主梁纵向预应力筋的估算与布置

第四章 主梁纵向预应力筋的估算与布置4.1 PRBP程序估算一、数据信息1、 材料信息： (1) 混凝土本设计中上部结构采用C50混凝土，根据桥规第2.1.3条： C50混凝土的抗压弹性模量为3.5104MPa； C50混凝土的抗弯压弹性模量为3.5104 MPa； C50混凝土的容重(含钢筋的平均容重)为2.6 t/m3。(2) 纵向预应力钢束本设计选定的预应力钢筋为1275的钢绞线，其，张拉控制应力=0.75R=1395Mpa，张拉时混凝土强度要达到80%的设计强度。初定预应力钢束的参数指标如下：a) 单束孔道的面积A1：A1=3.140.0922/4=0.006644(m2)b) 单根钢束的面积A2：A2=0.00167976m2c) 预应力钢束的弹性模量Eg：Eg=1.9105 Mpad) 预应力钢束的标准强度R：R=1860MPae) 张拉控制应力：=0.75R=0.751860=1395Mpaf) 钢束松弛终极值与控制应力比值为：0.045g) 孔道摩阻系数：0.35h) 孔道偏差系数：0.006i) 锚具变形与钢束回缩系数值（一端）：0.0062、荷载信息： (1) 恒载： a) 一期恒载：程序按截面尺寸信息自动计入 b) 二期恒载：含铺装层和栏杆重，按 3.2786t/m计入 (2)活载： 采用汽超20级，六车道，按规范，每列可布一辆重车和六辆标准车；采用挂120级时，全桥只布一辆挂车。3、温度变化的影响： 本设计估索阶段只考虑了一种情况的温度变化影响，按上下缘温差为5C的情况考虑。4、基础的不均匀沉降影响：本设计估索阶段不考虑，同时不计水平强迫位移和转角强迫位移。5、 收缩徐变的影响：本设计在估索阶段不考虑收缩徐变的影响 与环境有关的基本徐变系数：0 与材料有关的基本徐变系数：2 收缩速度系数：0.00625 收缩终极值：0.0015二、填卡注意事项本设计用PRBP程序对桥梁进行估索与成桥检算时，共填有二张卡，第一张卡用来估算一次成桥顶、底板的预应力钢筋数目，第二张卡为成桥检算卡。二张卡间既有区别又有联系，在填卡时注意如下几个方面：(1) 节点及单元控制信息是PRBP程序的控制信息，一次成桥填卡时，应对应填使用阶段纵向加载、估索，而在成桥检算时填全面进行成桥检算(2) 梁元坐标指整体坐标系下的端截面坐标值，单元上、下缘按I端到J端的局部坐标定义；(3) 一次成桥时可以先不考虑施工阶段及收缩徐变的因素，安装时视为一次施工完毕,在运营阶段的荷载信息填写荷载组合时可不考虑特载。4 估索时，不必要过分追求数据的可靠性，估索的结果可能不太准确，底板索用一次成桥的数据，顶板索用施工成桥的数据。5 填卡时输入数据繁多，易出错，为了避免出错和检查方便，可将整体坐标定义在结构的对称部位，Y坐标一般为正值较好。三、填写估索数据卡本设计在填写估索数据卡时，将支座处横隔板重量换算成集中力，作为运营阶段的集中荷载作用在支座单元上，考虑以下五种荷载组合： 第一种：汽车+二期恒载+第一组集中力+第一组强迫位移+第一组温度力 第二种：挂车+二期恒载第三种：汽车+二期恒载+第一组集中力+第二组强迫位移+第二组温度力第四种：满人+二期恒载+第一组集中力+第一组强迫位移+第一组温度力第五种：挂车+二期恒载+第一组集中力+第一组强迫位移+第一组温度力 其中汽车荷载为汽-超20，挂车荷载为挂-120，满布人群荷载集度为0.35t/m12 m=4.2 t/m, 数据卡的具体填写及估索结果参见附录一。3.2 估索阶段结构内力分析 本设计的内力分析计算由PRBP程序完成。PRBP程序是一个桥梁分析专用程序，在本设计中我们要用此程序进行估索、全面成桥检算，故需填两个数据卡，分别对以上两个阶段进行内力分析。两张卡既有联系又有区别，估束按一次成桥进行。结构内力主要有恒载内力、活载内力和结构次内力组成。其中恒载内力包括一期恒载产生的内力和二期恒载产生的内力。结构的内力与施工有密切的关系，预应力混凝土连续梁有各种不同的施工方法。它的施工方案是由桥址的地形、水流条件、施工设备等因素所决定的。一般说来，除满堂支架施工方法外，采用其他的施工方法的结构都面临着体系转换这一共同的问题。例如采用悬臂拼装或悬臂浇筑施工的连续梁，结构可能会经过悬臂刚构、单跨固定梁或悬臂梁、连续刚构等不同体系最后才形成多跨连续梁。从设计角度考虑考虑，在选择体系转换次序时应该使最终的连续梁体系的恒载内力分布最合理。结构的活载内力包括汽车、挂车和人群荷载所产生的内力。一、结构自重（一期恒载）引起的内力计算由于本设计采用悬臂施工法，结构自重引起的内力应按悬臂梁计算。而PRBP程序计算的结构自重引起的内力则是按一次成桥后的连续梁计算而得，故结构自重引起的内力不应采用PRBP程序的计算结果。结构自重引起的内力在施工阶段估索程序中已有计算，悬臂段的内力如下表所式：表4-1 结构自重产生的内力截 面 号弯矩值M（tm）截 面 号弯矩值M（tm）93924.58518-14078.01103601.48419-18107.73112867.343-20-21946.35121714.84121-26156.8813134.27222-30756.6614-1887.62123-32379.3615-4037.70924-35760.716-6590.41825-37519.1117-9589.466图4-1 结构自重产生的弯矩图二、二期恒载引起的内力计算由PRBP程序计算的二恒引起的内力如下表所示：表4-2 二期恒载产生的内力截面号剪力（t)弯矩（tm)截面号剪力(t)弯矩（tm)10044-4.9181187.839256.746-0.5945-18.0321141.938354.77932.86846-31.1471043.58447.402147.82247-44.261892.765537.567275.27548-57.375689.491627.731373.22149-70.49433.761717.895441.65950-83.604125.57288.059480.5951-95.079-187.1249-5.055486.59852-106.554-539.98410-18.17440.14853-118.03-933.00611-31.284341.24154-129.505-1366.1912-44.398189.87655-140.98-1839.5413-57.513-13.94756-150.816-2277.2314-70.627