层框架建筑在恒荷载作用下的内力计算

1、恒荷载作用下的内力计算§1梁的固端弯矩q图1计算简图1iM ab ql 彳（公式 3-1）; M ba qP （公式 3-2）1212集中荷载偏心引起的固端弯矩构成节点不平衡弯矩M集中荷载二一 Fe （公式3-3）；梁的固端弯矩可按下面方法求得: 六层:Mc6D6 工-1 24.51kN/m 6.62 工88.97kN m12D6C6-1 24.51kN/m 6.62 =88.97kN m12MD6E6 1 14.99kN/m 2.72 =-9.11kN m1212ME6D614.99kN/m 2.7 =9.11kN m121 2ME6F624.51kN/m 6.6288.97kN

2、m1212M f6e624.51 kN / m 6.688.97kN m12由图2知一到五层竖向受荷相同，则固端弯矩也相同，可只算第五层1 2Mc5D517.43kN / m 6.62 =-63.27kN m121 2MD5c5 17.43kN/m 6.62 =63.27kN m 121 2Md5E510.32kN/m 2.7 =-6.27kN m12ME5D510.32kN/m 2.72 =6.27kN m12ME5F517.43kN/m 6.62 工63.27kN m12M F5E5-1 17.43kN/m 6.62 =63.27kN m12集中荷载偏心引起的固端弯矩:MC6 =162,3

3、4KN 0.15m =24.35KN mMd6 二-182.14KN 0.15m 二-27.32KN mMe6 =182.14KN0.15m =27.32KN mMf6 - -162.34KN0.15m =24.35KN m一至五层受集中荷载相同，弯矩也相同MC -116.56KN0.15m -17.48KN mMd 二-172.21KN 0.15m = -25.83KN mMe =172.21KN0.15m =25.83KN mMf =-116.56KN0.15m =-17.48KN m§2弯矩分配系数的计算根据梁柱的相对线刚度，算出各节点的弯矩分配系数: 顶层：C轴:D轴:E轴F

4、轴”C6D6梁“D6C6 梁D6D5柱-E6D6梁LLE6E5柱F6F5 柱U.0.820.82 1= 0.45“C6C5 柱0.550.82 10.820.82 1 2.0= 0.214“D6E6 梁2.00.82 T 2.0二 0.5240.82 1 2.0 一0.2622.00.82 1 2.010.82 1 2.00.820.82 110.82 1=0.524二 0.262=0.45= 0.550.820.82 1 2.0= 0.214至五层:C轴:"cd梁0.821 0.82 1= 0.29"cc上柱0.3551 0.82 1-CC下柱11 0.82 1=0.35

5、5D轴:%C梁0.820.82 1 2.0 1-0.172.00.82 1 2.0 1=0.4 1 5-DD上柱10.82 1 2.0 1= 0.2 0 8L1_DD下柱10.82 1 2.0 1=0.2 0 8E轴：-EE下柱F轴：一层：C轴：D轴E轴：F轴：用弯矩 次即可JED梁"ee上柱2.00.4150.82 1 2.0 11 -0.2080.82 1 2.0 1 1-0.2080.82 1 2.0 1LL0.82、fe梁0.291+0.82+11下柱10.821心550.82C0D0 一 0.875 0.82 1.0 一 0.3040.875C0C-1 柱0.3250.87

6、5 0.82 1.0%0C0%0E0”D0D1 柱0.820.82 0.875 2.0 1.02.00.82 0.875 2.0 1.00.82丁梁=0.8212.01 = 0.17-FF上柱JC0C1 柱-= 0.175= 0.4260.82 0.875 2.0 1.0 一0.2130.875D0D- 0.82 0.8 7 5 2.0 1.0 _ 0.1 86%0F0E0D0JE0E1柱JE0E-1JF0E0F0F1 柱F0F-1 柱1 0.82 1 _ 0.3551.00.875 0.82 1.0020.82 0.875 2.0 1.0= 0.1750.82 0.875 2.0 1.0 一

