Constraints for Axial Strains in Frames

In the stiffness method of analysis, as applied to plane and space frames, axial strains in members may be systematically omitted using constraint conditions that prohibit length changes. With these conditions it is possible to solve for some of the unknown joint translations in terms of others. The number of dependent joint translations is equal to the rank of the coefficient matrix for the constraint equations. When these equations are combined with joint equilibrium equations, the number of the latter is reduced by eliminating the dependent joint translations and retaining the independent joint translations and rotations. A further reduction in the number of equilibrium equations is also accomplished by eliminating the joint rotations and keeping only the remaining joint translations as unknowns in the solution. The procedure developed pertains to both two- and three- dimensional frames and is suitable for automation on a digital computer.