	we	we	PRON
ap-6786	311	2	decided	decide	VERB
ap-6786	311	3	to	to	PART
ap-6786	311	4	select	select	VERB
ap-6786	311	5	them	they	PRON
ap-6786	311	6	by	by	ADP
ap-6786	311	7	means	mean	NOUN
ap-6786	311	8	of	of	ADP
ap-6786	311	9	the	the	DET
ap-6786	311	10	hamilton	hamilton	PROPN
ap-6786	311	11	minimum	minimum	PROPN
ap-6786	311	12	energy	energy	NOUN
ap-6786	311	13	principle	principle	NOUN
ap-6786	311	14	.	.	PUNCT
ap-6786	312	1	in	in	ADP
ap-6786	312	2	our	our	PRON
ap-6786	312	3	opinion	opinion	NOUN
ap-6786	312	4	,	,	PUNCT
ap-6786	312	5	from	from	ADP
ap-6786	312	6	the	the	DET
ap-6786	312	7	existing	exist	VERB
ap-6786	312	8	global	global	ADJ
ap-6786	312	9	optimization	optimization	NOUN
ap-6786	312	10	methods	method	NOUN
ap-6786	312	11	,	,	PUNCT
ap-6786	312	12	the	the	DET
ap-6786	312	13	most	most	ADV
ap-6786	312	14	promising	promising	ADJ
ap-6786	312	15	may	may	AUX
ap-6786	312	16	be	be	AUX
ap-6786	312	17	the	the	DET
ap-6786	312	18	clusterization	clusterization	NOUN
ap-6786	312	19	methods	method	NOUN
ap-6786	312	20	(	(	PUNCT
ap-6786	312	21	see	see	VERB
ap-6786	312	22	for	for	ADP
ap-6786	312	23	instance	instance	NOUN
ap-6786	312	24	törn	törn	NOUN
ap-6786	312	25	and	and	CCONJ
ap-6786	312	26	żilinskas	żilinskas	NOUN
ap-6786	312	27	[	[	X
ap-6786	312	28	35	35	NUM
ap-6786	312	29	]	]	PUNCT
ap-6786	312	30	)	)	PUNCT
ap-6786	312	31	.	.	PUNCT
ap-6786	313	1	the	the	DET
ap-6786	313	2	calculated	calculate	VERB
ap-6786	313	3	results	result	NOUN
ap-6786	313	4	conform	conform	VERB
ap-6786	313	5	to	to	ADP
ap-6786	313	6	the	the	DET
ap-6786	313	7	experimental	experimental	ADJ
ap-6786	313	8	ones	one	NOUN
ap-6786	313	9	.	.	PUNCT
ap-6786	314	1	the	the	DET
ap-6786	314	2	proposed	propose	VERB
ap-6786	314	3	approach	approach	NOUN
ap-6786	314	4	enables	enable	VERB
ap-6786	314	5	to	to	PART
ap-6786	314	6	evaluate	evaluate	VERB
ap-6786	314	7	the	the	DET
ap-6786	314	8	structural	structural	ADJ
ap-6786	314	9	safety	safety	NOUN
ap-6786	314	10	of	of	ADP
ap-6786	314	11	tower	tower	NOUN
ap-6786	314	12	-	-	PUNCT
ap-6786	314	13	like	like	ADJ
ap-6786	314	14	structures	structure	NOUN
ap-6786	314	15	with	with	ADP
ap-6786	314	16	rectangular	rectangular	ADJ
ap-6786	314	17	sections	section	NOUN
ap-6786	314	18	without	without	ADP
ap-6786	314	19	testing	test	VERB
ap-6786	314	20	the	the	DET
ap-6786	314	21	drilling	drilling	NOUN
ap-6786	314	22	-	-	PUNCT
ap-6786	314	23	out	out	ADP
ap-6786	314	24	cores	core	NOUN
ap-6786	314	25	taken	take	VERB
ap-6786	314	26	from	from	ADP
ap-6786	314	27	the	the	DET
ap-6786	314	28	structure	structure	NOUN
ap-6786	314	29	.	.	PUNCT
ap-6786	315	1	it	it	PRON
ap-6786	315	2	may	may	AUX
ap-6786	315	3	also	also	ADV
ap-6786	315	4	be	be	AUX
ap-6786	315	5	useful	useful	ADJ
ap-6786	315	6	in	in	ADP
ap-6786	315	7	the	the	DET
ap-6786	315	8	structural	structural	ADJ
ap-6786	315	9	design	design	NOUN
ap-6786	315	10	and	and	CCONJ
ap-6786	315	11	maintenance	maintenance	NOUN
ap-6786	315	12	.	.	PUNCT
ap-6786	316	1	references	reference	NOUN
ap-6786	316	2	[	[	X
ap-6786	316	3	1	1	NUM
ap-6786	316	4	]	]	PUNCT
ap-6786	316	5	m.	m.	NOUN
ap-6786	316	6	lechman	lechman	NOUN
ap-6786	316	7	,	,	PUNCT
ap-6786	316	8	p.	p.	NOUN
ap-6786	316	9	lewiński	lewiński	NOUN
ap-6786	316	10	.	.	PUNCT
ap-6786	317	1	generalized	generalized	ADJ
ap-6786	317	2	section	section	NOUN
ap-6786	317	3	model	model	NOUN
ap-6786	317	4	for	for	ADP
ap-6786	317	5	analysis	analysis	NOUN
ap-6786	317	6	of	of	ADP
ap-6786	317	7	reinforced	reinforce	VERB
ap-6786	317	8	concrete	concrete	ADJ
ap-6786	317	9	chimney	chimney	NOUN
ap-6786	317	10	weakened	weaken	VERB
ap-6786	317	11	by	by	ADP
ap-6786	317	12	openings	opening	NOUN
ap-6786	317	13	.	.	PUNCT
ap-6786	318	1	eng	eng	PROPN
ap-6786	318	2	trans	trans	PROPN
ap-6786	318	3	49(1):3–28	49(1):3–28	PROPN
ap-6786	318	4	,	,	PUNCT
ap-6786	318	5	2001	2001	NUM
ap-6786	318	6	.	.	PUNCT
ap-6786	319	1	250	250	NUM
ap-6786	319	2	vol	vol	NOUN
ap-6786	319	3	.	.	PUNCT
ap-6786	320	1	61	61	NUM
ap-6786	320	2	no	no	NOUN
ap-6786	320	3	.	.	PUNCT
ap-6786	321	1	1/2021	1/2021	NUM
ap-6786	321	2	global	global	ADJ
ap-6786	321	3	optimization	optimization	NOUN
ap-6786	321	4	to	to	PART
ap-6786	321	5	predict	predict	VERB
ap-6786	321	6	strains	strain	NOUN
ap-6786	321	7	in	in	ADP
ap-6786	321	8	rc	rc	PROPN
ap-6786	321	9	compressed	compress	VERB
ap-6786	321	10	columns	column	NOUN
ap-6786	321	11	[	[	X
ap-6786	321	12	2	2	NUM
ap-6786	321	13	]	]	PUNCT
ap-6786	321	14	m.	m.	NOUN
ap-6786	321	15	knauff	knauff	PROPN
ap-6786	321	16	.	.	PUNCT
ap-6786	322	1	calculations	calculation	NOUN
ap-6786	322	2	of	of	ADP
ap-6786	322	3	reinforced	reinforce	VERB
ap-6786	322	4	concrete	concrete	ADJ
ap-6786	322	5	structures	structure	NOUN
ap-6786	322	6	according	accord	VERB
ap-6786	322	7	to	to	ADP
ap-6786	322	8	ec	ec	PROPN
ap-6786	322	9	2	2	NUM
ap-6786	322	10	.	.	PUNCT
ap-6786	322	11	scientific	scientific	ADJ
ap-6786	322	12	publisher	publisher	NOUN
ap-6786	322	13	pwn	pwn	PROPN
ap-6786	322	14	,	,	PUNCT
ap-6786	322	15	warsaw	warsaw	PROPN
ap-6786	322	16	,	,	PUNCT
ap-6786	322	17	poland	poland	PROPN
ap-6786	322	18	,	,	PUNCT
ap-6786	322	19	2013	2013	NUM
ap-6786	322	20	.	.	PUNCT
ap-6786	323	1	[	[	X
