六层框架建筑在恒荷载作用下的内力计算

恒荷载作用下的内力计算 1 梁的固端弯矩图 1 计算简图11M = ql2（公式 3-1）；M = ql2（公式 3-2）ab 12 ba 12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 Fe公式 3-3）；梁的固端弯矩可按下面方法求得：六层：M=-丄 x 24.51kN / m x 6.62 =-88.97kN - mC6D6 12M=-!-x 24.51kN / m x 6.62 = 88.97kN - mD6C6 12M=-丄 x14.99kN / m x 2.72 =-9.11kN - mD6E6 12M=丄 x14.99kN / m x 2.72 = 9.11kN - mE6D6 12M = - x 24.51kN / m x 6.62 = -88.97kN - mE6F6 12M =-!-x 24.51kN / m x 6.62 = 88.97kN - mF6E6 12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M = -x 17.43kN / m x 6.62 = -63.27kN - mC5D5 12M =-!-x 17.43kN / m x 6.62 = 63.27kN - mD5C5 12M = -x 10.32kN / m x 2.72 = -6.27kN - mD5E5 12M=丄 x10.32kN / m x 2.72 = 6.27kN - mE5D5 12M = -x17.43kN / m x 6.62 = -63.27kN - mE5F5 12M=-!-x 17.43kN / m x 6.62 = 63.27kN - mF5E5 12集中荷载偏心引起的固端弯矩：M = 162,34KN x 0.15m = 24.35 KN - mC6M =182.14 KN x 0.15m = 27.32KN - m D6M = 182.14 KN x 0.15m = 27.32KN - m E6M = 162.34KN x 0.15m = 24.35 KN - m F6一至五层受集中荷载相同，弯矩也相同M = 116.56 KN x 0.15m = 17.48 KN - m CM =172.21KN x 0.15m = 25.83KN - m DM = 172.21KN x 0.15m = 25.83KN - mEM =116.56 KN x 0.15m = 17.48 KN - mF 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：0.82r = 0.45C6D6 梁 0.82 +10.82卩C6C5柱r = 0.214D6C6 梁0.82 +1 + 2.01RD6D5 柱0.82 +1 + 2.0 = 0.2622.0RE6D6 梁0.82 +1 + 2.0 = 0.5241r = 0.262E6E5 柱0.82 +1 + 2.00.82R = 0.45F6E6 梁 0.82 +11r = 0.55F6F5 柱0.82 +1h6梁E6F6 梁1 =0.55 0.82 +12.00.82 +1 + 2.0 - 0.524般去=0214二至五层：C 轴：r =082= 0.29CD梁CC上柱1 + 0.82 +1 = 0355D 轴：R dc梁0.82 +1 + 2.0 +1 = 0.172.0r = 0.355cc 下柱 1 + 0.82 +10.82卩 de 梁=0.82 +1 + 2.0 +1 = 0.4 1 5dd上柱0.82 +1 + 2.0 +1 _ 2 82.0%D下柱E 轴：%D梁=0.82 +1 + 2.0 +11= 0.415= =0.2 0 8 0.82 +1 + 2.0 +10.82=0.82 +1 + 2.0 +1 = *17卩 ee上柱0.82 +1 + 2.0 +1 _ 02081|lx = 0.208ee下柱0.82 +1 + 2.0 +10.82卩 =0.29fe 梁1 + 0.82 +11F 轴：ff 上柱1 + 0.82 +1= 0.355一层：C 轴：E 轴：F轴:唇下柱二伉聞=0.3550.82匕odo _ 0.875 + 0.82 +1.0 _ ，340.875coc-i柱0.875 + 0.82 +1.0 _。卫药0.82doco _ 0.82 + 0.875 + 2.0 +1.0 A152.0doeo _ 0.82 + 0.875 + 2.0 +1.0 _ 彳药1“D0D1 柱0.82 + 0.875 + 2.0 +1.0 _ 2130.875%od-1 _ 0.82 + 0.8 7 2.0 +1.0 QAS60.82eofo _ 0.82 + 0.875 + 2.0 +1.0 A152.0eodo _ 0.82 + 0.875 + 2.0 +1.0 _ 彳药1卩 eoei柱0.82 + 0.875 + 2.0 +1.0 Q2130.875%oe-1 _ 0.82 + 0.875 + 2.0 +1.0 _*1860.82%oeo _ 0.875 + 0.82 +1.0 _1.0Uof1 柱 _ 0.875 + 0.82 +1.0 _ ，3?10.875fof-1 柱 _ 0.875 + 0.82 +1.0 325C0C1 柱1.00.875 + 0.82 +1.0= 0.3 7 1用弯矩二次分配法计算恒荷载作用下的框架弯矩，传递系数为 1/2.各节点分配两 次即可。计算如下图 2：F*右衆F*业下逢#KY*d壬145I| D-2U1CLN1 ClN11 . 31ClK 10.21411 CL31 ClH21.s邑50*-HW-1 II乩II耳卫-m-501m-9*-3LS五壬B E且EE-5-E3-|Lat八 U.9L-L3-H-3-3-.53UTTy h至 -liTTLS.TT3-33IL21-14.91-IS.ee用1 5_S-五壬-B- 12一 l h-L U-E S-13 OS13 OS臣Stl ELI皿工i-EElEAS-S-23-3-S-9T五刃23. 