陳康非線性動(dòng)力反應(yīng)分析.doc

鋼筋混凝土非線性動(dòng)力反應(yīng)分析已知：結(jié)構(gòu)為一棟七層鋼筋混凝土框架結(jié)構(gòu)。結(jié)構(gòu)平面及尺寸如圖1所示。首層層高為3.75米，其余均為3米。柱截面尺寸皆為500mm500mm；所有主梁及主梁懸挑部分的截面尺寸皆為300mm500mm；沿軸線14方向的次梁及搭在主梁懸挑部分的次梁截面尺寸皆為300mm450mm；樓板厚皆為120mm?；炷翉?qiáng)度等級(jí)為：15層采用C40；6、7層采用C30。加載方向沿B軸線方向。抗震設(shè)防為8度，三類場(chǎng)地，設(shè)計(jì)地震分組為一組。圖1 七層框架結(jié)構(gòu)求：（1） 試采用基底剪力法，分別計(jì)算取中間B軸線一榀平面框架、以及A、B、C軸線三榀框架的三維整體結(jié)構(gòu)時(shí)， B軸線框架中產(chǎn)生的地震作用以及地震內(nèi)力（彎矩、剪力、軸力），并畫(huà)出相應(yīng)的荷載和內(nèi)力對(duì)比圖；（2） 采用SAP2000程序，計(jì)算該結(jié)構(gòu)沿X方向（B軸水平方向）的前五階振型以及相應(yīng)的自振周期；（3） 按照沿X方向的前三階振型，用振型分解法，計(jì)算B軸線框架中產(chǎn)生的地震作用和地震內(nèi)力，并與（2）結(jié)果進(jìn)行對(duì)比。1底部剪力法1.1重力荷載代表值計(jì)算1.1.1按整體結(jié)構(gòu)分析梁自重標(biāo)準(zhǔn)值： 板自重標(biāo)準(zhǔn)值： 柱自重標(biāo)準(zhǔn)值：剪力墻自重標(biāo)準(zhǔn)值：活載標(biāo)準(zhǔn)值： 各層重力荷載代表值Gj如下： 1.1.2取單榀框架B分析梁自重標(biāo)準(zhǔn)值： 板自重標(biāo)準(zhǔn)值： 柱自重標(biāo)準(zhǔn)值：剪力墻自重標(biāo)準(zhǔn)值：活載標(biāo)準(zhǔn)值： 各層重力荷載代表值Gj如下： 1.2側(cè)移剛度計(jì)算1.2.1框架線剛度A、C軸線外樓板挑出部分可以作為主梁翼緣，故主梁線剛度調(diào)整系數(shù)同B軸線主梁取值相同，=2。.1-5層主梁： 邊跨中間跨6-7層主梁:邊跨中間跨1.2.2各層側(cè)移剛度層號(hào)框架柱7邊柱5208031260312600.600 0.231 316029.349 中柱52080312603750031260375001.320 0.398 327612.158 6邊柱5208031260312600.600 0.231 316029.349 中柱52080312603750033860406201.375 0.407 328292.711 5邊柱5642033860338600.600 0.231 317363.156 中柱56420338604062033860406201.320 0.398 329910.752 4邊柱5642033860338600.600 0.231 317363.156 中柱56420338604062033860406201.320 0.398 329910.752 3邊柱5642033860338600.600 0.231 317363.156 中柱56420338604062033860406201.320 0.398 329910.752 2邊柱5642033860338600.600 0.231 317363.156 中柱56420338604062033860406201.320 0.398 329910.752 1邊柱45140338600.750 0.455 3.7517509.695 中柱4514033860406201.650 0.589 3.7522689.453 注：梁柱線剛度i單位為KNm，層高h(yuǎn)單位為m，柱側(cè)移剛度D單位KN/m。列表計(jì)算如下：1.3側(cè)移計(jì)算層號(hào)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：重力荷載代表值G和層剪力V單位為KN，層側(cè)移剛度D單位KN/m，位移u單位為m。1.4結(jié)構(gòu)基本周期近似計(jì)算 采用頂點(diǎn)位移法，對(duì)于質(zhì)量沿高度均勻分布的等截面剪切型懸臂桿，則按整體結(jié)構(gòu)分析時(shí)，取B軸框架分析時(shí)。1.5整體框架分析時(shí)地震作用計(jì)算1.5.1框架層剪力及位移驗(yàn)算8度（0.2g）設(shè)防，類場(chǎng)地，設(shè)計(jì)地震分組第一組，取阻尼比為0.05，根據(jù)建筑抗震設(shè)計(jì)規(guī)范5.1.4條，場(chǎng)地特征周期Tg取0.45s，地震影響系數(shù)。地震作用分布圖根據(jù)建筑抗震規(guī)范5.2.1條： ，故需考慮結(jié)構(gòu)頂部附加地震作用，頂部附加地震作用系數(shù) 每根柱剪力列表計(jì)算如下：層號(hào)層高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滿足要求滿足要求注：重力荷載代表值G地震作用F和剪力V單位為KN，層高h(yuǎn)和側(cè)移u單位為m，側(cè)移剛度D單位KN/m。