ap-6786	323	2	3	3	X
ap-6786	323	3	]	]	PUNCT
ap-6786	323	4	m.	m.	NOUN
ap-6786	323	5	knauff	knauff	PROPN
ap-6786	323	6	,	,	PUNCT
ap-6786	323	7	a.	a.	NOUN
ap-6786	323	8	golubiska	golubiska	NOUN
ap-6786	323	9	,	,	PUNCT
ap-6786	323	10	p.	p.	PROPN
ap-6786	323	11	knyziak	knyziak	PROPN
ap-6786	323	12	.	.	PUNCT
ap-6786	324	1	tables	table	NOUN
ap-6786	324	2	and	and	CCONJ
ap-6786	324	3	formulae	formulae	VERB
ap-6786	324	4	for	for	ADP
ap-6786	324	5	the	the	DET
ap-6786	324	6	design	design	NOUN
ap-6786	324	7	of	of	ADP
ap-6786	324	8	reinforced	reinforce	VERB
ap-6786	324	9	concrete	concrete	ADJ
ap-6786	324	10	structures	structure	NOUN
ap-6786	324	11	with	with	ADP
ap-6786	324	12	calculation	calculation	NOUN
ap-6786	324	13	examples	example	NOUN
ap-6786	324	14	.	.	PUNCT
ap-6786	325	1	scientific	scientific	ADJ
ap-6786	325	2	publisher	publisher	NOUN
ap-6786	325	3	pwn	pwn	PROPN
ap-6786	325	4	,	,	PUNCT
ap-6786	325	5	warsaw	warsaw	PROPN
ap-6786	325	6	,	,	PUNCT
ap-6786	325	7	poland	poland	PROPN
ap-6786	325	8	,	,	PUNCT
ap-6786	325	9	2013	2013	NUM
ap-6786	325	10	.	.	PUNCT
ap-6786	326	1	[	[	X
ap-6786	326	2	4	4	X
ap-6786	326	3	]	]	X
ap-6786	326	4	h.	h.	NOUN
ap-6786	326	5	nieser	nieser	PROPN
ap-6786	326	6	,	,	PUNCT
ap-6786	326	7	v.	v.	PROPN
ap-6786	326	8	engel	engel	PROPN
ap-6786	326	9	.	.	PUNCT
ap-6786	327	1	structure	structure	NOUN
ap-6786	327	2	of	of	ADP
ap-6786	327	3	industrial	industrial	ADJ
ap-6786	327	4	chimneys	chimney	NOUN
ap-6786	327	5	.	.	PUNCT
ap-6786	328	1	commentary	commentary	NOUN
ap-6786	328	2	on	on	ADP
ap-6786	328	3	din	din	VERB
ap-6786	328	4	1056	1056	NUM
ap-6786	328	5	.	.	PUNCT
ap-6786	329	1	german	german	PROPN
ap-6786	329	2	institute	institute	PROPN
ap-6786	329	3	for	for	ADP
ap-6786	329	4	standardization	standardization	NOUN
ap-6786	329	5	,	,	PUNCT
ap-6786	329	6	berlin	berlin	PROPN
ap-6786	329	7	,	,	PUNCT
ap-6786	329	8	germany	germany	PROPN
ap-6786	329	9	,	,	PUNCT
ap-6786	329	10	1986	1986	NUM
ap-6786	329	11	.	.	PUNCT
ap-6786	330	1	[	[	X
ap-6786	330	2	5	5	NUM
ap-6786	330	3	]	]	X
ap-6786	330	4	cicind	cicind	NOUN
ap-6786	330	5	.	.	PUNCT
ap-6786	330	6	model	model	PROPN
ap-6786	330	7	code	code	PROPN
ap-6786	330	8	for	for	ADP
ap-6786	330	9	chimneys	chimney	NOUN
ap-6786	330	10	,	,	PUNCT
ap-6786	330	11	part	part	NOUN
ap-6786	330	12	a	a	X
ap-6786	330	13	:	:	PUNCT
ap-6786	330	14	the	the	DET
ap-6786	330	15	shell	shell	NOUN
ap-6786	330	16	.	.	PUNCT
ap-6786	331	1	sec	sec	PROPN
ap-6786	331	2	.	.	PUNCT
ap-6786	332	1	ed	ed	PROPN
ap-6786	332	2	.	.	PROPN
ap-6786	332	3	,	,	PUNCT
ap-6786	332	4	rev	rev	PROPN
ap-6786	332	5	.	.	PROPN
ap-6786	332	6	1	1	NUM
ap-6786	332	7	.	.	X
ap-6786	333	1	cicind	cicind	PROPN
ap-6786	333	2	,	,	PUNCT
ap-6786	333	3	zurich	zurich	PROPN
ap-6786	333	4	,	,	PUNCT
ap-6786	333	5	switzerland	switzerland	PROPN
ap-6786	333	6	,	,	PUNCT
ap-6786	333	7	2001	2001	NUM
ap-6786	333	8	.	.	PUNCT
ap-6786	334	1	[	[	X
ap-6786	334	2	6	6	NUM
ap-6786	334	3	]	]	PUNCT
ap-6786	334	4	m.	m.	NOUN
ap-6786	334	5	lechman	lechman	NOUN
ap-6786	334	6	,	,	PUNCT
ap-6786	334	7	a.	a.	NOUN
ap-6786	334	8	stachurski	stachurski	PROPN
ap-6786	334	9	.	.	PUNCT
ap-6786	335	1	nonlinear	nonlinear	ADJ
ap-6786	335	2	section	section	NOUN
ap-6786	335	3	model	model	NOUN
ap-6786	335	4	for	for	ADP
ap-6786	335	5	analysis	analysis	NOUN
ap-6786	335	6	of	of	ADP
ap-6786	335	7	rc	rc	PROPN
ap-6786	335	8	circular	circular	ADJ
ap-6786	335	9	tower	tower	NOUN
ap-6786	335	10	structures	structure	NOUN
ap-6786	335	11	weakened	weaken	VERB
ap-6786	335	12	by	by	ADP
ap-6786	335	13	openings	opening	NOUN
ap-6786	335	14	.	.	PUNCT
ap-6786	336	1	struct	struct	VERB
ap-6786	336	2	eng	eng	PROPN
ap-6786	336	3	and	and	CCONJ
ap-6786	336	4	mech	mech	NOUN
ap-6786	336	5	20(2):161–172	20(2):161–172	PROPN
ap-6786	336	6	,	,	PUNCT
ap-6786	336	7	2005	2005	NUM
ap-6786	336	8	.	.	PUNCT
ap-6786	337	1	doi:/10.12989	doi:/10.12989	PROPN
ap-6786	337	2	/	/	SYM
ap-6786	337	3	sem.2005.20.2.161	sem.2005.20.2.161	PROPN
ap-6786	337	4	.	.	PUNCT
ap-6786	338	1	[	[	X
ap-6786	338	2	7	7	X
ap-6786	338	3	]	]	X
ap-6786	338	4	m.	m.	NOUN
ap-6786	338	5	lechman	lechman	PROPN
ap-6786	338	6	.	.	PUNCT
ap-6786	339	1	load	load	NOUN
ap-6786	339	2	-	-	PUNCT
ap-6786	339	3	carrying	carry	VERB
ap-6786	339	4	capacity	capacity	NOUN
ap-6786	339	5	and	and	CCONJ
ap-6786	339	6	dimensioning	dimensioning	NOUN
ap-6786	339	7	of	of	ADP
ap-6786	339	8	ring	ring	NOUN
ap-6786	339	9	cross	cross	NOUN
ap-6786	339	10	-	-	NOUN
ap-6786	339	11	sections	section	NOUN
ap-6786	339	12	under	under	ADP
ap-6786	339	13	eccentric	eccentric	ADJ
ap-6786	339	14	compression	compression	NOUN
ap-6786	339	15	.	.	PUNCT
ap-6786	340	1	scientific	scientific	ADJ
ap-6786	340	2	papers	paper	NOUN
ap-6786	340	3	of	of	ADP
ap-6786	340	4	the	the	DET
ap-6786	340	5	building	building	PROPN
ap-6786	340	6	research	research	PROPN
ap-6786	340	7	institute	institute	PROPN
ap-6786	340	8	,	,	PUNCT
ap-6786	340	9	dissertations	dissertations	PROPN
ap-6786	340	10	,	,	PUNCT
ap-6786	340	11	warsaw	warsaw	PROPN
ap-6786	340	12	,	,	PUNCT
ap-6786	340	13	poland	poland	PROPN
ap-6786	340	14	,	,	PUNCT
ap-6786	340	15	2006	2006	NUM
ap-6786	340	16	.	.	PUNCT
ap-6786	341	1	[	[	X
ap-6786	341	2	8	8	NUM
