直墙拱结构的设计计算步骤及实例

1、直墙拱结构的设计计算步骤一、计算步骤1. 计算结构的几何尺寸；2. 计算作用在结构上的荷载；3. 计算拱顶变位；4. 计算侧墙的弹性特征值a及换算长度l=ah，判别侧墙所属类型5. 计算墙顶的单位变位6. 计算墙顶力，7. 计算拱顶未知力，8. 考虑弹性抗力时，计算9. 计算拱圈截面内力10. 计算侧墙截面内力11. 绘制内力图，校核计算结果12. 计算拱圈、侧墙截面的内力和偏心距13. 计算拱圈和侧墙各截面的安全系数14. 计算配筋量15. 绘制结构施工图16. 计算工程量二、计算实例（一）设计基本资料结构断面如图所示。1、岩石特征软质石灰岩，隧道埋深H=50m，岩石坚硬系数，内摩擦角j=6

2、50，容重g=24kN/m3，侧向岩层地基系数K1=2.5×105kPa/m，基底岩层地基系数K2=3.125×105kPa/m。2被覆材料采用C20砼，弹性模量E=2.55×104MPa，容重g=25 kN/m3，砼轴心抗压强度设计值，弯曲抗压强度设计值，抗拉强度设计值。钢筋采用25MnSi钢：强度设计值，弹性模量。3结构尺寸净跨，拱顶砼厚度（预先确定），拱脚厚度，内拱矢高，侧墙厚度，内墙高，底板厚度，墙基埋深（二）结构几何尺寸计算1拱圈内圆几何尺寸内圆净跨：，内圆矢高内圆半径计算：，从而有：2拱圈轴线圆的几何尺寸拱脚截面与拱顶截面厚度之差：轴线圆与内圆的圆心距

3、：轴线圆半径：计算跨度：计算矢高：3拱圈外圆几何尺寸外圆跨度：外圆矢高：外圆半径：外圆与轴线圆的圆心距：4校核公式外圆与轴线的圆心距：5侧墙的几何尺寸拱脚中心到侧墙中心线的垂直距离：侧墙的计算长度（从拱脚中心算起）：结构总高：（三）计算拱顶单位变位采用分块总和法计算变位，将半拱轴线长分10等分，计算过程列于表1，故拱顶单位变位：校核计算：判别： 说明单位变位计算结果正确。表1 变截面圆拱拱顶单位变位计算（见附图）（四）计算拱顶载变位1计算荷载（1）岩石坚固系数，隧道半跨度：（考虑到有一定的间隙）隧道埋深H=50m>(2-2.5)h1，属于深埋因此围岩竖直压力：（采用均布荷载模式）（2）自

4、重计算因此：在实际设计中，外载还应包括超挖回填引起的拱顶荷载，一般取30cm回填高度，可忽略不计。2计算载变位先分别计算在均布荷载和三角形荷载作用下的载变位，然后叠加，计算过程列于表2。表2 变截面圆拱拱顶载变位计算(见附图)2计算载变位先分别计算在均布荷载作用下河三角形荷载作用下的载变位，然后叠加，计算过程列于表2.在均布荷载q作用下的载变位：在三角荷载作用下的载变位：拱顶总载变位：校核计算：，可见计算正确。 , 满足要求！（五）在荷载作用下多余未知力的计算1判别侧墙类型侧墙特征长度：，故侧墙属于长梁2计算墙顶单位变位3由外载引起的墙顶弯矩与水平力4计算多余未知力（六）弹性抗力作用下多余未知

5、力的计算1计算时引起的墙顶截面内力及变位通过积分可得到：因此墙顶内力（要考虑偏心距）：墙顶变位：2计算时的拱顶载变位采用分块总和法计算，将弹性抗力所分布拱轴线长对应圆心角四等分3计算时的多余未知力 4计算弹性抗力根据及从而可求得 5.在弹性抗力作用下多余未知力计算 （七）计算弹性抗力及外载共同作用下的多余未知力 将q=100.06kpa及=35.6kpa代入得 （八）计算拱圈内力1.拱圈任一截面的内力各截面的内力计算见表3（九）计算侧墙内力 侧墙为长梁，其任一截面的弯矩与轴力为现将侧墙分为6等分：侧墙各截面的内力计算见表4附表表1 变截面圆拱拱顶单位变位计算截面号化为弧度0000100.70.

6、34334.98542274116.1927150.1080830.1078730.9941646880.042597780.7033038370.34787959934.494693134212.385430.2161670.2144870.9767268540.169893970.713176790.36273678833.081838982318.578150.324250.3185980.9478900070.380402950.7295036360.38822400230.909989964424.770860.4323330.418990.9079906930.671667940.

7、7520938290.42541821128.207537192530.963580.5404160.5144930.8574945611.040289710.780683730.47580103825.220625954637.156290.64850.6039910.7969909321.48196620.8149396740.54122317522.171999582743.349010.7565830.6864410.7271859211.991542780.8544618750.6238469719.235486564849.541720.8646660.7608790.648894

8、1972.563072360.8987890840.72606143116.527527142955.734440.9727490.8264370.5630294723.189884850.9474039730.85036544714.1115799541061.927151.0808330.882350.4705938433.86466495111211.42857142934.9854227434.9854227001.42857142934.9854227434.985422745.687442311137.1736233137.9787735.877589110.2503722365.

