
книги из ГПНТБ / Кудзис А.П. Предварительно-напряженный полимерцементный бетон
.pdf£ Уп (^l)
уп(^г)> гуп (^i)
Ti), s 6 ( t u |
t x) |
£ y n |
(^2 ) |
£6 {T!, t2)
elastic strain in concrete due to prestressing in no time
the same at times t2 and t\ respectively
total strain in concrete including elastic, plastic and shrinkage at times t2 and U respectively elastic strain in concrete at time t2 due to a long time load
plastic strain in concrete at time T\ under a long time load
|
v (t 2) |
|
|
|
|
|
|
Ф(?х)=гуп(г1)/£б(Г1, Tx) |
|
|
|
||||||
|
|
coefficients |
of |
elastic |
strain |
in concrete |
at times |
||||||||||
|
|
to and |
/ 1 |
|
respectively |
|
|
|
|
|
|
|
|
||||
|
М Тг) = £yn(Ti)/£6 Oms, tx), |
фу(?1) = гуп(т1)/еб(г1,т1) |
|
|
|
||||||||||||
|
|
coefficients of conventional elastic strain in con |
|||||||||||||||
|
|
crete |
at |
|
times |
t 2 and |
t\ |
respectively |
|
|
|
||||||
|
h) = |
characteristic |
of |
plastic |
strain |
in |
concrete |
at |
|||||||||
|
|
time |
T\ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<*оЫ. «o(Ti)= |
average prestresses in reinforcement AH and /t„ |
||||||||||||||||
|
|
respectively |
at |
time ti |
(strain in |
adjoining con |
|||||||||||
|
|
crete layer being equal to zero) |
|
|
|
|
|||||||||||
|
<Jo(T2) =: |
the same at time t2 |
|
|
|
|
|
|
|
|
|||||||
®o(fl)* |
<Jo(/l) = |
the same at time t\ |
|
|
|
|
|
|
|
|
|||||||
Ы . |
стн (t2)=■ average |
actual |
stresses |
in |
|
prestressing |
steel |
AH |
|||||||||
|
|
and |
A'K |
respectively |
at |
time t2 |
|
|
|
|
|||||||
°hOi)> °н (*i)== the |
same |
|
at |
time |
t\ |
|
|
|
|
|
|
|
|
||||
®бЫ. ®бЮ= |
stresses in concrete adjacent to the centroids |
of |
|||||||||||||||
|
|
the prestressing steel ,A„ and |
respectively due |
||||||||||||||
|
|
to the transfer of prestressing farces in no time |
|||||||||||||||
|
®б(т8) |
the same at time t 2 |
|
|
|
|
|
|
|
|
|||||||
ff6 (^l)l |
^(^l)- |
the same at time t\ |
|
|
|
|
|
|
|
|
|||||||
.д(?2)> |
|
stresses on concrete layer adjacent to the cen |
|||||||||||||||
|
|
troids |
of |
the |
prestressing |
steel |
AK and |
re |
|||||||||
|
|
spectively due ta a long-time load |
|
|
|
||||||||||||
ffeW. ^б(г2) - : the |
same |
due |
to |
a long-time load and |
effective |
||||||||||||
|
|
prestresses |
|
|
|
|
|
|
|
|
|
|
|
||||
an.y(^i> Tl)_ |
losses of prestress due to |
|
shrinkage |
of |
concrete |
||||||||||||
<*п(*1» Tl) = : |
the same due to shrinkage and creep of concrete |
||||||||||||||||
N0 = N0(T) = |
prestressing |
force |
at |
time |
T. |
|
|
|
|
||||||||
e0 = e0(T)= |
eccentricity |
of |
prestressing |
force |
|
|
|
|
Ф0( П Фо’ (Т)= |
section |
characteristics — ratio |
of concrete stress |
||||||
|
to |
prestressing |
stress |
in |
adjacent |
steel |
A u and |
||
|
A „ |
respectively |
at time |
T |
|
|
|
||
ФН(Г), Ф'(Г) = |
the |
same with actual |
stress in |
steel |
A a |
and А 'а |
|||
Rap{T), R (Т)= |
prism and cube strengths of concrete at time T |
||||||||
RP(T)= |
tensile strength of concrete at time T |
|
|||||||
К ( Т )= |
the same after application of a long-time compres |
||||||||
|
sive force |
|
|
|
|
|
|
||
|
relative |
prestressing |
in concrete |
|
|
||||
/ . w = |
elastic |
instantaneous |
camber |
of |
the |
structural |
member just after transfer of prestressing force upward cambers of the structural member after prestress transfer at times r2 and ti respectively original deflection of the structural member due to a long-time load
(^i> ^г)— deflection of the structural member due to plastic strain in concrete caused by a long-time load deflection of the structural member due to a shorttime load
coefficient describing a camber change of the structural member due to plastic strain in con crete caused by prestressing
coefficient describing a deflection change of the structural member due to plastic strain in concrete caused by a long-time load
± м с.в — bending moment due to self-load (the upper sign being used when an increase in compressive con crete stresses in the steel zone Лн is caused by an action of the moment)
bending moment at time t\ due to added load and calculated in respect to a kern point
bending moment at cracking of structural member ultimate bending moment
INTRODUCTION
Prestressed concrete structures can be effectively constructed and built of concrete containing water-soluble polymer admixtures amounting to 1.5-2% of the weight of cement used in concrete mix. Polymercement concrete of this kind obtains improved physicomechanical properties.
