第七章--风荷载作用下的内力和位移计算

第7章风荷载作用下的内力和位移计算由设计任务资料知，该建筑为五层钢筋混凝土框架结构体系，室内外高差为0.45m基本风压20m/4.0KN，地面粗糙度为C类，结构总高度19.8+0.45=20.25m（基础顶面至室内地面1m）。计算主要承重结构时，垂直于建筑物表面上的风荷载标准值，应按下式计算，即ozszkww1、因结构高度H=20.25m30m,高宽比20.25÷18.2=1.11＜1.5,故可取0.1z；2、s为风荷载体型系数，本设计按《建筑结构荷载规范》（GB50009--2012）中规定，迎风面取0.8，背风面取0.5，合计s=1.3。3、z为风压高度变化系数，本设计的地面粗糙度类别为C类，按下表选取风压高度变化系数。7.1横向框架在风荷载作用下的计算简图6轴线框架的负荷宽度B=（6.6+6.6）/2=6.6m。各层楼面处集中风荷载标准值计算如表7.1：表7.1层号离地面高度Z（m）zzsW0(KN/m2)h下(m)h上(m)0(+)/2izszFwBhh下上（kN）14.650.651.01.30.44.653.99.5428.550.651.01.30.43.93.98.70312.450.651.01.30.43.93.98.70416.350.651.01.30.43.93.98.70520.250.741.01.30.43.91.06.22根据表7.1，画出6轴框架在风荷载作用下的计算简图，如图7.2所示：图7.2框架在风荷载作用下的计算简图7.2位移计算7.2.1框架梁柱线刚度计算考虑现浇楼板对梁刚度的加强作用，故对6轴线框架（中框架梁）的惯性矩乘以2.0，框架梁的线刚度计算：跨度为7.3m的梁（b×h=250mm×600mm）：)(109126.0250.0212bh24333mImKNLIEcb/105.33.7109108.2i437b跨度为3.3m的梁(b×h=200mm×400mm）：）（43-33m101.2124.02.0212bh2ImKNLIEcb/109.13.31013.2108.2i437b7.2.1.1框架柱的线刚度1、底层柱：A、D轴柱：)(1021.512500500433cmImKNhIEccc/100.32.51021.5100.3i437B、C轴柱：)(1021.512500500433cmImKNhIEccc/100.32.51021.5100.3i4372、上层柱：A、D轴柱：)(1021.512500500433cmImKNhIEccc/100.49.31021.5100.3i437B、C轴柱：)(1021.512500500433cmImKNhIEccc/100.49.31021.5100.3i4377.2.1.2侧移刚度D计算框架柱刚度修正系数a计算公式见表7.3:表7.3表7.4各层柱侧向刚度计算层次柱别KckN/mDijmKND/ij屋面层A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467四A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467三A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467二A0.8750.30946744180B1.350.4012623C1.350.4012623D0.8750.309467首层A1.170.53705630354B1.800.618121C1.800.618121D1.170.537056风荷载作用下框架的层间侧移可按下式计算，即有：ijjjDVu式中jV------第j层的总剪力标准；ijD--------第j层所有柱的抗侧刚度之和；ju--------第j层的层间侧移。各层楼板标高处的侧移值是该层以下各层层间侧移之和。顶点侧移是所有各层层间侧移之和，即有：第j层侧移：jjjiuu1顶点侧移：njjuu1框架在风荷载作用下侧移的计算过程详见表7.5：表7.5楼面()jFKN()jVKN(/)ijDKNm()jum()hm/juh56.226.22441800.00012293.90.000031548.7014.92441800.00033773.90.000086638.7023.62441800.00053463.90.000137128.7032.32441800.00073163.90.000187619.5441.86303540.00137914.650.000265200311.0u51jju侧移验算：由《高层建筑混凝土结构技术规程》（JGJ3-2010）表3.73可知，对于框架结构，楼层间最大位移与层高之比的限值为1/550=0.0018。本框架的层间最大位移与层高之比在底层，其值为0.00026520.0018，框架侧移满足要求。7.3内力计算框架在风荷载作用下的内力计算采用D值法。计算过程如下：7.3.1反弯点高度计算反弯点高度比按下式计算，即3210yyyyy式中0y-----标准反弯点高度；1y-----因上、下层梁刚度比变化的修正值；2y-----因上层层高变化的修正值；3y-----因下层层高变化的修正值。反弯点高度比的计算列于表7.6。