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M E C H A N I K A 
T E O R E T Y C Z N A 
I S T O S O W A N A 

2/3. 21 (1983) 

A N A L Y S I S O F T H E S T R E S S S T A T E I N T H E C Y L I N D R I C A L S H E L L S O F T H E 

C O N C R E T E T A N K S P R E S T R E S S E D B Y E X T E R N A L T E N D O N S 

A N D R Z E J S E R U G A 

Kraków 

1. Introduction 

The state of stress in cylindrical shells of the prestressed concrete tanks depends mailny 

o n : 

— the constructional and technological realization of the tank wall, 

— the method of joining the wall and the tank bottom, 

— the adapted method of prestressing of the cylindrical shell. 

The knowledge of the intensity degree o f the effect of the above mentioned agents 

on the statical work of the shell is very important in the process of the tank construction 

design. A n especially essential problem is the determination of the amount of prestressing 

tendons (wires) as well as the arrangement thereof along the tank wall height. In the 

practice, hitherto this task was being solved by means of the determination of the envelope 

curve of the circumferential forces exerted by the pressure o f a liquid under assumption 

that a determined value o f friction coefficient i n the joint of wall and the tank bottom 

exists. The analysis o f stress state within the cylindrical shell is then reduced only to chec-

king the circumferential stresses within the concrete for a prestressed tank, which in loaded 

by the liquid pressure, assuming that the load distribution due to the prestressing is o f 

the sectional uniform type. 

Moreover the resistance of concrete against the stress cracks for the maximum vertical 

bending moment results from the thrust of liquid or ground. However, the state o f stress 

produced by the total or partial prestressing of the tank wall is not analysed. Such a method 

o f design causes the following restrictions: 

— the distribution o f loads arising from the prestressing force is i n fact a disconti-

nuous one, thus an overloading of the shell may occur during prestressing, 

— the effect of the prestressing technology on the distribution o f the internal forces 

within the shell is not taken into account. It should be emphasized in this connec-

tion that the maximum vertical bending moments must not indispensably be o r i -

ginated, after the prestression of all circumferential tendons has been completed. 

M a n y cracks i n cylindrical shells of concrete tanks during prestressing were observed 

in the practice. Such phenomena make it necessary to carry out an exact analysis o f the 

effect of prestressing on the distribution of internal forces within the tank wall. 



220 Л . S F R U G A 

D u r i n g the recent 15 years in the Institute of Materials and Building Structures, Tech-
nical University of Cracow, very intensive investigation works have been carrying out 
to explain and determine the range of influence of the agents mentioned above on the 
behaviour of the tank wall during prestressing as well as during its exploitation. The 
results o f the above works can be found in papers [1, 2, 3, 4] i n which the necessity o f 
carrying out the proper analysis o f stress state i n the cylindrical shell of the tank was 
proved, assuming the load resulting from the prestressing consists of circular — symmetrical 
concentrated forces. 

In the present paper the estimation of one of the most used constructional realizations 
was made, based on an example of a tank with a capacity of 5000 cu m . 

2 . Experimental investigations 

2.1. Description of the construction. The constructional realization o f the tank was to 

some extent reduced because of the necessity to adapt an existing tank for drinking water. 

The design thickness for the floor slab was 0.40 m. The tank wall, with a height o f 

H = 5.6 m , the internal radius being l?j = 17.5 m and the thickness being / = 0.18 m, 
was made in monolithic system: the concrete works being executed in subsequent sections 

and the circumference was divided into 8 fields and 8 pilasters. The individual segments 

o f the wall were poured with the concrete using the platform — and — the movable 

formwork during one day cycle. The top o f the wall between the pilasters was made thicker 

to execute — during the next stage o f work — a r o o f ring beam o f reinforced concrete. 

The pilasters of the dimensions 5 . 6 x 1 . 2 x 0 . 3 8 m each were symmetrically arranged on 

the tank wall circumference. 

