第七章风荷载作用下的内力和位移计算

1、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00.4KN/m2，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,wkz szWo1、因结构高度 H=20.25mv30m, 高宽比 20.25 -18.2=1.11 1.5,故可取 z 1.0 ;5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5=1.3。I0.7-070 屯5 畑 77n

2、1*0(a)正多边形(包括矩形平面0. 650.51ISk 121+ IJ0,50.5111. 52K 230. 740. 51,301.67L 39o.ea0.511401. 79b 521. 00a. 60SOk B91. G21. 100.6960bGTh 7L1.2Q10, 771 3,05K 791.2SCK制ao12. 121k R?I. 36CL 9190 11Z” 1 甘k 931. 430” 9tiJOO J1辽四2* OQh 501. 04K地面成地面松枪度类别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

3、集中风荷载标准值计算如表7.1 :表7.1层号离地 面咼 度Z (m)zzsWo(KN/m 2)h下(m)h上(m)Fiz s zWoB(h下 +h上 )/2 ( 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:20,2501245016.5503爾4.650-0,4507300：A&

4、0jora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 Xh=250mm X600mm ):0.250 0.631210 3(m4)ibEclbL2.8107 9 10 37.33.5410 KN /m跨度为3.3m的梁(b Xh=200mmX400mm ):bh32120.2 0.43122.110-3(m4)ibEclbL2.8107 2.133.310 31.9 104KN/m7.2.1.1框架柱的线刚度1、底层柱:A、D轴柱:Ic5

5、00 5003125.21103 / 4,(m )icEcIch3.0107 5.215.210 33.0104KN /mB、C轴柱:Ic5001250035.21 10 3(m4)icEcIc3.0h73107 5.21 10 35.23.0104KN /m2、上层柱:A、D轴柱:,500 5003I c125.21 10 3(m4)-一 c Cic hEcIc 3.0 107 5.21 10 33.944.0 10 KN /mB、C轴柱：Ic3500 50012345.21 10 (m )icEclc 3.073105.21 104.0 104KN/m3.97.2.1.2侧移刚度D计算框架

6、柱刚度修正系数a计算公式见表7.3:表7.3kIniiLO.S + K “2 十 A：K J宀 耳K a =2+K表7.4各层柱侧向刚度计算层次柱别KcDj kN/mDjj KN /m屋面层A0.8750.30946744180B1.350.4012623C1 350 4012623D0 8750 309467四A0.8750.30946744180B1 350 4012623C1 350 4012623D0 8750 309467三三三A0 8750 30946744180B1 350 4012623C1 350 4012623D0 8750 309467二二二A0 8750 3094674

7、4180B1 350 4012623C1 350 4012623D0 8750 309467首层A1 170 53705630354B0618121C1 800 618121D1470537056Uj风荷载作用下框架的层间侧移可按下式计算，即有:VjDij第j层的总剪力标准;Dij第j层所有柱的抗侧刚度之和;Uj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:楼面Fj(KN)Vj(KN)Djj (KN /m)Uj(m)h(m)uj / h56.226.22441800.0001223.90.0000319548.7014.9244180

8、0.0003373.90.0000867638.7023.62441800.0005343.90.0001376128.7032.32441800.0007313.90.0001876619.5441.86303540.0013794.650.000265125uUj 0.00311j 1表7.5框架在风荷载作用下侧移的计算过程详见表7.5 :jUiUj第j层侧移：j 1nUUj顶点侧移：j 1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

9、.0002652V0.0018 ，框架侧移满足要求。裘玄工3楼JSS间最大位移与展高之比的限值給构体茶他限值框架1/550框架剪力墙，框架”核心筒，板柱剪力墙1/800筒中Sh剪力墙1/1000除框架结枸外的转换层11/10007.3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，即式中y。-标准反弯点高度;yi-因上、下层梁刚度比变化的修正值;y2-因上层层高变化的修正值;y3-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K =0.875y。=0.35K =1.35y0=0

10、.371 = 1y1 =01= 1y1 =03= 1y3 =03= 1y3=0五层y=0.35+0+0=0.35y=0.37+0+0=0.37K=0.875yo =0.40K =1.35y0=0.451 = 1y =01= 1y =02= 1y2=02= 1y2 =0四层3= 1y =03= 1y3=0y=0.40+0+0+0=0.40y=0.45+0+0+0=0.45K =0.875y0=0.45K =1.35y0=0.471 = 1y =01= 1y =02= 1y2 =02= 1y2 =0三层3= 1y3 =03= 1y3=0y=0.45+0+0+0=0.45y=0.47+0+0+0=0