9、621259972143.8563616149.9843232.80435374264.6238409966.16367811.240809861.9097458022.6753404277.4044878290.555043485.483180349117.1970824123.6399647.0330051417.891493784.926612682170.672965235.59746392.65924266651.2243624856.415074437.892196925.45097392.192404994.30727127157.65044215.12371380186.506

10、19827100.882504104.9470304109.17531563.767450984205.8295342419.95188032.45416938635.341765244.343999265.7163079397.389347141.558875006110.0603071273.16596224.68130892255.9511000276.9419462153.2331773305.17042742.475473178230.1751235688.57872822.22521616721.449232933.055054384.7224961217.14988830.936

11、957705117.7775504419.64993484.22206377931.7809416656.4463198180.0572605574.36192761.338403451236.5035803990.922768315.6471261131246.37597938179.22762190.22145856558.37597938283.9795807742.852731737.09585261527.97711427.142808293745.02155表2变截面圆拱拱顶载变位计算截面号x²x³垂直均布载q00.000000 0.000000 0.00000

12、0 0.000000 0.000000 0.000000 0.000000 0.00000010.78747250.6201130.4883219-31.024252748.49979527-4280.688312-182.347810148.0600040621.56575482.4515883.8385856-122.65294733.6035471-8115.170088-1378.71845692.0430594932.32576375.409176612.580466-270.621106874.142769-33459.58278-12728.12391385.353472643.

13、05862959.355214128.614133-468.0413627128.23051-26404.58829-17735.11547309.621234453.755799114.10602752.979404-705.7245338193.349187-71195.25797-74063.69413849.490620264.409136319.44048385.715738-972.6073496266.467767-43129.29949-63916.16408521.197827375.011016125.110282125.82803-1256.267404344.18285

14、-96659.65906-192501.84591171.66104385.554414230.851517171.3621-1543.501374422.877089-51020.5217-130769.2891610.604854596.032988836.396953219.58241-1820.939582498.887557-102785.338-327873.39261185.92873106.441154641.488473267.23367-2075.668308568.676249-24908.0197-96261.15066267.6155412-461958.1254-9

15、17409.84215441.576388垂直均布载q0.0000000.0000000.0000000.0000000.0000000.0000000.000000-4463.036122-0.8996423370.184858014-124.13155-5.2877280021.045234225-129.4192733-9493.888544-7.0718798211.453125991-467.90158-79.49365643.980239392-547.3952354-46187.70668-23.177169094.762432004-2865.6243-1090.0919132

16、4.75251108-3955.716168-44139.70376-52.7162177310.83209953-2973.9893-1997.53330226.15483647-4971.522646-145258.9521-97.604696120.05575947-9846.6061-10243.3230188.11611668-20089.92914-107045.4636-157.915300432.4483494-7002.5959-10377.6105163.46737317-17380.20646-289161.5049-231.814729547.63316359-1783

17、6.276-35521.70754162.1519552-53357.98398-181789.8108-315.702790664.87043643-10435.573-26747.1284593.66836004-37182.70133-430658.7306-404.539743583.12460482-22834.78-72840.31796197.5993503-95675.0977-121169.1704-492.3283243101.1633543-5907.9399-22832.2082147.60685164-28740.1481-1379367.967-80295.418-

18、181734.7023708.5428282-262030.12表3 拱圈各截面的M N值截面号057.8339700057.833970682.774157.8339729.0846550-31.9238950854.99473010678.7898007257.83397115.999180-129.724826844.1083280666.8837007357.83397259.729240-293.798275923.76493610647.1946518457.83397465.59740-520.75758052.673789520619.9524374557.83397750.2

19、8280-803.32922994.787540060585.4749911657.833971050.8480-1130.52265-21.840680544.1646863757.833971389.7740-1488.082134-40.4741640496.50364857.833971754.99120-1859.204164-46.3789940443.0480863957.833972121.652-9.00303-2225.479325-54.9963850.76911384.4218851057.833972464.693-16.80556-2567.996633-62.27

20、522310.08215321.30924040682.7742023.3458890975.39142868.684653287687.47445397588.10536323.2364273887.15539535.05667312701.94037382918.369209495.8133281922.67617978.90520099726.09985282938.295751117.736363773.869031139.0626099759.0150472150.8420348101.3157591832.693134213.4049468798.8799379482.979028

21、6502.4381133509.924315298.9161164843.0808027-968.5030939-1435.28881649.024524391.8160141888.319654-3114.160925-6201.98473024.001723487.7475251930.7956115-1533.060178-3929.34421344.003575582.0121615967.2031565-3104.343553-9902.49852299.183446669.83960311001.230994-747.3026701-2888.0744471566851-21816.65124689.09589表4 侧墙各截面M 、N值截面1100.000001.00000.00