The connection o f the bottom slab with the cylindrical shell was executed as a sliding 

joint, the friction coefficient being assumed in statical calculations to be  ц = 0.3. The 

tank wall was set o n the bottom o f the groove o f foundation ring, the depth being 0.2 m , 

using the slide layer made o f two layers o f bitumen board with glue. The internal chase 

o f foundation ring was filled with tallow cord and A b i z o l K F putty first to prestressing 

the tank wall. 

The prestressing o f the tank wall was executed using double­bay external tendons 

o f Freyssinet type 18 0 5 mm, running on the rolling pad of 12 mm dia. 

2.2. Characteristic of the building materials used 

Concrete 

D u r i n g pouring the concrete i n the tank wall formwork, the test specimens o f 15 x 30 

cm cylinder were sampled to determine the compressive strength as well as the modulus 

o f elasticity o f the concrete just in the moment o f prestressing the tank wall. The mean 

compressive strength o f concrete determined using 62 specimens is equal to 37.8 M P a , 

the standard deviation being  s  — 6.16 M P a , whereas coefficient o f variation was equal 

to r = 16.31% which would mean, that a concrete of В 35 class was obtained. The modulus 

o f elasticity i n compression was determined using 31 specimens, the full cycle o f load 

being assumed. The obtained values are listed below. 



PRESTRESSED C O N C R E T E T A N K S 221 

E 0 . 2  = 28080 M P a ; s = 2339 M P a ; v  = 8.33% 

Е 0 . з = 27400 M P a ; s  = 2220 M P a ; v = 8.10% 

E 0 . 4 = 26630 M P a ; s = 2044 M P a ; v  = 7.67% 

E p . s = 25760 M P a ; s = 2257 M P a ; v = 8.76% 

I 0 . 6 = 24500 M P a ; s = 2410 M P a ; v = 9.84% 

The results in question refer to a concrete made of a granite aggregate, whereas the 

first two segments of walls between the pilasters N o 3 and N o 4 as well as N o 4 ч ­ 5, res-

pectively were accomplished by use of basalt aggregate. The mean compressive strength 

of the concrete determined in analogous manner, is equal to 55.1 M P a . which means, 

that the concrete is of В 45 class. The modulus of elasticity in compression is E r = 36000 

M P a . 

Prestressing steel. 

Basing on the executed laboratory investigations the following mechanical properties 

o f steel with 5 mm dia. were determined: 

— the characteristic strength of steel, 

— the proof stress Rt . 0 . 2 <  

— the modulus of elasticity 

— the elongation of steel at rupture, 

— the number of contraflexures 

The strength of steel was determined using 38 samples taken at random, by means 

of multipurpose testing machine of Z D ­ 5 0 type, the measurement accuracy being 250 N . 

The obtained main value, the standard deviation as well as the coefficient of variation 

are respectively equal to: 

R = 1721.7 M P a ; s = 69,4 M P a ;  i> = 4.03% 

The strength characteristic of prestressing steel is 

Rvk = R ­ 1 . 6 4 ­ . V = 1607.9 M P a 

whereas the calculated strength is equal to 

R,. = j ' 2 5 • Kk = 1286.3 M P a 

The proof stress R t . u . 2 determined using 10 samples is 1478.3 M P a . 

The modulus of elasticity of the prestressing steel was determined on the level of loads 

equal to 0.4ч ­0.6 o f the tensile breaking stress. The adapted level of load (14ч ­20) k N 

corresponds approximately to the value 0.5 Rvk, which is below the admissible stress after 

immediate and rheological losses. The obtained results are as follows: 

E , = 202625 M P a ; s = 3069.5 M P a ; v = 1.51% 

Elongation at rupture A 1 0 0 = 5.7% 

Alternate bend test n = 5.35 

2.3. Program and methodology of the investigations. T o estimate the stati work of the shell 

the following investigations were considered to be necessary: 



222 A . SI;RIX;A 

— measurement of the radial displacements of the tank wall at the level of its connection 

with the foundation ring, 

— measurement of the radial displacements of the tank wall along the vertical section. 