ap-6786	341	3	]	]	PUNCT
ap-6786	341	4	m.	m.	NOUN
ap-6786	341	5	lechman	lechman	PROPN
ap-6786	341	6	.	.	PUNCT
ap-6786	342	1	resistance	resistance	NOUN
ap-6786	342	2	of	of	ADP
ap-6786	342	3	rc	rc	PROPN
ap-6786	342	4	annular	annular	PROPN
ap-6786	342	5	cross	cross	PROPN
ap-6786	342	6	-	-	NOUN
ap-6786	342	7	sections	section	NOUN
ap-6786	342	8	with	with	ADP
ap-6786	342	9	openings	opening	NOUN
ap-6786	342	10	subjected	subject	VERB
ap-6786	342	11	to	to	ADP
ap-6786	342	12	axial	axial	ADJ
ap-6786	342	13	force	force	NOUN
ap-6786	342	14	and	and	CCONJ
ap-6786	342	15	bending	bending	NOUN
ap-6786	342	16	.	.	PUNCT
ap-6786	343	1	eng	eng	PROPN
ap-6786	343	2	trans	trans	PROPN
ap-6786	343	3	56(1):43–64	56(1):43–64	PROPN
ap-6786	343	4	,	,	PUNCT
ap-6786	343	5	2008	2008	NUM
ap-6786	343	6	.	.	PUNCT
ap-6786	344	1	[	[	X
ap-6786	344	2	9	9	NUM
ap-6786	344	3	]	]	PUNCT
ap-6786	344	4	m.	m.	NOUN
ap-6786	344	5	lechman	lechman	NOUN
ap-6786	344	6	.	.	PUNCT
ap-6786	345	1	dimensioning	dimension	VERB
ap-6786	345	2	of	of	ADP
ap-6786	345	3	sections	section	NOUN
ap-6786	345	4	of	of	ADP
ap-6786	345	5	concrete	concrete	ADJ
ap-6786	345	6	members	member	NOUN
ap-6786	345	7	under	under	ADP
ap-6786	345	8	compression	compression	NOUN
ap-6786	345	9	according	accord	VERB
ap-6786	345	10	to	to	PART
ap-6786	345	11	eurocode	eurocode	NOUN
ap-6786	345	12	2	2	NUM
ap-6786	345	13	.	.	PUNCT
ap-6786	345	14	examples	example	NOUN
ap-6786	345	15	of	of	ADP
ap-6786	345	16	use	use	NOUN
ap-6786	345	17	.	.	PUNCT
ap-6786	346	1	building	build	VERB
ap-6786	346	2	research	research	PROPN
ap-6786	346	3	institute	institute	PROPN
ap-6786	346	4	publications	publication	NOUN
ap-6786	346	5	,	,	PUNCT
ap-6786	346	6	warsaw	warsaw	PROPN
ap-6786	346	7	,	,	PUNCT
ap-6786	346	8	poland	poland	PROPN
ap-6786	346	9	,	,	PUNCT
ap-6786	346	10	2011	2011	NUM
ap-6786	346	11	.	.	PUNCT
ap-6786	347	1	[	[	X
ap-6786	347	2	10	10	NUM
ap-6786	347	3	]	]	PUNCT
ap-6786	347	4	m.	m.	NOUN
ap-6786	347	5	lechman	lechman	PROPN
ap-6786	347	6	.	.	PUNCT
ap-6786	348	1	resistance	resistance	NOUN
ap-6786	348	2	of	of	ADP
ap-6786	348	3	reinforced	reinforce	VERB
ap-6786	348	4	concrete	concrete	ADJ
ap-6786	348	5	columns	column	NOUN
ap-6786	348	6	subjected	subject	VERB
ap-6786	348	7	to	to	ADP
ap-6786	348	8	axial	axial	ADJ
ap-6786	348	9	force	force	NOUN
ap-6786	348	10	and	and	CCONJ
ap-6786	348	11	bending	bending	NOUN
ap-6786	348	12	.	.	PUNCT
ap-6786	349	1	transportation	transportation	NOUN
ap-6786	349	2	res	re	NOUN
ap-6786	349	3	procedia	procedia	PROPN
ap-6786	349	4	14c:2411–2420	14c:2411–2420	NUM
ap-6786	349	5	,	,	PUNCT
ap-6786	349	6	2016	2016	NUM
ap-6786	349	7	.	.	PUNCT
ap-6786	350	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	350	2	/	/	SYM
ap-6786	350	3	j.trpro.2016.05.283	j.trpro.2016.05.283	PROPN
ap-6786	350	4	.	.	PUNCT
ap-6786	351	1	[	[	X
ap-6786	351	2	11	11	NUM
ap-6786	351	3	]	]	PUNCT
ap-6786	351	4	t.	t.	PROPN
ap-6786	351	5	majewski	majewski	PROPN
ap-6786	351	6	,	,	PUNCT
ap-6786	351	7	j.	j.	PROPN
ap-6786	351	8	bobiński	bobiński	PROPN
ap-6786	351	9	,	,	PUNCT
ap-6786	351	10	j.	j.	PROPN
ap-6786	351	11	tejchman	tejchman	PROPN
ap-6786	351	12	.	.	PUNCT
ap-6786	352	1	fe	fe	PROPN
ap-6786	352	2	analysis	analysis	NOUN
ap-6786	352	3	of	of	ADP
ap-6786	352	4	failure	failure	NOUN
ap-6786	352	5	behaviour	behaviour	NOUN
ap-6786	352	6	of	of	ADP
ap-6786	352	7	reinforced	reinforce	VERB
ap-6786	352	8	concrete	concrete	ADJ
ap-6786	352	9	columns	column	NOUN
ap-6786	352	10	under	under	ADP
ap-6786	352	11	eccentric	eccentric	ADJ
ap-6786	352	12	compression	compression	NOUN
ap-6786	352	13	.	.	PUNCT
ap-6786	353	1	eng	eng	PROPN
ap-6786	353	2	struct	struct	VERB
ap-6786	353	3	30(2):300–317	30(2):300–317	NUM
ap-6786	353	4	,	,	PUNCT
ap-6786	353	5	2008	2008	NUM
ap-6786	353	6	.	.	PUNCT
ap-6786	354	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	354	2	/	/	SYM
ap-6786	354	3	j.engstruct.2007.03.024	j.engstruct.2007.03.024	PROPN
ap-6786	354	4	.	.	PUNCT
ap-6786	355	1	[	[	X
ap-6786	355	2	12	12	NUM
ap-6786	355	3	]	]	X
ap-6786	355	4	e.	e.	PROPN
ap-6786	355	5	rodrigues	rodrigues	PROPN
ap-6786	355	6	,	,	PUNCT
ap-6786	355	7	o.	o.	PROPN
ap-6786	355	8	manzoli	manzoli	PROPN
ap-6786	355	9	,	,	PUNCT
ap-6786	355	10	l.	l.	PROPN
ap-6786	355	11	bitencourt	bitencourt	PROPN
ap-6786	355	12	jr	jr	PROPN
ap-6786	355	13	.	.	PROPN
ap-6786	355	14	,	,	PUNCT
ap-6786	355	15	et	et	PROPN
ap-6786	355	16	al	al	PROPN
ap-6786	355	17	.	.	PROPN
ap-6786	355	18	failure	failure	NOUN
ap-6786	355	19	behavior	behavior	NOUN
ap-6786	355	20	modeling	modeling	NOUN
ap-6786	355	21	of	of	ADP
ap-6786	355	22	slender	slender	ADJ
ap-6786	355	23	reinforced	reinforce	VERB
ap-6786	355	24	concrete	concrete	ADJ
ap-6786	355	25	columns	column	NOUN
ap-6786	355	26	subjected	subject	VERB
ap-6786	355	27	to	to	ADP
ap-6786	355	28	eccentric	eccentric	ADJ
ap-6786	355	29	load	load	NOUN
ap-6786	355	30	.	.	PUNCT
ap-6786	356	1	latin	latin	PROPN
ap-6786	356	2	amer	amer	PROPN
ap-6786	356	3	j	j	PROPN
ap-6786	356	4	of	of	ADP
ap-6786	356	5	solids	solid	NOUN
ap-6786	356	6	and	and	CCONJ
ap-6786	356	7	struct	struct	VERB
ap-6786	356	8	12(3):520–541	12(3):520–541	NUM
ap-6786	356	9	,	,	PUNCT
