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摘要: 分析了映射变换法与插值法的嵌套循环特性, 提出了抗力分项系数的双重迭代求解算法, 应用VB编制了计算程序, 计算了活恒载效应比为0.10、0.25、0.50、1.00、1.50、2.50六种工况下的构件抗力分项系数, 将分项系数乘以荷载效应组合值后得到修正抗力值, 针对修正抗力与荷载效应进行了可靠指标校核验算。计算结果表明: 应用双重迭代算法求得构件的可靠指标均大于目标可靠指标, 汽车一般运营状态下构件的可靠指标计算值与目标值的相对误差在0.62%~0.92%之间, 汽车密集运行状态下两者相对误差在0.62%~0.74%之间, 说明双重迭代算法计算结果可靠, 且偏于安全。Abstract: The characteristics of nested loop for reflection transformation method and interpolation method were analyzed, a double iteration solving method of resistance partial factor was presented, and its program was designed by using VB. The resistance partial factors of bridge components were calculated when the effect ratios of living load to dead load were 0.10, 0.25, 0.50, 1.00, 1.50, 2.50. The resistance was modified by multiplying load effect combination value by resistance partial factor, and the corresponding reliability index was checked. Computation result indicates that component reliability index computed by using the method is larger than its target index. Their relative deviation is between 0.62%-0.92% under general operation state for vehicle, and it is between 0.62%-0.74% under dense operation state for vehicle. The result shows that the method is reliable and emphasis on safety.
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Table 1. Target values of resistances for different type bridges
ρ 0.10 0.25 0.50 1.00 1.50 2.50 Dead load effect/ (kN·m) 100 Vehicle load effect/ (kN·m) 10 25 50 100 150 250 Resistance/ (kN·m) 134 155 190 260 330 470 
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Table 2. Statistical parameters of resistances and load effects
Force and effect Distribution type Statistical parameter Average Standard deviation Variation coefficient Resistance Lognormal 1.226 2 0.173 4 0.141 4 Dead load effect Normal 1.014 8 0.043 7 0.043 1 Vehicle load effect General state Extreme value I 0.686 1 0.107 6 0.156 9 Dense state 0.799 5 0.068 9 0.086 2
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Table 3. Reliability indexes
ρ 0.10 0.25 0.50 1.00 1.50 2.50 β Vehicle general state 2.787 3.166 3.570 3.854 3.909 3.921 Vehicle dense state 2.717 3.021 3.378 3.771 3.947 4.080
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Table 4. Computation result of resistance partial factors
ρ 0.10 0.25 0.50 1.00 1.50 2.50 βT Vehicle general state 3.7 1.143 1.082 1.020 0.973 0.959 0.952 4.2 1.230 1.164 1.102 1.065 1.061 1.065 Vehicle dense state 3.7 1.154 1.104 1.048 0.989 0.961 0.937 4.2 1.242 1.187 1.128 1.067 1.041 1.021
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Table 5. Adjusted resistances and checked result of reliability indexes
ρ 0.10 0.25 0.50 1.00 1.50 2.50 Vehicle general state βT=3.7 Modified resistance/ (kN·m) 153.832 168.485 194.750 254.280 318.120 449.790 β 3.730 3.732 3.730 3.730 3.725 3.723 β-βTβT-1/% 0.81 0.86 0.81 0.81 0.68 0.62 Average relative deviation/% 0.77 βT=4.2 Modified resistance/ (kN·m) 165.490 181.195 210.330 278.200 351.780 502.900 β 4.229 4.227 4.229 4.226 4.224 4.222 β-βTβT-1/% 0.69 0.64 0.69 0.62 0.57 0.52 Average relative deviation/% 0.62 Vehicle dense state βT=3.7 Modified resistance/ (kN·m) 155.306 171.895 200.070 258.440 318.780 442.740 β 3.727 3.730 3.731 3.731 3.730 3.734 β-βTβT-1/% 0.73 0.81 0.84 0.84 0.81 0.92 Average relative deviation/% 0.82 βT=4.2 Modified resistance/ (kN·m) 167.098 184.760 215.270 278.720 345.180 482.220 β 4.228 4.226 4.231 4.227 4.227 4.226 β-βTβT-1/% 0.67 0.62 0.74 0.64 0.64 0.62 Average relative deviation/% 0.65
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