9、210框架梁、柱配筋计算

1、2.10第1/1轴框架梁、柱配筋计算2.10.1承载力抗震调整根据高层建筑混凝土结构规范(JGJ3-2002)式(4.7.2-2)规定，有地震作用组合时，作用效应设计值S应采用下式表达式：S<R/Yre(2.3)式：Yre为构件承载力抗震调整系数，取值见表2.10-1：表2.10-1承载力抗震调整系数表构件类别梁轴压比小于0.15的柱轴压比不小于0.15的柱剪力墙各类构件节点受力状态受弯偏压偏压偏压局部承压受男、偏拉受男yre0.750.750.800.851.00.850.85具体调整见梁、柱配筋表。最小配筋率的确定：根据混凝土结构设计规范(GB50010-2002)11.3.6规定，

2、三级抗震时，框架梁正截面设计抗震要求的最小配筋率支座取0.25%和55ft/fy%=55X1.43/360=0.218%的较大值，跨中取0.20%和45ft/fy%=45X1.43/360=0.179%的较大值，所以支座取0.25%,跨中取0.20%。且梁端纵向受拉钢筋的配筋率不应大丁2.5%。2.10.2梁截面设计1).梁的正截面强度计算材料强度：C30(R=14.3N/mm2,ft=1.43N/mm2);HPB400级钢筋(fy=360N/mm2)。(1) AB跨梁正截面受弯承载力计算。从梁内力组合表中，挑出第一层AB梁跨中及支座截面的最不利内力。、MA=T71.68(79.08)kN.m

3、VA=114.80kNM中=90.8kN.mMB=T54.08(35.82)kN.mVB=T19.44kN、计算跨中截面。因梁板现浇，故跨中按T形截面hf=12m0n,h0=46m5n,hf/h0=12/06=50.2580.1,bf不受此限制，b+sn=4500mm,l0/3=6900/3=2300mm,故取bf=2300mm。''：1fcbfhf(国-hf/2)=1.014.32300120(465-120/2)_6.一故届第一类T形截面。：s90.81062=0.0128：1fcbfho1.014.323004652松=1一1_2：=1-1-20.0128=0.0129：

4、；b=0.518满足：x=h0=6.00mm：0.35h0=162.75mm：1fcb'fX：1fcbfh0As=fyfy1.014.323004650.02552=545.92mm360选用3118,入=763mm2,将跨中截面31118全部伸入支座。验算最小配筋率R:As'奇罗63矿0.61%土=0.20%满足要求。 、支座A右端负弯矩配筋，截面按矩形截面计算。171.681062 -2=0.222：1fcbh021.014.325046521 -.1-2：s=0.254：0.518,x=h0=103.23mm2a'=70mm满足：x£0.35h0=162

5、.75mmAs=业宜=1.0M32504650.254=1172.89mm2fy360=1598.4510N.mm=1598.45kN.mM=90.8kN.m选用4_20,A-1256mm2验算最小配筋率A:&=炫6=1.00%aPm。®%满足要求。bh250500 A's/As=763/1256=0.6070.3,满足要求154.08106支座B负弯矩配筋，截面按矩形截面计算。oo=0.199：1fcbh021.014.32504652二1-.1-2：s=0.2240.518,x=h0=104.16mm2a'=70mm：ifcbh0fy满足：x=h0=104

6、.16mm：0.35ho=162.75mm=1034.36mm21.014.32504650.224360选用420,A=1256mm2验算最小配筋率耳：A1256耳=1.00%APmin=0.25%两足要求A's/As=763/1256=0.607>0.3,满足要求（2）AB梁的斜截面强度计算：1）最少配筋率的确定根据高层建筑混凝土结构技术规程（JGJ3-20026.3.4规定，三级抗震设计时，框架梁沿梁全长箍筋的面积配筋率应符合下式要求：Ps0.26ft/fyv,由丁本设计混凝土采用C30,ft=1.43N/mm2,钢筋采用HRB235,侦=210N/mm2,所以Psvmin

7、=0.26x1.43/2140.17%O按AB梁问最大剪力设计值为119.44kN计算抗剪配筋：九/b=475/250=1.90：40.25诲万忸=0.251.014.3250475=424.53kNV=119.44kN截面尺寸满足要求。0.7ftbh0=0.71.43250475=118.86kN:V=119.44kN所以梁箍筋按构件配置即可。配双肢箍8,Av=101mm2由构造要求，非加密区取S=200mm,即*8200加密区取S=100mm，取*8100加密区取长度（1.5h、500的最大值），取900mm。验算箍筋的最小配筋率要求。表2.10-2梁正截面受弯承载力计算（第一层）awLa