A small amount of polymer resins improves the density, frost-resist ance and water-tightness of concrete and at the same time increases its durability under aggressive environmental conditions, such as harmful gas, sea-water, etc. High cracking resistance, compressive, tensile and fatigue strengths and elasticity are characteristic of polymer concrete. The use of concrete with polymer admixtures is especially expedient both for pre stressed concrete members in the open air or under aggressive environmen tal conditions and for water-tight structures.
Consideration is given to the principal mechanical properties of pol ymercement concrete and prestressed structural members. The test results of prestress losses due to shrinkage and creep of polymercement concrete, cracking resistance, deformations and ultimate strength of prestressed structures, including thermal treatment by infrared irradiation, are pre sented.
The algorithms for calculation of rational prestressed members by computers are given. The application efficiency of polymercement concrete in prestressed structures is considered.
The research was done at the Vilnius Civil Engineering Institute.
1. Some Technological Peculiarities
Water-soluble epoxy resins DEG-1, TEG-1 and TEG-17 are introduced into concrete mix together with water. Before this the resins are carefully mixed with a hardening agent, polyethylene-polyamine. Resins No. 89 and MF-17 are introduced into water without hardening agents.
192
Complex investigations of concretes and mortars with polymer ad mixtures have shown that introduction of water-soluble resins tends to decrease concrete porosity. The polymer resins effectively increase compac tion, density, water tightness, frost resistance and durability of concrete. Resin No. 89 effects considerably the resistance of concrete under alter nating conditions of humidity and dryness.
When evaluating the effects of polymer admixtures on physicomechanical properties of concrete and prestressed concrete, one should take into account that the polymers plastify concrete mixes and hence considerably improve their workability. Therefore, they allow to cut water consumption in the mix and to increase the strength of concrete. In comparison with conventional concrete the polymercement concrete of the same strength requires lower consumption of cement.
The influence of polymer admixtures on physicomechanical properties of concrete and reinforced concrete may be regarded as the effect No. 1 when polymercement and normal concretes are made of equally composed mixes differing from each other only by presence or absence of resins.
The effect |
No. 2 is evaluated |
either by reduction of water (case |
1) or |
both of cement |
and water (case |
2) in the polymercement mix with |
equal |
consumption of aggregates, provided that the mix workabilities of normal and polymercement concretes are identical as well.
Admixtures of water-soluble resins allow to reduce the duration of isothermal heat curing and to improve the quality of precast reinforced concrete products. They reduce the negative effect of heating immediately after casting on the physicomechanical properties of concrete. The inves tigation performed indicates that treatment by infrared irradiation intensi fies effectively the solidification of polymercement concrete. The data of full factor experiment of 23 type are shown in Table 4.
A number of versions is used in reinforcement of prestressed polymer
cement concrete structures. |
The author deals with a prestressed heat- |
||||
treated reinforcement made |
from |
steel |
of |
AT-V and AT-VI classes with |
|
the conventional yield |
points of |
800 |
and |
1000 MPa respectively. The |
|
maximum test losses of |
prestress due to relaxation of the steel were ^ 7 % . |
2. Principal Mechanical Properties of Polymercement Concrete
The quantitative evaluation of polymer resin effect No. 2 is of great interest. To this end were investigated the cracking resistance, stiffness and strength of prestressed flexural members made from three kinds of concrete mix, those of granite aggregates, quartz sand and portland cement.
193
The first type Б: normal mix on portland cement with water-cement ratio W/C=0.46.