ap-6786	356	10	2015	2015	NUM
ap-6786	356	11	.	.	PUNCT
ap-6786	357	1	doi:10.1590/1679	doi:10.1590/1679	NOUN
ap-6786	357	2	-	-	PUNCT
ap-6786	357	3	78251224	78251224	NUM
ap-6786	357	4	.	.	PUNCT
ap-6786	358	1	[	[	X
ap-6786	358	2	13	13	NUM
ap-6786	358	3	]	]	PUNCT
ap-6786	358	4	j.	j.	PROPN
ap-6786	358	5	kim	kim	PROPN
ap-6786	358	6	,	,	PUNCT
ap-6786	358	7	s.-s	s.-s	PROPN
ap-6786	358	8	.	.	PUNCT
ap-6786	359	1	lee	lee	PROPN
ap-6786	359	2	.	.	PUNCT
ap-6786	360	1	the	the	DET
ap-6786	360	2	behavior	behavior	NOUN
ap-6786	360	3	of	of	ADP
ap-6786	360	4	reinforced	reinforce	VERB
ap-6786	360	5	concrete	concrete	ADJ
ap-6786	360	6	columns	column	NOUN
ap-6786	360	7	subjected	subject	VERB
ap-6786	360	8	to	to	ADP
ap-6786	360	9	axial	axial	ADJ
ap-6786	360	10	force	force	NOUN
ap-6786	360	11	and	and	CCONJ
ap-6786	360	12	biaxial	biaxial	ADJ
ap-6786	360	13	bending	bending	NOUN
ap-6786	360	14	.	.	PUNCT
ap-6786	361	1	eng	eng	PROPN
ap-6786	361	2	struct	struct	VERB
ap-6786	361	3	22(11):1518–1528	22(11):1518–1528	NUM
ap-6786	361	4	,	,	PUNCT
ap-6786	361	5	2000	2000	NUM
ap-6786	361	6	.	.	PUNCT
ap-6786	362	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	362	2	/	/	SYM
ap-6786	362	3	s0141	s0141	PROPN
ap-6786	362	4	-	-	NOUN
ap-6786	362	5	0296(99)00090	0296(99)00090	NOUN
ap-6786	362	6	-	-	PUNCT
ap-6786	362	7	5	5	NUM
ap-6786	362	8	.	.	PUNCT
ap-6786	363	1	[	[	X
ap-6786	363	2	14	14	NUM
ap-6786	363	3	]	]	X
ap-6786	363	4	g.	g.	PROPN
ap-6786	363	5	campione	campione	PROPN
ap-6786	363	6	,	,	PUNCT
ap-6786	363	7	g.	g.	PROPN
ap-6786	363	8	.	.	PUNCT
ap-6786	364	1	minafo	minafo	PROPN
ap-6786	364	2	.	.	PUNCT
ap-6786	365	1	applicability	applicability	NOUN
ap-6786	365	2	of	of	ADP
ap-6786	365	3	over	over	ADP
ap-6786	365	4	-	-	PUNCT
ap-6786	365	5	coring	core	VERB
ap-6786	365	6	technique	technique	NOUN
ap-6786	365	7	to	to	ADP
ap-6786	365	8	loaded	load	VERB
ap-6786	365	9	rc	rc	PROPN
ap-6786	365	10	columns	column	NOUN
ap-6786	365	11	.	.	PUNCT
ap-6786	366	1	struct	struct	VERB
ap-6786	366	2	eng	eng	PROPN
ap-6786	366	3	and	and	CCONJ
ap-6786	366	4	mech	mech	NOUN
ap-6786	366	5	51(1):181–197	51(1):181–197	PROPN
ap-6786	366	6	,	,	PUNCT
ap-6786	366	7	2014	2014	NUM
ap-6786	366	8	.	.	PUNCT
ap-6786	367	1	doi:10.12989	doi:10.12989	PROPN
ap-6786	367	2	/	/	SYM
ap-6786	367	3	sem.2014.51.1.181	sem.2014.51.1.181	PROPN
ap-6786	367	4	.	.	PUNCT
ap-6786	368	1	[	[	X
ap-6786	368	2	15	15	NUM
ap-6786	368	3	]	]	X
ap-6786	368	4	g.	g.	PROPN
ap-6786	368	5	campione	campione	PROPN
ap-6786	368	6	,	,	PUNCT
ap-6786	368	7	m.	m.	NOUN
ap-6786	368	8	fossetti	fossetti	PROPN
ap-6786	368	9	,	,	PUNCT
ap-6786	368	10	m.	m.	NOUN
ap-6786	368	11	papia	papia	PROPN
ap-6786	368	12	.	.	PUNCT
ap-6786	369	1	behavior	behavior	NOUN
ap-6786	369	2	of	of	ADP
ap-6786	369	3	fiber	fiber	NOUN
ap-6786	369	4	-	-	PUNCT
ap-6786	369	5	reinforced	reinforce	VERB
ap-6786	369	6	concrete	concrete	ADJ
ap-6786	369	7	columns	column	NOUN
ap-6786	369	8	under	under	ADP
ap-6786	369	9	axially	axially	ADV
ap-6786	369	10	and	and	CCONJ
ap-6786	369	11	eccentrically	eccentrically	ADV
ap-6786	369	12	compressive	compressive	ADJ
ap-6786	369	13	loads	load	NOUN
ap-6786	369	14	.	.	PUNCT
ap-6786	370	1	aci	aci	PROPN
ap-6786	370	2	struct	struct	NOUN
ap-6786	370	3	j	j	PROPN
ap-6786	370	4	107(3):272–281	107(3):272–281	NUM
ap-6786	370	5	,	,	PUNCT
ap-6786	370	6	2010	2010	NUM
ap-6786	370	7	.	.	PUNCT
ap-6786	371	1	[	[	X
ap-6786	371	2	16	16	NUM
ap-6786	371	3	]	]	X
ap-6786	371	4	n.	n.	PROPN
ap-6786	371	5	lloyd	lloyd	PROPN
ap-6786	371	6	,	,	PUNCT
ap-6786	371	7	b.	b.	PROPN
ap-6786	371	8	rangan	rangan	PROPN
ap-6786	371	9	.	.	PUNCT
ap-6786	372	1	studies	study	NOUN
ap-6786	372	2	on	on	ADP
ap-6786	372	3	high	high	ADJ
ap-6786	372	4	-	-	PUNCT
ap-6786	372	5	strength	strength	NOUN
ap-6786	372	6	concrete	concrete	ADJ
ap-6786	372	7	columns	column	NOUN
ap-6786	372	8	under	under	ADP
ap-6786	372	9	eccentric	eccentric	ADJ
ap-6786	372	10	compression	compression	NOUN
ap-6786	372	11	.	.	PUNCT
ap-6786	373	1	aci	aci	PROPN
ap-6786	373	2	struct	struct	NOUN
ap-6786	373	3	j	j	PROPN
ap-6786	373	4	93(6):631–638	93(6):631–638	PROPN
ap-6786	373	5	,	,	PUNCT
ap-6786	373	6	1996	1996	NUM
ap-6786	373	7	.	.	PUNCT
ap-6786	374	1	[	[	X
ap-6786	374	2	17	17	NUM
ap-6786	374	3	]	]	PUNCT
ap-6786	374	4	j.	j.	PROPN
ap-6786	374	5	bonet	bonet	PROPN
ap-6786	374	6	,	,	PUNCT
ap-6786	374	7	m.	m.	PROPN
ap-6786	374	8	romero	romero	PROPN
ap-6786	374	9	,	,	PUNCT
ap-6786	374	10	p.	p.	PROPN
ap-6786	374	11	miguel	miguel	PROPN
ap-6786	374	12	.	.	PUNCT
ap-6786	374	13	effective	effective	ADJ
ap-6786	374	14	flexural	flexural	ADJ
ap-6786	374	15	stiffness	stiffness	NOUN
ap-6786	374	16	of	of	ADP
ap-6786	374	17	slender	slender	ADJ
ap-6786	374	18	reinforced	reinforce	VERB
ap-6786	374	19	concrete	concrete	ADJ
ap-6786	374	20	columns	column	NOUN
ap-6786	374	21	under	under	ADP
ap-6786	374	22	axial	axial	ADJ
ap-6786	374	23	forces	force	NOUN
ap-6786	374	24	and	and	CCONJ
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ap-6786	374	26	bending	bending	NOUN
ap-6786	374	27	.	.	PUNCT
ap-6786	375	1	eng	eng	PROPN
ap-6786	375	2	struct	struct	NOUN
ap-6786	375	3	33(3):881	33(3):881	NUM
ap-6786	375	4	–	–	PUNCT
