某實(shí)驗(yàn)教學(xué)樓建筑結(jié)構(gòu)豎向荷載作用下框架結(jié)構(gòu)的內(nèi)力計(jì)算案例(ー).計(jì)算單元確定取eq\o\ac(○,3)軸線橫向框架進(jìn)行計(jì)算，如下圖5-1所示。圖5-1橫向框架計(jì)算單元(二).荷載計(jì)算1.永久恒載永久荷載作用下各層框架梁上的荷載分布如下圖5-2所示：圖5-2恒荷載作用下框架梁的荷載分布圖（1）對(duì)于第5層和代表橫梁自重，為均布荷載形式．q1=0.3×0.6×25×1.05=4.725kN/mq1/=0.3×0.4×25×1.05=3.15kN/m和分別為屋面板和走道板傳給橫梁的梯形荷載和三角形荷載,由關(guān)系可得：q2=4.97kN/㎡×3.0m=14.91kN/mq2/=4.97kN/㎡×2.3m=11.43kN/mP1、P2分別由邊縱梁、中縱梁直接傳給柱的恒載，它包括主梁自重、樓板自重、次梁自重、女兒墻自重等重力荷載，計(jì)算如下P1=[（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5]×4.97（板）+4.725×6.0（縱梁）+6.6/2×3.94（次梁）+0.1×0.6×25×6.6（女兒墻）=112.08kNP2=[（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5+（12.2.3）/2×1.15]×4.97（板）+4.725×6.0（縱梁）+6.6/2×3.94（次梁）=129.90kN梁對(duì)柱節(jié)點(diǎn)的彎矩M1=P1×e1=112.08×(0.5.0.3)/2=11.21kN·mM2=P2×e2=129.90×(0.5.0.3)/2=12.99kN·m（2）對(duì)于2?4層、包括梁自重和其上橫墻自重，為均布荷載，其它荷載的計(jì)算方法同第5層．q1=4.725kN/m(同上)q1/=3.15kN/m(同上)和分別為樓面板和走道板傳給橫梁的梯形荷載和三角形荷載．q2=3.40×3.0=10.20kN/mq2/=3.40×2.3=7.82kN/mP1=[（（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5]×3.40（板）+6.0×4.725（縱梁）+6.6×3.94（次梁）+6.3×2.7×1.49（內(nèi)橫墻）+5.5×2.7×1.96×0.8（外縱墻）=144.60kNP2=[（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5+（12.2.3）/2×1.15]×3.40（板）+6.0×4.725（縱梁）+6.6×3.94（次梁）+6.3×2.7×1.27（內(nèi)橫墻）+5.5×2.7×1.96×0.8（外縱墻）=159.81kNM1=P1×e1=144.60×(0.5.0.3)/2=14.46kN·mM2=P2×e2=159.81×(0.5.0.3)/2=15.98kN·m（3）對(duì)于1層q1=4.725kN/mq1/=3.15kN/mq2=10.20kN/mq2/=7.82kN/mP1=144.60kNP2=159.81kNM1=P1×e1=156.31×(0.6.0.3)/2=21.69kN·mM2=P2×e2=159.81×(0.6.0.3)/2=23.97kN·m2.可變荷載可變荷載作用下各層框架梁上的荷載分布如圖5-3圖5-3活荷載作用下框架梁的荷載分布圖（1）、對(duì)于第五層（不上人屋面）（活荷載取0.5kN/㎡）q2=0.5×3.0=1.5kN/mq2/=0.5×2.3=1.15kN/mP1=[（（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5]×0.5=6.12kNP2=[（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5+（12.2.3）/2×1.15]×0.5=8.91kNM1=P1×e1=6.12×(0.5.0.3)/2=0.61kN·mM2=P2×e2=8.91×(0.5.0.3)/2=0.89kN·m同理，在屋面雪荷載(取0.5kN/㎡)的作用下：q2=0.5×3.0=1.5kN/mq2/=0.4×2.3=0.92kN/mP1=4.90kNP2=7.13kNM1=P1×e1=4.90×(0.5.0.3)/2=0.49kN·mM2=P2×e2=7.13×(0.5.0.3)/2=0.71kN·m（2）、對(duì)于第2?4層（走廊取2.5kN/m2，房間取2.0kN/m2）q2=2.0×3.0=6.0kN/mq2/=2.5×2.3=5.75kN/mP1=[（（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5]×2.0=24.48kNP2=[（（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5]×2.0+（12.2.3）/2×1.15×2.5=38.42kNM1=P1×e1=24.48×(0.5.0.3)/2=2.45kN·mM2=P2×e2=38.42×(0.5.0.3)/2=3.84kN·m（3）、對(duì)于第1層q2=2.0×3.0=6.0kN/mq2/=2.5×2.3=5.75kN/mP1=[（（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5]×2.0=24.48kNP2=[（（2.4×1.2×0.5）+（3.6×1.8×0.5）+（4.2+6.6）/2×1.2×0.5+（3+6.6）/2×1.8×0.5]×2.0+（12.2.3）/2×1.15×2.5=38.42kNM1=P1×e1=24.48×(0.6.0.3)/2=3.67kN·mM2=P2×e2=38.42×(0.6.0.3)/2=5.76kN·m將以上計(jì)算結(jié)果匯總?cè)绫?-1.5-2表5-1橫向框架恒載匯總表橫向框架恒載匯總表層次q1

