竖向荷载作用下的内力计算.docx

1、竖向荷载作用下的内力计算河南大学毕业设计第6章竖向荷载作用下内力计算6.1框架结构的荷载计算6.1.1.板传荷载计算计算单元见下图所示：因为楼板为整体现浇，本板选用双向板，可沿四角点沿45线将区格分为小块，每个板上的荷载传给与之相邻的梁，板传至梁上的三角形或梯形荷载可等效为均布荷载。一.AB,(CE)轴间框架梁：屋面板传荷载：恒载：7.6KN/m22.25122.25/6.62.25/6.623237.61.5121.5/6.61.5/6.622.44KN/m活载：2KN/m222.25122.25/6.62.25/6.632321.5121.5/6.61.5/6.66.36KN/m楼面板传荷

2、载：恒载：4.1KN/m22.25122.25/6.62.25/6.623234.11.5121.5/6.61.5/6.613.03KN/m33河南大学毕业设计活载：7.7KN/m22.25122.25/6.622.25/6.63237.71.5121.5/6.61.5/6.67.95KN/m梁自重：3.34KN/mAB,(CE)轴间框架梁均布荷载为：屋面梁：恒载梁自重板传荷载3.34KN/m+22.44KN/m=25.78KN/m活载板传荷载6.36KN/m楼面板传荷载：恒载梁自重板传荷载3.34KN/m+13.03KN/m=116.37KN/m活载板传荷载7.95KN/m二.BC轴间框架梁

3、：屋面板传荷载：恒载：4.2KN/m22.25122.25/7.222.25/7.23224.2KN/m1.5121.5/7.21.5/37.214.10KN.m活载：22.25122.25/7.222.25/7.23220.3KN/m1.5121.5/7.21.5/37.24.17KN.m楼面板传荷载：恒载：4.1KN/m22.25122.25/7.22.25/7.223224.1KN/m1.5121.5/7.21.5/37.213.38KN.m活载：2.5KN/m222.25122.25/7.22.25/7.23222.5KN/m1.5121.5/7.21.5/37.28.16KN.m梁自

4、重：3.34KN/mBC轴间框架梁均布荷载为：屋面梁：恒载梁自重板传荷载3.34KN/m+14.10KN/m=17.44KN/m活载板传荷载4.17KN/m楼面板传荷载：恒载梁自重板传荷载3.34KN/m+13.38KN/m=16.72KN/m活载板传荷载8.16KN/m三.A轴柱纵向集中荷载计算：顶层柱：34河南大学毕业设计顶层柱恒载女儿墙梁自重板传荷载6.6724.523.343.27.062.255/823.7514.5KN顶层柱活载板传荷载=25/82(22.252.251.51.5)18.28KN标准层柱恒载墙自重梁自重板荷载22=5.76(3.750.5)3.343.24.15/8

5、2(2.251.5)72.01KN准层柱活载板传荷载=2KN/m2.4m5/824.828.8KNa基础顶面荷载底层外纵墙自重基础自重=14.11(3.750.55)3.75(3.750.55)22.85KN四.C柱纵向集中力计算：顶层柱荷载=梁自重+板传荷载=3.13(3.75-0.5)+21.52)7.85/82(2.250.61.55/821.5=120.91KN顶层柱活载=板传荷载=22=25/82(2.2521.5)0.31.55/821.531.78KN标准柱恒载=墙梁自重板传荷载22=29.193.113(4.750.5)4.15/82(2.2521.5)114.32KN/m标准

6、层活载板传荷载=7.82.255/824.52.51.55/82345.70KN基础顶面恒载=底层内纵墙自重基础自重=46.953.75(3.750.55)58.95KN（3）.框架柱自重：柱自重：底层：边柱1.20.55m0.55m253KN/m5.4m=49.01KN中柱1.20.55m0.55m253KN/m5.4m=49.01KN标准层:边柱1.20.5m0.5m253KN/m3.6m=27KN中柱1.20.5m0.5m253KN/m3.6m=27KN顶层:边柱1.20.55m0.55m253KN/m3.9m=35.39KN中柱1.20.55m0.55m253KN/m3.9m=35.3