— measurement of the tank circumference shortening, i.e. the diminishing of the circum-

ference exerted by the elimination of distances between the pilasters and tank wall 

segments coming mutually to contact due to the prestressing, 

•—  measurement  of  the  strains  of  the  tank  wall  concrete  in  circumferential  and  vertical 

directions. 

2.3.1 Measurement of the radial displacements of the tank wall at the level of its connection with the foundation tint 

The  experimental  investigations were  carried out  for  the  connection sealed  with  the  tallow 

cord,  50 x 50 mm, tamped  therein,  which  then  was  covered with  the  A b i z o l  K F type  putty. 

The  measurements  were  carried  out  using 60  dial  gauges,  the  range  being 0.01  m  and  the 

measurement  accuracy  being  0.01  mm,  stabilised i n  foundation  ring  at  the  height  of  0.25 

m.  The  arrangement  o f measuring points  is shown in  F i g .  1. 

v 
i 

Fig. 1 

2.3.2. Measurement of the radial displacements of tank wall along the vertical section.  The  Values Of  the  tank 

wall  deflections  were  measured  using  dial  gauges  placed  at  the  following  heights:  0.25. 

0.6,  1.2,  1.8,  2.4, 3.0,  3.6,  4 . 2 ,  4.8, 5.2  and  5.6  m  within  ten  sections,  on  two  opposite  fields 

o f  the  tank.  The  arrangement  of the  measuring  points  was  made  possible  owing  to  a  steel 



PRESTRESSED C O N C R E T E T A N K S 223 

construction, made especially for this purpose, which could be connected with the floor 

slab in stable manner. The localization o f the measuring positions is shown in F i g . 1. 

2.3.3. Measurement of the tank circumference shortening Accordin g t O the adapted technology o f 

tank wall execution there were 16 vertical work contacts. By use of the installed dial gauges 

the total values of radial displacements were measured. The author decided to measure 

additionally the tank circumference shortening and to reduce properly the displacement 

values. The shortening of the circumference was determined by means o f D E M E C strain­

gauge measurement base of which was 12 inch. The measuring points were placed at the 

following heights: 0.25. 0.65, 1.05, 1.45, 1.85, 2.25, 2.65, 3.05, 3.45, 3.85, 4.25, 4.65, 

5.05, and 5.55 m. 

2.3.4. Measurement of the strains of the tank wall concrete in circumferential anil vertical directions. D u r i n g the 

prestressing the concrete strains were determined by means of a standard D E M E C 8 inch 

straingauge. The measuring points were placed on the inside face of the tank wall in six 

vertical sections. 

v 

w2 !3days) 
щ  
Wj !3rJays! 

Fig. 2 



224 A . S E R U G A 

The arrangement of the individual sections: 0­0, 1­1, 2­2, 3­3, 4­4 and 5­5, respectively 

is shown in F i g . 1. Additionally in the section 3­3 the measuring points on the outside 

face o f the tank wall were placed between the prestressing tendons. 

2.4. Results of the Investigations. A l l readings of the displacements as well as of the con-

crete strains were carried out at the morning before the sunrise at a constant temperature: 

the prestressing of tank wall was executed during a fortnight. 

2.4.1. The radial displacements of the tank wall at the level of 0.25 m. The prestressing o f the tank wall 

was executed according to the sequence shown i n F i g . 3, starting at the upper edge o f 

shell. The measurements o f the displacements were carried out as a rule i n three stages, 

i.e. after 5, 10 and 15 tendon circumferences have been prestressed. The distribution of 

displacement values for the 2­nd and 3­rd stage is shown i n F i g . 2. The displacements of 

the second stage, as well as the final ones o f the third stage were read after a 3­days period 

o f stabilization elapsed, whereas the initial displacements of the third stage were measured 

the next day after the prestressing completion. The mean values of displacements and the 

