Abstract— Two robust procedures evaluating all unstrained element lengths are presented to find one practically optimized initial shape of cable-stayed bridges under dead loads. An analytical method based on the continuous girder model accounting for P-Δeffects due to stay-cable tensions is first proposed to calculate optimized cable tensions and unstrained element lengths without recourse to refined nonlinear FE analysis method. And then it is addressed how the G.TCUD method  developed for suspension bridges should be applied to determine an optimized initial state of cable-stayed bridges. For this, the extended nonlinear formulations of the co-rotational frame element as well as the elastic catenary cable element are briefly summarized by adding unstrained lengths of all finite elements to the unknown. Finally, based on the unstrained lengths determined from two methods, the unstrained length methods are presented to effectively perform nonlinear FE analysis of cable stayed bridges subjected to various load combinations. Consequently accuracy and effectiveness of the proposed schemes are demonstrated by showing that not only the unstrained lengths of a long-span cable-stayed bridge model by the analytical method are nearly same as those by the G.TCUD method but also these two methods lead to essentially one optimized initial configuration which is in suit with the target geometry.
Keywords— Initial shaping, G.TCUD, elastic catenary cable element, co-rotational frame element, unstrained length, cable-stayed bridge