7、9KN6.2恒荷载作用下框架的内力6.2.1.恒荷载作用下框架的弯矩计算恒荷载作用下框架的受荷简图如图6-3所示，由于AE二轴的纵35河南大学毕业设计梁外边线分别与该柱的外边线齐平，故此二轴上的竖向荷载与柱轴线偏心，且偏心距离为75mm。则均布恒载和集中荷载偏心引起的固端弯矩构成框架节点不平衡弯矩。一.恒荷载作用下框架可按下面公式求得：均载M1：2M1/1ql2(61)abM1/12qlba2集中荷载Me：Me=-Fe(62)2故：MA61/1225.786.693.58KN.mMB6A693.58KN.mB62MB6C1/1217.447.275.34KN.mMC6B675.34KN.m6M

8、2A51/1259.426.659.42KN.mMB5A559.24KN.mB5A51/1259.426.659.42KN.mMB5A559.24KN.mM2B1/1216.727.272.23KN.m5MC5B572.23KN.mC5Me6114.50.12518.06KN.mMe572.850.1259.11KN.mMe472.010.1259.01KN.m所以梁固端弯矩为FMnMeM1恒荷载作用下框架的受荷简图如图6-3所示:图6-3竖向受荷总图：注：1.图中各值的单位为KN,2.图中数值均为标准值3.图中括号数值为活荷载36河南大学毕业设计图6-4：恒载作用下的受荷简图(2).根据梁，

9、柱相对线刚度，算出各节点的弯矩分配系数ij:ijiicib(63)/()分配系数如图65,图66所示：A柱：底层i00.977/(0.9421.00.977)0.335下柱i上柱7.9/(0.9421.00.977)0.342i左梁7.9/(0.9421.00.977)0.323标准层：i1.0/(0.9421.01.0)0.340上柱i下柱4.3/(0.9421.01.0)0.340i左梁4.3/(0.9421.01.0)0.32五层:i1.35/(1.350.9421.0)0.410上柱i1.0/(1.350.9421.0)0.304下柱i左梁0。942/(1.350.9421.0)0.2

10、86顶层：i下柱1.35/(0.9421.35)0.590i左梁7.3/(1.350.942)0.4137河南大学毕业设计B柱：底层：i0.942/(0.9420.8640.9771.0)0.250右梁i1.0/(0.9420.8640.9771.0)0.264上柱i下柱7.10/(0.9420.8640.9771.0)0.258i0.864/(0.9420.8640.9771.0)0.228左梁标准层：i1.0/(0.9421.01.00.864)0.63下柱i上柱7.10/(0.9421.01.00.864)0.63i右梁4.4/(0.9421.01.00.864)0.247i左梁4.4/

11、(0.9421.01.00.864)0.227顶层：i下柱1.0/(1.01.350.8640.94)20.241i上柱7.4/(1.01.350.8640.942)0.325i右梁14.11/(1.01.350.8640.942)0.227i左梁0.4/(1.01.350.8640.942)0.207顶层：i1.35/(1.350.8640.942)0.428下柱i左梁7.3/(1.01.350.8640.942)0.274i右梁4.18/(1.01.350.8640.942)0.294三.恒荷载作用下的弯矩剪力计算，根据简图（64）梁：M0A2MM1/2qlQ.l0ABBQMM/l1/2q

12、lBABM0B2MM1/2qlQ.l0ABAQMM/l1/2ql（64）AAB柱：M0MCMDQD.h0CQ(MM)/hDCDM0MMQ.h0DCDCQ(MM)/h（65）CCD38河南大学毕业设计四.恒荷载作用下的边跨框架的轴力计算，包括连梁传来的荷载及柱自重.N6=114.5+25.786.6/2=199.574KNN5=N6+72.81+16.377.2/2+35.39=361.795KNN4=N5+72.01+16.376.6/2+27=514.826KNN3=N4+72.01+16.376.6/2+27=667.857KNN2=N3+72.01+16.376.6/2+27=820.8

13、88KNN1=N2+72.01+16.376.6/2+27=973.92KN恒荷载作用下的中跨框架的轴力计算：N6=120.91+17.447.2/2+25.786.6/2=268.77KNN5=N6+114.32+16.376.6/2+16.727.2/2+35.39=532.69KNN4=N5+114.32+16.376.6/2+16.727.2/2+27=788.24KNN3=N4+114.32+16.376.6/2+16.727.2/2+27=1043.75KNN2=N3+114.32+16.376.6/2+16.727.2/2+27=1299.29KNN1=N2+114.32+16.

