竖向荷载作用下框架结构的内力计算

1、竖向荷载作用下框架结构的内力计算6.1计算单元的选择确定取轴线横向框架进行计算，如下图所示:图6.1框架计算简图计算单元宽度为6.4 m，由于房间内布置有次梁，故直接传给该框架的楼面荷载如图 中的水平阴影所示。计算单元范围内的其余楼面荷载则通过次梁和纵向框架梁以集中 力的形式传给横向框架，作用于各节点上。由于纵向框架梁的中心线与柱的中心线不 重合，所以在框架节点上还作用有集中力矩。6.2荷载计算6.2.1恒载作用下柱的内力计算：恒荷载作用下各层框架梁上的荷载分布如下图所示:图6.2恒荷载作用下各层框架梁上的荷载分布图、对于顶层屋面，q1、q代表横梁自重，为均布荷载形式。q1=0.3 X 0.7

2、5 X 25=5.625kN/mq=0.3 X 0.75 X25=5.625kN/mq2为屋面板传给横梁的梯形荷载。q2=5.29 X 3.2=16.928kN/mP】、P2分别由边纵梁、中纵梁直接传给柱的恒载，它包括主梁自重、次梁自重、楼板 重等重力荷载，计算如下：P=6.4*0.3*0.75*25+8.5/2*0.25*0.6*25+5.29*3.2*1.6+(5.3+8.5)*1.6*5.29/4=108.223KNP2=6.4*0.3*0.75*25+6.4/2*0.25*0.6*25+5.29*3.2*1.6 +(3.2+6.4)*1.6*5.29/4=95.398KNP3=6.4*

3、0.3*0.75*25+(8.5+6.4)*0.5*0.25*0.6*25+5.29*3.2*1.6*2+(3.2+6.4)*1.6*5.29/4= 190.64KN集中力矩M1=P1e1=108.223X(0.6 -0.3) /2=16.23kN - mM2=P2e2=147.23 X(0.6 -0.3) /2=14.31kN - m、对于3层，包括梁自重和其上横墙自重，为均布荷载，其它荷载的计算方法同第顶层。q1=5.635+0.2 X 3.7 X 10.3=13.257kN/mq1，=5.635+0.2 X 3.7 X 10.3=13.257kN/mq2为楼面板和走道板传给横梁的梯形荷载

4、。q2=3.85X3.2=12.32kN/mP=6.4*0.3*0.75*25+6.4/2*0.25*0.6*25+3.85*3.2*1.6+(3.2+6.4)*1.6*3.85/4+6.4*0.25*3.7*9.6=139.328KNP2=6.4*0.3*0.75*25+6.4/2*0.25*0.6*25+3.85*3.2*1.6 +(3.2+6.4)*1.6*3.85/4+6.4*0.25*3.7*9.6+(3.2+6.4)*1.6*5.29/4+6.4*0.25*3.7*9.6=139.32 8KNP3=6.4*0.3*0.75*25+6.4/2*0.25*0.6*25+3.85*3.2

5、*1.6+(3.2+6.4)*1.6*3.85/4+6.4*0.22*3.7*10.3+3.2*2.1*3.85+6.4*0.2*3.7*10.3=213.981KN 集中力矩M1=P1e1=139.328X(0.6-0.3) /2=20.90kN - mM2=P2e2=139.328X(0.6-0.3) /2=20.90kN - m、对于1层和2层，包括梁自重和其上横墙自重，为均布荷载，其它荷载的计算方法同第顶层。q1=5.635+0.2 X 3.3 X 10.3=12.433kN/mq1，=5.635+0.2 X3.3X 10.3=12.433kN/mq2为楼面板和走道板传给横梁的梯形荷载

