Structural Effects of Time Dependent Behaviour of Concrete
The procedures for the linear viscoelastic analysis of R.C. and P.C. structures with particular emphasis to bridge-structures are presented. After a brief discussion of the fundamental properties of the constitutive linear viscoelastic law, based on the s
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F. Mola Politechnic of Milan, Milan, Italy
ABSTRACT The procedures for the linear viscoelastic analysis of R.C. and P.C. structures with particular emphasis to bridge-structures are presented. After a brief discussion of the fundamental properties of the constitutive linear viscoelastic law, based on the superposition integral, the two simplified models, namely the classical model and the Dischinger model are presented and widely discussed, stating their stress-strain laws of differential type. The numerical algorithms and the approximate techniques allowing to express in a convenient way for the applications the integral constitutive law are then introduced and a particular discussion is devoted to the algebraic approximate procedures. The homogeneous structures are then examinated and the basic theorems of linear viscoelasticity are deduced, showing the results deriving from an exact analysis when loads or imposed deformations or additional restraints are applied to the structure. As regards the non homogeneous structures the very important class related to the homogeneous viscoelastic structures with elastic restraints is studied. With reference to bridge structures this class is very important as it includes the cable-stayed bridges or the bridge beams with P.C. or steelconcrete transverse sections. The problem of the evaluation the state of stress in cable stayed bridges or in P.C. or steel concrete sections is approached by means of the unified procedure, stated by the author and called Reduced Relaxation Function Method, which is here applied in its direct or inverse form.
G. Creazza et al. (eds.), Advanced Problems in Bridge Construction © Springer-Verlag Wien 1991
176
F.Mola
The method is explained in its fundamental aspects and approximate solutions of particular simplicity are suggested, defining the upper and lower bounds for the exact solution. In a wide number of actual cases these bounds are very close so that the approximate solutions can be recommended for practical purposes. Three numerical examples, related to cable stayed bridges and to a steel-concrete section are then discussed showing the marked effects of creep on the long term state of stress of this kind of bridge structures.
1 . INTRODUCTION Concrete exhibits time dependent deformations of two kinds: the first referred as shrinkage deformation is independent from the state of stress and the second called creep deformation is produced by the applied sustained stresses. These deformations have generally a not negligible influence on the behaviour of R.C. and P.C. structures and in many cases their effects can be very marked so .that they have interested in a large extent structural engineers, researchers and builders, as it is pointed out by the very high number of theoretical and experimental works published in the last three decades. The shrinkage deformation, more exactly called drying shrinkage, produces a time-developing volumetric shrinking of the hardened concrete and is essentially a consequence of the loss of water from the
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