第九章-梁的内力-习题答案

9−1图示简支梁，已知：均布荷载q=245kN/m，跨度l=2.75m，试求跨中截面C上的剪力和弯矩。解：由02,0RlqFFFCSAy得kN0875.336875.3362RASlqFFC由0812,02RCAOMqllFM（矩心O为C截面的形心）得kN.m6.23175.22458181812222RqlqllFMAC9−2用截面法求下列梁中指定截面上的剪力和弯矩。解：由q=245kN/mABC2.75m习题9−1图(a)6kN8kNABC1m1m2m11MCFSCFRAl/26kN8kNM1FS1第九章梁的内力2068,01SFFy得kN14681SF由03618,01MMO（矩心O为1截面的形心）得kN.m261881M解：由05,01SFFy得kN51SF由0215,01MMO（矩心O为1截面的形心）得kN.m3251M由kN0,02SFFy由02,02MMO（矩心O为2截面的形心）得kN.m22M5kNABC1m1m2kN.m221m1m(b)115kNBC2kN.mM1FS1C2kN.mM2FS2第九章梁的内力3解：支反力：kN2RAF，kN3RBF由0,0R1SAyFFF得kN2R1SAFF由03.,0R1AOFMM（矩心O为1截面的形心）得kN.m6323.R1AFM由0,0RS2ByFFF得kN3R2BSFF由02.,0RB2FMMO（矩心O为2截面的形心）得kN.m6232.RB2FM5kN11223m5mAB(c)FRB5kNFRAFRAM1FS1FRBM2FS2第九章梁的内力4解：支反力：kN4RAF，kN4RBF由0,0R1SAyFFF得kN4R1SAFF由01.,0R1AOFMM（矩心O为1截面的形心）得kN.m4141.R1AFM由0,0RS2ByFFF得kN4R2BSFF由05.1.,0RB2FMMO（矩心O为2截面的形心）得kN.m65.145.1.RB2FM10kN.m1m2.5mAB(d)1122FRBFRAFRAM1FS1FRBM2FS2第九章梁的内力59−3用简便法求下列梁中指定截面上的剪力和弯矩。解：支反力：aMFeA4R，aMFeC4RaMFFeA4R1S4.R1eAMaFMaMFFeA4R2SeAMaFM4.R203SFeMM3解：支反力：kN13RCF，kN35RDFkN5181336R1SCFFm.kN18627313636213.2R1CFMBAMeaa5a223311(a)12kN6kN.m6kN/m112m2m3m3mABCD(b)22MeFRAFRC12kN6kN.m6kN/mFRCFRD第九章梁的内力6kN23351212R2SDFFkN.m242122M解：支反力0AxF，20lqFAy，620lqMA201SlqFFAy6201lqMMA822.21002SlqlqF4832.82002lqllqM解：支反力aqFFBA0022.0001SaqaqaqFFA3432232.2.20202001aqaqaqaaqaFMA112a4aAB(d)q0Al/222l/2Bq0(c)11Bq0FAyMAFAxq0FAFB第九章梁的内力79−4图示某工作桥纵梁的计算简图，上面的两个集中荷载为闸门启闭机重量，均布荷载为自重、人群和设备的重量。试求纵梁在C、D及跨中E三点处横截面上的剪力和弯矩。解：求支反C截面kN5.347.1105.517.1.SqFFACkN165.187.1105.517.1.SFqFFACkN.m1.737.110217.15.517.1217.122qFMACD截面kN165.187.1105.517.1.SFqFFBCkN5.347.1105.517.1.SqFFBCkN.m1.737.110217.15.517.1217.122qFMBDE截面kN5.183.3105.513.3.SqFFAEkN.m9.856.15.183.310213.35.516.13.3213.322FqFMAE9−5试列出下列梁的剪力方程和弯矩方程，并画出剪力图和弯矩图。解：q=10kN/mABC3.2m习题9−4图DE1.7m1.7mF=18.5kNF=18.5kN20kN20kN.m6kN.m1m3mAB(a)Cq=10kN/mF=18.5kNF=18.5kNFA=51.5kNFB=51.5kN第九章梁的内力8①支反力kN2AF，kN22BF②内力方程：AC段kN2SAFxF（0x2）626.xxFxMA（0x≤2）CB段kN2220SAFxF（2x3）xxFxMB22463.20（2x≤3）③内力图FS图M图解：①支反力8qaFA，89qaFC②内力方程：AC段8SqaFxFA（0x4a）Aa5a(b)BCq20kN20kN.m6kN.mFAFB2kN22kN6kN.m20kN.m2kN.mABCqFAFC第九章梁的内力9xqaxFxMA8.（0≤x≤4a）CB段xaqxF5S（4ax≤5a）252xaqxM（4a≤x≤5a）③内力图FS图M图解：①支反力1211FFA，12FFC②内力方程：AC段1211SFFxFA（0x3l）xFxFxMA1211.