9竖向荷载作用下结构的内力分析9.1竖向荷载作用下框架内力分析1荷载及计算简图⑴计算方法框架在竖向荷载作用的内力计算可采用精确法(如弯矩分配法),也可采用近似法(如分层法).由于在竖向荷载作用下框架侧移很小,而且各层荷载对其他层杆件内力影响不大,本本工程手算采用弯矩二次分配法.⑵荷载计算计算以1轴为设计对象,板的受力计算简图如图①屋面梁的均布线荷载恒载计算------屋面板传来的梯型恒载0.5*3.6*5.5=9.90KN/m梁自重0.25*0.60*25=3.75KN/m女儿墙自重1.72*1.2=2.064KN/m活载计算------屋面板传来的梯型活载0.5*3.6*2.0=3.6KN/m②5~12层梁的均布线荷载恒载计算-------板传来的梯型恒载0.5*2.0*2.95=2.95KN/m0.5*3.6*2.95=5.31KN/m梁自重0.25*0.6*25=3.75KN/m外墙自重1.72*2.4=4.13KN/m集中力31.05KN活载计算------板传来的梯型活载0.5*2.0*2.0=2.0 KN/m0.5*3.6*2.0=3.6KN/m集中力 4.75KN③2~3层梁的均布线荷载恒载计算------板传来的梯型恒载0.5*3.6*2.95=5.31KN/m梁自重0.25*0.60*25=3.75KN/m外墙自重1.72*2.7=4.644KN/m 活载计算------板传来的梯型活载0.5*3.6*2.0=3.6KN/m 则1轴的横向框架恒荷载及活荷载分布如图:恒荷载示意图活载示意图⑶计算跨度框架梁、柱用轴线表示,节点间的水平距离为梁的计算跨度.柱计算高度对一般层可取层高,对底层取基础顶面与上层楼板顶面之间的高度.2内力计算⑴恒载作用下杆端弯矩计算 ① 框梁固端弯矩 屋顶框梁:Ⅰ梁自重、女儿墙自重1g =3.75+2.064=5.814KN/m2/ql R R B A ===5.814/2=2.907KNm KN ql M M B A .07.231290.6814.51222-=⨯-=-==Ⅱ板传来的梯型恒载m KN g /90.92=KN q a l R R B A 25.2590.928.19.62=⨯-=-== m KN l a l a ql M M B A .63.34)9.68.19.68.121(1290.69.9)21(123322233222-=+⨯-⨯⨯-=+--==4~12层框梁:Ⅰ梁自重、外墙自重1g =3.75+4.13=7.88KN/m2/ql R R B A ===7.88/2=3.94KNm KN ql M M B A .26.311290.688.71222-=⨯-=-==Ⅱ板传来的梯型恒载m KN g /31.52=KNc bc l c b l b lqc R A 36.4)458.148.17.529.68.17.5129.67.518(9.6128.131.5)45421218(12322323322323=⨯-⨯⨯-⨯+⨯-⨯⨯⨯⨯=--+-= mKN c l c bc ab lqc M A .725.3)158.129.68.18.17.537.52.118(9.6368.131.5)152318(363222232222-=⨯-⨯+⨯⨯-⨯⨯⨯⨯-=-+--= mKN c l c bc ab l qc M B .978.3)158.129.68.128.17.537.52.118(9.6368.131.5)1522318(363222232222-=⨯+⨯⨯-⨯⨯+⨯⨯⨯⨯-=+-+-=KN c bc l c b l b lqc R B 25.2)458.148.14.229.68.13.3129.63.318(9.6128.131.5)45421218(12322323322323=⨯-⨯⨯-⨯+⨯-⨯⨯⨯⨯=--+-= KN R qc R B A 53.225.228.131.52=-⨯=-=mKN c l c bc ab lqc M A .869.3)158.129.68.128.13.333.36.318(9.6368.131.5)1522318(363222232222-=⨯+⨯⨯-⨯⨯+⨯⨯⨯⨯-=+-+-=mKN c l c bc ab lqc M B .563.2)158.129.68.18.13.333.36.318(9.6368.131.5)152318(363222232222-=⨯-⨯+⨯⨯-⨯⨯⨯⨯-=-+--=KN bc l c b l b l qc R A 58.3)9.065.429.69.065.489.665.412(9.649.031.5)2812(42232322323=⨯⨯-⨯+⨯-⨯⨯⨯⨯=-+-⨯=KN R qc R B B 199.158.39.031.5=-⨯=-=m KN l c bc ab l qc M A .836.4)9.69.09.065.4365.425.212(9.61290.031.5)312(1222222222-=⨯+⨯⨯-⨯⨯⨯⨯-=+--= m KN l c bc ab l qc M B .885.4)9.69.029.065.4365.425.212(9.61290.031.5)2312(1222222222-=⨯⨯-⨯⨯+⨯⨯⨯⨯-=⨯-+-= 板传来的梯型恒载m KN g /95.22'=KNc bc l c b l b l qc R A 23.0)450.140.173.129.60.173.1129.673.118(9.6120.195.2)45421218(12322323322323=⨯-⨯⨯-⨯+⨯-⨯⨯⨯⨯=--+-= mKN c l c bc ab l qc M A .466.0)150.129.60.10.173.1373.117.518(9.6360.195.2)152318(363222232222-=⨯-⨯+⨯⨯-⨯⨯⨯⨯-=-+--= mKN c l c bc ab l qc M B .465.0)150.129.60.120.173.1373.117.518(9.6360.195.2)1522318(363222232222-=⨯+⨯⨯-⨯⨯+⨯⨯⨯⨯-=+-+-=KN c bc