陈康非线性动力反应分析.doc

钢筋混凝土非线性动力反应分析已知：结构为一栋七层钢筋混凝土框架结构。结构平面及尺寸如图1所示。首层层高为3.75米，其余均为3米。柱截面尺寸皆为500mm500mm；所有主梁及主梁悬挑部分的截面尺寸皆为300mm500mm；沿轴线14方向的次梁及搭在主梁悬挑部分的次梁截面尺寸皆为300mm450mm；楼板厚皆为120mm。混凝土强度等级为：15层采用C40；6、7层采用C30。加载方向沿B轴线方向。抗震设防为8度，三类场地，设计地震分组为一组。图1 七层框架结构求：（1） 试采用基底剪力法，分别计算取中间B轴线一榀平面框架、以及A、B、C轴线三榀框架的三维整体结构时， B轴线框架中产生的地震作用以及地震内力（弯矩、剪力、轴力），并画出相应的荷载和内力对比图；（2） 采用SAP2000程序，计算该结构沿X方向（B轴水平方向）的前五阶振型以及相应的自振周期；（3） 按照沿X方向的前三阶振型，用振型分解法，计算B轴线框架中产生的地震作用和地震内力，并与（2）结果进行对比。1底部剪力法1.1重力荷载代表值计算1.1.1按整体结构分析梁自重标准值： 板自重标准值： 柱自重标准值：剪力墙自重标准值：活载标准值： 各层重力荷载代表值Gj如下： 1.1.2取单榀框架B分析梁自重标准值： 板自重标准值： 柱自重标准值：剪力墙自重标准值：活载标准值： 各层重力荷载代表值Gj如下： 1.2侧移刚度计算1.2.1框架线刚度A、C轴线外楼板挑出部分可以作为主梁翼缘，故主梁线刚度调整系数同B轴线主梁取值相同，=2。.1-5层主梁： 边跨中间跨6-7层主梁:边跨中间跨1.2.2各层侧移刚度层号框架柱7边柱5208031260312600.600 0.231 316029.349 中柱52080312603750031260375001.320 0.398 327612.158 6边柱5208031260312600.600 0.231 316029.349 中柱52080312603750033860406201.375 0.407 328292.711 5边柱5642033860338600.600 0.231 317363.156 中柱56420338604062033860406201.320 0.398 329910.752 4边柱5642033860338600.600 0.231 317363.156 中柱56420338604062033860406201.320 0.398 329910.752 3边柱5642033860338600.600 0.231 317363.156 中柱56420338604062033860406201.320 0.398 329910.752 2边柱5642033860338600.600 0.231 317363.156 中柱56420338604062033860406201.320 0.398 329910.752 1边柱45140338600.750 0.455 3.7517509.695 中柱4514033860406201.650 0.589 3.7522689.453 注：梁柱线刚度i单位为KNm，层高h单位为m，柱侧移刚度D单位KN/m。列表计算如下：1.3侧移计算层号7589.373589.37387283.010.0067521622.7151622.7152618490.0061976815.5481404.92188644.120.0158492183.5653806.28265932.40.0143135815.5482220.46994547.820.0234852183.5655989.845283643.40.0211184815.5483036.01794547.820.0321112183.5658173.41283643.40.0288163815.5483851.56594547.820.0407372183.56510356.98283643.40.0365142815.5484667.11394547.820.0493622183.56512540.54283643.40.0442121839.7735506.88680398.30.0684952241.3914781.93241194.90.0612865506.8860.23679214781.930.212456注：重力荷载代表值G和层剪力V单位为KN，层侧移刚度D单位KN/m，位移u单位为m。1.4结构基本周期近似计算 采用顶点位移法，对于质量沿高度均匀分布的等截面剪切型悬臂杆，则按整体结构分析时，取B轴框架分析时。1.5整体框架分析时地震作用计算1.5.1框架层剪力及位移验算8度（0.2g）设防，类场地，设计地震分组第一组，取阻尼比为0.05，根据建筑抗震设计规范5.1.4条，场地特征周期Tg取0.45s，地震影响系数。地震作用分布图根据建筑抗震规范5.2.1条： ，故需考虑结构顶部附加地震作用，顶部附加地震作用系数 每根柱剪力列表计算如下：层号层高7321.751622.71535294.05206.1077293.959751.926882618490.0011230.00545521.0917436.332646318.752183.56540941.84239.0892533.0489121.801265932.40.0020040.00545536.6246664.64465315.752183.56534391.15200.835733.8838191.675283643.40.0025870.00545550.7221487.376824312.752183.56527840.45162.5807896.4645261.5491283643.40.0031610.00545561.67266106.2408339.752183.56521289.76124.32641020.791331.4232283643.40.0035990.00545570.04659120.6662236.752183.56514739.0686.072121106.863401.2973283643.40.0039020.00545575.84393130.65313.753.752241.398405.21349.084151155.947473.0218241194.90.0047930.00681893.85016121.6131182901.51068.095满足要求满足要求注：重力荷载代表值G地震作用F和剪力V单位为KN，层高h和侧移u单位为m，侧移刚度D单位KN/m。