**4**, 2, pp. 227–287, 1956

### Wpływ pełzania betonu na sprężone ustroje prętowe

**Concrete creep in prestressed beam structures**

This paper is concerned with some general methods of solution of problems under consideration.

In the first section the theoretical foundations are discussed according to Dischinger's theory of creep. In the second section structures prestressed with non-grouted cables are considered. A solution is obtained by means of the system (2.1.3) of differential equations for statically determinate, and the system (2.2.1) for statically indeterminate structures. The unknown functions of creep modulus *φ* are force changes in cables and the redundant forces.

For practical purposes the solution by means of power series (2.3.1) is convenient. The coefficients *x _{k}*

_{,r}are determined from the system of equations (2.3.3). Sufficient exactness for

*φ*< 4 is obtained with two terms, for small values of

*φ*one term is often sufficient.

In the third section structures prestressed with grouted cables are considered. In the first part, solution in the form of a series as well as an approximate solution are given for statically determinate structures. In the second part a general theory of statically indeterminate structures is developed. In order to find the redundant forces *X _{k}*(

*φ*) a system of integral equations (3.2.7) is established. The functions

*δ*

_{i}_{0}(

*φ*) represent the influence of plastic deformations due to the initial load (

*M*

^{0}

*and*

_{b}*N*

^{0}

*), and the functions*

_{b}*δ*(

_{ik}*φ*) – the influence of plastic deformations due to the permanently acting redundant force

*X*= 1. The solution of the system (3.2.7) is assumed in the form of the power series (3.2.10). The convergence of the series

_{k}*x*

_{k}_{,r}is slow in general; more rapidly convergent series

*w*

_{k}_{,r}are olbtained using (3.2.12), where the coefficient

*μ*should be assumed according to (3.2.13). For a degree of exactness of several percent two or three terms of the series

_{k}*w*

_{k}_{,r}are, in general, sufficient. The procedure, for statically indeterminate structures is illustrated by the numerical example 7. The first two tables present the computation of the changes Δ

*M*

^{0}

*and Δ*

_{b}*N*

^{0}

*of internal forces in the basic system ~ith the assumption that the redundant quantities*

_{b}*X*

_{1}(

*φ*) are equal to zero. The next tables are devoted to the computation of a redundant! quantity and its influence on the internal forces of the structure Δ

*M*

^{(X)}

*and Δ*

_{b}*N*

^{(X)}

*. In practice however the second part of the calculation can be reduced by some 30 to 50 percent.*

_{b}In the fourth section „combined” structures are discussed as well as the influence of reinforcement and the problem of friction in structures prestressed with non-grouted cables.

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#### References

W. Glanville, Studies on Reinforced Concrete. The Creep or FLow of Concrete under Load, Techn. Pap. 12. ,

R. Davis, Flow of Concrete under Sustained Comprssive Strress. J. Amer. Conc. Inst., 1928, 1931.

C. Whitney, Plain and Reinforced Arches, J. Amer. Conc. Inst., 1935.

F. Dischinger, Untersuchungen über die Knicksicherheit die elastische Verfornung und das Kriechen, Bauing., 1937.

F. Dischinger, Elastische und plastische, Verformung der Eisenbetontragwerke und insbesondere der Bogenbrücken, Bauing., 1937.

N. Arutiunian, Niekotoryje woprosy tieorji połzuczesti, Moskwa 1952.