Podstawy teorii pełzania ustrojów hiperstatycznych wstępnie sprężonych
The foundations of the theory of creep of statically indeterminate prestressed structures
Dealt with in this paper Pare the foundations of a general theory of creep in statically indeterminate prestressed structures, in particular the derivation of systems of equations enabling the determination of the redundant quantities as functions of time; a general discussion of methods for solving such equations is included.
The considerations are based on the Volterra-Boltzmann general theory of linear creep, leading to systems of linear equations [see the system (2.21)].
On the basis of accurate solutions, consideration is given to the principal ways in which the theory can be simplified. These ways are: simplification of the equations of internal statical indeterminacy (in the case of concentrated reinforcement); simplification of the equations of external statical indeterminacy (continuous beams); transition to a homogeneous system (together with the case of prestressing reinforcement allowed to slide in its channels); and replacement of integral equations by differential equations. No practical examples are solved in this investigation. They will constitute the subject of a separate paper.
References
N. Ch. Arutiunian, Niekotoryje woprosy tieorji potzuczesti, Moskwa Leningrad 1952.
R. Busemann, Kriechberechnung von Verbundtragern ureter Benutzung von zwei Kriechfasern, Bauing., 11 (1950).
Z. Bychawski, Resolving Kernel of the Volterra Equation in the Case of the Generalized Creep Function, Arch. Mech.. Stos. 2 (1957).
G. Colonnetti, Scienza de/le Construzioni, Turyn 1941.
G. Colonnetti, Deformazioni plastiche e deformazioni viscose, Pont. Ac. iSci. Acta, t. 6, 24.
F. Dischinger, Untersuchungen fiber die Knicksicherheit, die elastische Verformung und das Kriechen des Betons bei Bogenbriidken, Bauing. 35/36, 39/40 (1937).
A. Habel, Der Einfluss des Kriechens und Schwindens auf die statisch unbestimmten Grdssen vorgespannter Duichlauftrager und Zweigelenkrahmen, Bet. Stahlb., 4 (1955).
A.J. Iszlinski, Prodolnyje kolebanja stierżnia pri naliczii liniejnowo zakona poslediejstwja i relaksacji, Prikł. Mat. Mech. 1 (1940).
P. Lardy, Eigenspannungen und vorgespannter Beton, Schweiz. Baurtg, 5 (1943).
F. Leonhardt, Spannbeton für die Praxis, Berlin 1955.
F. Levi, Sulla valutazione degli effetti dell eLastizita ritardata nei solidi iperstatici, Giorn. Gen. Civ. 7/8 (1949).
F. Levi, G. Pizzetti, Fluage plasticite precontrainte, Pary2 1951.
W. Olszak i J. Litwiniszyn, Nieliniowe zjawisko pewnego przeplywu cieczy jako model reologiczny, Arch. Mech. Stos. 4 (1953).
W. Olszak, Z zagadnień teorii elementów uzwojonyah w świetle reologicznych własności materiałów, Arch. Mech. Stos. 2 (1954).
M. Ritter, P. Lardy, Vorgespannter Beton, Zurych 1946.
A.R. Rżanicyn, Niekotoryje woprosy miechaniki sistiem dieformirujuszczichsja wo wriemieni, Moskwa-Leningrad 1949.
K. Sattler, Kriechen und Schwinden bei vorgespannten Verbund-Stahlbetonkonstruktionen, Bet. Stahib., 1, 2 (1954).
V. Volterra, Sur requilibre des corps etastiques muttiptement connexes, Paryż 1907.
V. Volterra, Lecons sur les fonctions de ligne, Paryż 1913.