The second type П: similar mix as Б but with resin admixture and W/C = 0.42.
The third type П': |
similar mix with resin admixture but reduced |
|
amount |
of cement and |
W/C = 0.54. |
The |
concrete mix of |
all the types above was of equal slump (the |
workability index of concrete was approximately 20 s). Concrete hardening acceleration was carried out by infrared irradiation.
The investigations have shown that water-soluble polymer admixtures considerably increase the strength and deformative characteristics of
concrete. Thus the |
mean values for lower and |
upper microfailure limits |
of polymercement |
concrete under compression |
i?° and ЯУ increase by |
25-90 and by 15-60% respectively. Consequently the prestressed structural members are practically free of longitudinal cracks after transfer of prest ressing forces. Therefore, maximum values of compressive concrete prestresses may be increased by 10-20%.
Both prism and tensile strengths as well as bond strength of poly mercement concrete with water-soluble resins may be increased by 5-40% and elastic modulus by 5-15%. The intensity of increase depends on the ambient conditions (temperature and humidity).
3. Strains of Polymercement Concrete Due to Long-Time Loads
Numerous theories have been put forward to explain and express the mechanism of concrete creep. According to the theory of elastic creep
body, the creep-time relationship is expressed |
by the formulas (3.1), (3.2). |
it is shown that (3.8) is the general equation |
of the theory of elastic creep |
body. It estimates the change in concrete strain on account of its ageing and inheritance.
The relationship between the degree of concrete creep intensity and time is suggested to be expressed by (3.14). A comparison of the experi mental data shows that the form of concrete creep curves in (3.14) is more representative than in other equations. It is recommended that (3.14) be used to predict a long-time creep behaviour of concrete.
The water-soluble polymer admixtures do not exert any influence on concrete creep strains after constant compressive load in the case of resin
194
effect No. 1. But the polymers reduce concrete creep both by using big
compressive stresses and in the case of resin |
effect No. 2 (concrete mix |
with a resin admixture containing less cement |
and water). |
The experimental values of normal and polymercement concrete shrinkage strains after 100-1600 days are shown. A mathematical ana lysis of the data indicates that the formula (3.17) may be used to express the shrinkage-time relationship of cured concrete. Polymercement con crete strain values were less than the shrinkage of normal concrete with various percentages of relative humidity of the ambient atmosphere. But water-soluble admixtures practically did not affect concrete shrinkage over the period of 300 days.
Polymercement concrete uses less water and cement. The deformation properties of concrete are considerably improved while its creep and shrinkage strains decrease greatly.
4. Stress State of Prestressed Structural Members
Consideration is given to the stress state induced by prestressing ■structural members. Figures 12 and 13 indicate the states of camber deflec tion and deformation for prestressed concrete member at the transfer time •of eccentric prestressing force, of a longand short-time application. Elastic analysis of transformed cross-section members is given.
Concrete stresses on the centroid of reinforcement due to prestress transfer in no time and at time t2 are given by (4.1), (4.2) and (4.7), (4.8) respectively. Average actual stresses in reinforcement and section charac teristics at time x2 are expressed by (4.3), (4.4) and (4.9), (4.10) respec tively. In the case of axial prestressing force the calculation formulas are
(4.3a), (4.7a) |
and |
(4.1 la). |
The sizes of actual stresses in steel, concrete prestresses and section |
||
characteristics |
at time t\ due to a long-time eccentric prestressing force |
|
are given by |
(4.32), |
(4.33); (4.38), (4.39) and (4.40), (4.41) respectively. |
In the case of the axial prestressing force those sizes are expressed by (4.32a) , (4.38a) and (4.42a).
Concrete and reinforcement stresses due to long-time, short-time and effective prestresses at times t2 and T2 are expressed by (4.67), (4.68), (4.71), (4.72) and (4.69), (4.70) (4.73), (4.74) respectively.
