Deflection Calculation of New Type Composite Box Girder with Corrugated Steel Webs Based on Reddy Theory
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摘要: 为准确计算新型波形钢腹板（CSW）组合箱梁的挠度，基于Reddy高阶剪切变形理论，考虑钢-混接触面滑移变形和全截面高阶剪切变形效应，以形函数作为单元内高度变化的插值函数，利用最小势能原理推出新型CSW组合箱梁等参有限元行列式；以一根8.0 m新型波形钢腹板简支组合箱型试验梁为例，基于本文理论编制了相应的计算程序，计算了集中、均布荷载作用下该梁的竖向挠度，并通过模型试验和有限元模拟验证了本文解析计算方法的可靠性；最后分析了剪力键剪切刚度、波形腹板型号、子梁高度比、跨高比等参数对新型CSW组合箱梁挠度的影响程度. 研究结果表明：考虑新型CSW组合箱梁全截面剪切变形效应后的挠度值较初等梁理论值增大约10%，较Timoshenko理论值增大约1.87%. 全截面剪切变形效应对挠度贡献随跨高比逐渐增大而减小. 跨高比和剪力键剪切刚度越小或子梁高度比越大，剪切变形效应对结构竖向挠度的影响越发显著，而波形钢腹板型号对箱梁挠度影响较小.Abstract: In order to accurately calculate the deflection of a new type of composite box girder with corrugated steel webs (CSWs), Reddy high-order theory is used to analyze the slip deformation of the steel-concrete interface and the high-order shear deformation effect of the whole section; the isoparametric finite element determinant of the new-pattern composite box girder with CSWs is derived by the principle of minimum potential energy, using the shape function as the interpolation function of height variation in the element. Taking an 8.0 m long new-pattern simply supported composite box girder with CSWs as an example, the corresponding calculation program is compiled by the proposed methodology and applied to calculate vertical deflections of the beam under concentrated and uniform load. Results of the finite element simulation are then compared with those of model tests to verify the reliability of the analytical calculation method. Finally, influences of the shear stiffness of shear key, type of corrugated web, height ratio of sub-beams, and height-span ratio on the deflection of the new type of composite box girder with CSWs are analyzed. The results show that after taking into consideration the full-section shear deformation effect of the new type of composite box girder with CSWs, its deflection is increased by about 10% compared with the theoretical value of the elementary beam, and increased by about 1.87% compared with Timoshenko ’s theoretical value. As the span-to-height ratio increases gradually, the contribution of the full-section shear deformation effect to the deflection gradually decreases. With a smaller span-to-height ratio, a smaller shear stiffness of shear key, or a larger height ratio of sub-beams, shear deformation displays more significant effect on the vertical deflection of the structure, while the CSW type has little effect on the box deflection.
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Key words:
- Reddy theory /
- corrugated steel web /
- composite box girder /
- shearing deformation /
- deflection
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图 1 新型CSW组合箱梁轴向位移场假定
Figure 1. Axial displacement hypothesis of a new type of composite box girder with CSWs
图 7 关键参数对组合箱梁挠度的影响
Figure 7. Effect of key parameters on deflection of composite box girder
表 1 材料特性
Table 1. Material propoties
材料 Ei/GPa 质量密度 ρ/（kg•m−3） 混凝土 34.3 2556 Q235钢材 208.0 7860 
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表 2 箱梁跨中挠度（工况1）
Table 2. Midspan deflection of box girder (case 1)
mm 荷载/（kN•m−1） 初等梁理论 本文理论 FEM 值 Timoshenko 理论 实测 3 1.902 2.081 2.064 2.060 1.969 6 3.804 4.159 4.128 4.121 4.032 9 5.705 6.240 6.192 6.181 6.160
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表 3 箱梁跨中挠度（工况2）
Table 3. Midspan deflection of box girder (case 2)
mm 荷载/kN 初等梁理论 本文理论 FEM 值 Timoshenko 理论 实测 40 5.297 5.667 5.633 5.561 5.658 80 10.594 11.334 11.266 11.123 11.084 100 13.243 14.167 14.083 13.903 14.026
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