This paper presents a three-dimensional mixed beam element formulation for fully nonlinear distributed plasticity analysis of members composed of sections with no significant torsional warping such as steel angles and tees. This formulation is presented using a corotational total Lagrangian approach and implemented in the OpenSees corotational framework. In this context, a basic coordinate system is lined up with the element chord and translates and rotates as the element deforms. The element tangent stiffness matrix and resisting forces in the basic system are derived through linearization of the two-field Hellinger-Reissner variational principle. The displacement shape functions are cubic Hermitian functions for the transverse displacements and a linear shape function for the axial and torsional deformation. The generalized stress resultant shape functions are linear for moments and constant for axial force and torque with the P - $\delta$ effect considered, which are developed from equilibrium equations. The fiber section method with uniaxial constitutive laws is adopted to account for material nonlinearity. Since the degrees-of-freedom in the basic system are defined with respect to different reference points, all element responses are transformed to acting about the shear center before conducting the corotational transformation. The mixed element is validated through a number of experimental and numerical examples.

本文提出了一种三维混合梁单元公式，用于构件的完全非线性分布塑性分析，该构件由无明显扭转翘曲的截面（例如钢角和三通）组成。此公式是使用按比例的总拉格朗日方法表示的，并在OpenSees的比例框架中实现。在这种情况下，基本坐标系与元素弦对齐，并随着元素变形而平移和旋转。通过两场Hellinger-Reissner变分原理的线性化，得出基本系统中的单元切线刚度矩阵和抵抗力。位移形状函数是用于横向位移的三次Hermitian函数，而是用于轴向和扭转变形的线性形状函数。$\delta$考虑的效果，这是根据平衡方程得出的。采用具有单轴本构定律的纤维截面方法来解决材料非线性问题。由于基本系统中的自由度是针对不同的参考点定义的，因此在进行坐标转换之前，将所有单元响应转换为作用于剪切中心。通过许多实验和数值示例验证了混合元素。