发布时间 : 星期三 文章附录A 衬砌内力计算更新完毕开始阅读
a11??11??1?(21.061?138.889)?1022?6?159.95?10?6?6?6a12?a21??12?f?1?(63.324?7.839?138.889)?10a22??22?f?1?(327.454?7.839?138.889)?10a10??1p??ap?(?1????a?)?h??6?1152.075?10?6?8862.172?10?(90244.835?1235139.877?(36.893?1605.556)?h)?10??(1325384.712?1642.449?h)?10a20??2p?f?ap?(?2???f?a?)?h?6?6
??(436805.089?7.839?1235139.877?(253.765?7.839?1605.556)?h)?10??(10119066.58?12839.718?h)?10?6?6X1??a22a10?a12a20a12?a11a221152.075?159.95?8862.172?6221152.075?(10119066.58?12839.718?h)?8862.172?(1325384.712?1642.449?h)?(973.8?2.623?h)?10X2??a11a20?a12a10a12?a11a2221152.075?(1325384.712?1642.449?h)?159.95?(10119066.58?12839.718?h)1152.075?159.95?8862.172?62?(1015.234?1.79?h)?10 六 计算主动荷载和被动荷载σ1分别产生的衬砌内力
??Mp?X1p?yX2p?M计算公式为：?0N?Xcos??N?p2pp?0p
0?M??X??yX??M???1?2? ?0??N???X2??cos??N?A10 主、被动荷载作用下衬砌弯矩计算表
截面 yX 2p yX2? ? ? M? Mp 0 X1p Mp M?0 X1?? 0 0 1 (191) 2 (749) 3 (1635) 973.8 973.8 973.8 973.8 0 103 411 915 974 887 636 254 0.000 0.000 0.000 0.000 (2.623) (2.623) (2.623) (2.623) 0.000 0.182 0.725 1.613 (2.623) (2.441) (1.898) (1.010) 4 (2785) 5 (4120) 6 (5519) 7 (6854) 8 (7925) 9 (8625) 10 (8893) 973.8 973.8 973.8 973.8 973.8 973.8 973.8 1602 (209) 2455 (692) 3431 (1114) 4577 (1303) 5829 (1121) 7116 (535) 8362 443 0.000 0.000 (0.140) (1.098) (3.575) (7.292) (11.561) (2.623) (2.623) (2.623) (2.623) (2.623) (2.623) (2.623) 2.825 4.328 6.050 8.071 10.278 12.546 14.744 0.202 1.705 3.287 4.350 4.080 2.631 0.560 A11 主、被动荷载作用下衬砌轴力计算表
截面 0 Np0 39 154 334 566 831 1124 1461 1719 1871 1967 ? cos 0N? X2p Np (?h)X2??cos? N? ?1.79 1.77 1.70 1.59 1.43 1.24 0.96 0.56 0.35 0.44 0.78 0 1 2 3 4 5 6 7 8 9 10 1015 1002 963 899 812 705 566 349 113 (131) (366) 1015 1041 1117 1233 1378 1536 1690 1810 1832 1740 1600 0.00 0.00 0.00 0.00 0.00 0.00 (0.04) (0.05) 0.15 0.67 1.42 1.79 1.77 1.70 1.59 1.43 1.24 1.00 0.62 0.20 (0.23) (0.65)
七最大抗力值的求解
首先求出最大抗力方向内的位移。
??S???hpEh??????S?h?Eh???MIp(yh?yi)sin?hM?I
(yh?yi)sin?hA12 最大位移修正计算表
截面 0 (yh?yi ) Mp M?? I(145.722) MpI(yh? yi) M??I(yh? yi) I54100.000 4.509 243920.448 (657.017) 积分系数1/3 1 1 2 3 4 5 6 7 8 49254.751 35333.865 14118.451 (11628.111) (38445.963) (61877.120) (72378.654) ?hp?(135.591) (105.461) (56.106) 11.198 94.716 182.605 241.659 1.273.35?1074.407 4.104 3.608 2.931 2.091 1.129 0.000 ∑ 217056.944 145004.166 50932.766 (34078.847) (80385.767) (69850.710) 0.000 358828.481 ?6(597.528) (432.792) (202.406) 32.818 198.040 206.136 0.000 (1150.755) 4 2 4 2 4 2 4 ?358828.481?0.939?12773.544?10?1150.755?0.939??40.964?10?6位移值：
?h???1.273.35?107
最大抗力值的求解：
?h??hp1K??h??12773.544?1010.4?106?6?293.888
?6?40.964?10八、计算衬砌总内力 按下式计算衬砌总内力
??M?Mp??hM? ?N?N??N?ph??计算结果列入A13表，计算精度的校核为以下内容。
根据拱顶切开点的相对转角和相对水平位移为零的条件来检查：
?SEh?MI??a?0
?97027.843??3678.369?10?6?6?S式中：Eh?MI??1.273.35?107
?a?M10?0?26.778?138.889?10?3719.169?10?6闭合差：???SEh3719.169?3678.3693719.169?100%?1.1%
?yMI?f?a?0
?S式中：Eh闭合差：???yMI??1.273.35?10?67?446571.456?16929.724?10?6
f?a?17996.241?1017996.24117996.241?16929.724?100%?4.9%
A13 衬砌总内力计算表
截面 M Np Ne M/I My/I M p M ? N ? 0 974 1 886 2 632 3 245 4 (225) 5 (716) 6 (1148) 7 (1348) 8 (1179) 9 (605) 10 361 (771) (723) (582) (351) (36) 355 761 1005 852 349 (334) 203 162 50 (106) (261) (362) (386) (342) (327) (257) 27 1015 1041 1117 1233 1378 1536 1690 1810 1832 1740 1600 467 461 443 414 374 324 248 145 97 138 250 1483 1503 1560 1647 1752 1860 1938 1956 1929 1878 1850 0.137 0.108 0.032 (0.064) (0.149) (0.194) (0.199) (0.175) (0.170) (0.137) 0.014 ∑ 11274 9007 2754 (5902) (14521) (20085) (21457) (19027) (18181) (14251) 1488 (97028) 0 918 1115 (5319) (22914) (48562) (72521) (85788) (104394) (99883) 12254 (446571) 积分系数1/3 1 4 2 4 2 4 2 4 2 4 1
九、衬砌截面强度检算 1、拱顶（截面0） e=0.137<0.45d=0.27(可) α=1-1.53e/d=0.6575
k=αRabd/N=0.6575329.6310^330.6/1482.516=7.88>2.4（可）
Ra为混凝土的极限抗压强度，取29.6Mpa 2、截面7