kN/mq1/

kN/mq2

kN/mq2/

kN/mP1

kNP2

kNM1

kN·mM2

kN·m54.7253.1514.9111.43112.00129.9011.2012.992~44.7253.1510.207.82144.40159.8114.4415.9814.7253.1510.207.82144.40159.8121.6923.97表5-2橫向框架活載匯總表橫向框架活載匯總表層次q2

kN/mq2/

kN/mP1

kNP2

kNM1

kN·mM2

kN·m51.5(1.2)1.15(0.92)6.12(4.90)8.91(7.13)0.61(0.49)0.89(0.71)2~46.05.7524.4838.422.453.8416.05.7524.4838.423.675.76注：表中括號(hào)內(nèi)數(shù)值對(duì)應(yīng)于屋面雪荷載作用情況.(三).內(nèi)力計(jì)算1.梁端、柱端彎矩計(jì)算梁端、柱端彎矩采用彎矩二次分配法計(jì)算，由于結(jié)構(gòu)和荷載均對(duì)稱，故計(jì)算時(shí)可用半框架。圖5-4各層梁柱線剛度示意圖分布荷載轉(zhuǎn)化成等效荷載剛度分配：梁4×4.91/(4×4.91+4×4.18)=0.540柱4×4.18/(4×4.91+4×4.18)=0.460梁端彎矩MABr=ql2/12=（q1+q2E）l2/12=(4.725+13.11)×6.62/12=64.74kN?m(注：q2E=[1?2×(1.2/6.6)2+(1.2/6.6)3]×0.5×14.91+[1?2×(1.8/6.6)2+(1.8/6.6)3]×0.5×14.91=13.11kN/m)梁端彎矩MBCr=ql2/12=(3.15+5×11.43/8)×2.32/12=4.54kN?m表5-3恒載作用下彎矩恒載作用下上柱下柱右梁左梁上柱下柱右梁0.4600.5400.3790.2980.32311.20.64.7464.74.12.99.4.5424.62828.912.17.893.14.069.15.2494.252.8.946514.456.3.4570.0002.1592.535.4.1690.000.3.278.3.5530.00031.039.42.24057.1340.000.20.804.23.3420.3050.3050.3900.2930.2290.2290.24914.44.49.7149.71.15.98.3.5410.75710.75713.755.8.846.6.914.6.914.7.51712.3145.379.4.4236.8775.7.035.3.457.4.047.4.047.5.1751.0590.8280.8280.90019.02412.089.45.55348.801.13.121.9.543.10.1570.3050.3050.3900.2930.2290.2290.24914.44.49.7149.71.15.98.3.5410.75710.75713.755.8.846.6.914.6.914.7.5175.3795.379.4.4236.8775.3.457.3.457.1.932.1.932.2.470.0.011.0.008.0.008.0.0099.1839.183.33.99637.930.6.191.6.191.5.8990.3050.3050.3900.2930.2290.2290.24914.44.49.7149.71.15.98.3.5410.75710.75713.755.8.846.6.914.6.914.7.5175.3793.993.4.4236.8775.2.986.3.457.1.509.1.509.1.930.0.127.0.100.0.100.0.10814.62713.241.42.30847.615.10.000.10.471.11.1650.2850.3510.3640.2790.2190.2690.23721.69.49.7149.71.23.97.3.547.9869.83510.199.6.194.4.862.5.972.5.2615.379.3.975.100.1.729.0.402.0.495.0.513.0.941.0.738.0.907.0.79912.9639.340.43.99447.675.7.329.6.879.9.6004.670.3.440表5-4活載作用下彎矩活載作用下上柱下柱右梁左梁上柱下柱右梁0.4600.5400.3790.2980.3230.61.3.8303.830.0.71.0.2531.9222.256.1.357.1.067.1.1572.547.0.6791.128.1.572.0.859.1.008.0.1680.000.0.132.0.1433.610.4.2194.3910.000.2.771.1.6170.3050.3050.3900.2930.2290.2290.2492.45.19.15119.151.3.84.1.5845.0945.0946.513.4.022.3.143.3.143.3.4180.9612.547.2.0113.257.0.534.1.572.0.457.0.457.0.5840.3370.2640.2640.2875.5989.634.15.23318.723.6.556.4.451.4.4660.3050.3050.3900.2930.2290.2290.2492.45.19.15119.151.3.84.1.5845.0945.0946.513.4.022.3.143.3.143.3.4182.5472.547.1.2243.257.1.572.1.572.1.181.1.181.1.510.0.033.0.026.0.026.0.0286.4606.460.15.37218.353.4.741.4.741.5.0300.3050.3050.3900.2930.2290.2290.2492.45.19.15119.151.3.84.1.5845