On the inelastic failure of high strength steel I-shaped beams

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Abstract

Compactness and bracing provisions for the design of steel beams are formulated so as to ensure that the resulting beam exhibits adequate structural ductility. The specification of such compactness and bracing requirements involve assumptions about the constitutive nature of the structural steel being used. Such material response assumptions are valid in designs involving most structural steel grades. However, it appears from the current research that these same assumptions are not valid when used to predict the ductility of wide flange beams made from the high performance steel grade HSLA80. HSLA80 wide flange beams subjected to moment gradient loading display inelastic modes of failure, which do not lend themselves to a notional de-coupling of so-called local buckling and lateral-torsional buckling phenomena. Rather, the inelastic modes of failure of the HSLA80 beams tested herein display two distinct inelastic buckling patterns at failure, both of which exhibit localized and global buckling components. The structural ductility of the beams is very much dependent upon which of the two mode shapes govern at failure. Cross-sectional proportions, bracing configuration, and geometric imperfections all play a role in influencing which mode governs in the beam at failure. Currently held views as to the impact of cross-sectional compactness and bracing on structural ductility may not apply to HSLA80 beams.

Introduction

In the past, assumptions concerning the mechanical properties of structural steel were viewed as being somewhat canonical in nature. The historical norm in structural steel design has been a mild carbon steel which, when tested uniaxially, possesses yield stresses between 220 and 450 MPa and exhibits a well-defined yield plateau followed by a region of strain-hardening, ultimately ending in necking and rupture. Recently, interest in the class of high strength low alloy (HSLA) steels has emerged within the discipline of structural engineering, partially as result of the successful employment of this type of steel in advanced applications within naval architecture. The HSLA steels are appealing to the designer predominantly due to the high strength-to-weight ratio of this material. However, good weldability and adequate ductility further enhance this appeal. The material properties of the HSLA steels tend to be dramatically different from mild carbon steel in several key areas of the uniaxial stress–strain relationship as can be seen in Fig. 1. This figure displays a schematical representation (based on the tests of Sooi et al. [1]) of the uniaxial stress–strain response of HSLA80 steel superimposed over that of A36 steel. HSLA80 has neither a well-defined yield plateau nor a substantial strain-hardening modulus as compared with A36 steel. In general, HSLA80 steel is also somewhat less ductile than A36 steel.

It is these characteristic differences in the mechanical properties of HSLA steels which are at issue in light of the assumptions that the current AISC load and resistance factor design (LRFD) specification [2]makes in its prediction of the ultimate response of structural steel members. It is further noted that it may not be possible to make strict generalizations as to the constitutive nature of these new HSLA steels due to the fact that, unlike carbon steels, HSLA steels are sold on the basis of minimum mechanical properties, with the specific alloy content left to the discretion of the steel producer [3]. Variations in the chemical composition of steel may profoundly impact on the very mechanical properties which are deemed to be crucial in creating a favorable overall structural response at the component and system level within the structure.

Predicting the ultimate flexural response of wide flange beams manufactured from HSLA80 plate has been one area of recent interest. Research along these lines has been predominantly focused on demonstrating the ability of HSLA80 beams to resist flexural loading in a ductile manner as quantified by rotation capacity 4, 5, 6. This research activity has shown, both experimentally and analytically, that wide flanges produced from the 80 grade of HSLA steel can indeed exhibit a flexural rotation capacity of three as required by the AISC LRFD specification [2]. This rotation capacity of three is assumed to be adequate for accommodating moment redistribution within the structural system to develop the controlling plastic collapse mechanism at the system-wide level [7].

