Effects of beam axial deformations on storey-based critical gravity loads in tension-only semi-braced steel frames

Abstract

If the beams in a structural frame are not connected to slabs or other rigid diaphragms, the beams will axially deform when the frame is subjected to lateral loads, reducing the critical loads and increasing local deflections in the structure. The consideration of beam axial deformations always reduces the lateral stiffness of the frame, but has so far been neglected in storey-based stability methods. The lateral stiffness of a semi-braced (tension-only), semi-rigidly connected steel frame accounting for the axial deformations in its connecting beams is derived in this paper. The equations also apply to unbraced frames and/or idealized connections, which are commonly encountered or assumed in practice. It is demonstrated that the effect of beam axial deformation on the lateral stiffness of the frame can conveniently be accounted for using the concept of equivalent series and parallel springs. A lateral stiffness reduction factor is also introduced to predict the effects of beam axial deformations. The theoretical accuracy of the proposed method is verified via finite element analysis and the method is demonstrated via numerical examples. The effect of beam axial deformations on the critical gravity loads of frames was found to be significant in some cases, especially when the ratio of beam axial stiffness to column lateral stiffness is small – that is, within the order of 10². However, axial beam deformations have negligible effects on the critical gravity loads if the ratio is sufficiently large or where rotational buckling governs the failure mode, within the order of 10³ or above.