A new calculation method for losses of prestress due to concrete shrinkage and creep is being considered. The equation of losses of prestress immediately after the transfer of prestressing force at time x2 and after
195
the definite time t\ may be written by the forms (4.96) and (4.97) respec tively. The losses of prestress due to creep only may be calculated by using
(4.97) |
and the |
coefficient of conventional |
elastic |
strain |
of concrete |
vy (/j) |
given |
by (4.36) |
in place of the coefficient |
фу (/х) |
given |
by (4.34). |
|
The experiment results of prestressed structural members are pre |
||||||
sented. The members were cast from three kinds |
of concrete mix: Б |
(nor |
mal concrete), П and ГГ (polvmercement concrete). They were reinforced by a prestressed heat-treated steel. Concrete hardening acceleration was
carried out by infrared irradiation. The relative |
prestressing |
of concrete |
|||
at transfer was equal to |
q (ti) =0.2-1. After |
the |
transfer |
of |
prestressing |
force the specimens were |
stored for 100 and |
200 days at |
30, 60 and 80% |
of relative humidity where the temperature was maintained constant and
equal to 20±2 |
°C. |
|
The simplicity of the author’s method to predict the stress state of |
||
structural members has been |
experimentally verified and demonstrated. |
|
The comparison |
of measured |
and computed losses of prestress has shown |
a difference less than ±20%- The quantities of relative concrete and steel prestressing affected slightly the coefficient values фу(гх) given by (4.34). The water-soluble resin admixture reduced losses of prestress approximate'lv by 30%.
5. Deformations of Prestressed Concrete Members
The equations describing a camber curvature obtained from eccentric prestressing of a structural member in no time, at times тг and i\ are (5.8), (5.4) and (5.7) respectively. It is shown that the elastic theory can be used for practical calculations both of elastic instantaneous camber of the member and its upward deflection due to a long-time eccentric prestressing force. The coefficients describing a camber change of the structural member due to plastic strain of concrete caused by prestressing are expressed by (5.15), (5.16) and (5.17).
Consideration is given to deflection calculations of prestressed flexural' members according to the elastic theory using transformed section prop erties. The original deflection curvature caused by working load and the curvature due to plasticity of concrete under long-time loading are pre sented by (5.27) and (5.40) respectively, provided the member remains, uncracked. The coefficient describing a deflection change due to plastic strain of concrete caused by load may be calculated by using (5.44).
The total deflection of the prestressed flexural member due to prestress transfer and longand short-time loads can be reasonably expressed by
196
(5.48). The testing has demonstrated the ability of simple formula (5.48) to represent the deformations of prestressed structures, including members of polymercement concrete.
The values of cambers obtained from prestressing and deflections •caused by working load are less with water-soluble polymer admixtures of concrete used for structures working under dry environmental conditions. The resin admixtures allow to make considerable cement saving (in our structures cement consumption was reduced to 150 kg per 1 m3).
6.Cracking and Fracture Resistance of
Prestressed Concrete Members
The effect of water-soluble resin admixtures on cracking resistance of vibrate and centrifugate prestressed concrete members and on crack development and ultimate load is presented.
Mathematical methods are applied in the experiment planning in order to make an analysis of test data. In the given case a full-scale factor experiment of 2n type has been used. Factors of the experiment are as
sumed |
to be the |
following: |
1. |
Relation of |
steel prestressing to its conventional yield point |
По/Оо,2
2.Relation of prestressing force eccentricity to the distance from a centroid of cross-section to lower kern point е0/гя. H.
3.Quantity of polymer admixture ПД or the prism strength of poly mercement concrete.
4.Relative humidity of ambient atmosphere.
5.Kind of loading of structural members.
The levels of factors and varying intervals are given in Tables 20 and 26. The basic level of factors has been chosen on the basis of the respective literature recomendations and preliminary tests.
The availability |
of concrete mix of three types |
(Б normal, П and |
FT polymercement) |
and the application of external |
load of three kinds |
allowed to draw up some matrices for the experimental planning. The matrices permitted to reveal the effect of polymer admixture, environ mental conditions and preloading on the mechanical properties of prestress ed members.
An analysis of the mathematical models (6.2), (6.3), (6.4), (6.8) and (6.9) shows that polymer admixtures exert a positive influence on member
cracking resistance, especially in the case |
of strong prestressing and |
large eccentricities. The drier environmental |
conditions and external work |
197
ing load applied immediately at stress transfer, the bigger is the bending moment at which visible cracks appear.
The investigations have shown that resin admixtures allow to increase the cracking resistance of prestressed members by 10-40%, and that of strength by 5-20%. The polymers permit to avoid concrete micro-cracks, under isothermic heat curing and infrared irradiation of the members and allow to decrease essentially the crack width of flexural structures.
7. Rational Prestressed Concrete Members
Two types of reinforcement of flexural prestressed concrete members are considered: limit and those of rational reinforcement. The present chapter deals with the limit and rational amounts of steel in a cross-sec tion of definite shape and size by using the prestress distribution ex pressed by Fig. 33.
