Estimation of Critical Buckling Moments in Slender Reinforced Concrete Beams

At present, there are no recommendations in codes such as ACI 318 and BS 8110 to estimate the critical buckling moment in slender concrete beams. It is assumed that if the slenderness ratios of the beams are limited to the values prescribed by the codes, the failure moment of the beam will be dictated by flexure and not by buckling. Experimental studies carried out as part of the present study, however, show that the specified slenderness limits are not reliable, and failure by lateral instability can occur in slender beams designed according to the code. It is also shown that the existing formulations to predict critical buckling moments in beams, suggested by various researchers, grossly overestimate the capacities in the case of under-reinforced beams. In this paper, a modified formulation is proposed to predict theoretical buckling moment, and it is found to agree very closely with experimental results for both under-reinforced and over-reinforced beams.

Keywords: beams; buckling; reinforced concrete.

(ProQuest-CSA LLC: ... denotes formulae omitted.)

INTRODUCTION

Slender beams are occasionally encountered in reinforced concrete (RC) construction. Significant research has been carried out worldwide with regard to the behavior of slender columns, and on the basis of these research findings, appropriate provisions have been incorporated in the codes of practice with regard to the design of such members. With regard to slender RC beams, however, there are no comprehensive design provisions at present in the design codes. Some limits on slenderness have been prescribed in some codes, primarily to ensure that the failure of the beam occurs due to material failure and not due to buckling instability. But no such design provisions presently exist in the case of slender concrete beams. To develop a suitable design basis for such slender RC beams, it is necessary to predict the critical buckling moments of RC slender beams and to predict the conditions under which instability failure governs the ultimate load carrying capacity.

An ideal beam (free of imperfections), which is bent in the plane of its greatest flexural rigidity, may buckle laterally at a certain critical value of the load or applied moment (Fig. 1). As long as the applied load on such a beam is below a critical value, the beam is expected to be stable. When the critical load or moment is reached, a bifurcation state of equilibrium is possible, whereby the beam can either remain in the vertical plane (trivial solution) or suddenly bend laterally, accompanied with some twisting, as illustrated in Fig. 1(c). This buckling of the beam is associated with a loss in its lateral flexural rigidity, resulting in instability and collapse. The lowest load at which this critical condition occurs represents the critical load for the beam.1 The problem of lateral buckling has been widely studied with regard to the design of laterally unsupported steel beams with varying slenderness ratios.

The problem of lateral stability of RC beams was first studied by Marshall in 1948. He presented a theoretical study and concluded that RC beams are seldom expected to meet with the problem of lateral instability and the flexural behavior remains unaffected by high slenderness. These findings were to some extent substantiated by Hansell and Winter,2 who carried out tests on 10 slender RC beams and reported that no beam failed by instability, and the failure in each case was due to flexure in the vertical plane. Lateral deflections of the beams, however, were observed, indicating the presence of some slenderness effects. Later, in their theoretical study, they established that none of their test beams were long enough to produce instability failure. Hansell and Winter2 suggested that the slenderness limits of beams must be expressed in terms of Ld/b^sup 2^ rather than the simple L/b ratio.

Siev3 made an attempt to study the problem of lateral buckling in RC beams with initial imperfections. In his experimental study, he tested six slender RC beams having rectangular and inverted L sections. He established that the percentage of reinforcement also influences the slenderness behavior of the RC beams, in addition to their dimensions. Sant and Bletzacker4 tested 11 beams of different Ld/b^sup 2^ ratio, with a high percentage (3.85%) of tension steel. Instability failure was observed in nine of these over-reinforced beams, and only two beams failed by flexure. Although the experimental study was based on over-reinforced beams, Sant and Bletzacker4 proposed that their analytical expression to calculate the critical buckling moment is equally applicable to under-reinforced rectangular RC beams. They showed that the vulnerability of the RC beams to instability failure increases as the d/b ratio increases.

Massey5 attempted to address the problem of lateral instability with a theory that includes warping rigidity. He tested 11 overreinforced rectangular beams, both singly and doubly reinforced, made of mortar and established from the experimental results that the warping can be neglected if the ends of the beams are not restrained from warping. King et al.6,7 proposed a method of checking the lateral stability based on the equilibrium of the deformed position. Aydin and Kirac8 also developed an algorithm to generate the value of critical slenderness ratio (Ld/b^sup 2^) of any RC beam. A review of the literature available so far indicates that further analytical and experimental studies need to be done to explain the slenderness effects on the flexural capacity of the beams.