Exact and approximate formulas for deflections of an elastically fixed rod under transverse loading

An exact solution is obtained for the nonlinear bending problem of a thin rod elastically fixed at one end and loaded by a transverse concentrated load of constant direction at the other end. The solution is written in parametric form and expressed in terms of the Jacobi elliptic functions. Based on the exact solutions, approximate formulas are proposed for the de.ection of the rod tip.