6、。q2=3.85X3.2=12.32kN/mP=6.4*0.3*0.75*25+6.4/2*0.25*0.6*25+3.85*3.2*1.6+(3.2+6.4)*1.6*3.85/4+6.4*0.25*3.3*9.6=133.184KNP2=6.4*0.3*0.75*25+6.4/2*0.25*0.6*25+3.85*3.2*1.6+(3.2+6.4)*1.6*3.85/4+6.4*0.25*3.3*9.6=133.184KNP3=6.4*0.3*0.75*25+6.4/2*0.25*0.6*25+3.85*3.2*1.6+(3.2+6.4)*1.6*3.85/4+6.4*0.25*3.7*9

7、.6+3.2*2.1*3.85+6.4*0.2*3.3*10.3=202.563KN集中力矩M1=P1e1=133.184X(0.6-0.3) /2=19.98kN - mM2=P2e2=133.184X(0.6-0.3) /2=19.98kN - m6.2.2活载作用下柱的内力计算：活荷载作用下各层框架梁上的荷载分布如下图所示：图6.3活荷载作用下各层框架梁上的荷载分布图、对于顶层，q2, =2.0X3.2=6.4kN/mP1= (3.2X1.6 +8.5 X 1.6/2 )X2=23.84kNP2= (3.2X1.6+6.4X1.6/2)X2=20.48kN集中力矩M1=P1e1=23.8

8、4X(0.6-0.3) /2=3.58kN - mM2=P2e2=20.48 X(0.6-0.3) /2=3.07kN m、对于第1-3层，q2, =2.0X3.2=6.4kN/mP1= (3.2X1.6 +8.5 X 1.6/2 )X2=23.84kNP2= (3.2X1.6+6.4X1.6/2)X2=20.48kNP3=3.2*1.6*2+1.6*1.6*2+3.2*2.1=22.08kN集中力矩M1=P1e1 =23.84X(0.6-0.3)/2=3.58kN - mM2=P2e2=20.48X(0.6-0.3)/2=3.07kN m将计算结果汇总如下两表:横向框架恒载汇总表层次qi (

9、kN/m)q (kN/m)q2 (kN/m)P1 (kN)P2 (kN)M1 (kN m)M2 (kN m)45.6255.62516.928108.22395.39816.2314.31313.25713.25712.32139.328139.32820.920.91-212.43312.43312.32133.184133.18419.9819.98横向框架活载汇总表层次q： (kN/m)P1 (kN)P2 (kN)M1 (kN m)M2 (kN m)46.423.8420.483.583.071-36.423.8420.483.583.076.2.3恒荷载作用下梁的内力计算:恒荷载作用下

10、各层框架梁上的荷载分布如下图所示:等效于均布荷载与梯形的叠加。、对于第4层，MAC=-MCA=q1l21/12+q2l21 (1-2 a 2+ a 3)/12=5.625 X 8.52/12+16.928 X 8.52X 1-2X(0.19) 2+ (0.19) 3/12=129.13kN - mMCD=-MDC=q1； l22/12+q2l22 (1-2 a 2+ a 3) /12=5.625 X 6.42/12+16.928 X 6.42 X 1-2 X(0.25) 2+ (0.25) 3/12=70.66kN - m、对于第3层，MAC=-MCA=q1l21/12+q2l22 (1-2

11、a 2+ a 3) /12=13.257X 8.52/12+12.32X 6.42X 1-2X(0.19) 2+ (0.19) 3/12=119.12kN MCD=-MDC=q1，l22/12+q2l22 (1-2 a 2+ a 3) /12=13.257 X 6.42/12+12.32 X 6.42X 1-2 X(0.25) 2+ (0.25) 3/12 =82.70 kN、对于第1-2层，MAC=-MCA=q1l21/12+q2l21 (1-2 a 2+ a 3) /12=12.433 X 8.52/12+12.32X 6.42X 1-2X(0.19) 2+ (0.19) 3/12 =11

12、4.16 kNMCD=-MDC=q1，l22/12+q2l22 (1-2 a 2+ a 3) /12m=12.433 X 6.42/12+12.32 X 6.42 X 1-2 X(0.25) 2+ (0.25) 3/12 =82.52 kN6.2.4活荷载作用下梁的内力计算：活荷载作用下各层框架梁上的荷载分布如下图所示：图6.4活荷载作用下各层框架梁上的荷载分布图对于第4层，MAC=-MCA=q2l21(1-2 a 2+a 3)/12 =6.4X8.52X1-2X(0.19) 2+ (0.19) 3/12 =36.02 kN - mMCD=MDC=q2l22 (1-2a2+a3)/12 =6.

