Abstract: In order to solve the problem of the references for the geometric nonlinear analysis of prestressed concrete plane beam element，based on the conventional nonlinear balance equation of beam，prestressing tendon is regarded as truss element with rigid arm and prestressing force is taken into account in local coordinate system ( co-rotational coordinate system) ． According to the characteristics of the motion and deformation of rigid arm，geometric nonlinear tangent stiffness matrix of truss element with rigid arm in global coordinate system is acquired，a more exact expression of tangent stiffness matrix for composite elements is also derived for prestressed concrete plane beam． A computer program is developed to analyze the geometrical nonlinear behavior of a prestressed concrete cantilever beam． The results demonstrate that the proposed innovative element and algorithm are efficient and accurate together with satisfied convergence．

Key words: prestressing force, truss element with rigid arm, geometric nonlinear, non-conservative system, tangent stiffness matrix

摘要： 以常规的非线性平面梁元平衡方程为基础，将预应力束视为两端通过刚臂与混凝土梁元节点连接的平面杆 元，在局部坐标系(随转坐标系)中计入预应力，根据刚臂在受力后只有刚体运动而本身不变形的特点，采用微分方 法导出其在结构坐标系中的切线刚度矩阵，从而获得混凝土梁元与预应力束杆元在结构坐标系中的组合单元切线 刚度矩阵;编制了程序，对预应力钢筋混凝土悬臂梁进行几何非线性分析;与ANSYS计算结果比较表明，提出的方 法在非线性程度很高时仍能获得高精度数值解，具有对单元数量不敏感，预应力作为非保守荷载的特点容易被计入 的优点。

关键词: 预应力, 带刚臂的杆元, 几何非线性, 非保守系统, 切线刚度矩阵