Torsional analysis of tapered I–beams using Bernoulli-Euler beam theory

摘要

Previous investigations on the linear torsional analysis of a tapered I-beam indicate that thernconsideration of web-tapering effect on the torsional response may result in significant discrepancy. This studyrnintends to derive the governing equation of a torsional loaded I-beam with tapered section using the straightrnBernoulli-Euler beam theory. Regarding a tapered I-beam as the formation of three tapered narrow beams (therntop flange, web, and the bottom flange), one can directly express the total potential energy equation of therntapered I-beam by summing up all the potential energy equations of these narrow beams based on Yang et al.’srnwell-developed potential equation of a tapered solid beam. From the total potential energy presented, one canrnestablish the governing equation of a torsionally loaded I-beam, in which the effects of St. Venant torsion,rnwarping, and web-tapering have been included. Based on the differential equation derived herein, a closed formrnsolution for the linear torsional response of a taper I-beam will be investigated in the illustrated example.