-270.22757-160.651-2744.4315-82.102-537.50458-170.487-3241.1416-93.577-844.94459-173.766-3413.2717-105.053-1192.54660-180.323-3767.3618-116.528-1580.31261170.625-3949.3219-128.003-2008.2462167.346-3780.3320-137.839-2407.00263160.789-3452.221-147.674-2835.27164157.51-3293.0522-157.51-3293.04865147.674-2835.2723-160.789-3452.19866137.839-240724-167.346-3780.33267128.003-2008.2425183.602-3949.31868116.528-1580.3126180.323-3767.35569105.053-1192.5527173.766-3413.2677093.577-844.94428170.487-3241.147182.102-537.50429160.651-2744.4327270.627-270.22730150.816-2277.2327357.513-13.94731140.98-1839.5397444.398189.87632129.505-1366.1917531.284341.24133118.03-933.0067618.17440.14834106.554-539.984775.055486.5983595.079-187.12478-8.059480.593683.604125.57279-17.895441.6593770.49433.76180-27.731373.2213857.375689.49181-37.567275.2753944.261892.76582-47.402147.8224031.1471043.5883-54.77932.8684118.0321141.938841.967-0.59424.9181187.8398558.71404301191.527图4-2 二期恒载产生的剪力图 图4-3 二期恒载产生的弯矩图三、活载内力计算活载内力为基本可变荷载（包括汽车、履带车、挂车及人群等）在桥梁使用阶段所产生的内力。很显然，不管采用何种施工方法，这时结构已成为最终体系连续梁桥，因此力学计算图式已十分明确。当采用T形或箱形截面且肋数较多时，应根据结构空间受力特点进行活载内力计算；当采用单箱单室截面时，可直接按平面杆系结构进行活载内力分析。在本设计中采用的是单箱双室截面，故只需按平面杆系结构计算。连续梁桥为超静定结构，活载内力计算以影响线为基础。对于等截面连续梁或按某种规律变化的连续梁可先计算绘制影响线，然后进行影响线加载；如进行手工计算，一般将车辆荷载的最大轮载质量置于影响线的最大竖向坐标处即可求的最大活载内力；如编程电算，则可采用动态规划法进行计算。 直接在影响线上加载时：式中：主梁最大活载内力；汽车冲击系数汽车荷载折减系数荷载横向分布系数车队各轮载质量；主梁内力影响线坐标。 汽车活载产生的内力在PRBP程序的输出结果中含有汽车活载产生的内力项，但结果不明朗。在本设计中，将汽车活载、挂车活载和人群活载产生的内力项从PRBP挑出，并列表如下：表4-3 汽车活载产生的内力截面编号MAX-Q(t)MIN-Q(t)MAX-M(tm)MIN-M(tm)10-43.680020-43.680-26.2082168.326-57.490-26.2083164.927-57.33399.445-46.6274155.557-58.65440.498-181.4795146.704-61.156829.315-352.8046130.784-63.9741164.753-524.1297120.074-66.7591442.222-695.4538109.535-63.0571696.187-866.778996.073-73.0581989.789-1095.2121083.313-82.7652175.67-1323.6451171.445-94.5612257.14-1552.0781261.719-107.2372293.965-1780.5111352.603-119.3892248.65-2008.9451444.041-130.9532150.414-2237.3781536.763-141.6152015.316-2437.2571630.452-152.1871839.8-2637.1361725.485-165.041599.963-2837.0151820.769-175.6461318.645-3037.4031916.272-187.4491051.657-3317.5752012.581-196.443870.562-3599.3272113.51-209.455865.228-3932.1212212.263-216.803822.687-4314.1542311.842-221.345807.553-4448.842411.489-227.55775.352-4728.9112511.489-233.944778.036-4893.32525246.973-21.354778.036-4893.32526246.973-21.354756.682-4692.19527237.897-21.782751.566-4289.93528234.899-22.047748.855-4093.24429225.715-22.871739.462-3516.39530216.332-23.74603.798-3021.47231207.13-24.655705.417-2569.90232195.931-25.842816.053-2062.47633186.516-26.998957.952-1743.69934175.107-27.9271098.709-1461.82635165.445-32.1851295.15-1229.86936153.942-37.0931444.249-1043.14237142.754-42.9371647.688-883.31438131.516-49.2071877.359-815.40239120.297-55.9222088.724-779.