14、376.6/2+16.727.2/2+27=1554.82KN图67恒荷载作用下的计算简图五.弯矩分配及传递弯矩二次分配法比分层法作了更进一步的简化。在分层法中，用弯矩分配法计算分层单元的杆端弯矩时，任一节点的不平衡弯矩都将影响到节点所在单元中的所有杆件。而弯矩二次分配法假定任一节点的不平衡弯矩只影响至与该节点相交的各杆件的远端。因此可将弯矩分配法的循环次数简化到一次分配、一次传递、再一次分配。所以本框架设计采用弯矩分配法计算框架内力，传递系数为1/2。各节点分配两次即可，恒荷载作用下框架内力如表61所示39河南大学毕业设计图68恒荷载作用下的弯矩图单位（KN.m）表61恒荷载作用下的弯矩内力

15、二次分配表六.恒载作用下的的框架弯矩图对于无荷载直接作用的杆件（如柱），将其柱端的弯矩连以直线，即为该杆件的弯矩图；对于有荷载作用的杆件（如梁），则以杆端弯矩的连线为基线。叠加相应简支梁的弯矩图，即为该杆件的弯矩图。弯矩图如上图68所示7.11则梁跨中弯矩为：40河南大学毕业设计MAB1825.78/6.6212(49.13.101.9.)64.86.KNmKNmKNmKNm65中MBC1817.44/7.212(69.85.69.85.)43.16.KNmKNmKNmKNm256中MAB1816.37/6.612(42.54.71.15.)32.29.KNmKNmKNmKNm255中MBC1

16、816.72/7.212(85.18.85.18.)26.17.KNmKNmKNmKNm255中MAB1816.376.612(37.1971.24)34.92.2KNm44中MBC1816.72/7.212(86.16.86.15.)19.93.KNmKNmKNmKNm244中MAB1816.376.612(37.1971.19)34.94.KKNm233中MBC1816.727.212(86.1986.19)22.16.2KNm33中MAB1816.376.612(37.1971.19)34.94.KKNm222中MBC1816.727.212(86.1986.19)22.16.2KNm2

17、2中MAB1816.37/6.612(35.372.19)35.39.KNmKNm211中MBC188.095/2.712(16.36.16.36.)8.98.KNmKNmKNmKNm211中七.恒载作用下剪力计算7.12梁端剪力：QA6(MAMB)/L1/2ql(49.13101.9)/6.61/225.786.677.08KNQB6(MAMB)/L1/2ql(49.13101.9)/6.61/225.786.6182.62KNQA6(MAMB)/L1/2ql1/217.447.262.78KNQB6(MAMB)/L1/2ql62.78KNQA5(MAMB)/L1/2ql(42.5471.1

18、5)/6.61/216.376.649.69KNQB5(MAMB)/L1/2ql(42.5471.15)/6.61/216.376.658.35KNQA5(MAMB)/L1/2ql1/216.727.260.19KNQB5(MAMB)/L1/2ql60.19KNQA4(MAMB)/L1/2ql(37.1971.24)/6.61/216.376.648.86KNQB4(MAMB)/L1/2ql(37.1971.24)/6.61/216.376.659.18KNQA4(MAMB)/L1/2ql1/216.727.260.19KNQB4(MAMB)/L1/2ql60.19KN41河南大学毕业设计QA

19、3(MAMB)/L1/2ql(37.1971.19)/6.61/216.376.648.87KNQB3(MAMB)/L1/2ql(37.1971.19)/6.61/216.376.659.17KNQA3(MAMB)/L1/2ql1/216.727.260.19KNQB3(MAMB)/L1/2ql60.19KNQA2(MAMB)/L1/2ql(37.2271.19)/6.61/216.376.648.12KNQB2(MAMB)/L1/2ql(37.2271.19)/6.61/216.376.659.9348.12KNQA2(MAMB)/L1/2ql1/216.724.260.19KNQB2(MA

20、MB)/L1/2ql60.19KNQA1(MAMB)/L1/2ql(35.372.19)/6.61/2116.376.648.43KNQB1(MAMB)/L1/2ql(35.372.19)/6.61/2116.376.659.61KNQA1(MAMB)/L1/2ql1/216.727.260.19KNQB1(MAMB)/L1/2ql60.19KN2.柱端剪力：Q6(49.1329.0)/3.920.03KNQ6(6.035.65)/3.92.99KNQ5(13.5518.14)/3.68.8KNQ5(8.387.56)/3.64.43KNQ4(19.0618.14)/3.610.33KNQ4(

