Nonlinear analysis methods based on the unstrained element length for determining initial shaping of suspension bridges under dead loads

• G.TCUD is proposed by including the unstrained lengths of both the frame element and the cable element as unknown and deriving the extended tangential stiffness matrix of the bridge structure.
• Also, UELM is newly presented based the conventional Newton iteration method in which the stiffness matrix is symmetric and the unstrained lengths of all the elements are kept constant.
• Finally the accuracy and effectiveness of the proposed algorithms are demonstrated through the numerical application for two suspension bridges.

Two nonlinear analysis methods are newly presented for finding the initial shape of suspension bridges under dead load. For this, the extended tangential stiffness matrices of the nonlinear frame element as well as the elastic catenary cable element are derived by adding unstrained element lengths to the unknown. A G.TCUD (generalized target configuration under dead loads) method and an unstrained element length method are then proposed to get the minimized bending moment as well as to remove both lateral and axial deformations in the main girder and the tower. Finally the accuracy and effectiveness of the proposed schemes are demonstrated through two numerical examples.