Combined flexure and torsion of I-shaped steel beams

Abstract

Design standards provide little information for the design of I-shaped steel beams not loaded through the shear centre and therefore subjected to combined flexure and torsion. In particular, methods for determining the ultimate capacity, as is required in limit states design standards, are not presented. The literature on elastic analysis is extensive, but only limited experimental and analytical work has been conducted in the inelastic region. No comprehensive design procedures, applicable to limit states design standards, have been developed.From four tests conducted on cantilever beams, with varying moment–torque ratios, it is established that the torsional behaviour has two distinct phases, with the second dominated by second-order geometric effects. This second phase is nonutilizable because the added torsional restraint developed is path dependent and, if deflections had been restricted, would not have been significant. Based on the first-phase behaviour, a normal and shearing stress distribution on the cross section is proposed. From this, a moment–torque ultimate strength interaction diagram is developed, applicable to a number of different end and loading conditions. This ultimate limit state interaction diagram and serviceability limit states, based on first yield and on distortion limitations, provide a comprehensive design approach for these members. Key words: beams, bending moment, flexure, inelastic, interaction diagram, I-shaped, limit states, serviceability, steel, torsion, torque, ultimate.

Proposals for limit states torsional strength design of wide-flange steel members

“…Extensive tables in Appendix C of the AISC Design Guide 9 (AISC 2003) relate the y@ to the torsional load for a wide variety of boundary conditions and load profiles. The idea of the plastic model originates from the internal stress distribution in an I-section subjected to flexure and torsion proposed by Driver and Kennedy (1989) for Class 1 sections where the flange has sufficient potential of inelastic deformation without buckling to reach the ultimate stress of the steel, u (Fig. 3).…”

“…They noticed that as the bending moment approached the lateraltorsional buckling moment, beam twisting angles and warping normal and shear stresses became substantially higher than those predicted for these beams by first-order theory, and tended to infinity as moment M?M u . Driver and Kennedy (1989) pointed out that this resulted from two types of interaction. First, if the torque is caused by a vertical load acting at the top flange, the eccentricity increases as the section rotates.…”

“…Driver and Kennedy (1989) conducted four tests on cantilevered wide-flange Class 1 steel beams. The forces applied were strong-axis moment and torque only, with a different (but constant within each test) moment-torque ratio.…”

“…The only paragraph dealing with the strength of members in torsion is Clause 14.10.2, which makes a reference to ''moment-torque interaction diagrams'' but provides no immediate explanation as to what these diagrams are and how to construct them for a particular structure. The explanation is available in the Commentary to CSA S16 (CISC 2004) where two types of diagrams are referenced: one by by Driver and Kennedy (1989) and the other by Pi and Trahair (1995). These two types of diagrams will be considered in the following paragraphs.…”

Natural approach for thin‐walled beam‐columns with elastic‐plasticity

“…If the interpolation functions given by equations (49) are used in equations (50) to ( 5 9 , and if the results are used in the linear part of equation (20), then the following four simultaneous equations result:…”