拱壩應(yīng)力計算實例

鋼筋砼拱壩截面初擬尺寸計算計算方案1采用C30砼砌石拱壩加固擬沿原拱壩上游面新建一鋼筋砼拱壩，壩頂高程814.9m，最大壩高20m，壩頂中部有挑流堰，堰頂高程814.1m（計算時從堰頂高程算起），拱圈最大中心角108°，建基面高程794.1m，該拱圈與原拱壩同圓心。新建拱圈采用C30鋼筋砼，熱膨脹系數(shù)為1.0x10-51/℃，C30砼彈性模量3.0x104MPa，抗壓強度設(shè)計值為14.3MPa，抗拉強度設(shè)計值為1.43MPa，基巖彈性模量取1.4x104MPa，淤沙高程為800.7m，浮容重為10KN/m3，淤沙內(nèi)摩擦角15°。方案1-a：從溢流堰堰頂往下0～6.4m，拱厚0.8m；6.4m～19.2m，拱厚1.6m，C30砼。鋼筋砼等效彈性模量3.076x104MPa（假設(shè)按柱最小配筋率，2級鋼HRB335抗拉壓強度設(shè)計值均為300MPa）斷面圖及基本參數(shù)斷面截面分塊高度拱厚拱中心半半中心角上游面與壩軸線圖編號H(米)T(米)徑R(米)FA(度)之距LL(米)0/.837.459.412.1.837.443.422.1.837.438.4如圖132.21.637.8291.242.31.637.8271.252.31.637.8261.262.41.637.8241.272.91.637.8221.282.91.637.8201.2輸入變量水砂總荷載(千牛/米)砼熱膨脹系數(shù)L=.00001P(0)=0砼彈性模量EC=30760000P(1)=21.22基巖彈性模量EF=14000000P(2)=42.44淤砂浮容重RS=10P(3)=65.35淤砂摩擦角FS=15P(4)=88.84正常高水位HG=814.1P(5)=112.32壩頂高程HA=814.1P(6)=136.83建基面高程HI=794.9P(7)=183.88淤砂高程HZ=800.7延長系數(shù)C1=.45梁與拱冠梁間的夾角F=0水砂荷載引發(fā)的內(nèi)力及變位懸臂梁應(yīng)力(水、砂、自重、水重)千牛/米2彎矩(千牛-米)切力(千牛)上游面下游面M(0)=0.0Q(0)=0.0LS(0)=0.0LX(0)=0.0M(1)=-52.76Q(1)=-10.55LS(1)=565.86LX(1)=-444.07M(2)=-167.98Q(2)=-18.41LS(2)=1691.25LX(2)=-1479.23M(3)=-265.22Q(3)=19.37LS(3)=623.36LX(3)=-427.22M(4)=-432.07Q(4)=26.31LS(4)=1177.91LX(4)=-871.44M(5)=-515.92Q(5)=95.48LS(5)=1429.63LX(5)=-1012.76M(6)=-324.1Q(6)=254LS(6)=1037.65LX(6)=-505.58M(7)=638.94Q(7)=604.81LS(7)=-1149.88LX(7)=1821.15拱梁分載(千牛/米)分載圖水砂荷載拱分載扭分載梁分載P=0PD=31.26PH=0PF=-31.2721.2235.582.4-16.7642.4437.581.473.3865.3575.722.53-12.92如圖288.8470.513.115.22112.3259.774.1248.43136.8343.12.8290.9183.8816.641.69165.54拱冠應(yīng)力(千牛/米2)拱冠梁徑向變位(厘米)上游面下游面R=.33GS(1)=1577.4GX(1)=1372.6.37GS(2)=1899.8GX(2)=1444.7.39GS(3)=2069.8GX(3)=1450.9如圖3.38GS(4)=2649.8GX(4)=673.1.35GS(5)=2533GX(5)=472.29GS(6)=2174.1GX(6)=326.2.2GS(7)=1602.5GX(7)=115.6.07GS(8)=627.3GX(8)=-8.1拱座應(yīng)力(千牛/米2)拱座作用力上游面下游面軸向力(千牛)彎矩(千牛-米)剪力ZS(1)=1282.13ZX(1)=1670.07HA(1)=1180.88MA(1)=-20.7VA(1)=-1.5ZS(2)=1232.47ZX(2)=2116.89HA(2)=1339.74MA(2)=-47.17VA(2)=-4.85ZS(3)=1158.33ZX(3)=2368.93HA(3)=1410.9MA(3)=-64.57VA(3)=-7.58ZS(4)=-269.21ZX(4)=3633.66HA(4)=2691.57MA(4)=-832.62VA(4)=-128.31ZS(5)=-513.83ZX(5)=3