西安建筑科技大学学报(自然科学版)

为研究波形钢腹板预应力混凝土箱梁的剪力滞效应,引入β次曲线和近似余弦函数,根据变分原理推导出了简支梁和悬臂梁结构在典型荷载工况下的剪力滞系数计算公式,运用叠加法和肢解法将剪力滞计算方法推广应用到超静定桥梁的剪力滞系数求解中.采用有限元分析软件ANSYS和MIDAS/FEA建立波形钢腹板预应力混凝土箱梁空间模型,通过对比有限元计算结果,对能量变分解析方法进行了验证.对波形钢腹板PC箱梁开展了参数分析,得到了剪力滞系数随钢腹板厚度和宽跨比变化规律.研究结果表明:剪力滞系数值随纵向翘曲位移函数阶次的增加而增大,不宜引入高阶函数来求解波形钢腹板PC箱梁剪力滞问题; 悬臂箱梁的剪力滞系数随着宽跨比增大显著升高,均布荷载下的剪力滞系数比集中荷载下要大; 运用叠加法和肢解法解超静定桥梁的剪力滞问题简单高效,结果可靠.

In order to investigate the shear lag effect of prestressed concrete box girder with corrugated steel webs, β power curve and approximate cosine function were introduced, and the calculation formula of the shear lag coefficient of simple-supported beam bridge and cantilever girder bridge under typical load conditions was deduced according to the variational principle, and then the formula was extended to solve the shear lag coefficient in statically indeterminate bridges by the method of superposition or dismemberment. By means of the finite element software ANSYS and MIDAS/FEA, the corresponding 3D model was established, and the method of energy variational analysis was verified by comparing the results with the theoretical values in the paper. The geometric parameters affecting the shear lag effect of box birder were analyzed, and the variation of shear lag coefficient with steel web thickness and width span ratio was obtained. The results show that the shear lag coefficient increases with the increase of the order of the longitudinal warping displacement function, and it is not suitable to adopt the high-order function to solve the shear lag problem of PC box girder with corrugated steel webs; the shear lag coefficient of cantilever box girder increases with the increase of width-span ratio, and the shear lag coefficient under uniform load is larger than that under concentrated load. The study proves that the method of dismemberment or superposition is simple and efficient to settle the shear lag effect of statically indeterminate bridges, and the results are reliable.

引言
1 β次翘曲位移函数的变分解
2 近似余弦函数的变分解
3 算例分析
4 超静定桥梁的剪力滞解答
5 剪力滞效应的参数分析
6 结论

图1 波形钢腹板箱梁截面参数<br/>Fig.1 Section parameters of corrugated steel web box girder

图1 波形钢腹板箱梁截面参数
Fig.1 Section parameters of corrugated steel web box girder

表1 剪力滞系数实用计算公式汇总<br/>Tab.1 Summary of practical calculation formulas for shear lag coefficient

表1 剪力滞系数实用计算公式汇总
Tab.1 Summary of practical calculation formulas for shear lag coefficient

图2 有限元模型
Fig.2 Finite element model

表2 集中荷载20 kN下典型截面剪力滞系数<br/>Tab.2 Shear lag coefficient of typical section under concentrated load of 20 kN

表2 集中荷载20 kN下典型截面剪力滞系数
Tab.2 Shear lag coefficient of typical section under concentrated load of 20 kN

表3 均布荷载10 kN/m下典型截面剪力滞系数<br/>Tab.3 Shear lag coefficient of typical section under uniformly distributed load of 10 kN/m

表3 均布荷载10 kN/m下典型截面剪力滞系数
Tab.3 Shear lag coefficient of typical section under uniformly distributed load of 10 kN/m

图3 简支梁集中荷载下跨中截面剪滞系数分布<br/>Fig.3 Shear lag coefficient distribution of midspan section under concentrated load of simply supported beam

图3 简支梁集中荷载下跨中截面剪滞系数分布
Fig.3 Shear lag coefficient distribution of midspan section under concentrated load of simply supported beam

图4 悬臂梁根部剪力滞系数横向分布<br/>Fig.4 Transverse distribution of shear lag coefficient at the root of cantilever beam

图4 悬臂梁根部剪力滞系数横向分布
Fig.4 Transverse distribution of shear lag coefficient at the root of cantilever beam

表4 工况1典型截面剪力滞系数<br/>Tab.4 Shear lag coefficient of typical section under condition 1

表4 工况1典型截面剪力滞系数
Tab.4 Shear lag coefficient of typical section under condition 1

表5 均布荷载下典型截面剪力滞系数<br/>Tab.5 Shear lag coefficient of typical section under uniformly distributed load

表5 均布荷载下典型截面剪力滞系数
Tab.5 Shear lag coefficient of typical section under uniformly distributed load

图5 宽度比对悬臂梁根部剪力滞的影响<br/>Fig.5 Effect of width ratio on shear lag at the root of

图5 宽度比对悬臂梁根部剪力滞的影响
Fig.5 Effect of width ratio on shear lag at the root of

图6 波形腹板板厚对剪力滞的影响<br/>Fig.6 Effect of thickness of corrugated web on shear lag

图6 波形腹板板厚对剪力滞的影响
Fig.6 Effect of thickness of corrugated web on shear lag

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备注

引言

1 β次翘曲位移函数的变分解

2 近似余弦函数的变分解

3 算例分析

4 超静定桥梁的剪力滞解答

5 剪力滞效应的参数分析

6 结论

期刊信息