ap-6786	375	5	893	893	NUM
ap-6786	375	6	,	,	PUNCT
ap-6786	375	7	2011	2011	NUM
ap-6786	375	8	.	.	PUNCT
ap-6786	376	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	376	2	/	/	SYM
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ap-6786	376	4	.	.	PUNCT
ap-6786	377	1	[	[	X
ap-6786	377	2	18	18	NUM
ap-6786	377	3	]	]	PUNCT
ap-6786	377	4	m.	m.	NOUN
ap-6786	377	5	ye	ye	PROPN
ap-6786	377	6	,	,	PUNCT
ap-6786	377	7	y.	y.	PROPN
ap-6786	377	8	pi	pi	PROPN
ap-6786	377	9	,	,	PUNCT
ap-6786	377	10	m.	m.	NOUN
ap-6786	377	11	ren	ren	PROPN
ap-6786	377	12	.	.	PUNCT
ap-6786	378	1	experimental	experimental	ADJ
ap-6786	378	2	and	and	CCONJ
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ap-6786	378	4	investigation	investigation	NOUN
ap-6786	378	5	on	on	ADP
ap-6786	378	6	rc	rc	PROPN
ap-6786	378	7	columns	column	NOUN
ap-6786	378	8	with	with	ADP
ap-6786	378	9	distributed	distribute	VERB
ap-6786	378	10	-	-	PUNCT
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ap-6786	379	1	struct	struct	VERB
ap-6786	379	2	eng	eng	PROPN
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ap-6786	379	6	,	,	PUNCT
ap-6786	379	7	2013	2013	NUM
ap-6786	379	8	.	.	PUNCT
ap-6786	380	1	doi:10.12989	doi:10.12989	PROPN
ap-6786	380	2	/	/	SYM
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ap-6786	380	4	.	.	PUNCT
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ap-6786	381	2	19	19	NUM
ap-6786	381	3	]	]	X
ap-6786	381	4	c.	c.	PROPN
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ap-6786	381	6	,	,	PUNCT
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ap-6786	381	9	,	,	PUNCT
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ap-6786	381	12	,	,	PUNCT
ap-6786	381	13	et	et	PROPN
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ap-6786	381	23	under	under	ADP
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ap-6786	381	25	loading	loading	NOUN
ap-6786	381	26	.	.	PUNCT
ap-6786	382	1	eng	eng	PROPN
ap-6786	382	2	struct	struct	NOUN
ap-6786	382	3	126:78–91	126:78–91	NUM
ap-6786	382	4	,	,	PUNCT
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ap-6786	383	1	doi:10.1016	doi:10.1016	PROPN
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ap-6786	383	4	.	.	PUNCT
ap-6786	384	1	[	[	X
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ap-6786	384	6	,	,	PUNCT
ap-6786	384	7	m.	m.	NOUN
ap-6786	384	8	musiał	musiał	PROPN
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ap-6786	385	3	of	of	ADP
ap-6786	385	4	cfrp	cfrp	NOUN
ap-6786	385	5	materials	material	NOUN
ap-6786	385	6	strengthening	strengthening	NOUN
ap-6786	385	7	of	of	ADP
ap-6786	385	8	eccentrically	eccentrically	ADV
ap-6786	385	9	compressed	compress	VERB
ap-6786	385	10	reinforced	reinforce	VERB
ap-6786	385	11	concrete	concrete	ADJ
ap-6786	385	12	columns	column	NOUN
ap-6786	385	13	.	.	PUNCT
ap-6786	386	1	arch	arch	NOUN
ap-6786	386	2	of	of	ADP
ap-6786	386	3	civil	civil	ADJ
ap-6786	386	4	and	and	CCONJ
ap-6786	386	5	mech	mech	NOUN
ap-6786	386	6	eng	eng	PROPN
ap-6786	386	7	11(1):249–262	11(1):249–262	PROPN
ap-6786	386	8	,	,	PUNCT
ap-6786	386	9	2011	2011	NUM
ap-6786	386	10	.	.	PUNCT
ap-6786	387	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	387	2	/	/	SYM
ap-6786	387	3	s1644	s1644	PROPN
ap-6786	387	4	-	-	PUNCT
ap-6786	387	5	9665(12)60187	9665(12)60187	NUM
ap-6786	387	6	-	-	PUNCT
ap-6786	387	7	3	3	NUM
ap-6786	387	8	.	.	PUNCT
ap-6786	388	1	[	[	X
ap-6786	388	2	21	21	NUM
ap-6786	388	3	]	]	PUNCT
ap-6786	388	4	t.	t.	PROPN
ap-6786	388	5	trapko	trapko	PROPN
ap-6786	388	6	.	.	PROPN
ap-6786	388	7	effect	effect	NOUN
ap-6786	388	8	of	of	ADP
ap-6786	388	9	eccentric	eccentric	ADJ
ap-6786	388	10	compression	compression	NOUN
ap-6786	388	11	loading	loading	NOUN
ap-6786	388	12	on	on	ADP
ap-6786	388	13	the	the	DET
ap-6786	388	14	strains	strain	NOUN
ap-6786	388	15	of	of	ADP
ap-6786	388	16	frcm	frcm	NOUN
ap-6786	388	17	confined	confine	VERB
ap-6786	388	18	concrete	concrete	ADJ
ap-6786	388	19	columns	column	NOUN
ap-6786	388	20	.	.	PUNCT
ap-6786	389	1	constr	constr	NOUN
ap-6786	389	2	and	and	CCONJ
ap-6786	389	3	building	building	NOUN
ap-6786	389	4	mat	mat	NOUN
ap-6786	389	5	61:97–105	61:97–105	NUM
ap-6786	389	6	,	,	PUNCT
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ap-6786	389	8	.	.	PUNCT
ap-6786	390	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	390	2	/	/	SYM
ap-6786	390	3	j.conbuildmat.2014.03.007	j.conbuildmat.2014.03.007	PROPN
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ap-6786	391	1	[	[	X
ap-6786	391	2	22	22	NUM
ap-6786	391	3	]	]	PUNCT
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ap-6786	392	2	of	of	ADP
ap-6786	392	3	hollow	hollow	ADJ
ap-6786	392	4	core	core	NOUN
ap-6786	392	5	square	square	ADJ
ap-6786	392	6	reinforced	reinforce	VERB
ap-6786	392	7	concrete	concrete	ADJ
ap-6786	392	8	columns	column	NOUN
ap-6786	392	9	wrapped	wrap	VERB
ap-6786	392	10	with	with	ADP
ap-6786	392	11	cfrp	cfrp	NOUN
ap-6786	392	12	with	with	ADP
ap-6786	392	13	different	different	ADJ
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ap-6786	392	16	.	.	PUNCT
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ap-6786	393	5	50:62–73	50:62–73	PRON