（0≤x≤3l）CD段121211SFFFFFxFA（3lx≤32l）3123.12113..FlFxFlxFxFlxFxFxMAqa8qa22qa3lAB(c)FFl/43l3lCDFFl/4FAFB第九章梁的内力10（3l≤x32l）DB段12SFFxFB（32l≤xl）1212FxFlxlFxMB（32lx≤l）③内力图FS图M图解：①支反力43qlFC，43qlFD②内力方程：AC段qxxFS（0≤x4l）22qxxM（0≤x≤4l）CD段43SqlqxFqxxFC（4lx45l）16343242222qlqlxqxlxFqxxMCq4lABCD(d)l4l1211F12F3611Fl185Fl36FlqFCFD第九章梁的内力11（4l≤x≤45l）DB段xlqxF23S（45lx≤23l）2232xlqxM（45l≤x≤23l）③内力图FS图M图9−6用简便方法画出下列各梁的剪力图和弯矩图。解：①支反力kN3AF，kN3BF②FS图M图20kN.m8kN.m4mAB(a)2ql2ql4ql4ql3232ql322ql322ql85l20kN.m8kN.mFAFB3kN第九章梁的内力12解：①支反力kN10AF，kN10BF②FS图M图解：①支反力kN5AF，kN15AM②FS图(c)AC1m2.5mB5kN.m20kN8kN.m8kN.m2m2mAB(b)C20kN.m8kN.m20kN8kN.m8kN.mCFAFB10kN10kN12kN.m8kN.m8kN.mMA5kN.mFA5kN第九章梁的内力13M图解：①支反力23qaFA，23qaFB②FS图M图解：①支反力kN.m5.1AF，kN.m5.0BFqABCD(d)3aaaAB(e)1mq=2kN/m1m15kN.mqABCDFAFB892qa23qa23qa2aq=2kN/mFAFB第九章梁的内力14②FS图M图解：①支反力35FFB，3FFD②FS图M图解：q=6kN/mABCD(g)2mF=9kN2m6mAa2a(f)BCFFDa1.5kN0.5kN0.75m0.5625kN.mABCFFDFBFDCF32F3FFa3Fa第九章梁的内力15①支反力FC=28kN，FD=29kN②FS图M图解：①支反力30lqFA，60lqFB②FS图M图AlBq0(h)q=6kN/mABF=9kNFCFD9kN19kN17kN12kN18kN.m12kN.m12.08kN.m5.167mABq0FAFB0.423l0.04067q0l230lq60lq第九章梁的内力16解：①支反力4qlFA，23qlFB，4qlFD②FS图M图解：①支反力0AxF，0AyF，22qaMA，qaFC2②FS图qABCD(i)l0.5l0.5lqABCD(j)aF=qaaaqFAFBFD4ql4ql43ql43ql322ql322ql42ql4l4lqBCDF=qaFCFAyFAxMA第九章梁的内力17M图9−7用简便方法画出题9−2中各梁的剪力图和弯矩图。解：①支反力0AxF，kN14AyF，kN40AM②FS图M图解：qaqaqa20.5qa2(a)6kN8kNABC1m1m2m6kN8kNFAyFAxMA14kN6kN12kN.m40kN.m5kNABC1m1m2kN.m221m1m(b)115kN2kN.mFAyFAxMA第九章梁的内力18①支反力0AxF，kN5AyF，kN8AM②FS图M图解：①支反力0AxF，kN2AyF，kN3BF②FS图M图5kN2kN.m8kN.m5kN11223m5mAB(c)5kNFAyFAxFB3kN.m2kN6kN.m10kN.m1m2.5mAB(d)1122第九章梁的内力19解：①支反力0AxF，kN4AyF，kN4BF②FS图M图9−8用简便方法画出题9−3中各梁的剪力图和弯矩图。解：①支反力0AxF，aMFAy4e，aMFC4e②FS图M图10kN.mFAyFAxFB4kN6kN.m4kN.mBAMeaa5a223311(a)MeFAyFAxFCCaM4eMe第九章梁的内力20解：①支反力0CxF，kN13CyF，kN35DF②FS图解：①支反力0AxF，lqFAy021，2061lqMA②FS图12kN6kN.m6kN/m112m2m3m3mABCD(b)2212kN6kN.m6kN/mFCyFCxFD13kN12kN23kNAl/222l/2Bq0(c)11q0MAFAxFAylq021第九章梁的内力21③M图解：①支反力0AxF，aqFAy0，aqFB0②FS图③M图9−9解：最大正弯矩在跨中28422222maxqlaqllqlalqlM最大负弯矩在两个吊点处22maxqaM由maxmaxMM得112a4aAB(d)q0FAxFAyFB2061lq2aq0aq0a2034aq第九章梁的内力2222822qaqlaql解得la207.09−10已知简支梁的剪力图如图所示，试作梁的弯矩图和荷载图（已知梁上无集中力偶作用）。解：荷载图M图解：荷载图M图5kN1kN4kN2m2m2m(a)6.5kN0.5kN3.5kN2m2m(b)4kN5kN6kN3kN8kN.m10kN.m6.5kN7kN.m3.5kN4kN3kN/m第九章梁的内力239−11已知简支梁的弯矩图如图所示，试作梁的剪力图和荷载图。解：荷载图M图解：荷载图M图10kN.m1m1m1m(a)10kN.m10kN.m2m2m2m(b)40kN.m10kN10kN2