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-1-表16层间侧移i层号横向纵向ViDiδi=Vi/Diδi/hViDiδi=Vi/Diδi/h(kN)(kN/m)(mm)l/x(kN)(kN/m)(mm)l/x61054.317.7281E+051.364324191114.618.6098E+051.2946254951621.147.7281E+052.097715731713.858.6098E+051.9906165842087.937.7281E+052.701712212207.348.6098E+052.5638128732454.707.7281E+053.176314172595.098.6098E+053.0141149322721.447.7281E+053.521512782877.088.6098E+053.3416134712905.025.3743E+055.405411103071.166.2248E+054.933712163.框架侧移验算由于本工程高宽比小于4,柱轴向变形引起的侧移忽略不计,梁柱弯曲变形引起的层间侧移计算见表16。从结果看,层间位移均满足要求。以上结果汇总于图7中。地震作用地震剪力水平侧移地震作用地震剪力水平侧移横向纵向图7地震作用、地震剪力与水平侧移4.框架剪力标准值横向共有8榀框架,纵向共有4榀框架,由于每榀框架总刚度不同,应按照各框架柱在总刚度中的比例将层地震剪力分配至各框架柱。横向4轴框架的各柱剪力分配计算见表17。表17横向6轴框架柱剪力分配层号层剪力层抗侧刚度边柱1、2中柱1、2ViDiDijVij=vi*dij/diDijVij=vi*Dij/Di(kN)(kN/m)(kN/m)(kN)(kN/m)(kN)61054.317.7281E+051.9793E+0427.002.6167E+0435.70-2-51621.147.7281E+051.9793E+0441.522.6167E+0454.8942087.937.7281E+051.9793E+0453.482.6167E+0470.7032454.707.7281E+051.9793E+0462.872.6167E+0483.1222721.447.7281E+051.9793E+0469.702.6167E+0492.1512905.025.3743E+051.3593E+0473.481.5935E+0486.137水平地震作用下框架内力计算以横向4轴框架为例,采用D值法进行计算。其计算步骤如下:1.根据柱剪力及反弯点高度计算柱端弯矩柱反弯点距柱下端的高度yh按式(5-2-2)计算,即:yh=(y0+y1+y2+y3)h;柱端弯矩按式(5-2-5)计算。柱下端弯矩:Mb=Vij·yh;柱上端弯矩:Mt=Vij·(h-y)h。计算结果见表18。表18横向6轴框架柱柱端弯矩计算层号柱位置柱剪力Vij反弯点相对高度y层高h柱端弯距(kN*m)(kN)Ky0y1y2y3y(m)下端Mb上端Mt6边柱1、227.00271.94710.400000.00000.00000.40003.638.8858.33中柱1、235.69853.750.450000.00000.00000.45003.657.8370.685边柱1、241.52021.94710.450000.00000.00000.45003.667.2682.21中柱1、254.89113.750.500000.00000.00000.50003.698.8098.804边柱1、253.47551.94710.497400.00000.00000.49743.695.7696.76中柱1、270.69643.750.500000.00000.00000.50003.6127.25127.253边柱1、262.86911.94710.500000.00000.00000.50003.6113.16113.16中柱1、283.11503.750.500000.00000.00000.50003.6149.61149.612边柱1、269.70081.94710.500000.0000-0.04680.45323.6113.72137.20中柱1、292.14673.750.500000.00000.00000.50003.6165.86165.861边柱1、273.47552.43390.578300.00000.57836.0254.95185.91中柱1、286.13494.68750.550000.00000.55006.0284.25232.562.计算梁端弯矩及梁剪力利用节点平衡条件,梁端弯矩按式(5-2-6)计算,梁剪力由梁两端的弯矩之和除以梁跨度求得。计算结果见表19。表19横向6轴框架梁端弯矩、剪力计算-3-层号654321A轴∑MCol,A58.33121.09164.02208.92250.36299.63LABMA58.33121.09164.02208.92250.36299.63VAB16.6627.3134.7344.1134.7741.62MB,L19.2842.7261.6575.5186.04108.66B轴∑MCol,B70.68156.63226.05276.86315.47398.42LBCMB,R51.40113.91164.40201.35229.43289.76VBC34.2775.94109.60134.24152.96193.17MC,L51.40113.91164.40201.35229.43289.76C轴∑MCol,C70.68156.63226.05276.86315.47398.42LCDMC,R19.2842.7261.6575.5186.04108.66VCD10.7822.7531.3439.5046.7256.71MD58.33121.09164.02208.92250.36299.63D轴∑MCol,D58.33121.09164.02208.92250.36299.633.