9640109.185-64.0482254.518-744.5184198.533-72.7282371.513-709.0764288.876-81.8312423.748-674.5774385.723-84.9482441.696-661.2194481.842-88.8952419.242-671.0694572.773-98.592369.951-706.0734664.13-109.4792269.116-741.0764756.22-120.6442115.872-776.084849.521-131.9071900.924-811.0844943.265-143.1941663.879-886.5575037.434-154.6041467.476-1043.1425132.859-164.3671306.925-1229.7555228.469-175.8471148.419-1460.2495327.287-185.41995.349-1739.955426.143-197.303853.661-2057.6185524.922-208.193745.79-2549.6245624.016-220.599646.505-3006.7895723.156-228.207787.623-3503.9775822.341-237.853798.527-4068.4165922.078-243.191801.744-4269.0066021.976-247.065811.264-4675.1366121.976-250.622833.241-4878.20161228.862-14.714833.241-4878.20162222.428-14.714823.737-4715.94363218.321-15.483849.718-4438.67964214.687-15.907861.957-4305.90565203.589-17.211895.447-3924.11966194.891-16.089889.774-3590.27667185.851-19.781062.634-3308.85668175.702-24.2771311.77-3029.79969163.363-28.9931597.153-2816.74970152.261-33.961835.653-2631.61871139.945-40.5732010.211-2446.48772130.765-47.4142158.368-2261.35673119.21-55.972251.586-2049.77774107.064-65.082285.615-1838.1997594.391-74.7982255.629-1626.627682.31-86.5222178.225-1415.0427772.603-99.2631988.102-1203.4647862.602-112.7081690.983-991.8857966.299-123.2261431.968-883.2018063.509-134.1281158.706-674.5178160.689-143.96832.344-515.8348257.85-155.023442.032-357.158356.99-164.38998.679-42.3248454.99-167.7640-26.2088443.6800-26.2088543.68000图4-4 汽车活载产生的剪力包络图图4-5 汽车活载产生的弯矩包络图 挂车活载产生的内力由PRBP程序计算的挂车活载内力如下表所示：表4-4 挂车活载产生的内力截面编号MAX-Q（t）MIN-Q（t）MAX-M(tm)MIN-M(tm)10-30002112.393-300-182112.393-26.90-183110.982-26.966.632-17.7864105.69-26.9301.416-76.665598.692-26.9577.752-157.364691.795-26.9812.989-238.64785.038-26.91008.488-318.764878.448-27.2391168.359-399.464969.958-36.2481330.45-507.0631061.869-44.9471432.654-614.6631154.222-53.2841480.744-72.2631247.036-61.2011480.67-89.8621340.305-68.0671438.062-937.4641434.017-75.6691367.115-1045.061528.851-81.4241276.822-1139.211623.968-86.8541161.348-1233.361719.343-91.9711023.376-1327.511814.949-96.81864.504-1421.661910.774-101.39568.25-1515.81207.347-105.144519.271-1596.51216.716-108.73418.773-1677.21226.716-112.175438.922-1757.91236.716-113.292445.639-1784.81246.716-115.482459.072-1838.07256.716-116.568465.788-1865.5125117.838-12.844465.788-1865.5126117.158-112.844458.944-1789.0727115.755-12.844427.257-1638.8128115.038-12.844414.413-1556.2829112.805-12.844375.881-1353.1530110.448-12.844328.094-1150.1131107.951-12.844455.277-957.0832104.859-12.844595.738-760.80133101.557-12.844728.717-715.8483498.032-15.67853.289-670.8943594.266-19.008968.77-625.9413690.259-22.571074.637-580.9873795.38-26.9371180.606-535.6123880.201-31.6281276.384-478.2363976.76-36.6291353.87-426