竖向荷载作用下交错桁架结构的内力计算

CALCULATION OF INTERNAL FORCES OF STAGGERED TRUSS STRUCTURES SUBJECTED TO VERTICAL LOADS

以位移为未知量,根据平衡条件建立了竖向荷载作用下端部固定的空腹桁架节点转角和节间侧移迭代计算公式与固端弯矩的计算方法。运用节点力学平衡和各节间相对侧移之和为零这两个条件,建立了端部固定的空腹桁架在某端发生单位转角时节点转角和节间侧移的迭代计算公式以及空腹桁架转动刚度和传递系数的计算方法。在此基础上,将空腹交错桁架结构简化为无侧移刚架,提出了包含空腹桁架转动刚度、传递系数和固端弯矩的结点转角的迭代计算公式和构件内力计算方法。还以力法为基础,提出了只包含3个赘余力的混合交错桁架结构内力的力学计算模型,并给出了赘余力的计算公式和内力计算方法。空腹交错桁架结构的计算实例表明引入桁架转动刚度和传递系数的概念后,把单榀横向框架简化为无侧移刚架,使得参与迭代的构件数量大大减少,迭代收敛速度提高。因此,本文方法计算工作量少、计算方便实用。将计算结果与ANSYS分析结果比较,吻合良好。

Iterative formulas of nodal rotational angle and lateral deflection of truss panel and fixed-moment in end-fixing Vierendeel truss subjected to vertical loads were presented. Iterative formulas of nodal rotational angle and lateral deflection caused by unit rotational angle in one end of end-fixing Vierendeel truss and methods for calculating rotational stiffness and transfer coefficient were provided by use of the conditions that the forces on each node were in equilibrium and that the summation of relative lateral deflection of truss panel was zero. As a result, the staggered truss structure is simplified as a rigid frame with no lateral deflection and iterative formulas of nodal rotational angle including rotational stiffness, transfer coefficient and fixed-moment and methods for calculating member forces are developed. With consistent displacement principle, a calculation model of Pratt staggered truss including three unknown forces and formulas of unknown forces and calculation methods of member forces were proposed. Results show that the number of members involved in interaction is decreased greatly and iterative convergent rate is improved greatly. Thus, the method adopted in this paper needs less computational effort and is convenient for application. The results obtained by the present method are in good agreement with the those of software ANSYS.