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独立式螺旋楼梯(图1)的内力计算,视上、下端支座形式的不同而异。对于上、下端为简支的情况,计算较为简单,在文献中均有介绍。对上、下端为固定的情况,在文献中虽亦有介绍,但计算过程尚嫌烦琐,还须有一定的高等数学知识,不便为设计人员使用,且该方法只能解决具有对称性的情况。对这两种支座形式的螺旋楼梯受均布荷载时的内力进行比较,结果表明,按固定支座情况的内力值,除支座处有竖向平面弯矩(简支时此弯矩当然等于另)及竖向剪力略高外,其余各内力的最大值均比简支情况的各内力的最大值要小。自然,按此情况设计,钢筋和水泥的用量也可减少。本文用最一般的方法对固定支座受均布荷载的情况进行了研究,导出了具体的计算方法。为便于设计人员使用,把必需的计算表达式,表成简明的形式。此外,用此方法,不但可研究具有对称性的情况,还可研究任意空间曲线形的杆件受任意荷载作用的情况。最后,举了一个数字例题,绘了内力分布图。
The calculation of the internal force of a freestanding spiral staircase (Figure 1) varies depending on the type of upper and lower bearings. For the case where the upper and lower ends are simply supported, the calculation is relatively simple and is described in the literature. Although the upper and lower ends are fixed, they are introduced in the literature. However, the calculation process is still tedious and requires some advanced mathematics knowledge. It is inconvenient for designers to use it, and this method can only solve the problem of symmetry. . Comparing the internal forces of the two types of bearings in the form of abutment with uniformly distributed loads, the results show that, in addition to the internal forces of the fixed bearings, there are vertical plane bending moments at the support (in case of simple support, the bending moment is of course Equal to the other) and the vertical shear force is slightly higher, and the maximum values of the remaining internal forces are all smaller than the maximum values of the internal forces in the simple support case. Naturally, according to this design, the amount of reinforcing steel and cement can also be reduced. In this paper, the most common method is used to study the situation of fixed supports under uniform load, and a specific calculation method is derived. For the convenience of the designer, the necessary calculation expressions are presented in concise form. In addition, with this method, it is possible not only to study the case of symmetry, but also to study the case where any spatially curvilinear rod is subjected to an arbitrary load. Finally, a numerical example was given and the distribution of internal forces was plotted.