8、bLbcLcd左端跨中右端左端跨中右端左端跨中右端顶面底面顶面底面顶面底面顶面底面顶面底面顶面底面混凝土强度14.3014.3014.3014.3014.3014.3014.3014.3014.3014.3014.3014.3014.3014.3014.30钢筋强度360360360360360360360360360360360360360360360M171.6879.0890.80154.0835.82135.3173.8267.96135.3169.11154.0835.8290.80171.6879.08b或bf250230023002502300250700700250700250

9、230023002502300h(mm)500500500500500350350350350350500500500500500h0(mm)465465465465465325325325325325465465465465465hf'120.00120.00120.00100.00100.00100.00120.00120.00120.001598.451598.451598.45275.28275.281598.451598.451598.45截面类型矩形第一类T形第一类T形矩形第一类T形矩形第一类T形第一类T形矩形第一类T形矩形第一类T形第一类T形矩形第一类T形as=M/a1f

10、cbf'h0人20.22210.01110.01280.19930.00500.35830.06980.06430.35830.06540.19930.00500.01280.22210.0111£=1-(1-2as)人20.25450.01120.01290.22450.00500.46770.07240.06650.46770.06770.22450.00500.01290.25450.0112£b0.5180.5180.5180.5180.5180.5180.5180.5180.5180.5180.5180.5180.5180.5180.518.，.'

11、一、%=岳儡0吼2）1175.08475.06545.921036.83214.521509.50654.65600.831509.50611.361036.83214.52545.921175.08475.06选筋4ll203北183。1841203118412231183*184112231184“203118318420318实际As125676376312567631520763763152076312567637631256763p1=As/bh(%)1.00%0.61%0.61%1.00%0.61%1.74%0.87%0.87%1.74%0.87%1.00%0.61%0.61%1.

12、00%0.61%pmin(%)0.250%0.250%0.200%0.250%0.250%0.250%0.250%0.200%0.250%0.250%0.250%0.250%0.200%0.250%0.250%表2.10-3梁斜截面受弯承载力计算（第一层）梁号LabLbcLcd时(kN)119.44138.19119.44b(mm)250250250h0(mm)4753254750.25&fcbh°424.53290.47424.530.7ftbho118.8681.33118.86nAsv1?reV0.7ftbh0s1.25fyvh0按构造配筋SM150mm(28)按构造配

13、筋选筋（双肢）J8200l815018200实际Asvi(mm2)50.350.350.3实际nAsWs1.011.011.01s=nAsv1/(sb)(%)0.5030.6710.503psv,min=24ft/fyv(%)0.1630.1630.163注：梁端加密区的长度max(1.5hb,500)=max(1.5500,500)=750mm,取900mm,选用1：81002.10.3柱的截面设计1).柱的正截面强度计算(1) 柱的计算长度本工程采用现浇式楼盖，根据混凝土结构设计规范(GB50010-2002)7.3.11规定，框架各层柱的计算长度对丁底层柱取：l0=1.0H=1.0x52

14、50=5250mm,其余各层柱取：l0=1.25H层高=1.25x3900=4875mm。(2) 最小配筋率的确定因本工程为三级抗震，根据建筑抗震设计规范(GB50011-2001)6.3.8规定，柱纵向钢筋的最小总配筋率为0.7%,同时，每一侧配筋率不应小丁0.2%。(3) 据建筑抗震设计规范(GB50011-2001)6.2.2规定，一、二、三级框架的梁柱节点处，柱端组合的弯矩设计值应符合下式要求。£McfEMb(2.5)式中：nc为柱端弯矩增大系数，一级抗震时取1.4,二级取1.2,三级取1.1,由丁设计为三级抗震，所以气取为1.1；ZMb为节点左右梁截面反时针或顺时针方向组合