1.5.2柱反弯点高度计算柱底至反弯点的高度可由下式得到：倒三角形荷载作用下标准反弯点高度比y0如下：层号边柱中柱70.600 0.31.320 0.38260.600 0.41.375 0.4550.600 0.451.320 0.46640.600 0.451.320 0.46630.600 0.51.320 0.520.600 0.551.320 0.510.750 0.71.650 0.618框架梁线刚度和层高变化不大，上下横梁线刚度比对反弯点高度影响y1和层高变化对反弯点影响y2 、y3值均为零，故。1.5.3地震作用计算地震作用下柱端弯矩：有节点平衡条件知：式中为节点处左右梁端弯矩，为节点上下柱端弯矩， 为节点左右梁线刚度。以各梁为脱离体，将梁左右端弯矩之和除以该梁跨度即得到梁剪力，自上而下逐层叠加节点左右的梁端剪力即得到柱轴力。列表计算如下：地震作用下梁柱内力计算表层号h边柱柱端弯矩中柱柱端弯矩yVej边上端下端yVej中上端下端7 30.317.99503-37.790-16.1960.38230.998244-57.471-35.5246 30.432.13007-57.834-38.5560.4556.711407-93.574-76.5605 30.4544.9245-74.125-60.6480.46677.389476-123.978-108.1904 30.4554.87683-90.547-74.0840.46694.533924-151.443-132.1583 30.562.48743-93.731-93.7310.5107.64438-161.467-161.4672 30.5567.75632-91.471-111.7980.5116.72086-175.081-175.0811 3.750.783.91671-94.406-220.2810.618108.74115-155.772-252.008层号ib边/(ib边+ib中)边跨梁中跨梁左端弯矩右端弯矩剪力左端弯矩右端弯矩剪力边柱轴力中柱轴力7 0.45537.79026.149-10.65631.32231.322-12.529-10.656-1.8726 0.45574.03058.740-22.12870.35870.358-28.143-32.785-7.8875 0.455112.68291.245-33.988109.293109.293-43.717-66.772-17.6174 0.455151.195118.133-44.888141.500141.500-56.600-111.660-29.3293 0.455167.815133.599-50.236160.026160.026-64.010-161.896-43.1042 0.455185.202153.129-56.389183.419183.419-73.367-218.285-60.0821 0.455206.204150.538-59.457180.315180.315-72.126-277.742-72.751注：层高单位h为m，剪力、轴力单位为KN，弯矩单位为KNm。1.6单榀框架分析时地震作用计算1.6.1框架层剪力及位移验算地震作用分布图地震影响系数 ，需考虑结构顶部附加地震作用，顶部附加地震作用系数 每根柱剪力列表计算如下：层号层高7321.75589.37312818.86371.452005104.40218.85993687283.01380.00119610.00545519.1732233.027796318.75815.54815291.52585.234559189.636644.95747288644.12010.00213930.00545534.2916260.526665315.75815.54812844.88171.59703261.233671.05500894547.8160.0027630.00545547.9740382.642774312.75815.54810398.23757.9595319.1931978160.0033760.00545558.61795100.9786339.75815.5487951.59344.321971363.5151123.2500894547.8160.00384480.00545566.75742115.0001236.75815.5485504.94930.684441394.1995149.3476294547.8160.00416930.00545572.39244124.707313.753.75839.7733149.148817.553272411.7528176.2203580398.2950.00512140.00681889.67436116.20267959.197378.97满足要求满足要求注：重力荷载代表值G地震作用F和剪力V单位为KN，层高h和侧移u单位为m，侧移刚度D单位KN/m。1.6.2柱反弯点高度计算柱底至反弯点的高度可由下式得到：倒三角形荷载作用下标准反弯点高度比y0如下：层号边柱中柱70.600 0.31.320 0.38260.600 0.41.375 0.4550.600 0.451.320 0.46640.600 0.451.320 0.46630.600 0.51.320 0.520.600 0.551.320 0.510.750 0.71.650 0.618框架梁线刚度和层高变化不大，上下横梁线刚度比对反弯点高度影响y1和层高变化对反弯点影响y2 、y3值均为零，故。1.6.3地震作用计算地震作用下柱端弯矩：有节点平衡条件知：式中为节点处左右梁端弯矩，为节点上下柱端弯矩， 为节点左右梁线刚度。以各梁为脱离体，将梁左右端弯矩之和除以该梁跨度即得到梁剪力，自上而下逐层叠加节点左右的梁端剪力即得到柱轴力。