21、7.377.56)/3.64.15KNQ3(19.0618.14)/3.610.33KNQ3(7.697.56)/3.64.22KNQ2(19.0621.11)/3.611.16KNQ2(7.78.44)/3.64.48KNQ1(13.198.45)/5.44.01KNQ1(4.773.5)/5.41.53KN42河南大学毕业设计注：由于该框架结构左右对称，所以竖向荷载作用下框架剪力图反对注：由于该框架结构左右对称，所以竖向荷载作用下框架轴力图对称43河南大学毕业设计6.3活荷载作用下框架的内力6.3.1活载作用下的框架内力同恒载作用下用弯矩分配法计算框架内力，折减系数为1/2，各节点分配两次

22、即可。活荷载作用下框架内力如表62所示。6.3.2活荷载作用下框架的内力计算活荷载作用下框架可按下面公式求得：均载M1：2M1/1ql2(61)abM1/12qlba2集中荷载Me：Me=-Fe(62)2故：MA1/126.366.623.09KN.m6B6MB6A623.09KN.mMe618.280.1252.29KN.m2MAB1/127.956.628.86KN.m55MB6A628.86KN.mMe622.850.1252.86KN.m2Mb6c1/124.176.618.01KN.mMC6B618.01KN.m62MB5C1/128.167.235.25KN.mMC5B535.25

23、KN.m5Me28.80.0752.16.FeKNmFMMeM1所以梁固端弯矩为FMnMeM。1表62活荷载作用下的弯矩内力二次分配表46河南大学毕业设计47河南大学毕业设计二.活载作用下的的框架弯矩图对于无荷载直接作用的杆件（如柱），将其柱端的弯矩连以直线，即为该杆件的弯矩图；对于有荷载作用的杆件（如梁），则以杆端弯矩的连线为基线。叠加相应简支梁的弯矩图，即为该杆件的弯矩图。弯矩图如上图69所示则梁跨中弯矩为：MAB186.36/6.612(14.7.24.72.)14.92.KNmKNmKNmKNm266中121MBC2(22.71.22.71.)4.31.4.17KN/m7.2KNmKN

24、mKNm66中8MAB187.95/6.612(20.83.33.71.)16.02.KNmKNmKNmKNm255中121MBC2(38.28.38.28.)14.60.7.1116KN/m7.2KNmKNmKNm5中85MAB187.95/6.612(19.59.33.96.)16.51.KNmKNmKNmKNm244中121MBC2(38.29.38.29.)14.59.7.1216KN/m7.2KNmKNmKNm4中84MAB187.95/6.612(19.74.33.94.)16.45.KNmKNmKNmKNm233中121MBC2(38.3.38.3.)14.58.4.516KN/

25、m7.2KNmKNmKNm33中8MAB187.95/6.612(19.74.33.94.)16.45.KNmKNmKNmKNm222中121MBC2(38.3.38.3.)14.58.4.5KN/m7.2KNmKNmKNm22中8MAB187.95/6.612(18.16.34.27.)17.08.KNmKNmKNmKNm211中121MBC2(38.08.38.08.)14.08.7.5KN/m7.2KNmKNmKNm1中81三.活荷载作用下的框架剪力计算根据简图（64）和推导公式计算其活荷载作用下的剪力如图（69）所示：14.12梁端剪力：QA6(MAMB)/L1/2ql(14.7024

26、.72)/6.61/26.366.619.47KNQB6(MAMB)/L1/2ql(14.7024.72)/6.61/26.366.622.51KN48河南大学毕业设计QA6(MAMB)/L1/2ql1/24.177.215.01KNQB6(MAMB)/L1/2ql15.01KNQA5(MAMB)/L1/2ql(20.8333.71)/6.61/27.956.624.29KNQB5(MAMB)/L1/2ql(20.8333.71)/6.61/27.956.628.19KNQA5(MAMB)/L1/2ql1/28.167.229.38KNQB5(MAMB)/L1/2ql29.38NQA4(MAMB)/L1/2ql(19.5933.96)/6.61/27.956.624.06KNQB4(MAMB)/L1/2ql(19.5933.96)/6.61/27.956.628.41KNQA4(MAMB)/L1/2ql1/28.167.229.38KNQB4(MAMB)/L1/2ql29.38KNQA3(MAMB)/L1/2ql(19.7433.94)/6.61/27.956.624.08KNQB3(MAMB)/L1/2ql(19.7433.94)/6.61/27.956.628.39KNQA3(MAMB)/L1/2