15、的弯矩设计值之和；ZMc为节点上下柱端截面顺时针或反时针方向组合的弯矩设计值之和，上下柱端的弯矩设计值，可按弹性分析分配。(4) 截面参数的计算根据混凝土结构设计规范(GB50010-2002)7.3.3规定，附加偏心距ea应取20mm和偏心方向截面最大尺寸的1/30两者的较大值。轴向压力对截面重心的偏心距e°=M/N；轴向压力作用点至纵向普通受拉钢筋的合力点距离e=hei+h/2-a，其中偏心受压构件考虑二阶影响的轴向压力偏心距增大系数n=1+1''0&2(2.6)1400e/h°.hj式中：匚产0.5fcA，当匚11.0时取匚1=1.0;N匚2为

16、构件长细比对截面曲率的影响系数；当NaNb=%fcbtbbh0时，为小偏心受压，否则为大偏心受压。(5) 现以一层B轴柱来说明柱截面的配筋过程，从表B柱的内力挑选中，挑出第1层B柱截面的最不利内力组。混凝土强度等级：C30(fc=14.3N/mm2,ft=1.43N/mm2);HPB335级钢筋(fy=300N/mm2),HRB235级车冈筋(fy=210N/mm2)第一组：上端：Mma<=-140.24kN,N=685.17kN,V=66.77kN下端：Mmax=-159.70kN,N=714.93kN,V=66.77kN第二组：上端：M=9.63kN,Nmax=1216.43kN,V

17、=6.80kN下端：M=26.20kN,Nmax=1250.26kN,V=-6.80kN第三组：上端：M=-140.24,N=685.17kN,Vmax=66.77N下端：M=-159.70kN,N=714.93kN,Vmax=66.77kN柱的轴压比及剪跨比用最大轴力设计值验算轴压比:Nmaxfcbh1250.2610314.3450450=0.432：0.9Hn2h0(5.25-0.5)1032415=5.6a2,为长柱柱截面的配筋计算见表2.10-4,表2.10-4底层B柱截面的配筋计算1层柱上端柱下端M(kN.m)140.249.36140.24159.7026.20159.70N(k

18、N)685.171216.43658.17714.931250.26714.93X106.481189.03102.28111.10194.29111.10&h0(mm)214.97214.97214.97214.97214.97214.97偏压类型大偏压大偏压大偏压大偏压大偏压大偏压轴压比0.2410.420.230.250.430.25b(mm)450.00450.00450.00450.00450.00450.00h(mm)450.00450.00450.00450.00450.00450.00hg(mm)415.00415.00415.00415.00415.00415.00e

19、c(mm)204.687.69213.08223.3820.96223.38ea(mm)20.0020.0020.0020.0020.0020.00ei(mm)224.6827.69233.08243.3840.96243.38l0(mm)5250.005250.005250.00P5250.005250.005250.00l0/h11.6711.6711.6711.6711.6711.67司1.0011.001.001.001.001.001.001.001.001.001.001.00门1.182.461.171.171.991.17e(mm)455.031258.04463.42P473

20、.73271.30473.73/2、As(mm)467.12555.23479.01597.22425.45597.22Nx=-1fcb685.171031.014.3450=106.48mm第一组1层B柱顶的配筋计算:根据已知条件X<讥=0.51841B214.97mm所以为大偏心受压Meee0=204.68mmNea取h/30=450/30=15mm及20mm中的较大者，即e=20mmei=&ea=224.68mm因x2a=70mm，故将x代入式采用对称配筋林"1fcbx(h0,-0.5x)=467.12mm2fy(h0-a)八46712八:=0.23%：|min-

21、0.7%450450所以应该按构造配置纵向钢筋。三级框架柱纵向配筋率不应大丁5%,且不小丁0.7%,每侧不应小丁0.2%。一20.007bh°=0.007450415=1307mm实际每侧配筋2此18+1也6(P=710.1=0.355%>0.2%)，共配4业18+6140050016(总配筋面积为2223mm2>1307mm2)。同理：求得B柱截面设计如下表2.10-5:表2.10-5B柱截面设计1层柱上端柱下端M(kN.m)140.249.36140.24159.7026.20159.70N(kN)685.171216.43685.17714.931250.26714

22、.93X106.48189.03106.48111.10194.29111.10"(mm)214.97214.97214.97214.97214.97214.97偏压类型大偏压大偏压大偏压大偏压大偏压大偏压轴压比0.240.420.240.250.430.25b(mm)450.00450.00450.00450.00450.00450.00h(mm)450.00450.00450.00450.00450.00450.00h0(mm)415.00415.00415.00415.00415.00415.00e0(mm)204.687.69204.68223.3820.96223.38ea