Fig. 3 



PRESTRESSED C O N C R E T E T A N K S 225 

distribution parameters corresponding with them are respectively: 

Щ = 0.0467 mm,  s = 0.0632 mm,  v = 135.3% 

w2  = 0.4217 mm,  s = 0.1212 mm,  v = 28.75% (3 days) 

w3 = 1.7333 mm,  s = 0.9809 mm,  v = 56.59% 

w3  = 2.0833 mm.  s  = 1.1873 mm,  v  = 56.99% (3 days) 

2.4.2. The radial displacements of the tank wall along the vertical section. A s the Cracks Were Originated 

i n the tank wall at the final stage of prestressing, e.g. on the circumference part between 

the pilasters N o 7 and N o 8, the measured displacement values were worked up i n separate 

manner for opposite measurement positions. The obtained mean values o f displacements 

for individual loading stages are listed in Table 1. Moreover, this table contains also the 

values of radial displacements corresponding with the measured shortening of the tank 

wall circumference as well as the reduced values of displacements for total prestressing 

of the cylindrical shell. The distribution o f the mean values of displacements along the 

height of the tank wall is shown i n F i g . 3 and F i g . 4 respectively. 

2.4.3. strains of the tank waii concrete. The measurements of concrete strains were carried out 

two times, i.e. firstly at the beginning of the prestressing and then after a three — days 

period of stabilization, since the completion of the prestressing. The obtained results 

i Him] 

wlmm] 

Fig. 4 



1,915 

2,291 

2,636 

3,039 

3,348 

3,602 

3,741 

3,601 

2,962 

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a?
 

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0,841 

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2,035 

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0,908 

0,217 

o
 

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St 

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0,145 

0,221 

0,354 

0,514 

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0,824 

0,953 

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3,726 

4,030 

3,867 

3,163 

1,936 

1,109 

of tensioning t 

wall w [mm] 

crete tank w. 

of tensioning t 

Й '2 
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1 0 x 4 

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1,759 

2.204 

2.769 

3,196 

3,400 

3,249 

2,711 

1,869 

0,913 

0,427 

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. 

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U
 

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5 x 4 

2,051 

2,017 

1,974 

1,823 

1,556 

1,213 

0,900 

0,619 

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r~. 
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: 

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_ 

1,443 

1,713 

1,959 

2,244 

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ti­

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2,650 

2,780 

1
 

2,420 

1,727 

о
 

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r>
 

o
' 

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О
 

Z
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j. I Щ
 

IS
 

II 

1,546 

1,726 

1,919 

2,176 

2,403 

2,571 

2,735 

2,697 

2,294 

1,555 

1,159 

1 displacements of the 

sters No 3­

i 
­

I 

. Radia 

sters No 3­

0,060 

0,145 

0,221 

0,354 

0,514 

0,700 

0,824 

0,953 

1,072 

1,028 

0,892 

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1 between pila 

tendons 

W3  ' 

Stage П1 

1 5 x 4 

1
 

1,871 

2,140 

2,530 

2,917 

3,271 

3,559 

3,650 

3,366 

2,583 

2,051 

Concrete tank wa 

of tensioning 

Й '2 
Stage II 

1 0 x 4 

2,300 

2,493 

2,696 

006'Г 

3,009 

3,010 

2,820 

2,350 

1,681 

0,856 

0,461 

Concrete tank wa 

Number 

Stage I 

5 x 4 

2,397 

2,333 

2,289 

2,074 

•* 
v>

 
r­

1,417 

1,049 

0,691 

0,401 

0,163 

0,039 

Height 

of the 

tank 

wall 

H [m] 

5,60 

5,20 

4,80 

4,20 

3,60 

3,00 

2,40 

08'I 

1,20 

0,60 

0,25 

0,00 

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[229] 



230  A .  S E R U G A 

of concrete strains in circu liferential and vertical direction are listed in Table 2, whereas 
the distribution of strains along the height of the tank wall are shown in F i g . 5 and F i g . 6. 
respectively. The concrete strains on the outside face of the tank wall according to the 
section 3­3 were measured only in circumferential direction, as there occured difficulties 
resulting from the use of band — shaped prestressing tendons. 

