基于改进三弯矩方程的钢-混凝土混合变截面连续梁桥钢箱梁段合理长度研究

为简便估算恒载作用下钢-混凝土混合梁变截面连续梁合理钢箱梁长度，基于现有三弯矩方程推导了适用于变截面连续梁的改进三弯矩方程，建立了基于改进三弯矩方程的变截面连续梁弯矩简化计算方法，并采用MATLAB软件编制了计算程序。构建了不同跨径的变截面钢-混凝土混合连续梁桥标准结构，运用改进三弯矩方程分析了恒载作用下不同跨径钢-混凝土混合连续梁桥关键截面弯矩随钢箱梁段长度变化的规律，建立了主跨跨径150m~300m间钢-混凝土混合变截面连续梁桥钢箱梁段合理长度预估公式。不同跨径的钢-混凝土混合连续梁的墩顶负弯矩和跨中正弯矩均随钢箱梁段长度的增大而减小；主跨跨径150m、200m、250m、300m的变截面钢-混凝土混合连续梁桥钢箱梁段长度与主跨跨径的比例分别为0.35、0.40、0.40、0.45时，主跨跨中正弯矩减小趋势变缓；研究结果表明：基于改进三弯矩方程的变截面连续梁弯矩计算结果与有限元计算结果的偏差小于10%，可便捷且准确地计算恒载下变截面连续梁弯矩；预估公式计算得到的钢箱梁段合理长度与实桥使用的钢箱梁段长度之间的误差在12.5%以内，预估公式具有良好适用性。

Study on the reasonable length of steel box girder for steel-concrete hybrid continuous beam bridge based on improved three-moment equation

For easy to estimate the reasonable length of steel box girder for steel-concrete hybrid continuous beam bridge, based on the existing three-moment equation, this paper deduces the improved three-moment equation which is suitable for three-span variable cross-section continuous beam, the simplified calculation method of bending moment of variable cross-section continuous beam which based on the improved three moment equation is proposed, and the corresponding calculation program is compiled using MATLAB software. The standard steel-concrete hybrid continuous beam bridges with different spans are proposed, and the modified three-moment equation is used to analyze the law of the bending moment of the key section of steel-concrete hybrid continuous beam bridge with different spans under the action of dead load. The formula for estimating reasonable length of steel box girder in steel-concrete hybrid continuous beam bridges with span between 150 m and 300 m is proposed. The negative bending moments in pier top and the positive bending moments in midspan of the steel-concrete hybrid continuous girder bridges with different spans are decreasing with the increasing of steel box girder length. The decreases of positive bending moments in midspan trend to slow down when length ratio of steel box girder of hybrid bridge with spans of 150m, 200m, 250m and 300m increase to 0.35, 0.40, 0.40 and 0.45. The research results show that the simplified calculation method based on the improved three-moment equation which can be used to calculate the bending moment of prestressed concrete and steel-concrete hybrid continuous beam, and the calculation accuracy is within 10%; The lengths of steel box girder employed in existing bridges can be accurately estimated by proposed estimation formula with the errors within 12.5%, the proposed estimation formula has wide applicability.