根据梁端剪力计算柱轴力边柱轴力nkkiijVN;中柱轴力nkRk,Lk,iijVVN。计算结果见表21。表20横向6轴框架柱轴力计算层号各梁剪力各柱轴力(受拉为正)VABVBCVCDNANBNCND616.6634.2710.7816.6617.61-17.61-16.66527.3175.9422.7543.9766.24-66.24-43.97434.73109.6031.3478.70141.11-141.11-78.70344.11134.2439.50122.81231.24-231.24-122.81234.77152.9646.72157.58349.42-349.42-157.58141.62193.1756.71199.20500.98-500.98-199.204.绘制内力图左震作用下,横向4轴框架的内力图见图8。右震作用下,内力相同,方向-4-相反。8竖向荷载作用下框架内力计算与水平地震作用下相同,取横向4轴框架进行计算。作用在梁上的竖向荷载按照各自的负荷范围计算,导算为作用在梁及梁柱节点上的荷载,荷载值详见表22。由纵向传来的作用在梁柱节点上的竖向荷载值见表23。荷载简图如图9所示,括号内为活荷载。表21横向6轴框架梁竖向荷载取值层号主梁自重pb传递荷载方式板荷载等效宽度板恒载ps板活载qs墙自重pw等效均布恒荷载p等效均布活荷载qAB跨65.28梯形2.812515.891.4121.171.4155.28梯形2.812510.275.638.3223.875.6345.28梯形2.812510.275.638.3223.875.6335.28梯形2.812510.275.638.3223.875.6325.28梯形2.812510.275.638.3223.875.6315.28梯形2.812510.275.638.3223.875.63BC跨63.2175三角形1.26.780.6010.000.6053.2175三角形1.24.933.008.153.0043.2175三角形1.24.933.008.153.0033.2175三角形1.24.933.008.153.0023.2175三角形1.24.933.008.153.0013.2175三角形1.24.933.008.153.00CD跨65.28梯形2.812515.891.4121.171.4155.28梯形2.812510.275.638.3223.875.6345.28梯形2.812510.275.638.3223.875.63-5-35.28梯形2.812510.275.638.3223.875.6325.28梯形2.812510.275.638.3223.875.6315.28梯形2.812510.275.638.3223.875.63表22横向6轴框架梁柱节点处由纵向框架传来的竖向荷载取值(kN)传至A、D柱传至B、C柱层号62~5162~51每根柱自重(kN)34.5534.5558.3123.9923.9940.48纵向框架梁自重(kN)29.2129.2129.2129.2129.2129.21次梁自重(kN)9.089.089.089.089.089.08楼板恒载(kN)30.7619.8719.87134.9467.3067.30楼板活载(kN)2.7210.8910.8911.9458.0458.04纵向墙重(kN)0.0065.6165.610.0045.2945.29纵梁传恒载G(kN)69.05123.77123.77173.23150.88150.88偏心距(m)0.000.000.000.000.000.00恒载节点力偶(kN-m)0.000.000.000.000.000.00纵梁传活载Q(kN)2.7210.8910.8911.9458.0458.04活载节点力偶(kN-m)0.000.000.000.000.000.00-6-弯矩(kN·m)剪力(kN)轴力(kN)图8横向4轴框架内力图-7-图9作用在横向4轴框架上的竖向荷载8.1竖向恒载作用下框架内力计算采用二次弯矩分配法。计算步骤如下:1.计算竖向荷载作用下各层梁端固端弯矩(表23)。表23恒载(活载)作用下横向6轴框架梁端固端弯矩(kN·m)层号M恒M活左端右端左端右端AB跨6-99.2399.23-6.616.614~5-111.89111.89-26.3926.392~3-111.89111.89-26.3926.391-111.89111.89-26.3926.39BC跨6-4.804.80-0.290.294~5-3.913.91-1.441.442~3-3.913.91-1.441.441-3.913.91-1.441.44CD跨6-99.2399.23-6.616.614~5-111.89111.89-26.3926.392~3-111.89111.89-26.3926.39-8-1-111.89111.89-26.3926.392.根据梁柱线刚度求梁柱转动刚度,并确定各节点处的分配系数,详见图11。n1kkkiiiiSS其中,Sik为节点k第iSik为节点k各杆件的转动刚度之和。杆件的转动刚度的计算方法如下:梁柱节点处为刚接,当杆件的另一端为刚节点时,第j根杆件的转动刚度为Sj=4i;当利用结构对称性而将杆件的另一端取为定向支座时,第j根杆件的转动刚度为Sj=2i,i为杆件的线刚度。3.进行弯矩的分配和传递,求得各节点处的杆端弯矩值。需要注意的是,A轴柱外侧的悬臂是静定结构,并不参节点弯矩的分配和传递。具体计算过程见图11。-9-图10用二次弯矩分配法计算竖向恒载作用下框架弯矩4.根据静力平衡条件计算各梁跨中弯矩。跨中弯矩取荷载实际分布并按两端简支的计算值与梁端弯矩叠加求得。跨中最大弯矩并不一定在跨度
本文标题:框架结构设计例题第二部分
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