Wpływ Pełzania Betonu na Zespolone Ustroje Prętowe
The calculation methods of the influence of creep of concrete in statically determinate structures are discussed in the second Article.
Accurate solutions are given by Eqs. (2.7). For practical purposes, however, approximate solutions, (2.9) and (2.11), are proposed, the approximation being good for cross-sections with thin slabs.
The third Article is devoted to the theory of statically indeterminate structures. Using the well-known virtual work method we obtain the system of integral equations (3.5) in which the unknown functions are the redundant forces. The notations are taken from the stress method; do(p) represents the influence of plastic deformations due to the initial load (acting from ϕ=0) and δik(p) that of plastic deformations due to the constant action of the redundant force. The solution of the system of equations (3.5) is, in principle, possible, the number of equations being equal to that of the unknowns. This may be achieved by transforming (3.5) into a system of differential equations with constant coefficients (or by using the Laplace transformation). In the case of constant cross-section of all members the differential equations are of the second order (if the accurate formulae of the second Article are used), or of the first order (if approximate formulae are used). If the cross-section is sectionally variable the order of the equations is equal to the number of different cross-sections. In view of the above, solutions can easily be obtained only in the most simple cases [Eqs. (3.10) and (3.15); numerical examples 4, 5 and 6]. A method enabling the solution of most complicated cases by the use of arithmetic operations only is obtained with the aid of power series. The unknowns are taken in the form (3.16). The successive terms of the series xk,r are obtained from systems of algebraic equations. The series (3.16) is usually slowly convergent. In order to obtain rapidly convergent series the solution should be represented in the form (3.22). The best convergence is secured by the assumption of the coefficient pr according to (3.23). Then, one term is usually sufficient and the solution can be represented with a sufficient accuracy by the equation (…).
A slower convergence may appear in the rare cases where the redundant force passes through its maximum value or changes the sign (Figs. 12c and 12e). Three terms, however, are always sufficient for ϕ <4. The series calculation method is illustrated by the examples 7 and 8; the results are compared with accurate solutions.
A. Chudzikiewicz, Wpływ pełzania betonu na sprężone ustroje prętowe, Rozpr. Inzyn. 2 (1956).
K. Klöppel, Die Theorie der Stahlverbundbauweise in statisch unbe-stimmten Systemen unter Berücksichtigung des Kriecheinflusses, Der Stahlbau (1951).