562.23HA(5)=2438.72MA(5)=-869.56VA(5)=-144.27ZS(6)=-559.27ZX(6)=3098.44HA(6)=2031.34MA(6)=-780.32VA(6)=-134.59ZS(7)=-599.12ZX(7)=2348.56HA(7)=1399.56MA(7)=-628.84VA(7)=-117.75ZS(8)=-314.4ZX(8)=947.06HA(8)=506.13MA(8)=-269.12VA(8)=-55.08溫度荷載引發(fā)的內(nèi)力及變位懸臂梁應(yīng)力(溫度)彎矩(千牛-米)切力(千牛)上游面下游面M(0)=0.0Q(0)=0.0LS(0)=0.0LX(0)=0.0CT(1)=-3450.41M(1)=-19.67Q(1)=67.68LS(1)=184.36LX(1)=-184.37CT(2)=-3450.41M(2)=-53.8Q(2)=61.8LS(2)=504.37LX(2)=-504.38CT(3)=-3450.41M(3)=-29.97Q(3)=127.8LS(3)=70.22LX(3)=-70.23CT(4)=-2897.24M(4)=-106.18Q(4)=131.09LS(4)=248.84LX(4)=-248.85CT(5)=-2897.24M(5)=-91.79Q(5)=176.46LS(5)=215.12LX(5)=-215.13CT(6)=-2897.24M(6)=161.72Q(6)=285.85LS(6)=-379.06LX(6)=379.05CT(7)=-2897.24M(7)=1001.19Q(7)=503.19LS(7)=-2346.55LX(7)=2346.54CT(8)=-2897.24拱梁分載(千牛/米)分載圖溫度當(dāng)量荷載拱分載扭分載梁分載P=73.02PD=81.58PH=0PF=-8.5773.0275.822.89-5.773.0268.15.75-.84120.09121.296.5-7.72如圖4120.09100.362.2117.51120.0976.092.3341.65120.0949.4.4970.19120.0917.13-1.25104.2拱冠應(yīng)力(千牛/米2)梁徑向變位上游面下游面R=.87GS(1)=4116.6GX(1)=3582.8GS(2)=4048.6GX(2)=3078.8.72GS(3)=3751GX(3)=2629.3如圖5.61GS(4)=4244.5GX(4)=1078.1.5GS(5)=3605.3GX(5)=671.9.37GS(6)=2767.7GX(6)=415.3.23GS(7)=1836.6GX(7)=132.5.07GS(8)=645.6GX(8)=-8.3拱座應(yīng)力(千牛/米2)拱座作用力上游面下游面軸向力(千牛)彎矩(千牛-米)剪力ZS(1)=3345.93ZX(1)=4358.33HA(1)=3081.7MA(1)=-54VA(1)=-3.9ZS(2)=2626.46ZX(2)=4511.22HA(2)=2855.07MA(2)=-100.53VA(2)=-10.34ZS(3)=2099.17ZX(3)=4293.08HA(3)=2556.9MA(3)=-117.01VA(3)=-13.74ZS(4)=-431.21ZX(4)=5820.35HA(4)=4311.32MA(4)=-1333.67VA(4)=-205.53ZS(5)=-731.36ZX(5)=5070.33HA(5)=3471.18MA(5)=-1237.7VA(5)=-205.35ZS(6)=-711.99ZX(6)=3944.52HA(6)=2586.03MA(6)=-993.39VA(6)=-171.34ZS(7)=-686.65ZX(7)=2691.69HA(7)=1604.04MA(7)=-720.72VA(7)=-134.95ZS(8)=-323.58ZX(8)=974.73HA(8)=520.92MA(8)=-276.98VA(8)=-56.69最大壓應(yīng)力，發(fā)生在第4拱圈拱座下游面，不滿足規(guī)定。最大拉應(yīng)力，發(fā)生在懸臂梁最底層拱圈上游面。方案1-b：從溢流堰堰頂往下0～6.4m，拱厚0.8m；6.4m～19.2m，拱厚2.2m，C30砼。