11、.47K =0.875y =0.50K =1.35y =0.501 = 1y1 =01= 1y1 =02= 1y2 =02= 1y2 =03= 1.33y =03= 1.33y =0y=0.50+0+0+0=0.50y=0.50+0+0+0=0.50K=1.17yo=0.65K =1.80y =0.651 = 1y1 =01= 1y1 =02= 0.75y2 =02= 0.75y2=0y=0.65+0+0=0.65y=0.65+0+0=0.65二层一层732弯矩及剪力计算jVjDij jVij 风荷载作用下的柱端剪力按下式计算，即： 式中Vij -第j层第i柱的层间剪力；Vj -第j层的总剪力

12、标准值;Dij第j层所有柱的抗侧刚度之和;Dij -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Mc上Vij(1 y)hMc下Vij yh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V（KN）Dij(KN/m)Dij(KN/m)DijVij(KN)yyh(m)Mc上(KN m)Mc下(KN m)DijA轴边柱56.229467441800.2141.330.351.373.371.82414.929467441800.2143.190.401.567.464.98323.629467441800.2145.050.451.7610.838.89232.32

13、9467441800.2146.920.501.9513.4913.49141.867056303540.2329.710.653.3817.6732.82B56.2212623441800.2861.780.371.444.372.56轴414.9212623441800.2864.270.451.769.167.52中323.6212623441800.2866.760.471.8313.9712.21柱232.3212623441800.2869.240.501.9518.0218.02141.868121303540.26811.220.653.3820.4237.92C轴中柱56.2

14、212623441800.2861.780.371.444.372.56414.9212623441800.2864.270.451.769.167.52323.6212623441800.2866.760.471.8313.9712.21232.3212623441800.2869.240.501.9518.0218.02141.868121303540.26811.220.653.3820.4237.92D轴边柱56.229467441800.2141.330.351.373.371.82414.929467441800.2143.190.401.567.464.98323.6294674

15、41800.2145.050.451.7610.838.89232.329467441800.2146.920.501.9513.4913.49141.867056303540.2329.710.653.3817.6732.82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K右/左Kb/右（Mc下 jiMc 上 j）K b K bK左M b左ij左右（ M c下j 1 M c上j）M b右ij中柱：Kb Kb式中:Me下j 1、MM b左ij

16、、M知-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; K：-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;岀-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。7.321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M AB、Mdc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M DC(kN.m )5/3.373.37/3.373.373.373.3741.829.289.281.829.289.287.467.4634.9815.8115.814.9815.8115.8110.8310.8328.89

17、22.3822.388.8922.3831.1622.3813.4913.49113.4931.1631.1613.4931.1617.6717.67梁端弯矩 Mba=M cd、Mbc=M cb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 )M ba(kN.m )M bc(kN.m )54.373.5x10 41.9x10 42.831.544.3742.5611.723.5x10 41.9x10 47.604.129.1637.5221.493.5x10 41.9x10 413.937.5613.97212.2130.233.5x10 41.9x10 4

18、19.5910.6418.02118.0238.443.5x10 41.9x10 424.9113.5320.427.10所示。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272564 125.1710.7.607X4 1? 16T5右U2皿 7,4也+冷g15- SI7.5 A7S41呻1席0；?23呂12.i1IQ.佔HIn.671.1637.2图 7.1017135 i2J .Z121S115 913.?7呂12.211予Ep1S.0；ia.?iB.4?31 16框架在风荷载作用下的弯矩图（单位:KN.m):77.322风荷载作用下的梁端剪力计算见详表7.11表 7.11楼层M AB（kN/m ）M BA（kN/m）Vab=V ba（kN）M BC（kN/m）M CB（kN/m ）Vbc=V cb（kN）53.372.83-0.851.541.54-0.9349.287.60-2.314.124.12-2.50315.8113.93-4.077.567.56-4.58222.3819.59-5.7510.6410.64-6.45131.1624.91-7.6813.5313.53-8.20依据表7.11，画出框架在风荷载作用下的剪力图，如图7.12所示。图7.12 框架在风荷载作用下的剪力图（单位：kN）733轴力计算由梁柱节点的平衡条件