Wen-Hao Pan

This study presents an extended matrix stiffness method for the exact flexural–torsional buckling analysis of non-funicular thin-walled beam-columns under general loading conditions. The formulation is built upon the well-established second order stiffness matrix proposed by Yang and McGuire, which is widely recognized as a robust and accurate benchmark for the geometric nonlinear analysis of thin-walled members. However, the original formulation does not explicitly account for the effects of uniformly distributed transverse loads at arbitrary heights on the cross section. To overcome this limitation, in this study, a superposition principle is introduced to incorporate the eccentricity of the distributed load into the total potential energy expression. The validity of this superposition approach is further confirmed by an independent variational derivation in the appendix. The refined total potential energy is then used to derive an improved element second order stiffness matrix. The proposed method is implemented within a standard matrix stiffness framework and validated using three representative problems: beam columns under combined axial and bending loads, beams subjected to moment gradients, and beams carrying uniformly distributed loads applied at varying heights. The results demonstrate excellent agreement with classical analytical solutions and high-fidelity shell finite element models. Thus, the proposed matrix stiffness method provides a consistent and computationally efficient tool for the exact stability analysis of non-funicular thin-walled structural systems.

In order to establish a three-dimensional dynamic stability analysis of beam-column systems, this paper presents an exact second-order dynamic stiffness matrix of axially-loaded members considering the natural frequency and axial compression effect. First, dynamic equilibrium analysis is developed for torsion and warping of an axially-loaded member. A fourth-order differential equation governing twist angle is derived, where a dimensionless quantity [ ] associated with the natural frequency is defined for the dynamic effect, and another dimensionless quantity [ ] indicates the Saint Venant torsion and axial load effect. Then, the exact element dynamic stiffness matrix defining the correlation between the element-end torsional stress resultants (torques and bimoments) and the associated deformations (angles and rates of twist) is obtained. Exact element dynamic torsional stiffness matrices for three configurations of warping restraints at the ends of the element are then developed via the matrix structural analysis. Moreover, for structural three-dimensional analysis, a 14-order exact element second-order dynamic stiffness matrix is derived through analogies between dynamic axial–torsional and axial–flexural problems.

Beam string structures (BSS) are frequently employed in large-span spatial structures due to their high load-carrying efficiency and elegant appearance. Owing to the neglect of the influence of prestress, the natural frequency of the BSS is often overestimated which could be crucial to the dynamic behavior of BSS. This paper presents an exact matrix stiffness analysis method (MSM) for investigating the relationship between prestress and the natural frequency of the planar BSS. A novel dynamic stiffness matrix of beam–columns considering the natural frequency and axial force is used to develop the MSM. The dynamic analysis of the structural vibration stability of BSS is performed by using the global structural stiffness matrix which is assembled from the element stiffness matrices in the global coordinate system. The proposed MSM with the exact dynamic element stiffness matrix for the dynamic analysis of the BSS is verified by comparing with previous results based on the finite element method. The illustrative examples demonstrate that the prestress in the cable has a negative effect on the natural frequency of the BSS and should be considered in the dynamic analysis. As the axial force increases from zero to the buckling load [ ], the natural frequency of the BSS decreases from the maximum vibration frequency to zero. The influence of prestress on the vibration frequencies of BSS is particularly significant when the prestress to balance the loads is large, especially in the case of large dead and live loads (e.g. floor slabs).

This paper optimizes the design of a novel large-span cable-supported steel–concrete composite floor system in a simply supported single-span, single-strut configuration, aiming for cost-effective solutions and minimal steel consumption. The optimization considers various cross-sectional dimensions, adhering to building standards and engineering practices, and is based on a non-linear programming (NLP) algorithm. Parameters of live loads ranging from 2 to 10 kN/m² and spans from 20 to 100 m are considered. The optimization results show that cable-supported composite floors with a single strut exhibit robust economic feasibility for spans of less than 80 m and live loads under 8 kN/m². Compared to conventional composite floors with welded I-beams, the cable-supported system offers more cost-effective cross-sections and reduces steel consumption. The savings in economically equivalent steel consumption range from 20% to 60%. Discussion on the area ratio of cables to steel beam in the optimal cross-section reveals that the secondary load-bearing system (i.e., bending of the main beam with an effective span length of L/2) may require more steel in cases of ultra-large spans. Therefore, the economical efficiency of cable-supported composite beams with multiple struts and smaller effective span lengths warrants further exploration in future studies.