1.5.2柱反彎點(diǎn)高度計(jì)算柱底至反彎點(diǎn)的高度可由下式得到：倒三角形荷載作用下標(biāo)準(zhǔn)反彎點(diǎn)高度比y0如下：層號(hào)邊柱中柱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框架梁線剛度和層高變化不大，上下橫梁線剛度比對(duì)反彎點(diǎn)高度影響y1和層高變化對(duì)反彎點(diǎn)影響y2 、y3值均為零，故。1.5.3地震作用計(jì)算地震作用下柱端彎矩：有節(jié)點(diǎn)平衡條件知：式中為節(jié)點(diǎn)處左右梁端彎矩，為節(jié)點(diǎn)上下柱端彎矩， 為節(jié)點(diǎn)左右梁線剛度。以各梁為脫離體，將梁左右端彎矩之和除以該梁跨度即得到梁剪力，自上而下逐層疊加節(jié)點(diǎn)左右的梁端剪力即得到柱軸力。列表計(jì)算如下：地震作用下梁柱內(nèi)力計(jì)算表層號(hào)h邊柱柱端彎矩中柱柱端彎矩yVej邊上端下端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層號(hào)ib邊/(ib邊+ib中)邊跨梁中跨梁左端彎矩右端彎矩剪力左端彎矩右端彎矩剪力邊柱軸力中柱軸力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：層高單位h為m，剪力、軸力單位為KN，彎矩單位為KNm。1.6單榀框架分析時(shí)地震作用計(jì)算1.6.1框架層剪力及位移驗(yàn)算地震作用分布圖地震影響系數(shù) ，需考慮結(jié)構(gòu)頂部附加地震作用，頂部附加地震作用系數(shù) 每根柱剪力列表計(jì)算如下：層號(hào)層高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滿足要求滿足要求注：重力荷載代表值G地震作用F和剪力V單位為KN，層高h(yuǎn)和側(cè)移u單位為m，側(cè)移剛度D單位KN/m。1.6.2柱反彎點(diǎn)高度計(jì)算柱底至反彎點(diǎn)的高度可由下式得到：倒三角形荷載作用下標(biāo)準(zhǔn)反彎點(diǎn)高度比y0如下：層號(hào)邊柱中柱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框架梁線剛度和層高變化不大，上下橫梁線剛度比對(duì)反彎點(diǎn)高度影響y1和層高變化對(duì)反彎點(diǎn)影響y2 、y3值均為零，故。1.6.3地震作用計(jì)算地震作用下柱端彎矩：有節(jié)點(diǎn)平衡條件知：式中為節(jié)點(diǎn)處左右梁端彎矩，為節(jié)點(diǎn)上下柱端彎矩， 為節(jié)點(diǎn)左右梁線剛度。以各梁為脫離體，將梁左右端彎矩之和除以該梁跨度即得到梁剪力，自上而下逐層疊加節(jié)點(diǎn)左右的梁端剪力即得到柱軸力。列表計(jì)算如下：地震作用下梁柱內(nèi)力計(jì)算表層號(hào)h邊柱柱端彎矩中柱柱端彎矩yVej邊上端下端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層號(hào)ib邊/(ib邊+ib中)邊跨梁中跨梁左端彎矩右端彎矩剪力左端彎矩右端彎矩剪力邊柱軸力中柱軸力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：層高單位h為m，剪力、軸力單位為KN，彎矩單位為KNm。1.7荷載和內(nèi)力對(duì)比圖1.7.1地震作用對(duì)比1.7.2整體結(jié)構(gòu)分析內(nèi)力圖1.7.2整體結(jié)構(gòu)分析內(nèi)力圖通過(guò)對(duì)比可以看出，按整體結(jié)構(gòu)分析時(shí)B軸線框架的地震作用和內(nèi)力比取單榀框架分析時(shí)小。2 SAP2000程序計(jì)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 振型分解反應(yīng)譜法3.1地震作用計(jì)算由： 得由得各陣型下各質(zhì)點(diǎn)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內(nèi)力計(jì)算各陣型下的柱剪力列表計(jì)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單位為KN，側(cè)移剛度D單位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單位為KN，側(cè)移剛度D單位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單位為KN，側(cè)移剛度D單位KN/m。根據(jù)SRSS法疊加后各柱剪力如下（KN）：內(nèi)力計(jì)算如下表：地震作用下梁柱內(nèi)力計(jì)算表層號(hào)h邊柱柱端彎矩中柱柱端彎矩yVej邊上端下端yVej中上端下端7 30.315.198-31.915-13.6780.38226.179-48.536-30.00