Abstract
This chapter analyzes the stability and failure of individual members of frames. It is common, in dealing with rigid-jointed frames, to calculate deflexions and bending moments by a linear analysis. When this is done, the equations of equilibrium are established by considering the geometry of the structure in its undeformed state. The chapter describes the effect of various end conditions. The elastic critical load may be obtained for columns with end conditions other than those of a pin-ended strut by solving the differential equation and obtaining the constants of integration by reference to the boundary conditions. A readier solution is, however, obtained by observing that the solution of the differential equation can always be represented as a part of the continuous sine wave y = A sin αx referred to suitable axes. The axial thrust that makes the sinusoidal deformation of the member possible is then the elastic critical load for the given end conditions.
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