Finite extensional deformation of a rigid plastic arch

The exact, nonlinear extensional theory of a rigid perfectly plastic arch is used to determine the complete load-deflection behavior of a clamped semicircular arch under the action of a vertical upward point load at the crown. A rate formulation of the problem is discussed. Solution of the rate problem at the yield-point state provides the basis for the construction of exact solutions for thin and for thick arches. Numerical results are presented in graphical form. These results consist of load-deflection curves for three thin arches and one thick arch. The plots together with formulas presented herein show that the slope of the load-deflection curve at the yield-point state is nonzero and positive for upward loading. This result deviates from the zero slope predicted by the usual methods of limit analysis in which geometry changes are neglected.