Small strain deformation of slender beam structures is analyzed with the aid of nonlinear Total Lagrangian finite element analysis, wherein rotation vector increments are measured from the reference configuration so that a consistent Total Lagrangian finite element formation is obtained. Comparison shows an excellent agreement of the current FEM solution with the exact solution obtained from the shooting method. The tangent stiffness would be exactly the first derivative of the internal force under consorrative bading if no terms were neglected in linearization. However, the tangent stiffness, with some small term neglected in linearizing is still accurate for not too large deformations, and it may be used to detect the bifurcation point when the prebuckling deformations are not too large.