鋼筋砼等效彈性模量3.077x104MPa斷面圖及基本參數(shù)斷面截面分塊高度拱厚拱中心半半中心角上游面與壩軸線圖編號H(米)T(米)徑R(米)FA(度)之距LL(米)0/.837.459.412.1.837.443.422.1.837.438.4如圖132.22.238.1291.842.32.238.1271.852.32.238.1261.862.42.238.1241.872.92.238.1221.882.92.238.1201.8輸入變量水砂總荷載(千牛/米)砼熱膨脹系數(shù)L=.00001P(0)=0砼彈性模量EC=30770000P(1)=21.22基巖彈性模量EF=14000000P(2)=42.44淤砂浮容重RS=10P(3)=65.84淤砂摩擦角FS=15P(4)=89.51正常高水位HG=814.1P(5)=113.17壩頂高程HA=814.1P(6)=137.86建基面高程HI=794.9P(7)=185.27淤砂高程HZ=800.7延長系數(shù)C1=.45梁與拱冠梁間的夾角F=0水砂荷載引發(fā)的內(nèi)力及變位懸臂梁應(yīng)力(水、砂、自重、水重)千牛/米2彎矩(千牛-米)切力(千牛)上游面下游面M(0)=0.0Q(0)=0.0LS(0)=0.0LX(0)=0.0M(1)=-49.1Q(1)=-8.6LS(1)=531.54LX(1)=-409.75M(2)=-138.94Q(2)=-5.69LS(2)=1419LX(2)=-1206.98M(3)=-170.41Q(3)=50.27LS(3)=197.58LX(3)=-34.56M(4)=-308.19Q(4)=57.77LS(4)=530.59LX(4)=-257.3M(5)=-336.05Q(5)=140.03LS(5)=620.32LX(5)=-236.64M(6)=-31.78Q(6)=319.89LS(6)=300.72LX(6)=198.16M(7)=1143.77Q(7)=695.16LS(7)=-1086.96LX(7)=1725.05拱梁分載(千牛/米)分載圖水砂荷載拱分載扭分載梁分載P=0PD=29.4PH=0PF=-29.4121.2230.452.55-11.7942.4429.385.547.5265.8476.076.59-16.82如圖289.5165.573.0420.88113.1751.653.5757.94137.8635.21.53101.12185.2712.92-.34172.68拱冠應(yīng)力(千牛/米2)拱冠梁徑向變位(厘米)上游面下游面R=.31GS(1)=1483.7GX(1)=1291.32GS(2)=1626GX(2)=1236.5.31GS(3)=1618.1GX(3)=1134.2如圖3.27GS(4)=2060.7GX(4)=232.8.22GS(5)=1804.4GX(5)=78.8.17GS(6)=1428.6GX(6)=10.1.11GS(7)=976GX(7)=-68.2.03GS(8)=353.4GX(8)=-53.6拱座應(yīng)力(千牛/米2)拱座作用力上游面下游面軸向力(千牛)彎矩(千牛-米)剪力ZS(1)=1205.96ZX(1)=1570.86HA(1)=1110.73MA(1)=-19.47VA(1)=-1.41ZS(2)=1054.87ZX(2)=1811.86HA(2)=1146.69MA(2)=-40.38VA(2)=-4.16ZS(3)=905.54ZX(3)=1851.95HA(3)=1103MA(3)=-50.48VA(3)=-5.93ZS(4)=-631.48ZX(4)=2977.41HA(4)=2580.53MA(4)=-1455.59VA(4)=-222.55ZS(5)=-740.07ZX(5)=2672.83HA(5)=2126.04MA(5)=-1376.54VA(5)=-226.59ZS(6)=-664.13ZX(6)=2143.66HA(6)=1627.48MA(6)=-1132.48VA(6)=-193.8ZS(7)=-566.06ZX(7)=1503.94HA(7)=1031.67MA(7)=-834.91VA(7)=-155.1ZS(8)=-248.21ZX(8)=559.79HA(8)=342.75MA(8)=-325.9VA(8)=-66.18溫度荷載引發(fā)的內(nèi)力及變位懸臂梁應(yīng)力(溫度)彎矩(千牛-米)切力(千牛)上游面下游面M(0)=0.0Q(0)=0.0LS(0)=0.0LX(0)=0.0CT(1)=-3450.41M(1)=-5.21Q(1)=74.7LS(1)=48.84LX(1)=-48.85CT(2)=-3450.41M(2)=13.44Q(2)=87.31LS(2)=-126.02LX(2)=126.01CT(3)=-3450.41M(3)=161.85Q(3)=202.94LS(3)=-200.65LX(3)=200.64CT(4)=-2586.27M(4)=142.34Q(4)=221.48LS(4)=-176.46LX(4)=176.45CT(5)=-2586.27M(5)=274.