l c b l b l qc R B 43.1)450.140.123.629.60.123.6129.623.618(9.6120.195.2)45421218(12322323322323=⨯-⨯⨯-⨯+⨯-⨯⨯⨯⨯=--+-= KN R qc R B A 05.043.120.195.22=-⨯=-=mKN c l c bc ab l qc M A .814.0)150.129.60.120.123.6323.667.018(9.6360.195.2)1522318(363222232222-=⨯+⨯⨯-⨯⨯+⨯⨯⨯⨯-=+-+-= mKN c l c bc ab l qc M B .785.0)150.129.60.10.123.6323.667.018(9.6360.195.2)152318(363222232222-=⨯-⨯+⨯⨯-⨯⨯⨯⨯-=-+--=KN bc l c b l b l qc R A 10.0)4.02.129.64.02.189.62.112(9.644.095.2)2812(42232322323=⨯⨯-⨯+⨯-⨯⨯⨯⨯=-+-⨯=KN R qc R B B 08.110.04.095.2=-⨯=-=m KN l c bc ab l qc M A .205.0)9.64.04.02.132.17.512(9.6124.095.2)312(1222222222-=⨯+⨯⨯-⨯⨯⨯⨯-=+--=m KN l c bc ab l qc M B .202.0)9.64.024.02.132.17.512(9.61240.095.2)2312(1222222222-=⨯⨯-⨯⨯+⨯⨯⨯⨯-=⨯-+-= Ⅲ次梁传来的集中力F=31.05KNKN b a l Pb R A 66.8)4.25.43(9.64.205.31)3(3232=+⨯⨯=+= m KN l Pab M A .904.169.64.25.405.312222-=⨯⨯-=-=m KN l b Pa M B .696.319.64.25.405.312222-=⨯⨯-=-= 2~3层框梁Ⅰ梁自重、女儿墙自重1g =3.75+4.644=8.394KN/m96.282/9.6394.82/=⨯===ql R R B A KNm KN ql M M B A .303.331290.6394.81222-=⨯-=-==Ⅱ板传来的梯型恒载m KN g /31.52=KN q a l R R B A 54.1331.528.19.62=⨯-=-== mKN l a l a ql M M B A .574.18)9.68.19.68.121(1290.631.5)21(123322233222-=+⨯-⨯⨯-=+--==活载产生的梁固端弯矩(计算方法同上) 同上计算结果列于力矩二次分配法表中.⑵根据梁、柱线刚度,计算各节点弯矩分配系数 顶层(12层)边框架边节点13A ：13131313131213131313131244219130.39110.609444(2191334200)A B A B AA ABA B A A i i i μμμ⨯====-=+⨯+注:AiBi μ为i 层梁板框架梁A 节点分配系数,1-AiBi μ为i 层梁板框架柱A 节点分配系数.11层~9层边框架边节点10~12A121212121213121112121211121344219130.2420.3794444(21913342002)A B A B A A A A A B A A A A i i i i μμμ⨯=====++⨯+⨯8层边框架边节点9A :999991098999109844234780.2090.3040.4874444(234783420054705)A B A B A A A A A B A A A A i i i i μμμ⨯=====++⨯++7层~5层边框架边节点6~8A :8888898788898744234780.1760.4124444(23478254705)A B A B A A A A A B A A A A i i i i μμμ⨯=====++⨯+⨯4层边框架边节点5A :5555565455565444246520.1600.3540.4864444(246525470575144)A B A B A A A A A B A A A A i i i i μμμ⨯=====++⨯++3~2层边框架边节点3~4A :4444454344454344246520.1400.4304444(24652275144)A B A B A A A A A B A A A A i i i i μμμ⨯=====++⨯+⨯1层边框架边节点2A :2222232122232144246520.1860.5670.2474444(246527514432844)A B A B A A A A A B A A A A i i i i μμμ⨯=====++⨯++⑶纵向框梁产生的柱轴力R 及柱偏心弯矩M纵向框梁,按简支梁计算的支反力R 反向作用于柱上 恒载:1g --梁自重; 2g --板传来的; 3g --墙自重屋面:KN R A 88.13=; 5~12: KN R A 62.15= 2~4: KN R A 55.16= 屋面:m KN M A .74.1125.088.13=⨯= 9~12:m KN M A .95.1125.062.15=⨯= 5~8: m KN M A .34.215.062.15=⨯= 2~4: m KN M A .90.2175.055.16=⨯= 活载:m KN q l q o /8.12==; KN lqR 62.12==9~屋面: m KN M A .20.0125.062.1=⨯= 5~8: m KN M A .24.015.062.1=⨯= 2~4: m KN M A .29.0175.062.1=⨯=⑷弯矩二次分配①恒载作用下弯矩二次分配②活载作用下弯矩二次分配恒载作用下框架弯矩图M(kN m)活载作用下框架弯矩图M(kN m)⑸梁端剪力及柱轴力计算对与梁剪力的求解要根据以上梁实际受荷情况梁已求的梁端弯矩，再由实际受荷与弯矩求剪力。