7、0.4260.82 0.875 2.0 1.0 一0.2130.8750.82 0.875 2.0 1.00.820.875 0.82 1.0-0.186= 0.3041.00.875 0.82 1.00.8750.875 0.82 1.0= 0.371= 0.3 2 5次分配法计算恒荷载作用下的框架弯矩, 计算如下图2：传递系数为1/2.各节点分配两F*F逢MSr*下醴D.3 H4EI Cl J14Lclw1 tsa1 dShClX2ties0.S3Ta.s电痢->Bs担III9. IV羽酸-J3L3s.m-iila-HITs.sX> 3.SiiHilk xzHIEa e-5.Q

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14、3 -EMDsin七13-SSID-1£图2 弯矩分配法计算恒载作用下框架弯矩（kN.m）59 3(16.1219.55Efi &7$4,12TmrmnT Uh<皿 JFJF45.3056.57H.5556,571.5556.6B19 453 7115.1211?IS 511.CBbi.e心“加 书站叫IW昨荀334.SS1讪吨uu皿1山山忤,J413那十叫Hl州II |皿衍莎33 71astK也511.>311.DBI俩山屮”1沾5rrmTlT芬-wuiu山川山屮沪仇蒔MAB怛55皿山川1川11叮而34刖6-37旳出现山川11叱也册34.775519.£

15、;3.5I1K63.5flK151O.Bta.o叮.T 7山川| |山屮*业丽39,03俪 zouimiuu尸阳&63Jllhr34.IBa E：7U11U11U山四"谥Tn汇"_”祁应甩扇则川川川屮妊I39.031213.3lM图3 恒载作用下的弯矩图（单位：kN.m）§3恒荷载作用下的剪力计算图4计算简图梁:刀 MA=0 刀 MB=0柱:刀 MC=0MA- MB-ql2/2-QBI=0MA- MB+ql2/2-QAI=0-MC- MD-QD X h=0刀MD=0 -MC- MD+QD X h=0由上面计算简图和推到公式进行计算如下:QB=(MA-MB)

16、/I-qI/2 (公式 3-4) QA=(MA- MB)/I+qI/2 (公式 3-5) QD=-(MC+ MD)/h (公式 3-6) QC=-(MC+ MD)/h (公式 3-7)六层:66.64-86.92 1Qc6D6 = -Qf6E624.51 6.6 = 77.82KN6.6 266.64-86.921Qd6C6 = -Qe6F624.51 6.6 = -83.95KN6.6 230.630.61Qd 6E6 =Qe 6D 614.99 2.7= 20.24 KN2.72Qc6C5iQF6F5 QD6D5_QE 6E542.3 25.718.91KN 3.613.98 23.641

17、0.45KN3.6五层:QC5D5- QF5E5QD 5C5QE5F559.38 -64.121 ,17.43 6.6 = 56.79KN 259.38 -64.121 人17.43 6.6 = -58.24KN26.66.6QD 5E5-_QE 5D 513.98-13.98110.32 2.7 =13.93KN2QC 5C4-Qf5F42.7贬竺5 二-9.91KN3.6Qd 5D4=- Qe5E4空38 =5.95KN3.6QcdQdeQcc三、四层:二-Qef-Qff-_Qee一层:Qc1D1QD1E1QC1C056.57-63.5117.43 6.6 =56.47KN 256.57-

18、63.51.17.43 6.6 =-58.27KN26.6-Qf1 E1 -Qe1F1-QE1D1-QF1 fo-QE1E0负一层:6.615.5-15.5110.32 2.7 =13.93KN2.7219.55 19.5510.86KN3.6迪上辱6.16KN3.656.68-63.711.17.43 6.6 =56.46KN6.6 256.68-63.71117.43 6.6 =-58.58KN26.615-15 110.32 2.7 =13.93KN2.7219.42 23.111.81KN3.6空g6.35KN3.6Qcodo-Qfoeo-QeofoQD0E0-iQE0D053.71 -63 117.43 6.6 =56.11KN6.6 253.71-63117.43 6.6 =-58.92KN6.6 217.32 -17.321 “10.32 2.7 =13.93KN2Qcoc-i=一 Qf20F-12.713.12 6.56 二-4.69KN4.2QC0C-1=- Qfof-i7.73 3.°6 = 2.57KN4.2恒荷载作用下的剪力和轴力图如下:77.622O.2t33.951S.9156.79=10A