出于使用功能的考虑，在多高层结构中多层楼板抽空后形成通高区。在通高区内，外筒框架柱无任何面外支撑，其面外失稳常常控制结构的设计。该文针对通高区多层群柱的基本组成单元——两层两跨的十字型刚架中轴压柱的面外稳定性能进行了研究，提出了其面外稳定性设计方法。首先，剖析了十字型刚架中轴压柱发生面外失稳的主要影响因素，并按照面外支撑刚度相等的原则提出了等效研究模型，即柱跨中带侧向弹簧支撑的轴压柱。然后，通过对等效模型的弹性屈曲研究发现：当弹簧支撑刚度 低于其弹性临界值 ，柱子的屈曲荷载随弹簧刚度 线性增加；而当 时，柱子的屈曲荷载保持不变。据此特征该文建立了柱子的屈曲荷载和计算长度系数与柱跨中弹簧刚度 的简化关系式，并给出了弹性临界支撑刚度 的计算公式。最后，通过对等效模型的弹塑性极限承载力研究，验证了采用该文提出的计算长度系数计算公式并结合我国钢结构设计规范中柱子稳定曲线对轴压柱进行稳定性设计是适合的，但对中小长细比的柱子太过富裕。同时，极限承载力研究还发现了等效研究模型弹塑性失稳对应临界支撑刚度 弱于弹性柱子对应的 ，而且当实际支撑刚度小于 时，柱子的稳定系数也表现为随弹簧刚度线性变化。通过深入剖析，提出了 的计算公式，并基于此建立了更加简便、精确的轴压柱稳定性简化设计公式，从而构建起了一种新的设计方法。
A cross frame was selected as a most simple and typical case of the multi-storey and multi-span frames which buckle in the out-plane direction. In this paper, the out-plane buckling behavior of the axial loaded column in the cross frame was investigated theoretically and its design criterion was presented. Firstly, the column in the cross frame could be treated as an equivalent model of a compressed column with a lateral spring support at mid height of the column. The elastic buckling load and the effective slenderness of the column in the equivalent model was obtained by theoretical derivation and finite element analysis. Afterward, the ultimate load-carrying capacity of the column with single and two wave imperfections was obtained by using finite element analysis. It was proved that the ultimate load-carrying capacity of the equivalent model could be predicted by the column curve in the current design code for steel structures (GB50017-2003) directly, depending on the effective slenderness obtained herein. In addition, it was found that the full bracing requirement at mid height of the inelastic column was lower than that of the elastic one, hence a deep analysis was carried out and an equation to determine the inelastic critical stiffness was proposed. Based on this inelastic critical bracing stiffness, a new design formula was conducted for the purpose of a more simplified and accurate application in the design of the bracing column loaded axially.