FIELD SOLUTIONS FOR 2-DIMENSIONAL FRAMEWORKS

Closed form solutions are given for a variety of problems associated with the stress, deflection and buckling analysis of two-dimensional lattices of flexural members. The component frame of a multi-story building is one example of the type of system analyzed; that is, a regular orthogonal framework with rigid joint connections which is subject to in-plane loads only. The mathematical model in each case is a partial difference equation. The solutions are in the forms of single and double finite Fourier series and are general as regards loading and numbers of stories and bays. The formulas are in different categories depending upon the actions taken into account such as joint rotation, lateral displacement, in-plane buckling, etc. Various classes of boundary and support conditions are investigated and two of the solutions are numerically illustrated. In the Appendix, a basis for the extended use of general finite sinusoidal series is given. The characteristic functions and parameters are catalogued for all possible boundary conditions. © 1968.