The iimit reinforcement corresponds to the maximum value of bending moment just after cracking of structural members under working load
given by (7.41). The limit value of |
relative prestressing of concrete t] ( t i ) |
|||
is dependent |
on |
prestress in |
longitudinal steel and concrete strength at |
|
the transfer |
of |
prestressing |
force. |
The values of coefficient r] (mi) are |
presented in |
Table 29. |
|
|
|
The design of prestressed concrete structures under bending only or |
||||
bending with |
axial load may |
directly be computed, i.e. it is unnecessary |
to know the size of concrete I cross-section and the amount of longitudinal steel in advance. A calculus algorithm of rational cross-section of pre stressed structures is given in page 171. The initial values of mechanical concrete and steel properties may be changed automatically with the help of electronic computers. Therefore, it is easy to choose a rational variant of solution according to the criterion set.
Application efficiency of polymercement concrete in prestressed struc tures may be revealed by comparing the rational cross-section members and using the efficiency coefficient given by (7.72).
198
|
|
|
|
|
О Г Л А В Л Е Н И Е |
|
ВВЕДЕНИЕ ......................................................................................................................... |
|
|
|
5 |
||
Основные |
обозначения |
...................................................................................................... |
|
7 |
||
Г л а в а 1. |
НЕКОТОРЫЕ ТЕХНОЛОГИЧЕСКИЕ ОСОБЕННОСТИ |
|
||||
1.1. |
Полимерные |
добавки ...................................................................................................... |
|
ц |
||
1.2. |
Тепловая обработка ...................................................................................................... |
|
15 |
|||
1.3. Арматура ......................................................................................................................... |
|
|
|
25 |
||
Г л а в а 2. |
ОСНОВНЫЕ МЕХАНИЧЕСКИЕ СВОЙСТВА ПОЛ ИМЕРЦЕМЕНТ- |
|||||
|
|
НОГО БЕТОНА |
|
|
||
2.1. |
Границы микроразрушения .......................................................................................... |
31 |
||||
2.2. Прочность и |
деформационность ............................................................................... |
39 |
||||
2.3. Сцепление с |
арматурой ............................ |
|
48 |
|||
Г л а в а 3. |
ДЕФОРМАЦИИ |
ПОЛИМЕРЦЕМЕНТНОГО БЕТОНА |
ПРИ ДЛИ |
|||
|
|
ТЕЛЬНОМ НАГРУЖЕНИИ |
|
|||
3.1. Вопросы теории упруго-ползучего тела ................................................................... |
53 |
|||||
3.2. Ползучесть бетона |
.......................................................................................................... |
|
58 |
|||
3.3. Усадка |
бетона .............................................................................................................. |
|
|
64 |
||
Гл а в а 4. |
НАПРЯЖЕННОЕ СОСТОЯНИЕ ПРЕДВАРИТЕЛЬНО-НАПРЯЖЕН |
|||||
|
|
НЫХ ЭЛЕМЕНТОВ |
|
|||
4.1. Общие |
сведения ............................................................................................................. |
|
|
71 |
||
4.2. Кратковременное обжатие |
.......................................................................................... |
75 |
||||
4.3. Длительное |
обжатие .................................................................................................. |
|
84 |
|||
4.4. Действие внешней |
нагрузки ...................................................................................... |
93 |
||||
4.5. Потери |
предварительного |
напряжения ................................................................... |
97 |
|||
Г л а в а 5. |
ДЕФОРМАЦИИ ПРЕДВАРИТЕЛЬНО-НАПРЯЖЕННЫХ |
ЭЛЕМЕН |
||||
|
|
ТОВ |
|
|
|
|
5.1. Выгиб при внецентренном обжатии ....................................................................... |
106 |
|||||
5.2. Прогиб |
изгибаемых |
элементов .................................................................................. |
113 |
|||
5.3. Расчет элементов по деформациям ........................................................................... |
121 |
|||||
Г л а в а 6. ТРЕЩИНОСТОЙКОСТЬ И ПРОЧНОСТЬ ПРЕДВАРИТЕЛЬНО-НА |
||||||
|
|
ПРЯЖЕННЫХ ЭЛЕМЕНТОВ |
|
|||
6.1. Трещиностойкость |
вибрированных элементов ....................................................... |
124 |
||||
6.2. Трещиностойкость |
центрифугированных элементов ............................................ |
135 |
||||
6.3. Раскрытие трещин |
и прочность балок ..................................................................... |
137 |
199