Refined second-order analysis of frames with members under lateral and axial loads

Loads such as those caused by wind, snow, and dead weight act along members in a frame structure. This type of member loads is extremely common in the practical design and analysis of structures. However, most research studies on the second-order and nonlinear analysis of frames idealize all loads as nodal forces and moments. Unlike in a linear analysis, the stress due to the nodal moments and forces in a second-order ananlysis cannot be simply superimposed on the stress created by the loads along members to obtain the final bending moment and force diagrams, because they affect the nonlinear element stiffness. Without careful consideration of the interactive and nonlinear response of the element with member and nodal loads, the accuracy of a nonlinear analysis for realistic problems is questionable. This paper presents the formulation of a proficient element for the second-order analysis of frames accounting for the nonlinear interaction between the element stiffness, the nodal load, and the member load. The degree of accuracy satisfies the requirement for practical applications, while the simplicity allows the approach to be easily coded in a computer program for the practical analysis of steel frames.