# Upper and Lower Bounds of Elastic Critical Loads

*The elastic critical load of a plane frame is that at which the resistance offered by the frame to any random disturbance is nil. For this state the stiffness matrix corresponding to all possible disturbances is singular. The elements of this matrix are in terms of the physical properties of the members and the modified stability functions tabulated by Livesley and Chandler. The usual method adopted is one of trial and error. A load trial is chosen, the value of the stiffness of the frame is then calculated, and the critical load is that at which the stiffness of the structure vanishes. Several load trials must be made before the critical load is predicted.
S. Z. Al-Sarraf*