.0945.0946.513.4.022.3.143.3.143.3.4182.5472.206.1.0113.257.1.572.1.588.1.141.1.141.1.459.0.028.0.022.0.022.0.0246.5006.159.15.10818.378.4.692.4.753.5.0260.2850.3510.3640.2790.2190.2690.2373.67.19.15119.151.5.76.1.5844.4125.4345.635.3.294.3.176.3.176.2.7982.547.1.6472.818.1.572.0.2570.316.0.328.0.348.0.273.0.335.0.2956.7025.750.15.49118.327.5.021.3.511.4.6771.875.1.756表5-5雪荷載作用下彎矩雪荷載上柱下柱右梁左梁上柱下柱右梁0.4600.5400.3790.2980.3230.490.3.8303.830.0.710.0.2531.5361.804.1.087.0.854.0.9262.547.0.5440.902.1.572.0.921.1.0820.2370.0000.1860.2023.162.3.6523.8820.000.2.240.0.9770.3050.3050.3900.2930.2290.2290.2492.45.19.15119.151.3.84.1.5845.0945.0946.513.4.022.3.143.3.143.3.4180.7682.547.2.0113.257.0.427.1.572.0.398.0.398.0.509.0.369.0.288.0.288.0.3135.4647.243.15.15818.017.3.858.5.001.5.3150.3050.3050.3900.2930.2290.2290.2492.45.19.15119.151.3.84.1.5845.0945.0946.513.4.022.3.143.3.143.3.4182.5472.547.1.2243.257.1.572.1.572.1.181.1.181.1.510.0.033.0.026.0.026.0.0286.4606.460.15.37218.353.4.741.4.741.5.0300.3050.3050.3900.2930.2290.2290.2492.45.19.15119.151.3.84.1.5845.0945.0946.513.4.022.3.143.3.143.3.4182.5472.206.1.0113.257.1.572.1.588.1.141.1.141.1.459.0.028.0.022.0.022.0.0246.5006.159.15.10818.378.4.692.4.753.5.0260.2850.3510.3640.2790.2190.2690.2373.67.19.15119.151.5.76.1.5844.4125.4345.635.3.294.3.176.3.176.2.7982.547.1.6472.818.1.572.0.2570.316.0.328.0.348.0.273.0.335.0.2956.7025.750.15.49118.327.5.021.3.511.4.6771.875.1.756圖5-5豎向恒載作用下框架彎矩圖圖5-6豎向活載作用下框架彎矩圖2.梁端剪力和柱軸力計(jì)算：以第4、5層恒載作用(下表)為例說明計(jì)算過程（注意：計(jì)算剪力時(shí)梯形、三角形荷載按實(shí)際大小計(jì)算）：(1).第五層：荷載引起的剪力：VAB跨=0.5（2.3+6.6）/2×q2+0.5×6.6×q1=0.5×（2.3+6.6）/2×14.91+0.5×6.6×4.725=48.77kNVBC跨=0.5（1.15q2、+2.3q1、）=0.5×（1.15×11.43+2.3×3.15）=10.19kN彎矩引起的剪力：AB跨：（Mbl.Mbr）/l=(42.240.57.134)/6.6=?2.26kNBC跨：Mbl.Mbr=0總剪力：AB跨：VA=48.77?2.26=46.51kNVB=48.77+2.26=51.03kNBC跨：VB=VC=10.19kN柱軸力：A柱：N頂=P1+VA=112+46.51=158.51kNA柱重G柱=0.5×0.5×3.3×25=20.625kNN底=N頂+G柱=158.51+20.625=179.135kNB柱：N頂=P2+VB（AB跨）+VC=129.9+51.03+10.19=194.12kNB柱重G柱=0.5×0.5×3.3×25=20.625kNN底=N頂+G柱=194.12+20.625=214.75kN(2).第四層：荷載引起的剪力：VAB跨=0.5（2.3+6.6）/2×q2+0.5×6.6×q1=0.5×（2.3+6.6）/2×10.20+0.5×6.6×4.725=38.29kNVBC跨=0.5（1.15q2、+2.3q1、）=0.5×（1.15×7.82+2.3×3.15）=8.12kN彎矩引起的剪力:AB跨：（Mbl.Mbr）/l=(45.553.48.801)/6.6=.0.49kNBC跨：Mbl.Mbr=0總剪力：AB跨：VA=38.29.0.49=37.8kNVB=38.29+0.49=38.78kNBC跨：VB=VC=8.12kN柱軸力：A柱：N頂=P1+VA+N底(5層)=144.4+37.8+179.135=362.32kNA柱重G柱=0.5×0.5×3.3×25=20.625kNN底=N頂+G柱=362.315+20.625=382.94kNB柱：N頂=P2+VB（AB跨）+VC+N底(5層)=159.81+38.78+8.12+214.75=421.46kNB柱重G柱=0.5×0.5×3.6×25=20.625kNN底=N頂+G柱=421.64+20.625=442.08kN表5-6恒載作用下梁端剪力及柱軸力（kN）層次荷載引起的

剪力彎矩引起的

剪力總剪力柱軸力AB跨BC跨AB跨BC跨AB