列表计算如下：地震作用下梁柱内力计算表层号h边柱柱端弯矩中柱柱端弯矩yVej边上端下端yVej中上端下端730.319.17322-40.264-17.2560.38233.02779-61.234-37.850630.434.29162-61.725-41.1500.4560.52666-99.869-81.711530.4547.97403-79.157-64.7650.46682.64277-132.394-115.535430.4558.61795-96.720-79.1340.466100.9786-161.768-141.168330.566.75742-100.136-100.1360.5115.0001-172.500-172.500230.5572.39244-97.730-119.4480.5124.7073-187.061-187.06113.750.789.67436-100.884-235.3950.618116.202-166.459-269.298层号ib边/(ib边+ib中)边跨梁中跨梁左端弯矩右端弯矩剪力左端弯矩右端弯矩剪力边柱轴力中柱轴力70.45540.26427.861-11.35433.37233.372-13.349-11.354-1.99560.45578.98162.662-23.60775.05775.057-30.023-34.961-8.41050.455120.30797.418-36.287116.687116.687-46.675-71.249-18.79840.455161.485126.173-47.943151.130151.130-60.452-119.192-31.30730.455179.270142.719-53.665170.949170.949-68.380-172.857-46.02120.455197.866163.600-60.244195.961195.961-78.384-233.101-64.16110.455220.331160.852-63.530192.669192.669-77.067-296.631-77.698注：层高单位h为m，剪力、轴力单位为KN，弯矩单位为KNm。1.7荷载和内力对比图1.7.1地震作用对比1.7.2整体结构分析内力图1.7.2整体结构分析内力图通过对比可以看出，按整体结构分析时B轴线框架的地震作用和内力比取单榀框架分析时小。2 SAP2000程序计算第1振型 =0.917s 第2振型 =0.294s 第3振型 =0.163s 第4振型 =0.105s 第5振型 =0.075s 3 振型分解反应谱法3.1地震作用计算由： 得由得各阵型下各质点水平地震作用如下：,(KN)(KN)10.177839.77316.25020.374815.54833.31430.561815.54849.98640.724815.54864.46450.853815.54875.98460.946815.54884.25171.000589.37364.360,(KN)(KN)1-0.500839.77333.9172-0.869815.54857.2803-0.911815.54860.0324-0.594815.54839.1375-0.036815.5482.40260.566815.548-37.31071.000589.373-47.621,(KN)(KN)10.827839.77324.68120.917815.54826.56130.113815.5483.2634-0.799815.548-23.1535-0.911815.548-26.3916-0.059815.548-1.71771.000589.37320.9353.2内力计算各阵型下的柱剪力列表计算如下：716029.34927612.15887283.01464.36011.81920.360616029.34928292.71188644.120148.61126.87347.432517363.15629910.75294547.816224.59541.24571.052417363.15629910.75294547.816289.05853.08491.445317363.15629910.75294547.816339.04462.264107.259217363.15629910.75294547.816372.35968.381117.798117509.69522689.45380398.295388.60984.634109.671注：剪力V单位为KN，侧移刚度D单位KN/m。716029.34927612.15887283.014-47.621 -8.746 -15.065 616029.34928292.71188644.120-84.932 -15.358 -27.108 517363.15629910.75294547.816-82.530 -15.156 -26.109 417363.15629910.75294547.816-43.393 -7.969 -13.728 317363.15629910.75294547.81673.919 13.575 23.385 217363.15629910.75294547.81616.639 3.056 5.264 117509.69522689.45380398.295107.836 23.485 30.433 注：剪力V单位为KN，侧移刚度D单位KN/m。716029.34927612.15887283.01420.9353.8456.623616029.34928292.71188644.12019.2183.4756.134517363.15629910.75294547.816-7.174-1.317-2.269417363.15629910.75294547.816-30.327-5.569-9.594317363.15629910.75294547.816-27.063-4.970-8.562217363.15629910.75294547.816-0.502-0.092-0.159117509.69522689.45380398.29524.1785.2666.823注：剪力V单位为KN，侧移刚度D单位KN/m。根据SRSS法叠加后各柱剪力如下（KN）：内力计算如下表：地震作用下梁柱内力计算表层号h边柱柱端弯矩中柱柱端弯矩yVej边上端下端yVej中上端下端7 30.315.198-31.915-13.6780.38226.179-48.536-30.00