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钢梁的弹性挠度是钢结构设计中经常要考虑并验算的问题,对此《钢结构设计规范》(GB 50017—2003)第3.5节和附录A明确提出了受弯构件的挠度容许值。为了计算钢梁的挠度值,通常的方法是采用结构力学图乘法进行推导,但这种推导需要针对具体的荷载形式和边界条件。由于实际结构中钢梁支座既可能是刚接也可能是铰接,甚至可能是滑动支座,另一方面楼板传递来的荷载形式也较为多样,一般包括均布荷载、三角型荷载以及梯形荷载,针对所有情况全部采用结构力学方法进行推导是一项非常繁杂的工作,不进行简化处理则难以满足各种实际情况的需要。本文研究了一种基于局部二次有限元分析的钢梁挠度计算方法,可直接接力整体有限元分析,对梁上的荷载形式及支座条件均可一致处理,有效避免复杂的推导与计算,计算结果在有限元舍入误差范围内是精确的,不存在人为引入的简化假定。另外该方法计算效率较高,可给出钢梁任意点的挠度值,是一种值得推广的挠度算法。目前,该方法已集成到北京市建筑设计研究院有限公司自主研发的结构设计软件Paco中,取得了良好的应用效果。
The elastic deflection of steel beams is a problem that often needs to be considered and checked in the design of steel structures. The tolerances for deflection of the flexural members are explicitly stated in Section 3.5 and Appendix A of the “Specifications for Design of Steel Structures” (GB 50017-2003). In order to calculate the deflection value of a steel beam, the general method is to use structural mechanics diagram multiplication to derive, but this derivation needs to be specific to the load form and boundary conditions. As the actual structure of the steel beam support may be just or may be hinged, and may even be a sliding bearing, on the other hand the form of load transmitted from the floor is also more diverse, generally including uniform load, triangular load and trapezoidal load It is a very complicated task to use all structural mechanics methods for all cases. It is difficult to meet the needs of various practical situations without simplifying the process. In this paper, a method for calculating the deflection of steel beams based on local quadratic finite element analysis is studied. The direct finite element analysis can be applied directly to the entire beam. The load forms and support conditions on the beam can be processed in unison, effectively avoiding complicated derivation and calculation. The calculation result is accurate within the finite element rounding error range, there is no artificially introduced simplified assumption. In addition, this method has high computational efficiency and can give the deflection value of any point of steel beam. It is a deflection algorithm worthy of generalization. At present, this method has been integrated into Paco, a structural design software independently developed by Beijing Architectural Design and Research Institute Co., Ltd., and has achieved good application results.