Stiffness Expressions for Element with Central and End Springs

The force‐deformation equations of a two‐noded three‐dimensional (3‐D) beam‐column element with both central and end rotational springs, which take account of the effects of the axial load on the lateral element stiffness, are derived. Current position‐based equations are developed that give both the nodal forces and end shortening for a deformed element under the action of a significant axial force. The tangent stiffness matrix for this element is derived from the force‐deformation relations by following the procedures adopted by Oran for a two‐noded beam‐column prismatic element. Where appropriate, a successful analytical comparison with either Oran's or Chilton's expressions is made for the cases of no axial force, infinite end joint stiffness, and finite/infinite central joint stiffness. The stiffness expressions of this element can be used to represent several commonly used members in real structures by employing the appropriate stiffnesses of the central and end springs. The use of the new equations presented can lead to a significant saving in the core storage required for the analysis of structural assemblies with flexible joints.