ap-6786	393	6	,	,	PUNCT
ap-6786	393	7	2014	2014	NUM
ap-6786	393	8	.	.	PUNCT
ap-6786	394	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	394	2	/	/	SYM
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ap-6786	395	1	[	[	X
ap-6786	395	2	23	23	NUM
ap-6786	395	3	]	]	PUNCT
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ap-6786	395	8	m.	m.	PROPN
ap-6786	395	9	el	el	PROPN
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ap-6786	395	11	,	,	PUNCT
ap-6786	395	12	b.	b.	PROPN
ap-6786	395	13	abdel	abdel	PROPN
ap-6786	395	14	-	-	PUNCT
ap-6786	395	15	magid	magid	PROPN
ap-6786	395	16	.	.	PUNCT
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ap-6786	396	5	-	-	ADJ
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ap-6786	396	12	performance	performance	NOUN
ap-6786	396	13	of	of	ADP
ap-6786	396	14	reinforced	reinforce	VERB
ap-6786	396	15	concrete	concrete	ADJ
ap-6786	396	16	members	member	NOUN
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ap-6786	396	18	with	with	ADP
ap-6786	396	19	carbon	carbon	NOUN
ap-6786	396	20	fiber	fiber	NOUN
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ap-6786	396	22	reinforced	reinforce	VERB
ap-6786	396	23	polymers	polymer	NOUN
ap-6786	396	24	.	.	PUNCT
ap-6786	397	1	mat	mat	NOUN
ap-6786	397	2	and	and	CCONJ
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ap-6786	397	5	,	,	PUNCT
ap-6786	397	6	2010	2010	NUM
ap-6786	397	7	.	.	PUNCT
ap-6786	398	1	doi:10.1016	doi:10.1016	PROPN
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ap-6786	399	1	[	[	X
ap-6786	399	2	24	24	NUM
ap-6786	399	3	]	]	PUNCT
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ap-6786	399	9	.	.	PUNCT
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ap-6786	400	7	loading	loading	NOUN
ap-6786	400	8	.	.	PUNCT
ap-6786	401	1	comp	comp	PROPN
ap-6786	401	2	struct	struct	NOUN
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ap-6786	401	4	,	,	PUNCT
ap-6786	401	5	2012	2012	NUM
ap-6786	401	6	.	.	PUNCT
ap-6786	402	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	402	2	/	/	SYM
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ap-6786	402	4	.	.	PUNCT
ap-6786	403	1	[	[	X
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ap-6786	403	3	]	]	PUNCT
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ap-6786	404	7	short	short	ADJ
ap-6786	404	8	columns	column	NOUN
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ap-6786	404	10	using	use	VERB
ap-6786	404	11	gfrp	gfrp	PROPN
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ap-6786	404	13	.	.	PUNCT
ap-6786	405	1	struct	struct	VERB
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ap-6786	405	7	2011	2011	NUM
ap-6786	405	8	.	.	PUNCT
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ap-6786	406	4	.	.	PUNCT
ap-6786	407	1	[	[	X
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ap-6786	407	3	]	]	PUNCT
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ap-6786	407	7	a.	a.	PROPN
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ap-6786	408	2	study	study	NOUN
ap-6786	408	3	of	of	ADP
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ap-6786	408	5	rc	rc	PROPN
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ap-6786	408	7	strengthened	strengthen	VERB
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ap-6786	408	10	composites	composite	NOUN
ap-6786	408	11	under	under	ADP
ap-6786	408	12	eccentric	eccentric	ADJ
ap-6786	408	13	loading	loading	NOUN
ap-6786	408	14	.	.	PUNCT
ap-6786	409	1	j	j	PROPN
ap-6786	409	2	for	for	ADP
ap-6786	409	3	comp	comp	NOUN
ap-6786	409	4	for	for	ADP
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ap-6786	409	7	,	,	PUNCT
ap-6786	409	8	2010	2010	NUM
ap-6786	409	9	.	.	PUNCT
ap-6786	410	1	doi:10.1061/(asce)cc.1943	doi:10.1061/(asce)cc.1943	PROPN
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ap-6786	410	4	.	.	PUNCT
ap-6786	411	1	[	[	X
ap-6786	411	2	27	27	NUM
ap-6786	411	3	]	]	PUNCT
ap-6786	411	4	r.	r.	PROPN
ap-6786	411	5	eid	eid	PROPN
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ap-6786	411	8	paultre	paultre	NOUN
ap-6786	411	9	.	.	PUNCT
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ap-6786	412	2	behaviour	behaviour	NOUN
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ap-6786	412	5	-	-	PUNCT
ap-6786	412	6	confined	confine	VERB
ap-6786	412	7	reinforced	reinforce	VERB
ap-6786	412	8	concrete	concrete	ADJ
ap-6786	412	9	columns	column	NOUN
ap-6786	412	10	.	.	PUNCT
ap-6786	413	1	eng	eng	PROPN
ap-6786	413	2	struct	struct	NOUN
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ap-6786	413	4	,	,	PUNCT
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ap-6786	413	6	.	.	PUNCT
ap-6786	414	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	414	2	/	/	SYM
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ap-6786	414	4	.	.	PUNCT
ap-6786	415	1	[	[	X
ap-6786	415	2	28	28	NUM
ap-6786	415	3	]	]	X
ap-6786	415	4	y.	y.	PROPN
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ap-6786	415	6	,	,	PUNCT
ap-6786	415	7	c.	c.	PROPN
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ap-6786	415	9	.	.	PUNCT
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ap-6786	416	2	of	of	ADP
