Design Methods for Flexural Capacity of Variable Cross-Section Inverted Trapezoidal Steel Beams
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摘要: 变截面倒梯形钢梁作为一种新型钢梁,其凭借良好的力学性能和较低的成本,在大型空间结构中得到广泛应用。相比于常规H型钢梁、箱形截面梁和圆钢管构件,其具有更加复杂的几何形态。影响该类杆件几何形态的因素很多,导致此类杆件的承载能力存在很大差异。而GB 50017—2017《钢结构设计标准》中并未给出其抗弯承载力计算方法,工程应用中缺少理论计算方法。以深圳市大运城市综合交通枢纽工程中的变截面倒梯形次梁为例,给出其截面特性计算公式,利用ABAQUS建立数值模型,进行参数化分析,分析其受力机理及变化规律,提出变截面倒梯形钢梁承载力系数β,基于参数分析结果提出抗弯承载力理论计算式,给出设计流程。通过建立两段式变截面倒梯形钢梁的标准模型,设置合适的端部截面参数,得到变截面倒梯形钢梁抗弯承载力的变化规律,重点研究了翼缘宽厚比、腹板高厚比、倒梯形截面上下宽度比值、楔率对于变截面倒梯形钢梁抗弯承载力的影响,揭示了各因素下截面塑性发展机理,结果表明倒梯形钢梁抗弯承载力随上下翼缘宽度比值和楔率的增大而上升,随腹板高厚比和翼缘宽厚比的增大而减小。基于端部截面弹性极限弯矩,提出变截面倒梯形钢梁承载力系数β,充分考虑构件的弹塑性抗弯承载力,通过多元线性回归分析推导出变截面倒梯形钢梁在集中荷载和分布荷载作用下的抗弯承载力理论计算公式,将公式与数值模拟结果进行对比,二者拟合较好。针对变截面倒梯形钢梁的工程应用,总结出变截面倒梯形钢梁的设计流程,分析其整体稳定性,给出截面强度和局部稳定验算公式,为实际工程应用提供了设计依据。Abstract: As a new type of structural member, variable cross-section inverted trapezoidal steel beams have been widely used in large space structures due to their favorable mechanical properties and cost-effectiveness. These beams possess a more complex geometric configuration compared to conventional structural members such as H-shaped beams, box-section beams, and circular steel tubes. There are many factors affecting the geometrical form of such members, resulting in a great difference in their bearing capacity. However, the Standard for Design of Steel Structures(GB 50017—2017) does not provide a calculation method for their flexural capacity, resulting in a lack of theoretical calculation methods for engineering applications. This study investigates the secondary variable cross-section inverted trapezoidal steel beams in the Shenzhen Dayun Integrated Transportation Hub project. Formulae for calculating sectional properties were derived, and finite element models were developed using ABAQUS for parametric analysis. The mechanical mechanism and variation patterns were examined, leading to the proposal of a flexural capacity coefficient β for such beams. Based on the parametric analysis results, a theoretical formula for calculating flexural capacity was established, and a design procedure was outlined. A standard model for two-segment variable cross-section inverted trapezoidal steel beams was established with appropriately defined end-section parameters to study the variation law of flexural capacity. The research focused on the effects of the flange width-to-thickness ratio, web height-to-thickness ratio, ratio of top-to-bottom flange widths in the inverted trapezoidal section, and taper rate on the flexural capacity. The mechanisms of sectional plastic development under these parameters were revealed. Results demonstrated that the flexural capacity increased with the ratio of top-to-bottom flange widths and the taper rate, while it decreased with an increase in the web height-to-thickness ratio and flange width-to-thickness ratio. The bearing capacity coefficient β was proposed based on the elastic limit moment of the end sections, comprehensively considering the member's elastoplastic flexural capacity. Through multiple linear regression analysis, a theoretical formula for calculating the flexural capacity under both concentrated and distributed loads was derived. Comparison with numerical simulation results showed good agreement. For engineering applications, a design procedure was summarized, incorporating overall stability analysis and providing formulae for checking cross-sectional strength and local stability, thereby offering a design basis for practical projects.
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