Torsion constant for matrix analysis of structures including warping effect

Abstract

In this research, an effective torsion constant, Jeff, for a wide-flanged member with different warping restraint conditions at the ends is developed. In order to derive Jeff, the boundary conditions for different warping restraint conditions at the ends, as imposed by the use of different types of connections in steel structures, are employed in the general equation of torsional rotation, ø. This effective torsion constant can be used directly instead of the St Venant torsion constant, J, in the conventional member stiffness matrix. The use of Jeff will account for the effect of warping when using the commercial computer programs which employ either a 6 x 6 member stiffness matrix for grid or a 12 x 12 member stiffness matrix for space frame. A table for factor F, which is the ratio of Jeff to J, is presented for different member properties and warping restraint conditions for the easy and rapid torsional analysis of structures composed of wide-flanged members by the matrix method. The solutions of a sample grid problem using Jeff are compared with well known solutions to demonstrate its application.