表7.6楼层A、D轴边框架柱B、C轴中框架柱五层K=0.8750y=0.351=11y=03=13y=0y=0.35+0+0=0.35K=1.350y=0.371=11y=03=13y=0y=0.37+0+0=0.37四层K=0.8750y=0.401=11y=02=12y=03=13y=0y=0.40+0+0+0=0.40K=1.350y=0.451=11y=02=12y=03=13y=0y=0.45+0+0+0=0.45三层K=0.8750y=0.451=11y=02=12y=03=13y=0y=0.45+0+0+0=0.45K=1.350y=0.471=11y=02=12y=03=13y=0y=0.47+0+0+0=0.47二层K=0.8750y=0.501=11y=02=12y=03=1.333y=0y=0.50+0+0+0=0.50K=1.350y=0.501=11y=02=12y=03=1.333y=0y=0.50+0+0+0=0.507.3.2弯矩及剪力计算风荷载作用下的柱端剪力按下式计算，即：jijijijVDDV式中ijV----第j层第i柱的层间剪力；jV----第j层的总剪力标准值；ijD-----第j层所有柱的抗侧刚度之和；ijD----第j层第i柱的抗侧刚度。风荷载作用下的柱端弯矩按下式计算，即hyMijc)1(V上yhMijcV下一层K=1.170y=0.651=11y=02=0.752y=0y=0.65+0+0=0.65K=1.800y=0.651=11y=02=0.752y=0y=0.65+0+0=0.65风荷载作用下的柱端剪力和柱端弯矩计算列于下表7.7。表7.7柱楼层jV（KN）ijD(KN/m)ijD（KN/m）ijijDDVij（KN）yyh(m)cM上(KNm)cM下(KNm)A轴边柱56.229467441800.2141.330.351.373.371.82414.929467441800.2143.190.401.567.464.98323.629467441800.2145.050.451.7610.838.89232.329467441800.2146.920.501.9513.4913.49141.867056303540.2329.710.653.3817.6732.82B轴中柱56.2212623441800.2861.780.371.444.372.56414.9212623441800.2864.270.451.769.167.52323.6212623441800.2866.760.471.8313.9712.21232.3212623441800.2869.240.501.9518.0218.02141.868121303540.26811.220.653.3820.4237.92C轴中柱56.2212623441800.2861.780.371.444.372.56414.9212623441800.2864.270.451.769.167.52323.6212623441800.2866.760.471.8313.9712.21232.3212623441800.2869.240.501.9518.0218.02141.868121303540.26811.220.653.3820.4237.92D轴边柱56.229467441800.2141.330.351.373.371.82414.929467441800.2143.190.401.567.464.98323.629467441800.2145.050.451.7610.838.89232.329467441800.2146.920.501.9513.4913.49141.867056303540.2329.710.653.3817.6732.82梁端弯矩及剪力计算由节点平衡条件，梁端弯矩之和等于柱端弯矩之和，将节点左右梁端弯矩之和按左右梁的线刚度比例分配，可求出各梁端弯矩，进而由梁的平衡条件求出梁端剪力。风荷载作用下的梁端弯矩按下式计算，即中柱：）（上下右左左左jcjcbbbijbKMMMKK1）（上下右左右右jcjcbbbijbKMMMKK1边柱：）（上下总jcjcijbMMM1式中：ijbM左、ijbM右--表示第j层第i节点左端梁的弯矩和第j层第i节点右端梁的弯矩；左bK、右bK--表示第j层第i节点左端梁的线刚度和第j层第i节点右端梁的线刚度；jcjc上下、MM1--表示第j层第i节点上层柱的下部弯矩和第j层第i节点下层柱的上部弯矩。7.3.2.1风荷载作用下的梁端弯矩计算列于表7.8和7.9梁端弯矩ABM、DCM计算表7.8楼层柱端弯矩柱端弯矩之和MAB（kN.m）柱端弯矩柱端弯矩之和MDC（kN.m）5/3.373.37/3.373.373.373.3741.829.289.281.829.289.287.467.4634.9815.8115.814.9815.8115.8110.8310.8328.8922.3822.388.8922.3822.3813.4913.49113.4931.1631.1613.4931.1631.1617.6717.67梁端弯矩MBA=MCD、MBC=MCB计算：表7.9楼层柱端弯矩柱端弯矩之和KB左（kN.m）KB右（kN/m）MBA（kN.m）MBC（kN.m）5——4.373.5x1041.9x1042.831.544.3742.5611.723.5x1041.9x1047.604.129.1637.5221.493.5x1041.9x10413.937.5613.97212.2130.233.5x1041.9x10419.5910.6418.02118.0238.443.5x1041.9x10424.9113.5320.42依据表7.8—表7.9，画出框架在风荷载作用下的弯矩图，如图7.10所示。图7.10框架在风荷载作用下的弯矩图（单位：KN.m）7.3.2.2风荷载作用下的梁端剪力计算见详表7.11表7.11楼层MAB（kN/m）MBA（kN/m）VAB=VBA(kN)MBC（kN/m）M