6 第三章 框架内力计算.docx

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1、第三章框架内力计算3.1恒载作用下的框架内力3.1.1弯矩分配系数（1）弯矩分配系数：节点：A13472MAC=0.239a,ao4(0.868+1.333+0.424)5332.朋=0.368,4(0.868+1.333+0,424)5.696八CCC=0.393A4(0.868+1.333+0,424)节点：B15332为=0.247“21.61+2x3.5555.696八4aia2=263,221.61711朋切=329,n,21.6140.868nrAIAC=0.161,021.61节点：A21.424IAa21=43=4181=03411333A282=318a2b24.181节点：

2、B253322a2=224必223.8341.4244n_oi=3=23834=0.23942D2=3355x2=0298r1d223.834节点:A41.3334八皿uar-=0.484a(1.3331.424)41.424八4a4a3-2757057节点：B45332m4=029418.1381.4244八NRaR13144318.1388皿=3555x2=0392w418.138A3与B3与相应的A2,B2相同。(2)杆件固端弯矩横梁固端弯矩：i)顶层横梁自重作用：MA4B4=-M444=一,夕尸=_!_乂4_08x7.2?=17.63kNm1212171)Mb4D4=一一q12一一2.

3、841.352=-1.73iWm33MD4B4=1/2MB4D4=0.863XJVm板传来的恒载作用：MA4B4=-M4U11220.5MB4D4=MD4B4=ii）二四层横梁自重作用：2 2/ /-4夕5%32=/2(1-22/2+3/Z3)7.22(1-22.12/7.22+2.1363)=-75.69kNm5,=X11.80X2.7?=-4.48析加96=-11.82.72=-2.69kNm3211Maiai=-M创A1=一一q12一一X4.08X7.22=-17.63kNm1212Mf11Di=-72=-i2.841.352=-1.737V33Mdb=1/2fB1D1=0.863AJV

4、m板传来的恒载作用：Af八484=-Mb4A4=f2(12a2/12+a3/3)=15.517.22X().855=-57.29m125O5、Mf1iDi=q128.62X2.72=-3.T1kNnkN9696Moim=q128.622.72=-96kNm3232纵梁引起柱端附加弯矩：(边框架纵梁偏向外侧，中框架梁偏向内侧)(逆时针为正)顶层外纵梁：Ma4=-Md4=57.54().125=7.19/W加楼层外纵梁：Mm=-M0=30.45X().125=3.81WVm顶层中纵梁：M4=-Mc4=-52.530.125=-6.57kN-m楼层中纵梁：Mm=-MG=-42.8x0.125=-5.

5、35雨m(3)节点不平衡弯矩横向框架的节点不平衡弯矩为通过该节点的各杆件(不包括纵向框架梁)在节点处的固端弯矩之和，根据平衡原则，节点弯矩的正方向与杆端弯矩方向相反，一律以逆时针方向为正，如图4-1。20.515.5115.51g6CO15.51g6CO72001350a）恒载三b972001350b）恒载产生的节点不平衡弯矩图4-2横向框架承担的恒载及不平衡弯矩节点的不平衡弯矩：Ma4b4+MA,纵梁=-17.63-75.69+7.19=-86.13kN.m（4）内力计算根据对称原则，只计算AB、BC跨。在进行弯矩分配时，应将节点不平衡弯矩反号后再进行杆件弯矩分配。节点弯矩使相交于该节点杆件

6、的近端产生弯矩，同时也使各杆件的远端产生弯矩，近端产生的弯矩通过节点弯矩分配确定，远端产生的弯矩由传递系数C（近端弯矩与远端弯矩的比值）确定。传递系数与杆件远端的约束形式有关。恒载弯矩分配过程如图3-2。根据所求出的梁端弯矩，再通过平衡条件，即可求出恒载作用下梁剪力、柱轴力,结果见表4-1、表4-2、表4-3、表4-4。AB跨梁端剪力（kN）表3-1层q（kNm）1传来荷t作用）g（kN/m）（自重作用）1(m)g1/2u=q14MAB(kNm)MBA(kNm)EMik匕A=g-3t-U-EMij12Vb=TgU2+ZMik1)420.54.087.214.6952.28-62.4687.14

7、3.4363.54-70.40315.514.087.214.6939.55-66.8170.760.5553.69-54.79215.514.087.214.6939.55-63.4570.891.0353.21-55.27115.514.087.214.6939.55-57.7970.021.7052.54-55.97BC跨梁端剪力（kN）表3-2层q（kNm）反传来荷载作用）g（kNm）（自重作用）1(m)g1/21q/4VB=g12+1q/4VC=-g12+1q/4411.802.842.73.837.9711.80-11.8038.622.842.73.835.829.65-9.65

8、28.622.842.73.835.829.65-9.6518.622.842.73.835.829.65-9.65AB跨跨中弯矩（kN）表3-3层q（kNm）反传来亍载作g(kN/m)(自1(m)g1/2u=1q/4MAB(kNm)Mik/1Va=g?u-Mik1M=(g12+u)i+/4MAB%a*”2用)重作用)420.54.087.214.6952.28-62.463.4363.54-84.95315.514.087.214.6939.55-66.810.5553.69-58.50215.514.087.214.6939.55-63.451.0353.21-60.14115.514.0

9、87.214.6939.55-57.791.7052.54-63.38柱轴力(kN)表3-4层边柱A4油、D轴中柱B轴、C轴横梁口部压力纵梁口部压力柱重柱轴力横梁端部压力纵梁端部压力柱重柱轴力4柱顶63.5457.5424.375121.0882.2052.5324.38134.73柱底145.46159.113柱顶53.6930.4924.375229.6464.4442.8024.38266.35柱底254.01290.732柱顶53.2130.4924.375337.7164.9242.8024.38398.45柱底362.09422.831柱顶52.5430.4924.375445.1

10、265.5942.8040.00531.22柱底485.12571.22736294334.3B4M93.32魏1.51黑窝 19.12心嗯-14.47翅70.318道2|卬)6.81a A-7-7.13.唠 6州一,293Bq3.11A-712/ 217914.O.230B2B1篇膀-23.17318器 G A-722.-6-463411,16希 4a524期822禽 21.0.4)121.7120.S-27.15.S5 1- - 73ffi1B1,9B比127.19 “ A74-7.24QL-5239 正 Z a 160.7伯A1-71.11BoOA1363B ACdQ Oa节点分配顺序：

11、（A4、B3、A2、B1）;（B4、A3、B2、AD0.517A4阳44.37.5)3Z5520.341AW22.2714.991.62-0.B3850.341A2A324.275-4.而26.0.39BAIf1Q12.C26.32-2.3B1.1937.25图3-2恒载弯矩分配过程图3-5恒载作用下弯矩图（kN.m）121.0863.54-70.40134.7311.80-11.8070.45134.73-63.54121.08159.11159.11145.4653.49-54.799.65-9.6554.79-53.59145.46229.64266.35266.35229.64290.33290.33254.0153.21-55.279.65-9.6555.27-53.21254.01337.71398.45398.45337.71422.83422.83362.0952.54-55.949.65-9.8555.94-52.54362.09445.12531.22531.22445.12485.12571.22571.22485.12图3-6恒载作用下梁剪力、柱轴力(kN)3.2活载作用下的框架内力1)梁固端弯矩：顶层：1MA4B4=-MB4A4=2(17.CT/