ap-6786	416	3	load	load	NOUN
ap-6786	416	4	eccentricity	eccentricity	NOUN
ap-6786	416	5	on	on	ADP
ap-6786	416	6	the	the	DET
ap-6786	416	7	stress	stress	NOUN
ap-6786	416	8	-	-	PUNCT
ap-6786	416	9	strain	strain	NOUN
ap-6786	416	10	relationship	relationship	NOUN
ap-6786	416	11	of	of	ADP
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ap-6786	416	13	-	-	PUNCT
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ap-6786	417	1	comp	comp	PROPN
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ap-6786	417	4	,	,	PUNCT
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ap-6786	417	6	.	.	PUNCT
ap-6786	418	1	doi:10.1016	doi:10.1016	PROPN
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ap-6786	418	4	.	.	PUNCT
ap-6786	419	1	[	[	X
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ap-6786	419	3	]	]	PUNCT
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ap-6786	419	9	.	.	PUNCT
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ap-6786	420	2	of	of	ADP
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ap-6786	420	8	cfrp	cfrp	NOUN
ap-6786	420	9	systems	system	NOUN
ap-6786	420	10	under	under	ADP
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ap-6786	420	13	.	.	PUNCT
ap-6786	421	1	constr	constr	NOUN
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ap-6786	421	10	.	.	PUNCT
ap-6786	422	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	422	2	/	/	SYM
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ap-6786	423	1	[	[	X
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ap-6786	423	9	,	,	PUNCT
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ap-6786	423	14	park	park	PROPN
ap-6786	423	15	.	.	PUNCT
ap-6786	424	1	structural	structural	ADJ
ap-6786	424	2	performance	performance	NOUN
ap-6786	424	3	of	of	ADP
ap-6786	424	4	rectangular	rectangular	ADJ
ap-6786	424	5	section	section	NOUN
ap-6786	424	6	confined	confine	VERB
ap-6786	424	7	by	by	ADP
ap-6786	424	8	squared	square	VERB
ap-6786	424	9	spirals	spiral	NOUN
ap-6786	424	10	with	with	ADP
ap-6786	424	11	no	no	DET
ap-6786	424	12	longitudinal	longitudinal	ADJ
ap-6786	424	13	bars	bar	NOUN
ap-6786	424	14	influencing	influence	VERB
ap-6786	424	15	the	the	DET
ap-6786	424	16	confinemen	confineman	NOUN
ap-6786	424	17	.	.	PUNCT
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ap-6786	425	8	,	,	PUNCT
ap-6786	425	9	2016	2016	NUM
ap-6786	425	10	.	.	PUNCT
ap-6786	426	1	doi:10.1016	doi:10.1016	PROPN
ap-6786	426	2	/	/	SYM
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ap-6786	426	4	.	.	PUNCT
ap-6786	427	1	[	[	X
ap-6786	427	2	31	31	NUM
ap-6786	427	3	]	]	PUNCT
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ap-6786	427	8	v.	v.	PROPN
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ap-6786	427	10	.	.	PUNCT
ap-6786	428	1	strengthening	strengthen	VERB
ap-6786	428	2	of	of	ADP
ap-6786	428	3	axially	axially	ADV
ap-6786	428	4	loaded	load	VERB
ap-6786	428	5	columns	column	NOUN
ap-6786	428	6	using	use	VERB
ap-6786	428	7	stainless	stainless	ADJ
ap-6786	428	8	steel	steel	NOUN
ap-6786	428	9	wire	wire	NOUN
ap-6786	428	10	mesh	mesh	NOUN
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ap-6786	428	14	numerical	numerical	ADJ
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ap-6786	428	16	.	.	PUNCT
ap-6786	429	1	struct	struct	VERB
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ap-6786	429	5	60(6):979	60(6):979	PROPN
ap-6786	429	6	–	–	PUNCT
ap-6786	429	7	999	999	NUM
ap-6786	429	8	,	,	PUNCT
ap-6786	429	9	2016	2016	NUM
ap-6786	429	10	.	.	PUNCT
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ap-6786	431	17	http://dx.doi.org/10.1061/(asce)cc.1943-5614.0000100	http://dx.doi.org/10.1061/(asce)cc.1943-5614.0000100	VERB
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ap-6786	431	20	http://dx.doi.org/10.1016/j.conbuildmat.2010.07.034	http://dx.doi.org/10.1016/j.conbuildmat.2010.07.034	NOUN
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ap-6786	432	1	[	[	X
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ap-6786	432	7	a.	a.	NOUN
ap-6786	432	8	stachurski	stachurski	NOUN
ap-6786	432	9	.	.	PUNCT
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ap-6786	433	2	of	of	ADP
ap-6786	433	3	stresses	stress	NOUN
ap-6786	433	4	in	in	ADP
ap-6786	433	5	rc	rc	PROPN
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ap-6786	433	7	compressed	compress	VERB
ap-6786	433	8	members	member	NOUN
ap-6786	433	9	using	use	VERB
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ap-6786	433	11	methods	method	NOUN
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ap-6786	434	2	computer	computer	NOUN
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ap-6786	434	4	in	in	ADP
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ap-6786	434	16	computer	computer	NOUN
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ap-6786	434	22	conference	conference	NOUN
ap-6786	434	23	proceedings	proceeding	NOUN
ap-6786	434	24	,	,	PUNCT
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ap-6786	434	28	,	,	PUNCT
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ap-6786	435	2	.	.	PUNCT
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ap-6786	436	5	,	,	PUNCT