75Q(5)=296.6LS(5)=-340.61LX(5)=340.6CT(6)=-2586.27M(6)=763.41Q(6)=452.03LS(6)=-946.39LX(6)=946.38CT(7)=-2586.27M(7)=2074.13Q(7)=736.15LS(7)=-2571.25LX(7)=2571.24CT(8)=-2586.27拱梁分載(千牛/米)分載圖溫度當(dāng)量荷載拱分載扭分載梁分載P=73.02PD=74.9PH=0PF=-1.8873.0267.012.933.0773.0257.8314.24.93145.14140.1315.17-10.16如圖4145.14112.482.4730.18145.1482.091.7861.27145.1451.62-1.6395.14145.1417.29-4.93132.77拱冠應(yīng)力(千牛/米2)梁徑向變位上游面下游面R=.8GS(1)=3779.3GX(1)=3288.5.71GS(2)=3578.4GX(2)=2721.3.61GS(3)=3185.5GX(3)=2232.9如圖5.5GS(4)=3796.1GX(4)=428.9.39GS(5)=3095.1GX(5)=135.2.28GS(6)=2270.5GX(6)=16.1.16GS(7)=1431.3GX(7)=-100.05GS(8)=473GX(8)=-71.7拱座應(yīng)力(千牛/米2)拱座作用力上游面下游面軸向力(千牛)彎矩(千牛-米)剪力ZS(1)=3071.78ZX(1)=4001.23HA(1)=2829.2MA(1)=-49.58VA(1)=-3.58ZS(2)=2321.43ZX(2)=3987.3HA(2)=2523.49MA(2)=-88.85VA(2)=-9.14ZS(3)=1782.69ZX(3)=3645.83HA(3)=2171.41MA(3)=-99.37VA(3)=-11.67ZS(4)=-1163.27ZX(4)=5484.81HA(4)=4753.7MA(4)=-2681.4VA(4)=-409.97ZS(5)=-1269.43ZX(5)=4584.66HA(5)=3646.76MA(5)=-2361.15VA(5)=-388.66ZS(6)=-1055.48ZX(6)=3406.84HA(6)=2586.51MA(6)=-1799.81VA(6)=-307.99ZS(7)=-830.12ZX(7)=2205.51HA(7)=1512.94MA(7)=-1224.37VA(7)=-227.45ZS(8)=-332.2ZX(8)=749.24HA(8)=458.74MA(8)=-436.18VA(8)=-88.57最大壓應(yīng)力，發(fā)生在第4拱圈拱座下游面，滿足規(guī)定。最大拉應(yīng)力，發(fā)生在懸臂梁最底層拱圈上游面。計算方案2采用C25砼砌石拱壩加固擬沿原拱壩上游面新建一鋼筋砼拱壩，壩頂高程814.9m，最大壩高20m，壩頂中部有挑流堰，堰頂高程814.1m（計算時從堰頂高程算起），拱圈最大中心角108°，建基面高程794.1m，該拱圈與原拱壩同圓心。新建拱圈采用C25鋼筋砼，熱膨脹系數(shù)為1.0x10-51/℃，C25砼彈性模量2.8x104MPa，抗壓強度設(shè)計值為11.9MPa，抗拉強度設(shè)計值為1.27MPa，基巖彈性模量取1.4x104MPa，淤沙高程為800.7m，浮容重為10KN/m3，淤沙內(nèi)摩擦角15°。方案2-a：從溢流堰堰頂往下0～6.4m，拱厚1.2m；6.4m～19.2m，拱厚2.6m，C25砼。鋼筋砼等效彈性模量2.878x104MPa斷面圖及基本參數(shù)斷面截面分塊高度拱厚拱中心半半中心角上游面與壩軸線圖編號H(米)T(米)徑R(米)FA(度)之距LL(米)0/1.237.659.612.11.237.643.622.11.237.638.6如圖132.22.638.329242.32.638.327252.32.638.326262.42.638.324272.92.638.322282.92.638.3202輸入變量水砂總荷載(千牛/米)砼熱膨脹系數(shù)L=.00001P(0)=0砼彈性模量EC=28780000P(1)=21.33基巖彈性模量EF=14000000P(2)=42.67淤砂浮容重RS=10P(3)=66.17淤砂摩擦角FS=15P(4)=89.95正常高水位HG=814.1P(5)=113.73壩頂高程HA=814.1P(6)=138.54建基面高程HI=794.9P(7)=186.18淤砂高程HZ=800.7延長系數(shù)C1=.45梁與拱冠梁間的夾角F=0水砂荷載引發(fā)的內(nèi)力及變位