3 .  The  comparative  analysis  of  the  obtained  results  and  the  final  conclusions 

T o carry out the analysis of the results of investigations the statical — and — strength 

calculations were made loading the tank wall with single prestressing tendons according 

to the accepted sequence of tensioning. The calculation method presented in the paper 

[2] was used for this purpose. 

The value of the prestressing force  Nv was determined basing on the measured strain 

values of the prestressing steel. The electric resistance wires were glued o n three wires 

selected at random in each of the 15 tendons placed along the height of the tank wall 

between the pilasters N o 7 and N o 8. 

The obtained results were worked up using statistical methods and the mean value, the 

standard deviation and the coefficient of variation were determined. Assuming that the 

mean value of strains to be decisive the value of effective prestressing force was calculated, 

which was equal to: 

N„ = « • ! „• 18­ Щ = 280.56 k N 

Taking into account many cracks in the tank wall occurring on the inside face except 

of two segments of wall which were made of concrete using the basalt aggregate ( N o 3 

to N o 5), the statical calculations were carried out for two different calculations scheme. 

Scheme I 

The tank wall made of concrete using basalt aggregate, slidingly jointed to foundation 

ring the friction coefficient being  fi  = 0.7 and  ц = 0.8. The modulus of elasticity of con-

crete i n bending was E f c = 30000 M P a 

Scheme II 

The tank wall made o f concrete using granite aggregate was jointed in hinge type 

manner to the foundation ring. The modulus of elasticity of the concrete in bending was 

E b = 22500 M P a . 

For both calculations schemes the tank wall was considered to be a cylindrical shell 

of a constant thickness / = 0.18 m at the height of  H = 5.6 m as well as to be cylindrical 

shell of thickness  t at the height  H = 5.35 m with the top stiffening ring of 0.25x0.38 m. 

The obtained values o f the tank wall displacements for both calculation schemes are 

given in the Table 1 as well as they are shown properly i n F i g . 3 and 4. 

The measured values of concrete strains in the compression along the section between 

the pilaster N o 7 and 8 are shown i n F i g . 5. When comparing the mean values o f concrete 

strains with the distribution of circumferential forces the conformity of the nature of both 

curves is stated. 

T a k i n g into account the modulus of elasticity o f concrete in compression to be E = 

= 27000 M P a as well as the mean values concrete strains along the vertical section 3­3 



PRESTRESSED  C O N C R E T E  T A N K S  231 

(inside and outside of the tank wall) the experimental distribution of circumferential 
forces were determined and are shown in F i g . 5. The occurring differences may be explained 
by: 

— the presence of pilasters, which bring disturbances in the static work of cylindrical 

shell, 

— the increased strains of concrete, exerted by partial damage of the concrete structure 

due to the cracks appearing at several levels. 

Basing on the executed analysis the following final conclusions can be presented: 

— A special care must be taken of the quality of execution of the joint of wall and 

tank foundation ring. The effect of pilasters, which introduce considerable distur-

bances in the static work of shell can be eliminated to appreciable extent, i f the 

sliding layer is executed carefully. The F i g . 2 exemplifies the comparison of radial 

displacements of the pilasters N o 1 and N o 8. 

— The used sealing materials must not be used second time when further similar con-

structional and technological realizations are executed. Their presence within the 

joint of wall and bottom generated considerable increase o f boundary disturbances 

corresponding with the coefficient of friction,  ц  = 0.7^­0.8 

— Prestressing of walls of the cylindrical tanks should be commenced at the bottom 

edge of the shell. If not, the discontinuity stresses, generated at the subsequent 

tensioning o f tendons, combined with the boundary disturbances may exert the 

cracking of the tank wall, in spite of considerable displacements of the wall (see 

vertical section 0­0). 

