Large Inelastic Deformations Of T-beams Subjected To Impulsive Loads

Abstract

Experimental test results on T-section aluminium alloy beams with fully clamped ends, which are subjected to a uniform impulsive load distributed over the entire span, are presented in this paper. A theoretical method, which was developed previously for beams with rectangular cross-sections, is modified to predict the behaviour of beams having a T-shaped cross-section. A satisfactory correlation is found between the theoretical predictions and the corresponding experimental results, with the experimental data generally bounded by the theoretical predictions which use inscribing and circumscribing curves to the exact yield surfaces. NOTATION m n N/No t Flange and web thicknesses B Flange width H Beam depth I Total impulse L Beam half span M Bending moment MQ Fully plastic bending moment N Axial force NQ Fully plastic axial force VQ Initial impulsive velocity = I/u2L Wf Final mid-point deflection A dimensionless impulsive velocity u Y Distance of equal area axis from top of flange as shown in Figure 1 Transactions on the Built Environment vol 8, © 1994 WIT Press, www.witpress.com, ISSN 1743-3509 192 Structures under Shock and Impact y Mass per unit length of beam p Density of material DO Static uniaxial yield stress Oy Dynamic uniaxial yield stress INTRODUCTION The theoretical rigid-plastic predictions for the dynamic plastic response of impulsively loaded fully clamped beams with rectangular shaped cross-sections were found to give favourable agreement with the permanent transverse displacements recorded on ductile metal beams [1j. Schubak et al . [2], using a finite-element approach, have presented numerical predictions for beams with both rectangular and I shaped cross-sections. For these doubly-symmetric cross-section beams, Schubak et al . [3] also reported that the interaction relations of all practical doubly-symmetric sections can be adequately approximated by a linear interaction in N-M space, that is a straight line segment passing through the axis points N = NQ with M = 0 and M = MQ with N = 0. However, the effect of the asymmetry of the beam cross-sections on the dynamic plastic response has not been reported in the literature. This paper presents some recent experimental results on beams with asymmetric cross-sections and makes comparisons with a theoretical rigid plastic method of analysis. Only large inelastic deformations are examined, while the results of investigations into the ductile fracture of doublyand singlysymmetric sections will be reported separately by the authors in due course. Two sets of experimental data are presented for aluminium alloy extruded T-sections (flange width 10.5 mm, nominal total height 11.2 mm and web and flange thickness of 3.2 mm) with fully clamped spans of 150 and 200 mm, respectively. ANALYSIS The theoretical analysis used for the predictions of the permanent transverse deflections of the T-beams is based on the approximate theoretical method developed for rigid, perfectly plastic beams with rectangular cross-sections [1], but modified to account for the asymmetry of the T-section. In Reference [1], the maximum permanent transverse displacement is given as Wf = {(1 + 3A/4X/2 l}(H/2) (1) for a rigid, perfectly plastic beam of depth H, which is fully clamped across a span 2L, and subjected to a dimensionless impulsive velocity Transactions on the Built Environment vol 8, © 1994 WIT Press, www.witpress.com, ISSN 1743-3509 Structures under Shock and Impact 193 Equation (1), which was developed for a beam with a rectangular cross-section, caters for the strengthening influence of finite transverse displacements, or geometry changes. It is evident for the particular case of the T-shaped cross-section in Figure 1 that U = {Bt + (H-t)tJp (3) and that the fully plastic bending moment carrying capacity is MQ/OQ = BY = /2 + B(t-Y)*/2 + (H-t) (H-2Y + t)t/2 , (4) Y = (B +Ht)t/2B (5) where is the distance to the equal area axis for pure bending shown in Figure 1. The fully plastic axial force for the crosssection in Figure 1 is = 2YB (6) It may be shown for the particular case of a T-shaped cross-section having t « H and B = H that equation (5) predicts Y = t, while equations (4) and (6) give the ratio MO/NO = HA. As noted previously, equation (1) was developed for a beam with a rectangular cross-section for which MQ/NQ = HA so that NO in the various equations leading to equation (1) was replaced by 4Mo/H. Thus, equation (1) is also valid for the T-shaped cross-section in Figure 1 when B = H and t « H.