M.N. Pavlović

Strain-softening of concrete in uniaxial compression

0025-5432/97

Symbolic computation in structural engineering

Abstract Nowadays computers can perform symbolic calculations––in addition to mere numerical computations for which they were originally designed––and this opens up exciting possibilities in structural engineering and mechanics. Until relatively recently, this computer-algebra option was hardly exploited except for a handful of pioneering enthusiasts. As symbolic computations are finally beginning to experience a reasonably widespread awareness––and usage––it seems timely to review their past applications to structural-mechanics problems and to point to areas where significant advances are yet to come. What emerges is a picture where areas of classical analysis––increasingly neglected since the advent of computers––now re-emerge as attractive computational options, as well as a more balanced view that no longer sees analytical techniques and numerical methods as incompatible opposites but combines their usage in a rational way.

Bending of clamped orthotropic rectangular plates: a variational symbolic solution

Abstract The Galerkin method is herein applied to the classical bending problem of a uniformly-loaded orthotropic rectangular plate with clamped edges, a problem for which, to our knowledge, no exact analytical solution in its general form exists. The tedious and error-prone computations inherent in such an approach are facilitated through the use of a computer algebra system; and several solutions, based on different approximations for the infinite series representing the assumed deflection function for the plate, are worked out, thereby extending previous work in the literature. The accuracy and convergence of the present formulation are assessed on the basis of solutions corresponding to the special case of material isotropy; and one such existing, manually-derived, result is shown to be incorrect.

Shear-lag revisited: The use of single fourier series for determining the effective breadth in plated structures

Abstract The problem of shear lag is tackled by means of a classical technique which, in its present form, appears to offer a simpler and more direct approach, yielding a closed-form solution for the longitudinal stress distribution in wide flanges of box girders and ensuing effective-breadth ratios. The method is particularly suited to parametric studies and a number of these are undertaken, both for purposes of computational illustration and so as to study cases of practical relevance. Some of the salient features in the latter are highlighted, especially as an aid to engineers at the preliminary design stage of plated structures.

Single Fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of colinear compression. Part 1: Closed-form solution and convergence study

Abstract This paper considers certain types of classical plane-stress problems, concentrating on their solutions by means of the simple, although usually approximate, single Fourier series technique. While this approach is well known, no systematic studies based on it seem to have been carried out in the past. Such a study is presently undertaken with reference to the problem of a colinearly compressed rectangular plate so as to reach some conclusions regarding (ordinary) convergence rates for stresses, as well as to investigate possible ways of improving convergence. In addition, a truly closed-form solution for the single Fourier series technique is given (thus bypassing the need to repeatedly solve systems of equations) which encompasses completely arbitrary normal and/or shear loading along two opposite edges. In a follow-up paper (Tahan et al., Thin Walled Structures 17 (1) (1993)), the present findings will be used to conduct an investigation of the stress distribution in a plate subject to colinear compression .

Deformational behaviour of concrete specimens in uniaxial compression under different boundary conditions

This paper reports experimental data produced by a series of uniaxial compression tests on cylindrical specimens of concrete. The specimens were tested under four different boundary conditions, with their deformational behaviour carefully recorded to study the ensuing strain-softening behaviour.

Size effects in structural concrete: A numerical experiment

Abstract The paper forms part of a programme of investigation into the causes of size effects in structural-concrete behaviour. It is postulated that one of the causes of size effects is load-induced non-symmetrical cracking which is inherent in concrete due to its heterogeneous nature. The validity of this postulate is supported by the results—presently reported—of non-linear finite element analysis, in which the model used to describe cracking is capable of inducing non-symmetrical cracking in symmetrical structural members subjected to symmetrical loading. The results demonstrate that the package used can also provide a close fit to experimental values and, moreover, that the presence of stirrups (designed so as to prevent shear failure) is sufficient to diminish the effect of non-symmetrical cracking and hence eliminate size effects.

Single fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of colinear compression. Part 2: Stress distribution

Abstract In this, the second paper of a two-part report on colinearly compressed rectangular plates, a study of the mechanical aspects of the problem is conducted in order to obtain a reasonably general picture of the stress distribution as the relevant geometric and load parameters are varied. Special emphasis is placed on the degree of error inherent in the approximate single Fourier series scheme, and on what constitutes a ‘long’ plate for the sort of systems in question. Finally, a possible practical implication for estimating the tensile strength of brittle materials through compression testing is suggested.

The effect of prior flexural prestrain on the stability of structural steel columns

Abstract Prior large bending deformations may cause a significant reduction in the buckling stress of a mild steel strut subjected to direct compression. Although the work arose in investigating the properties of mangled bars, that is bars which have been deliberately deformed so as to reduce initial geometric imperfections, the conclusions are equally applicable to other instances of plastic strain reversal, such as those which might arise due to earthquake or shock waves. Particular attention is drawn to the possibly potentially dangerous situation which may arise when a severely deformed element is straightened and then subjected to loading conditions which would be regarded as safe for a previously undeformed element. Buckling stresses have been computed from material data for the prestrained specimens and these values are compared with actual test results.

Transverse-stiffener requirements for the post-buckling behaviour of a plate in shear

Abstract The optimum stiffener rigidity in a transversely-stiffened web under pure shear is sought in the post-critical range. An energy-based large-deflection scheme is employed to study the post-critical strength of the system up to the initiation of material yielding for the usual range of plate geometries and varying stiffener rigidities. Several criteria for “optimum” rib stiffness are assessed including stiffener deflection, the effective halving of the plate length and, finally, the strength of the plate itself. Tentative conclusions are reached on the basis of comparing optimal rib rigidities for the two instances of elastic and post-buckling regimes.