This paper deals with the equilibrium problem of the Mises truss, with out-of-plane lateral linear spring, analyzed as a three DOF system. It is shown that, as a consequence of the geometry of the structure, the system can undergo three buckling modes which are asymmetric in-plane buckling, symmetric out-of-plane buckling and asymmetric out-of-plane buckling. The analysis takes into account the influence of local buckling and yielding of bars on global instabilities.

The Green–Lagrange strain is adopted as the strain measure and the theorem of the stationarity of the total potential energy is employed to derive the nonlinear equilibrium equations. The tangent stiffness matrix is derived and, through the solution of the eigenvalue problem, the stability of the equilibrium solutions is investigated. Analytical formulations for the instabilities of the truss are presented.

For the numerical approach, a linear elastic constitutive model is assumed for the uniaxial stress–strain relationship of the truss bars. To take into account the yielding of bar elements, a perfect elastoplastic model is assumed. A computer program was developed in Fortran to perform comparisons with the results of the theoretical formulation. Finally, the numerical results obtained demonstrate the accuracy and effectiveness of the presented truss element.

The main novelty of this paper is the introduction of an additional DOF in the Mises truss which allows to study a more complex scenario of equilibrium paths and instabilities.

本文处理具有平面外横向线性弹簧的 Mises 桁架的平衡问题，作为三自由度系统进行分析。结果表明，作为结构几何形状的结果，系统可以经历三种屈曲模式，即非对称平面内屈曲、对称平面外屈曲和非对称平面外屈曲。该分析考虑了局部屈曲和钢筋屈服对全局不稳定性的影响。

采用格林-拉格朗日应变作为应变测度，并利用总势能平稳性定理推导出非线性平衡方程。推导出切线刚度矩阵，并通过求解特征值问题，研究平衡解的稳定性。介绍了桁架不稳定性的分析公式。

对于数值方法，假设桁架杆的单轴应力-应变关系为线弹性本构模型。考虑到杆单元的屈服，假设了一个完美的弹塑性模型。在 Fortran 中开发了一个计算机程序来与理论公式的结果进行比较。最后，获得的数值结果证明了所提出的桁架单元的准确性和有效性。

本文的主要新颖之处在于在 Mises 桁架中引入了一个额外的自由度，它允许研究更复杂的平衡路径和不稳定性场景。