Tapering I-Section Frames

A doubly symmetric I-section member of constant flange thickness, web thickness, and flange breadth but with linearly varying depth is a common structural element particularly in steel frames for industrial buildings. It is usual in elastic analysis to assume that conventional Bernoulli-Euler bending theory continues to hold for such members. Even so, it is not possible to obtain a stiffness matrix for major axis bending by exact algebraic integration of the governing differential equation. To overcome this difficulty, power functions have been commonly used to represent, in an approximate manner, the variation of the moment of inertia along the member. Numerical integration or displacement functions can also be employed to obtain the stiffness matrix, although such methods are less convenient to use. A further approximate approach is to treat the member as a series of stepped prismatic segments, but this procedure will result in a large stiffness matrix if more than just a few segments are used.