Second order moments in torsion members

This paper is concerned with the elastic flexural buckling of structural me mbers under torsion, and with second-order moments in torsion members. Prev ious research is reviewed, and the energy method of predicting elastic buck ling is presented. This is used to develop the differential equilibrium equ ations for a buckled member. Approximate solutions based on the energy meth od are obtained for a range of conservative applied torque distributions an d flexural boundary conditions. A comparison with the limited range of inde pendent solutions available and with independent finite element solutions s uggests that the errors in the approximate solutions may be as small as 1%. The predicted linear elastic buckling torques may be used to approximate t he second-order bending moments caused by torsion in members under more gen eral loading. A method is developed for approximating these second-order mo ments. This is used as the basis of a method of estimating when these secon d-order moments may be significant by comparing the actual member slenderne ss with a reference value. Reference values of slenderness are calculated f or two examples involving an equal angle member and a circular hollow secti on member (both simply supported), and the importance of second-order torsi on effects in an I-section member is estimated. The reference values of sle nderness are found to be very high, and it is concluded that second-order m oments caused by torsion in typical structural steel members with slenderne ss ratios L/r(y) <300 are very small and may be neglected. (C) 2001 Elsevie r Science Ltd. All rights reserved.