The present study is restricted to the numerical testing of HSLA80 wide flange beams subjected to a moment gradient loading. Nonlinear finite element modelling is the vehicle by which the numerical testing is accomplished. The nonlinear finite element modelling techniques implemented in this research are consistent with experimentally verified techniques used in earlier studies by the author 4, 8, 9. From the numerical test results, it has become apparent that the notions of local buckling of the constituent cross-sectional plate elements, and the global lateral torsional mode, are so closely inter-related as to render them indivisible from each other in their manifestations within the context of HSLA80 beams under moment gradient. Two distinct modes, each possessing definite attributes of both local and global buckling, are identified and studied. The two modes differ from each other in the manifestation of their mode shapes, which appear to be directly related to the ability of the beam to develop adequate ductility in the form of plastic hinge rotation capacity. Furthermore, the sensitivity of the mode shapes to inevitable imperfections in cross-sectional dimensions are studied. Bracing stiffness requirements are also investigated, as is the impact of a new bracing scheme for use with these HSLA80 wide flange beams.

Section snippets

Overview of modelling techniques

The commercially available multipurpose finite element software package abaqus [10]is used for all of the numerical studies reported herein. Both geometric and material nonlinearities are considered in all of the finite element models. The subsequent nature of the nonlinearities are severe in that they are associated with inelastic global and local buckling phenomena. Hence, a very refined model must be used in the incremental solution of these types of problems. As a result, all analyses are

Geometries of specimens

All numerical tests reported herein are limited to simply supported beams having a wide flange cross-sectional shape and loaded with a moment gradient which varies linearly along the longitudinal axis in a fashion that is consistent with the structural geometry displayed in Fig. 4. In the studies reported here, L/d varies from 13.8 to 22, where L is the total span length, and d is the cross-sectional depth. The variation of this parameter is only an artifact of the change in specimen length

Preliminary results

Preliminary finite element studies of HSAL80 beams subjected to a moment gradient loading were conducted so as to develop a notional understanding of potential underlying mechanisms associated with the ultimate response of such beams. The results of these early studies were seen to run counter to expectations concerning the influence that cross-sectional proportioning has on structural ductility as quantified by plastic hinge rotation capacity. The definition of rotation capacity is consistent

Manifestations of the inelastic modes

Based on the foregoing discussion concerning the preliminary finite element studies associated with this research, a subsequent comprehensive modelling program is carried out. From this work it appears that the ultimate response of an HSLA80 wide flange cross-section is governed by one of two distinct possible inelastic buckling modes. These two modes will be referred to, respectively, as mode 1 and mode 2. Fig. 6, Fig. 7 display a typical mode 1 wide flange inelastic buckled shape, while Fig. 8

Imperfection sensitivity

Evidence from the current study of HSLA80 wide flange beams under moment gradient suggests that a sensitivity to cross-sectional imperfections exists. The cross-sectional imperfections used in this modelling are of the order of those that are deemed to be of an acceptable level by the literature. Such cross-sectional imperfections are based on the Standard Mill Practice as outlined in the LRFD Manual [2]and are displayed in Fig. 5. It is noted here that for a given beam length and

Strength and stiffness of mid-span bracing

Bracing a beam against premature failure due to lateral-torsional-buckling is typically achieved by restraining the out-of-plane translation and twisting of the cross-section at discreet points along the longitudinal axis of the beam. In the case of a beam subjected to a moment gradient loading, the bracing point is often chosen as the point of maximum moment. Once the bracing point location is known, strength and stiffness requirements for the bracing member must be specified.

The strength of

Alternative bracing scheme

In this portion of the research, alternative bracing configurations are sought based on the quantification of dimensions associated with mode 2 inelastic buckling manifestations. A series of measurements are made on the post-processed geometry of the HSLA80 wide flange beams exhibiting mode 2 failure so that trends in the geometry of the mode shape may be identified. The measurements consist of noting the distance from the mid-span stiffener to the centerline of the localized buckling wave

Conclusions

HSLA80 wide flange beams subjected to a moment gradient loading may behave differently at failure than similarly proportioned steel beams made from more traditional types of structural steel. The impacts that cross-sectional slenderness and unbraced length have on the plastic deformation capacity of HSLA80 beams seem to contradict conventional views about the influence of such parameters on plastic deformation capacity. Investigations into the source of these apparent discrepancies leads to the

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