.8614069.115-41.9181413.328-375.4854163.336-47.4491453.054-324.114257.503-53.1571471.91-272.7344355.32-55.321472.584-253.4694453.157-57.5031471.91-272.7344547.449-63.3361453.054-324.114641.918-69.1151413.328-375.4854736.629-74.761353.87-426.8614831.628-80.2011276.384-478.2364926.937-85.381180.606-535.6125022.57-90.2591074.637-580.9875119.008-94.266968.77-625.9415215.67-98.032853.289-670.8945312.844-101.557728.717-715.8485412.844-104.859595.738-760.8015512.844-107.951455.277-957.085612.844-110.448328.094-1150.115712.844-112.805375.881-1353.155812.844-115.038414.413-1556.285912.844-115.755427.257-1638.816012.844-117.158458.944-1789.076112.844-117.838465.788-1865.5161116.568-6.716465.788-1865.5162115.492-6.716459.072-1838.0763113.292-6.716445.639-1784.8164112.175-6.716438.922-1757.9165108.73-6.716418.773-1677.2166105.144-7.734519.271-1596.5167101.395-10.77468.25-1515.816896.81-14.949864.504-1421.666991.971-19.3431023.376-1327.517086.854-23.9681161.348-1233.367181.424-28.8511276.822-1139.217275.669-34.0171367.115-1045.067368.667-40.3051438.062-937.4647461.201-47.0361480.67-89.8627553.284-54.2221480.744-72.2637640.947-61.8691432.654-614.6637736.248-69.9581330.45-507.0637827.239-78.4481168.359-399.4647926.9-85.0381008.488-318.7648026.9-91.795812.989-238.648126.9-98.692577.752-157.3648226.9-105.69301.416-76.6658326.9-110.98266.632-17.7868426.9-112.9330-18843000-188530000 图4-6 挂车活载产生的剪力包络图图4-7 挂车活载产生的弯矩包络图(三)人群活载产生的内力由PRBP程序计算的人群活载内力如下表所示：表4-5 人群活载产生的内力截面编号MAX-Q(t)MIN-Q(t)MAX-M(tm)MIN-M(tm)10-0.0420020-2.4780-0.7312134.177-61.45979.793-37.6133131.675-61.45979.793-37.6134122.55-61.78365.522-175.8285111.034-62.86713.355-360.1156100.258-64.681023.359-544.401790.214-67.2311295.562-728.688880.891-70.5031529.977-912.974969.55-75.9561783.744-1158.691059.415-82.6151970.281-1404.411150.43-90.4252089.618-1650.11242.536-99.3252141.756-18951335.667-109.2522126.693-2141.551429.759-120.1392044.421-2387.271525.328-130.4041917.308-2602.271621.544-141.3161738.754-2817.271718.371-152.841508.749-3032.271815.778-164.9431250.564-3270.541913.733-177.5961039.265-3607.162012.396-188.856897.775-3976.262111.427-200.485794.166-4421.032210.81-212.466733.987-4947.082310.682-216.536723.99-5140.892410.536-224.789721.067-5558.162510.518-228.97728.638-5782.1425255.246-20.088728.638-5782.1426251.058-20.099709.896-5530.2827242.75-20.19680.802-5047.5928238.631-20.271670.56-4816.8229226.421-20.659654.716-4164.643024.437-21.275660.802-3572.2331202.694-22.129687.668-3038.3832189.314-23.448743.309-2487.6433176.303-25.134926.217-1612.1534163.685-27.214926.217-1612.1535151.486-29.7131052.214-1280.1136139.736-32.661201.217-1034.5437126.896-36.6161403.383841.89638114.725-41.2421681.789-792.70239103.268-46.5811942.189-792.7024092.564-52.6732135.389-792.7024