懸臂梁應(yīng)力(水、砂、自重、水重)千牛/米2彎矩(千牛-米)切力(千牛)上游面下游面M(0)=0.0Q(0)=0.0LS(0)=0.0LX(0)=0.0M(1)=-60.76Q(1)=-13.85LS(1)=324.4LX(1)=-202.61M(2)=-177.1Q(2)=-17.41LS(2)=854.32LX(2)=-642.34M(3)=-246.43Q(3)=34.38LS(3)=214.17LX(3)=-27.41M(4)=-377.52Q(4)=65.42LS(4)=495.51LX(4)=-198.48M(5)=-354.45Q(5)=168.45LS(5)=530.23LX(5)=-122.8M(6)=43.46Q(6)=366.04LS(6)=234.66LX(6)=287.97M(7)=1374.19Q(7)=756.15LS(7)=-876.87LX(7)=1538.7拱梁分載(千牛/米)分載圖水砂荷載拱分載扭分載梁分載P=0PD=34.52PH=0PF=-34.5321.3333.692.8-15.1742.6731.66.374.6966.17667.6-7.44如圖289.9557.043.529.39113.7344.743.8165.17138.5430.471.27106.79186.1811.16-.97175.98拱冠應(yīng)力(千牛/米2)拱冠梁徑向變位(厘米)上游面下游面R=.26GS(1)=1208.6GX(1)=982.25GS(2)=1274.6GX(2)=845.5.24GS(3)=1244.6GX(3)=729如圖3.21GS(4)=1549.3GX(4)=61.8.17GS(5)=1347.8GX(5)=-38.8.13GS(6)=1056.5GX(6)=-68.3.08GS(7)=711.1GX(7)=-99.2.02GS(8)=252.5GX(8)=-55拱座應(yīng)力(千牛/米2)拱座作用力上游面下游面軸向力(千牛)彎矩(千牛-米)剪力ZS(1)=882.54ZX(1)=1311.69HA(1)=1316.54MA(1)=-51.5VA(1)=-3.7ZS(2)=646.5ZX(2)=1480.48HA(2)=1276.19MA(2)=-100.08VA(2)=-10.24ZS(3)=486.6ZX(3)=1495.22HA(3)=1189.09MA(3)=-121.04VA(3)=-14.13ZS(4)=-637.82ZX(4)=2299.12HA(4)=2159.69MA(4)=-1654.48VA(4)=-251.64ZS(5)=-693.25ZX(5)=2049.04HA(5)=1762.54MA(5)=-1544.83VA(5)=-252.96ZS(6)=-600.16ZX(6)=1626.36HA(6)=1334.06MA(6)=-1254.28VA(6)=-213.52ZS(7)=-483.48ZX(7)=1122.89HA(7)=831.25MA(7)=-904.93VA(7)=-167.23ZS(8)=-201.24ZX(8)=409.17HA(8)=270.32MA(8)=-343.87VA(8)=-69.46溫度荷載引發(fā)的內(nèi)力及變位懸臂梁應(yīng)力(溫度)彎矩(千牛-米)切力(千牛)上游面下游面M(0)=0.0Q(0)=0.0LS(0)=0.0LX(0)=0.0CT(1)=-2946.98M(1)=-1.02Q(1)=98.31LS(1)=4.21LX(1)=-4.22CT(2)=-2946.98M(2)=41.74Q(2)=122.67LS(2)=-173.93LX(2)=173.92CT(3)=-2946.98M(3)=238.6Q(3)=238.35LS(3)=-211.79LX(3)=211.78CT(4)=-2258.2M(4)=287.8Q(4)=275.83LS(4)=-255.45LX(4)=255.44CT(5)=-2258.2M(5)=524.83Q(5)=368.45LS(5)=-465.83LX(5)=465.82CT(6)=-2258.2M(6)=1165.61Q(6)=540.67LS(6)=-1034.57LX(6)=1034.56CT(7)=-2258.2M(7)=2713.13Q(7)=841.01LS(7)=-2408.11LX(7)=2408.1CT(8)=-2258.2拱梁分載(千牛/米)分載圖溫度當(dāng)量荷載拱分載扭分載梁分載P=92.57PD=91.51PH=0PF=1.0592.5780.973.897.7192.5769.4118.334.82148.26134.919.24-5.89如圖4148.26107.992.637.66148.26