Abstract: A nonlinear differential equation with the effect of dead loads taken into account is formulated by the virtual work principle. Based on the equation, the effect of key physical factors, including the magnitude of dead loads, the height and span of the arch beam, the moment of inertia and the radius of inertia, etc, on the static characteristics of the arch beam, are discussed by using the Galerkin method. The equation is validated through comparing with the analytical solution for a straight beam presented by Takabatake and the numerical results for arch beams, which are presented, based on finite element method, in other articles by the author. The conclusion shows the differential equation can be applied to both arch and straight beams, the initial dead loads have a deterrent effect on the static responses of the arch beams with live loads, and such an effect relates to the magnitude of dead loads and the stiffness of the structures. In addition, some suggestions for the design of lightweight structures are proposed.