Instead of the usual neglecting, this study takes advantage of the second-order axial strain terms in the elastic constitutive equation of three-dimensional truss. This leads to higher-order terms on the resulting unbalanced force and on its corresponding tangent stiffness. The finite element procedure and updated Lagrangian descriptions are utilized with the new stiffness matrix. Furthermore, governing equilibrium equations are solved by using cylindrical arc-length approach. The validity of the proposed algorithm is checked by numerical examples. The outcomes indicate that the authors' formulation possesses the ability to trace the equilibrium path completely. Moreover, the obtained answers are identical with the exact results of other researchers.

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