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IDB-S-XS3-S-a壬图 2 弯矩分配法计算恒载作用下框架弯矩 (kN.m)66.6586.ABBB.aB42.30InrnnrJrimT66.*5559.3116.125A.5756.5719.5555719.5519.4253.715fi.69JF6LQ lrrnTTn-r-.64.1233.1?B3.513-59.3810.3310.3：IK16.1233.71I34,aat3.5blK.出zui川止山山呼11朋34.3B11.OBTrTrTT Illi”；,” rrTTrirTTl3.5也穿7山山|11 111屮仇观34.3 B63.7忸砧FUlUll |山山屮他册34.7263.0110811.DB15.B15.M.D811.Q815.05.615.10.B23.112.08 7335.D3|kM卄皿叫Ulllllll山山片也比34.B83.5si.aa1炯现山山山山屮尸阳北34.BB佰飙皿皿皿HI尸13.5534.?2疋常现UHIIIIIJll叱 m3P.03S.M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=OEMB=0柱：EMC=0MA- MB-ql2/2-QBl=0MA- MB+ql2/2-QAl=0-MC- MD-QD X h=0E 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)/l-ql/2QA=(MA- MB)/l+ql/2 QD=-(MC+ MD)/h QC=-(MC+ MD)/h（公式 3-4）（公式 3-5（公式 3-6）公式 3-7）Q= -QC6D6F6E6Q= -QD6C6E6F6Q= -QD6E6E6D6Q= -QC6C5F6F5Q= -QD6D5E 6E 5五层Q= -QC5D5F5E5Q= -QD5C5E5F5Q= -QD5E5E5D5Q= -QC5C4F5F4QD5D4= -QE 5E4六层：二、QCD66.64 - 86.921 ,=+ x 24.51 x 6.6 = 77.82KN6.6 266.64-86.921=-x 24.51 x 6.6 = -83.95KN6.6 230.6-30.61=+ x 14.99 x 2.7 = 20.24KN2.7242.3+25.7=-=-18.91KN3.613.98+23.64=-=10.45KN3.659.38-64.121=+ x 17.43 x 6.6 = 56.79KN6.6259.38-64.121=-x 17.43 x 6.6 = -58.24KN6.6213.98-13.981=-+ X10.32 x 2.7 = 13.93KN2.72=-16.12 +19.55 = -9.91KN3.6=133 + ll.8 = 5.95KN3.6QDCQDEQCC三、四层：=-q = 56.57 - 65 + % 17.43 x 6.6 = 56.47KN fe6.6256.57 -63.51=x 17.43 x 6.6 = -58.27KN6.6 2=15.5 -15.5 + - x 10.32 x 2.7 = 13.93KN 2.7219.55+19.55=-=-10.86 KN= -Qef= -Qed= -QffQDD一层= _Qee3.6=IL。8 * a08 = 6.16 KN3.656.68 -63.711Q= -Q=+ x17.43 x 6.6 = 56.46KNC1D1 F1E16.6256.68 -63.71 1Q= -Q=- x 17.43 x 6.6 = -58.58KND1C1 E1F16.62Q=-Q= 15 -15 +1 x10.32 x 2.7 = 13.93KND1E1E1 D12.72QC1C0 =-QF1F019.42*23.1=-=11.81KNQ=-QD1D0E1E0负一层：3.6=183 +12.8 = 6.35KN3.6QC0D0 =-QF0E0=53.71-63 * 丄 17.43 x 6.6 = 56.11KN6.6 2n 1 /TO 1Q =-Q =- X17.43 x 6.6 = -58.92KND0C0E0F06.6217.32 -17.321Q = -Q=+ x10.32 x 2.7 = 13.93KND0E0 E0 D02.72C0C-1F20F-113.12 + 6.564.2= -4.69KNQ=-Q= 7.73 + 3.06 = 2.57KNC0C-1F0F-14.2恒荷载作用下的剪力和轴力图如下：W.9177.82IffnnrrTTH 全711111120.2i.03.95rnTTrm- =9.91W.8610.8610.86W.8956.79THIrnntT56.47lIHtTrnTrirrT-56.47UrRlTnrTrr-I 56.47 = IirlTTTTTm-g 56.47 ItRrfTnrnrr4.69587413.9310.431D.t3Tfrrrh-L5.955.55TftTTTh-w.58.2713.93MsHl582713.93sa.f?13.93IWfrnTrr- 7T8220.2458.仏j-ffnTTinTrtTT13.9358.27RHTTTTrTTrr9.9118.91BBBSBB58.2713.9356.11nurtTm 5S?9Zpf13.9358.27Snninitn56.47HTnnnTrtTrSlVr-2.5710.06W.S62.5713.935B.27liWlTnrn13.9358.92ltTnnrni-n13.93图5恒荷载作用下的剪力图（单位：kN）HE5&.47W.8656.4756.rr10.894.69240.16286.33240.162B6.33图 6 恒荷载作用下的轴力图（单位 kN）