Application Study on Grillage Method for Multiple-Cells Box Girder with Transverse Slope
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摘要: 为了研究多箱室箱梁基于梁格法计算的影响因素，考虑了横坡构造对多箱室箱梁的受力特性进行了分析.对梁格法理论的应用进行拓展，推导了适用于具有横坡构造的多箱室箱梁梁格截面特性值计算公式，并讨论考虑横坡的合理性；采用数值模拟的方法进行参数分析，通过改变加载位置、箱梁宽跨比、横坡大小等参数，对研究对象的受力特性进行了对比分析.研究结果表明：考虑横坡时，梁格截面刚度特征值更加接近实际，减小了12.12%的误差；具有横坡构造的多箱室箱梁的梁格模型与实体有限元模型计算结果吻合程度好，但仍无法反映箱梁在承受荷载时产生的畸变；考虑横坡构造的梁格法计算精度的提高主要体现在截面横向位移计算结果上；当箱梁宽跨比大于0.8时，采用梁格法计算时需要考虑横坡的影响；随着横坡大小从0增加到2%时，截面的竖向位移最大差值增加了758%，呈线性递增.Abstract: Mechanical properties of multiple-cells box girder with the transverse slope were analyzed in order to study the factors when using the grillage method. Based on the grillage method, formulas for multiple-cells box girder with tte transverse slope were derived while rationality of considering the transverse slope was discussed. Parameter analysis was done by adopting numerical simulation. Contrastive analysis on mechanical characteristic were done by changing the parameters such as loading positions, width-span ratios of box girder, cross slope angles. The results show that the error in computing characteristic value of grillage section rigidity is decreased up to 12.12% when the transverse slope is considered. The calculated results of grillage model fit the results of solid model, however, distortion cannot be reflect in the grillage model of multiple-cells box girder. The improvement of calculation precision is mainly appear on lateral displacement. Transverse slope would be considered in the grillage model if width-span ratio is greater than 0.8. Vertical displacement of cross section is increased linearly up to 758% when the transverse slope is change from 0 to 2%.
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图 3 跨中荷载作用下1/2跨与1/4跨截面位移
Figure 3. Displacement of 1/2 span and 1/4 span section under effect of loadings in 1/2 span
图 4 1/4跨荷载作用下跨中截面位移
Figure 4. Displacement of mid-span section under the effect of loadings in 1/4 span.
图 5 1/2荷载作用下1/2跨与1/4跨截面顶、底板应力
Figure 5. Stress at the top and bottom of 1/2 span and 1/4 span section under the effect of loadings in 1/2 span
图 6 1/4跨中心荷载作用下跨中截面顶、底板应力对比图
Figure 6. Stress value contrast at the top and bottom of 1/2 span section under the effect of centric load in 1/4 span
图 7 9箱室梁在自重作用下跨中截面位移
Figure 7. Displacement in 1/2 span section of 9 cells box girder under the effect of self-weight
图 9 1/2跨截面位移最大差值与横坡的关系
Figure 9. Relationship between displacement of 1/2 span section and transverse slope
表 1 纵、横向梁格截面特征值
Table 1. Characteristic value of the longitudinal and transverse girder section
梁格 0横坡, 1.5%横坡(纵向梁格) 0横坡, 1.5%横坡(横向梁格) Iy/m4 Jx/m4 As/m2 Ix/m4 Jy/m4 Ash/m2 ① 3.84, 3.43 5.21, 4.77 1.12, 1.07 2.87, 2.71 5.74, 5.42 0.01, 0.01 ② 4.81, 4.67 7.34, 7.14 1.12, 1.10 2.87, 2.87 5.74, 5.74 0.01, 0.01 ③ 4.81, 4.95 7.34, 7.55 1.12, 1.13 2.87, 3.03 5.74, 6.06 0.01, 0.01 ④ 4.81, 5.24 7.34, 7.98 1.12, 1.16 2.87, 3.12 5.74, 6.23 0.01, 0.01 
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表 2 参数要素
Table 2. Specification of parameter factor
参数 箱梁宽跨比 横坡大小/% 加载位置 1 1.6(9箱室) 0 自重 2 1.3(7箱室) 1.0 中心荷载 3 1.0(5箱室) 1.5 偏载1 4 0.7(3箱室) 2.0 偏载2
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表 3 位移误差分析
Table 3. Tolerance analysis of displacement
因素 自重 中心荷载 偏载1 偏载2 无横坡 有横坡 无横坡 有横坡 无横坡 有横坡 无横坡 有横坡 均差/mm 0.244 0.174 0.004 0.005 0.006 0.006 0.012 0.010 方差 1.0×10-1 4.5×10-2 2.1×10-5 2.8×10-5 4.5×10-5 4.4×10-5 2.8×10-4 1.8×10-4 相关系数 0.958 0.991 0.999 0.999 0.987 0.987 0.998 0.998
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表 4 应力误差分析
Table 4. Tolerance analysis of stress
位置 因素 自重 中心荷载 偏载1 偏载2 无横坡 有横坡 无横坡 有横坡 无横坡 有横坡 无横坡 有横坡 顶板 均差/kPa 108.21 88.49 7.71 7.06 1.70 1.59 1.62 1.65 方差 1.7×104 9.4×104 1.2×102 1.1×102 3.4 3.5 3.1 3.5 相关系数 0.988 0.995 0.938 0.941 0.998 0.999 0.999 0.999 底板 均差/kPa 128.27 81.38 5.82 5.86 6.63 6.64 10.69 9.92 方差 4.6×104 1.8×104 4.8×101 5.3×101 9.1×101 1.2×102 3.6×102 3.0×102 相关系数 0.977 0.974 0.998 0.997 0.988 0.993 0.999 0.999
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