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ap-6786	436	7	,	,	PUNCT
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ap-6786	436	9	,	,	PUNCT
ap-6786	436	10	2018	2018	NUM
ap-6786	436	11	.	.	PUNCT
ap-6786	437	1	doi:10.1063/1.5019133	doi:10.1063/1.5019133	NOUN
ap-6786	437	2	.	.	PUNCT
ap-6786	438	1	[	[	X
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ap-6786	438	3	]	]	PUNCT
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ap-6786	438	5	.	.	PUNCT
ap-6786	439	1	1992	1992	NUM
ap-6786	439	2	-	-	SYM
ap-6786	439	3	1	1	NUM
ap-6786	439	4	-	-	SYM
ap-6786	439	5	1	1	NUM
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ap-6786	439	7	2	2	NUM
ap-6786	439	8	:	:	PUNCT
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ap-6786	439	13	part	part	NOUN
ap-6786	439	14	1	1	NUM
ap-6786	439	15	-	-	SYM
ap-6786	439	16	1	1	NUM
ap-6786	439	17	:	:	PUNCT
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ap-6786	439	24	.	.	PUNCT
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ap-6786	440	2	research	research	NOUN
ap-6786	440	3	center	center	NOUN
ap-6786	440	4	,	,	PUNCT
ap-6786	440	5	eurocodes	eurocode	NOUN
ap-6786	440	6	,	,	PUNCT
ap-6786	440	7	european	european	PROPN
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ap-6786	440	11	.	.	PUNCT
ap-6786	441	1	[	[	X
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ap-6786	441	3	]	]	PUNCT
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ap-6786	441	5	stachurski	stachurski	NOUN
ap-6786	441	6	.	.	PUNCT
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ap-6786	442	2	to	to	ADP
ap-6786	442	3	optimization	optimization	NOUN
ap-6786	442	4	,	,	PUNCT
ap-6786	442	5	(	(	PUNCT
ap-6786	442	6	in	in	ADP
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ap-6786	442	8	:	:	PUNCT
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ap-6786	442	13	.	.	PUNCT
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ap-6786	443	2	house	house	PROPN
ap-6786	443	3	of	of	ADP
ap-6786	443	4	the	the	DET
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ap-6786	443	6	university	university	PROPN
ap-6786	443	7	of	of	ADP
ap-6786	443	8	technology	technology	PROPN
ap-6786	443	9	,	,	PUNCT
ap-6786	443	10	warsaw	warsaw	PROPN
ap-6786	443	11	,	,	PUNCT
ap-6786	443	12	poland	poland	PROPN
ap-6786	443	13	,	,	PUNCT
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ap-6786	443	15	.	.	PUNCT
ap-6786	444	1	[	[	X
ap-6786	444	2	35	35	NUM
ap-6786	444	3	]	]	PUNCT
ap-6786	444	4	a.	a.	NOUN
ap-6786	444	5	törn	törn	NOUN
ap-6786	444	6	,	,	PUNCT
ap-6786	444	7	a.	a.	NOUN
ap-6786	444	8	żilinskas	żilinskas	PROPN
ap-6786	444	9	.	.	PUNCT
ap-6786	445	1	global	global	ADJ
ap-6786	445	2	optimization	optimization	NOUN
ap-6786	445	3	.	.	PUNCT
ap-6786	446	1	springer	springer	PROPN
ap-6786	446	2	verlag	verlag	PROPN
ap-6786	446	3	,	,	PUNCT
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ap-6786	446	5	,	,	PUNCT
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ap-6786	446	10	1989	1989	NUM
ap-6786	446	11	.	.	PUNCT
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ap-6786	447	4	polytechnica	polytechnica	PROPN
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ap-6786	447	6	,	,	PUNCT
ap-6786	447	7	2021	2021	NUM
ap-6786	447	8	1	1	NUM
ap-6786	447	9	introduction	introduction	NOUN
ap-6786	447	10	1.1	1.1	NUM
ap-6786	447	11	motivation	motivation	NOUN
ap-6786	447	12	to	to	PART
ap-6786	447	13	study	study	VERB
ap-6786	447	14	the	the	DET
ap-6786	447	15	strains	strain	NOUN
ap-6786	447	16	in	in	ADP
ap-6786	447	17	rc	rc	PROPN
ap-6786	447	18	compressed	compress	VERB
ap-6786	447	19	structure	structure	NOUN
ap-6786	447	20	members	member	NOUN
ap-6786	447	21	2	2	NUM
ap-6786	447	22	formulation	formulation	NOUN
ap-6786	447	23	of	of	ADP
ap-6786	447	24	the	the	DET
ap-6786	447	25	equilibrium	equilibrium	NOUN
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ap-6786	447	31	in	in	ADP
ap-6786	447	32	the	the	DET
ap-6786	447	33	rectangular	rectangular	ADJ
ap-6786	447	34	sections	section	NOUN
ap-6786	447	35	2.1.1	2.1.1	NUM
ap-6786	447	36	equations	equation	NOUN
ap-6786	447	37	for	for	ADP
ap-6786	447	38	sections	section	NOUN
ap-6786	447	39	wholly	wholly	ADV
ap-6786	447	40	in	in	ADP
ap-6786	447	41	compression	compression	NOUN
ap-6786	447	42	2.1.2	2.1.2	NUM
ap-6786	447	43	section	section	NOUN
ap-6786	447	44	under	under	ADP
ap-6786	447	45	combined	combined	ADJ
ap-6786	447	46	compression	compression	NOUN
ap-6786	447	47	with	with	ADP
ap-6786	447	48	bending	bend	VERB
ap-6786	447	49	3	3	NUM
ap-6786	447	50	computational	computational	ADJ
ap-6786	447	51	solution	solution	NOUN
ap-6786	447	52	and	and	CCONJ
ap-6786	447	53	numerical	numerical	ADJ
ap-6786	447	54	results	result	NOUN
ap-6786	447	55	4	4	NUM
ap-6786	447	56	comparison	comparison	NOUN
ap-6786	447	57	of	of	ADP
ap-6786	447	58	experimental	experimental	ADJ
ap-6786	447	59	and	and	CCONJ
ap-6786	447	60	numerical	numerical	ADJ
ap-6786	447	61	results	result	NOUN
ap-6786	447	62	5	5	NUM
ap-6786	447	63	conclusions	conclusion	NOUN
ap-6786	447	64	and	and	CCONJ
ap-6786	447	65	comments	comment	NOUN
ap-6786	447	66	references	reference	NOUN