References 

I  H .  N O W A K , The Influence of Defor inability of the Bottom Edge of Shell on the Internal Forces Distribution 

in Concrete Tanks Prestressed by Separate Tendons Using Sectional System,  Ph.  D .  Thesis,  Technical 

University  of  Cracow,  1971. 

2.  J .  M I C H N O , Reaction of Prestressing Cable at the Cylindrical Tank Wall, Inż ynieria  i  Budownictwo,  N o 

5,  pp.  180­  183,  1977. 

3.  A .  S E R U G A , An Experimental Evaluation of the Internal Forces Distribution in Cylindrical Shells of Pre­

stressed Concrete Reservoirs, Ph.  D .  Thesis,  Technical  University  of  Cracow,  1978. 

4.  A .  S E R U G A , Prefabricated Prestressed Concrete Tanks,  Inż ynieria  i  Budownictwo,  N o  8 ­ 9 ,  pp.  185  ­  188, 

1982. 

P  e  3  ю  M  e 

А Н А Л ИЗ  Н А П Р Я Ж Е Н Н О ГО  С О С Т О Я Н ИЯ  В  Ц И Л И Н Д Р И Ч Е С К ИХ  О Б О Л О Ч К АХ  

Б Е Т О Н Н ЫХ  Р Е З Е Р В У А Р ОВ  П Р Е Д В А Р И Т Е Л Ь НО  Н А П Р Я Ж Е Н Н ЫХ  В Н Е Ш Н И МИ  

К А Б Л Я МИ  

В  п у б л и к а ц ии  п р е д с т а в л е на  о ц е н ка  к о н с т р у к т и в н о ­ т е х н о л о г и ч е с к о го  р е ш е н ия  ц и л и н д р и­

ч е с к о го  р е з е р в у а ра  е м к о с т ью v  =5000  м .3 ,  п од  д е й с т в и ем  н а г р у з ки  о т  п р е д в а р и т е л ь н о го  н а п р я­

ж е н ия  в н е ш н и ми  к а б л я ми  18  0  5  м м. 

С р а в н и т е л ь н ый  а н а л на  э к с п е р и м е н т а л ь н ых  и  а н а л и т и ч е с к их  р е з у л ь т а т ов  д а ет  о с н о ву  д ля  

в ы в о д ов  о т н о с и т е л ь но  с т а т и ч е с к ой  р а б о ты  о б о л о ч е к,  а т а к же  т е х н о л о г ии  н а п р я ж е н ия  к о н с т р у к ц и и. 

8» 

\ 



232  A .  S E R U G A 

S t r e s z c z e n i e 

A N A L I Z A  S T A N U N A P R Ę Ż E N IA W  P O W Ł O K A C H  W A L C O W Y C H  B E T O N O W Y C H 

Z B I O R N I K Ó W S P R Ę Ż O N Y CH P A S M O W Y M I C I Ę G N A MI Z E W N Ę T R Z N Y MI 

W pracy przeprowadzono o c e n ę r o z w i ą z a n ia konstrukcyjno­technologicznego zbiornika cylin­

drycznego o p o j e m n o ś ci  V = 5000 m 3 , s p r ę ż o n e go pasmowymi c i ę g n a mi z e w n ę t r z n y mi typu 18 0 5 mm. 

W oparciu o  d o k o n a ń ^  a n a l i z ę  p o r ó w n a w c z ą  w y n i k ó w  otrzymanych  z  b a d a ń  d o ś w i a d c z a l n y ch  z  war­

t o ś c i a mi  obliczonymi,  w y s u n i ę to  wnioski  k o ń c o we  d o t y c z ą ce  dalszego  stosowania  podobnych  r o z w i ą z ań  

a  t a k ż e  technologii  sprę ż ania  konstrukcji. 

Praca została złoż ona w Redakcji dnia 7 marca 1983 roku