182.644-59.552261.389-792.7024273.53-67.2332320.14-792.7024370.323-70.3232324.816-792.7024467.233-73.532320.14-792.7024559.55-82.6442261.389-792.7024652.673-92.5642135.389-792.7024746.581-103.2681942.189-792.7024841.242-114.7251681.789-792.7024936.616-126.8961403.383841.8965032.66-139.7361201.217-1034.545129.713-151.7861052.214-1280.115227.214-163.685926.217-1612.155325.134-176.303743.309-2487.645423.448-189.314687.668-3038.385522.129-202.694660.802-3572.235621.275-214.437654.716-4164.645720.659-226.421670.56-4816.825820.271-238.631680.802-5047.595920.192-242.75709.896-5530.286020.099-251.058728.638-5782.146120.088-255.246728.638-5782.1461228.97-10.518728.638-5782.1462224.789-10.536721.067-5558.1663216.536-10.682723.99-5140.8964212.466-10.81733.987-4947.0865200.485-11.427794.166-4421.0366188.856-12.396897.775-3976.2667177.596-13.7331039.265-3607.1668164.943-15.7781250.564-3270.5469152.84-18.3711508.749-3032.2770141.316-21.5441738.754-2817.2771130.404-25.3281917.308-2602.2772120.139-29.7592044.421-2387.2773109.252-35.6672126.693-2141.557499.325-42.5362141.756-18957590.425-50.432089.618-1650.17682.615-59.4151970.281-1404.417775.956-69.551783.744-1158.697870.503-80.8911529.977-912.9747967.231-90.2141295.562-728.6888064.68-100.2581023.359-544.4018162.86-111.034713.355-360.1158261.78-122.55365.522-175.8288361.459-131.67579.793-37.6138461.444-134.17779.793-37.613842.47800-0.731850.042000 图4-8 人群活载产生的剪力包络图图4-9 人群活载产生的弯矩包络图四、估索阶段的组合内力 在本设计估索阶段考虑五种荷载组合，将运营阶段各种荷载组合的最大组合内力挑出，如下表所示： 表4-7 估索阶段的组合内力截面编号Max-Q（t）Min-Q（t）Max-M(tm)Min-M(tm)100001-41.75-41.75-12.52-12.522555.06528.02-12.52-12.522513.31486.27307.99291.763513.31486.27307.99291.763449.07422.031390.661313.614449.07422.031390.661313.614363.41336.372609.372451.215363.41336.372609.372451.215277.75250.723571.113331.846277.75250.723571.113331.846192.09165.064275.883955.57192.09165.064275.883955.57106.4479.44723.684322.198106.4479.44723.684322.198-7.9-34.934920.834411.29-7.9-34.934920.834411.29-123.02-150.064659.434041.6610-123.02-150.064659.434041.6610-239.73-266.773934.533208.6111-239.73-266.773934.533208.6111-358.52-385.552738.811904.7512-358.52-385.552738.811904.7512-480.17-507.211062.57120.3713-480.17-507.211062.57120.3713-605.49-632.53-1107.46-2157.814-605.49-632.53-1107.46-2157.814-724.25-751.29-3430.19-4575.1615-724.25-751.29-3430.19-4575.1615-858.86-885.9-6195.71-7435.3116-858.86-885.9-6195.71-7435.3116-998.2-1025.23-9447.73-1078217-998.2-1025.23-9447.73-1078217-1136.74-1163.77-13182.2-1461118-1136.74-1163.77-13182.2-1461118-1281.39-1308.42-17412-18935.519-1281.39-1308.42-17412-18935.519-1410.68-1437.71-21448.8-23053.420-1410.68-1437.71-21448.8-23053.420-1545.46-1572.5-25881.6-27567.321-1545.46-1572.5-25881.6-27567.321-1685.98-1713.02-30727.3-32494.122-1685