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'七、水平荷载(风荷载)计算1、设计资料基本风压:,地面粗糙度类别为C类。房屋高度H=21.9m。2、荷载计算风荷载近似按阶梯形分布,首先应将其简化为作用在框架节点上的节点荷载。作用在屋面梁和楼面梁节点处的集中风荷载标准值:式中——风荷载标准值(KN/m²);——高度z处的风振系数,结构高度H=21.9m<30m,故取βZ=1.0;——风荷载体型系数,对于矩形截面=1.3;——风压高度变化系数(地面粗糙度类别为C类);——基本风压(KN/m²);风压高度变化系数可查荷载规范取得。将风荷载换算成作用与框架每层节点上的集中荷载,计算过程如下表所示。表中z为框架节点至室外地面的高度,A为一榀框架各层节点的受风面积表4.1层次A(m2)PK(kN)=A×61.01.30.351.000.465.852.6951.01.30.350.840.3814.635.5641.01.30.350.840.3816.886.4131.01.30.350.740.3416.25.5121.01.30.350.740.3416.25.5111.01.30.350.740.3424.38.26
故风荷载下的计算简图为:图4.13风荷载计算简图3.风荷载下的横向框架内力计算—反弯点法3.1各柱剪力按刚度分配法计算公式为:式中,——为该平面框架i层总剪力;——为i层第j根柱分配到的剪力;——为i层第j根柱的抗侧刚度;
——为i层s根柱的抗侧刚度之和。3.2各层柱的剪力分配和柱端弯距的计算第六层:V=2.69KNG柱:KN/MH柱:KN/MJ柱:KN/ML柱:KN/MKN/MG柱剪力:H柱剪力:J柱剪力:L柱剪力:第五层:V=3.34+5.56=8.25KNG柱:KN/MH柱:KN/MJ柱:KN/ML柱:KN/MKN/MG柱剪力:H柱剪力:J柱剪力:
L柱剪力:第四层:V=2.69+5.56+6.41=14.66KNG柱:KN/MH柱:KN/MJ柱:KN/ML柱:KN/MKN/MG柱剪力:H柱剪力:J柱剪力:L柱剪力:第三层:V=2.69+5.56+6.41+5.51=20.17KNG柱剪力:H柱剪力:J柱剪力:L柱剪力:第二层:V=2.69+5.56+6.41+5.51+5.51=25.68KNG柱剪力:H柱剪力:J柱剪力:L柱剪力:第一层:V=2.69+5.56+6.41+5.51+5.51+8.26=33.94KN
G柱:KN/MH柱:KN/MJ柱:KN/ML柱:KN/MKN/MG柱剪力:H柱剪力:J柱剪力:L柱剪力:3.3水平风荷载作用下楼层层间位移验算表4.2层次62.692.691348000.01226001/21666655.568.25460000.07339001/5342446.4114.66572000.17036001/2117635.5120.17572000.26736001/13483
25.5125.68572000.36336001/991718.2633.94578000.50246001/9163最大层间弹性位移角=1/9163<1/550,满足规范要求。3.4风荷载框架内力计算近似取上部各层柱子的反弯点在柱子中点,因为底层柱的底端为固定端,底层反弯点设在处。根据各柱分配到的剪力及反弯点位置yh计算第i层第j个柱端弯矩上端弯矩:M=Vh(1-y)下端弯矩:M=Vhy各柱柱端弯距见下表:(单位:KN·m)表4.3层次端点G柱H柱J柱L柱6上0.41×1.3=0.530.94×1.3=1.220.94×1.3=1.220.41×1.3=0.53下0.41×1.3=0.530.94×1.3=1.220.94×1.3=1.220.41×1.3=0.535上1.35×1.95=2.632.78×1.95=5.422.78×1.95=5.421.35×1.95=2.63下1.35×1.95=2.632.78×1.95=5.422.78×1.95=5.421.35×1.95=2.634上2.36×1.8=4.254.90×1.8=8.824.90×1.8=8.822.36×1.8=4.25下2.36×1.8=4.254.90×1.8=8.824.90×1.8=8.822.36×1.8=4.25
