Effect of inclination on bending of variable-arc-length beams subjected to uniform self-weight

This paper presents the effect of inclination on the static behaviors of inclined variable-arc-length (VAL) beams. An updated Lagrangian formulation of the VAL beams has been developed via the variational approach. The first variation of the total potential energy is evaluated to establish the system of nonlinear finite element equations. These equations are then solved by using the iterative process to obtain static configurations. The second variation of the total potential energy is performed to determine the tangent stiffness matrix of the VAL beams. The critical values of uniform self-weight of the inclined VAL beams are obtained by equating the determinant of the tangent stiffness to zero. The critical uniform self-weights obtained from the finite element method are validated by those derived from the shooting method. The effects of inclination on the deflection, bending moment diagram, and axial force diagram at critical state are investigated herein.