13、4 X 6.42X 1-2 X(0.25) 2+ (0.25) 3/12 =19.46 kN - m对于第1-3层，MAC=-MCA=q2l21 (1-2 a 2+a 3) /12 =6.4X8.52X1-2X(0.19) 2+ (0.19) 3/12 =36.02 kN - mMCD=-MDC=q2l22(1-2a2+a3)/12=6.4 X 6.42 X 1-2 X( 1/3) 2+ (1/3) 3/12=19.46 kN - m梁端固端弯矩统计梁端固端弯矩MAC (kN m)MCA (kN m)MCD (kN m)MDC (kN m)顶层165.15-165.1590.12-90.123

14、层155.14-155.14102.16-102.161-2层150.18-150.18101.98-101.986.3框架梁端、柱端弯矩计算梁端、柱端弯矩采用弯矩二次分配法计算，矩计算如下表所示: 矩分配与传递计算表19.341-11.67 061.7360.39659.47127.032-7.90978.59519.20619.824 -6.748011.67-9.07762.219 -123950.2950.309-150.18 044.303 46.406-7.061-5.891-6.17138.412-117.00 721.025 -3.1260.6900.429-2.924 -17

15、.4390.4290.916158.39 -11.0894-10.88 -136.43230.2930.1820.1350.390150.180-14.12 -8.7723-101.98 0-6.507 -18.79823.203 -4.1930.0030.002-19.0190.0010.004159.26 -12.9634-3.253.“a -139.79-6.506 30.373101.98 011.223 10.7969.763-9.432-38.03 -36.7193-9.399 -16.7764.306 -44.06669.360 -34.36-8.965 211.61-12.23

16、 810.796-34.99 30.3600.267-27.22 96.989-20.24 0-10.12 0图6.5框架弯矩图6.4梁端剪力和柱轴力的计算6.4.1恒载作用下：例：第4层：荷载引起的剪力：VA=VC左=(16.928X(5.3+1.6) +5.625X8.5) /2 =82.31kNVC=VD右=(16.928X(3.2+1.6) +5.628X6.4) /2 =58.64kN本方案中，弯矩引起的剪力很小，可忽略不计。A 柱： N 顶=108.22+82.31=190.53kN柱重：0.6X0.6X3.7X25=33.3kNN 底=N 顶+33.3=223.83kND 柱：N

17、 顶=95.40+58.64=154.04kNN 底=N 顶+33.3=187.34kNC 柱：N 顶=190.64+82.31+58.64=331.59kNN 底=N 顶+23.13=354.72kN 恒载作用下梁端剪力及柱轴力（kN）层次荷载引起的剪力柱轴力AC跨CD跨A柱3D柱VA=VC左(kN)VC=VD右(kN)N顶（kN）N底（kN）N顶（kN）N底（kN）N顶（kN）N底顷482.3158.64190.53223.83331.59354.72197.968231.268381.2352.27428.708495.308716.41762.67409.286475.886279.0050.52657.232757.1321083.661153.05611.82711.72179.0050.52885.7521018.9521450.911543.43814.354947.5546.4.2活载作用下：例：第4层：荷载引起的剪力：AC 跨：VA=Vc 左=6.4X(5.3+1.6)/2=22.08kNCD 跨：VC 右=VD=6.4X(3.2+1.6)/2=15.36kNA 柱：N 顶=N 底=22.08+23.