3上3.24×1.8=5.836.84×1.8=12.316.84×1.8=12.313.24×1.8=5.83下3.24×1.8=5.836.84×1.8=12.316.84×1.8=12.313.24×1.8=5.832上4.13×1.8=7.438.71×1.8=15.688.71×1.8=15.684.13×1.8=7.43下4.13×1.8=7.438.71×1.8=15.688.71×1.8=15.684.13×1.8=7.431上6.12×1.2=7.3410.86×1.2=13.0310.86×1.2=13.036.12×1.2=7.34下6.12×2.4=14.6910.86×2.4=26.0610.86×2.4=26.066.12×2.4=14.69当计算出了框架在水平力作用下的柱端弯矩值后,求梁端弯矩时,由柱端弯矩,并根据节点平衡来求。对于边跨梁端弯矩:M=M+M对于中跨,由于梁的端弯矩与梁底线刚度成正比,因此,M=(M+M)M=(M+M)
表4.4层次GH跨HJ跨JL跨左端右端左端右端左端右端60.531.22-0.28=0.941.22-0.28=0.940.5350.53+2.63=3.161.22+5.42-1.51=5.131.22+5.42-1.51=5.130.53+2.63=3.1642.63+4.25=6.885.42+8.82-3.23=11.015.42+8.82-3.23=11.012.63+4.25=6.88
34.25+5.83=10.088.82+12.31-4.79=16.348.82+12.31-4.79=16.344.25+5.83=10.0825.83+7.43=13.2612.31+15.68-6.35=21.6412.31+15.68-6.35=21.645.83+7.43=13.2617.43+7.34=14.7715.68+13.03-6.51=22.215.68+13.03-6.51=22.27.43+7.34=14.77
图4.14左风荷载弯矩图(单位:KN·m)剪力计算表4.5层次梁柱GH跨HJ跨JL跨GHJL6(0.53+0.28)/7.8=0.10(0.94+0.94)/2.4=0.78(0.53+0.28)/7.8=0.100.53×2/2.6=0.411.22×2/2.6=0.941.22×2/2.6=0.940.53×2/2.6=0.415(3.16+1.51)/7.8=0.60(5.13+5.13)/2.4=4.28(3.16+1.51)/7.8=0.602.63×2/3.9=1.355.42×2/3.9=2.785.42×2/3.9=2.782.63×2/3.9=1.354(6.88+3.23)/7.8=1.30(11.01+11.01)/2.4=9.16(6.88+3.23)/7.8=1.304.25×2/3.6=2.368.82×2/3.6=4.908.82×2/3.6=4.904.25×2/3.6=2.36
3(10.08+4.79)/7.8=1.91(16.34+16.34)/2.4=13.62(10.08+4.79)/7.8=1.915.83×2/3.6=3.2412.31×2/3.6=6.8412.31×2/3.6=6.845.83×2/3.6=3.242(13.26+6.35)/7.8=2.51(21.64+21.64)/2.4=18.03(13.26+6.35)/7.8=2.517.43×2/3.6=4.1315.68×2/3.6=8.7115.68×2/3.6=8.717.43×2/3.6=4.131(14.77+6.51)/7.8=2.73(22.20+22.20)/2.4=18.5(14.77+6.51)/7.8=2.73(7.34+14.69)/3.6=6.12(13.03+26.06)/3.6=10.86(13.03+26.06)/3.6=10.86(7.34+14.69)/3.6=6.12图4.15左风荷载剪力图(单位:KN)柱的轴力以受压为负,受拉为正:表4.6柱
层次GHJL60.100.10-0.78=-0.680.78-0.10=0.680.1050.10+0.60=0.70-0.68+0.60-4.28=-4.360.68+4.28-0.60=4.360.10+0.60=0.7040.70+1.30=2.00-4.36+1.30-9.16=-12.224.36+9.16-1.30=12.220.70+1.30=2.0032.00+1.91=3.91-12.22+1.91-13.62=-23.9312.22+13.62-1.91=23.932.00+1.91=3.9123.91+2.51=6.42-23.93+2.51-18.03=-39.4523.93+18.03-2.51=39.453.91+2.51=6.4216.42+2.73=9.15-39.45+2.73-18.50=-55.2239.45+18.50-2.73=55.226.42+2.73=9.15
图4.16左风荷载轴力图(单位:KNm注:右风荷载作用下的内力与左风荷载下的内力大小相等方向相反'