23、(mm)20.0020.0020.0020.00P20.0020.00ei(mm)224.6827.69224.68243.3840.96243.38lo(mm)5250.005250.005250.005250.005250.005250.00lo/h11.6711.6711.6711.6711.6711.671.001.001.001.00一1.001.001.001.001.001.001.001.001.182.461.181.171.991.17e(mm)455.03258.04455.03473.73271.30473.732、As(mm)467.12-555.23467.1259

24、7.22-425.45597.22选筋21118+1业162业18+1业162业18+1业162业18+1业162业18+1业16坦18+1业16实际As(mm2)710.1710.1710.1710.1710.1710.1M%)0.3550.3550.3550.3550.3550.355p侧min(%)0.20.20.20.20.20.23层柱上端柱下端M(kN.m)112.3232.53112.3296.5333.5696.53N(kN)397.24615.59397.24419.35643.86419.35X61.7395.6661.7365.17100.0665.17$h°(

25、mm)214.97214.97214.97214.97214.97214.97偏压类型大偏压大偏压大偏压大偏压大偏压大偏压轴压比p0.140.210.140.140.220.14b(mm)450.00450.00450.00450.00450.00450.00h(mm)450.00450.00450.00450.00450.00450.00h°(mm)415.00415.00415.00415.00415.00415.00e0(mm)282.7552.84282.75230.1952.12230.19ea(mm)20.0020.0020.0020.0020.0020.00ei(mm)

26、302.7572.84302.75250.1972.12250.19l°(mm)4875.004875.004875.004875.004875.004875.00l0/h10.8310.8310.8310.8310.8310.8341.001.001.001.001.001.001.001.001.001.001.001.001.111.481.111.141.481.14e(mm)147.54297.63147.5494.98296.9194.982、As(mm)428.43-312.91428.43291.15-320.33291.15选筋21J_18+1业162业8+1业16

27、2业18+1业162业18+1业1621L18+1业16型18+1业16实际As(mm2)710.1710.1710.1710.1710.1710.1仞()0.3550.3550.3550.3550.3550.355p侧min(%)0.20.20.20.20.20.2顶层柱上端柱下端M(kN.m)95.352.2195.371.8738.2771.87N(kN)231.17323.92231.17253.29352.19253.29X35.9250.3435.9239.3654.7339.36"(mm)214.97214.97214.97214.97214.97214.97偏压类型大

28、偏压大偏压大偏压大偏压大偏压大偏压轴压比p0.080.110.080.090.120.09b(mm)450.00450.00450.00450.00450.00450.00h(mm)450.00450.00450.00450.00450.00450.00h°(mm)415.00415.00415.00415.00415.00415.00e0(mm)412.25161.18412.25283.75108.66283.75ea(mm)20.0020.0020.0020.0020.0020.00e(mm)432.25181.18432.25303.75128.66303.75l°

29、(mm)4875.004875.004875.004875.004875.004875.00l0/h10.8310.8310.8310.8310.8310.831.001.001.001.001.001.0021.001.001.001.001.001.001.081.191.081.111.271.11e(mm)277.0425.97277.04148.54-26.55148.54“/一2、As(mm)468.1561.49468.15275.02-68.35275.02选筋2山8+1业162乩8+1业162业18+1业162业18+1业162业18+1虹16疝8+但16实际As(mm2)7

30、10.1710.1710.1710.1710.1710.1P1(%)0.3550.3550.3550.3550.3550.355p侧min(%)0.20.20.20.20.20.22.9.4柱的节点设计本框架抗震等级为三级，只需要按高层建筑混凝土结构技术规程（JGJ3-20026.4.10的要求在节点加密区设置水平箍筋，配筋特征值七不宜小丁0.08,体积配箍率不宜小丁0.4%,不必专门进行抗剪承载力的计算，所以配*810002).柱的斜截面强度计算：(1) 最小配筋率的确定：根据混凝土结构设计规范(GB50010-2002)11.4.17规定，柱箍加密区箍筋的体积配筋率3-，式中、为最小配箍特征值，按混凝土结构设计规范(GB50010-2002)土11.4.17规定采用。(2) 框架柱的计算剪跨比的确定：根据混凝土结构设计规范(GB50010-200211.4.9规定，框架柱的计算剪跨比当框架结构中的框架柱的反弯点在柱层高范围内时，可取人=Hn/(2h0)。(3) 保证强剪弱弯，根据建筑抗震设计规范(GB50011-2