結(jié)構(gòu)力學(xué)題目整合第九章力矩分配法知識(shí)題解答

**1、清華5-6 試用力矩分配法計(jì)算圖示連續(xù)梁，并畫其彎矩圖和剪力圖。kN kNA20·55·CAC2iB清華iEIBEI題5-6題9-1b35M圖15M圖(kN·m)(kN·m)59027.5

17.5V圖 8.75 V圖32.5分配系數(shù)0.60.4分配系數(shù)0.50.5固端彎矩0(20)0固端彎矩0(55)067.50450分與傳0-52.5-35-17.5分與傳0-50-500最后彎矩015-35-17.5最后彎矩0-5-500解：（1）計(jì)算分配系數(shù)：s32isBA0.6BAs32i4iBABCs4iBC0.4BCss32i4iBABC（2）計(jì)算固端彎矩：固端彎矩僅由非結(jié)點(diǎn)荷載產(chǎn)生，結(jié)點(diǎn)外力偶不引起固端彎矩，結(jié)點(diǎn)外力偶逆時(shí)針謝謝閱讀為正直接進(jìn)行分配。MF0AB3Pl3606MF67.5kNmBA1616（3）分配與傳遞，計(jì)算列如表格。（4）疊加固端彎矩和分配彎矩或傳遞彎矩，得各桿端的最后彎矩，作彎矩圖如圖所示。精品文檔放心下載（5）根據(jù)彎矩圖作剪力圖如圖所示。**VV0MABMBA3001527.5kNABABl6VV0MABMBA3001532.5kNBABAl6VVMBCMCB3517.58.75kNBCCBl62、利用力矩分配法計(jì)算連續(xù)梁，并畫其彎矩圖和剪力圖。謝謝閱讀kNkN/m20kNM圖15.713020(kNm)7.14·AEIBEICD202m2m4m1m題9-1b原結(jié)構(gòu)28.93kNmkN/m20kN·V圖7.8620AkN(kN)EIBEICD12.1431.07kNkN/mA20kNmEIBEIC·分配系數(shù)0.5710.429簡(jiǎn)化結(jié)構(gòu)固端彎矩-1010-30+1020-20分與傳2.865.714.2900最后彎矩-7.1415.71-15.7120-20EI,4,3iiiS解：（1）計(jì)算分配系數(shù)：令4BABCBABCs4is3iBA0.429BC0.571BAss4i3iBCss4i3iBABCBABC（2）計(jì)算固端彎矩：CD桿段剪力和彎矩是靜定的，利用截面法將外伸段從C處切開(kāi)，讓剪力直接通過(guò)精品文檔放心下載支承鏈桿傳給地基，而彎矩暴露成為BC段的外力偶矩，將在遠(yuǎn)端引起B(yǎng)、C固端彎矩。謝謝閱讀MFPl20410kNm,MF=10kNmAB88BAMFql2Nm,MF20kNmBCCB（3）分配與傳遞，計(jì)算列如表格。（4）疊加固端彎矩和分配彎矩或傳遞彎矩，得各桿端的最后彎矩，作彎矩圖如圖所示。感謝閱讀（5）根據(jù)彎矩圖作剪力圖如圖所示。**VV0MABMBA207.1415.717.86kNABABl24VV0MABMBA207.1415.7112.14kNBABAl24VV0MBCMCB15415.712028.93kNBCBCl24VV0MBCMCB15415.712031.07kNCBCBl243、9-2a利用力矩分配法計(jì)算連續(xù)梁，并畫其彎矩圖。45kNq=15kN/m40kN解：（1）計(jì)算分配系數(shù)：A0.75B1.5EICD令EI4EIEIB結(jié)點(diǎn)：題9-2a2m4m4m4m3m3m分配系數(shù)0.40.60.60.4S40.75EIEI2,S41.5EI3EI3BA62BC84固端彎矩-4020-8080-450s212243618分BA0.4-31.8-21.2配-15.9BAss233.186.369.54BABC與4.773-1.43s-2.86-1.91傳BC0.6遞0.290.570.860.43BCss23-0.24-0.16BABC最后彎矩-24.5368.28-68.280C結(jié)點(diǎn)：50.93-50.9341.5EI3EI3，S3EIEI26050.9368.28SCB84CD62M圖24.5360s3(kNm)CB0.6·CBss32CBCD2120sCD0.4CDss32CBCD（2）計(jì)算固端彎矩：固端彎矩僅由非結(jié)點(diǎn)荷載產(chǎn)生。Pab245242Pba245422MF40kNm,MF20kNmABl262BAl262ql21582MF80kNmMF1080kNm,BC1212CBMF3Pl340645kNm,MF0CD1616DC**（3）分配與傳遞，計(jì)算列如表格。（4）疊加固端彎矩和分配彎矩或傳遞彎矩，得各桿端的最后彎矩，作彎矩圖如圖所示。精品文檔放心下載4、9-3c利用力矩分配法計(jì)算剛架，并畫其彎矩圖。精品文檔放心下載q=5kN/m10kN·m10kNq=5kN/m10kN·m40kN10kNq=5kN/m10kN·m40kN40kNBC10kN·m10kN·mA2EI2EIDA2EIB2EICA2EIB2EICm(a1.5EI原結(jié)構(gòu)1.5EI1.5EI4題9-3cEE(b)E4m3m3m1mABABEBCC102530100.3750.3750.25B(-10)A15CD100-45+10/210601515107.502515-3010EM圖(d)(c)(kN·m)E07.57.5解：（1）計(jì)算分配系數(shù)：S32EI1.5EI3,S32EIEI2,S41.5EIEI2BA4BC6BE6令EI2則，S3,S2,S2BABCBEBAss30.375sBAS332BABCBE2BCss0.25sBCS332BABCBE3BCss0.375sBES332BABCBE（2）計(jì)算固端彎矩：剛結(jié)點(diǎn)處力偶不引起固端彎矩，結(jié)點(diǎn)外力偶逆時(shí)針為正直接進(jìn)行分配。CD桿段剪精品文檔放心下載力和彎矩是靜定的，利用截面法將外伸段從C處切開(kāi)，讓剪力直接通過(guò)支承鏈桿傳給地基，而彎矩暴露感謝閱讀成為BC段的外力偶矩，將在遠(yuǎn)端引起B(yǎng)、C固端彎矩。感謝閱讀**MFql25423Plm3406100，MF810kNmMF40kNm,ABBA8BC162162MF10kNmMFMF0kNmABEBBE（3）分配與傳遞，計(jì)算如圖所示。（4）疊加固端彎矩和分配彎矩或傳遞彎矩，得各桿端的最后彎矩，作彎矩圖如圖所示。感謝閱讀9-3d利用力矩分配法計(jì)算剛架，并畫其彎矩圖。10kNG.5EIq=10kN/m2m4EI3AB4EICD4EI4EIm題9-3d4EF2m4m4m(a)2058.50.5205.5124.5M圖(kN·m)1(c)

10kN10kNGG.5EI.5EI20kN·mq=10kN/m20kN·mq=10kN/m4EI2.5kN2.5kN4EI4EICDB4EICDB4EI4EI4EI4EI簡(jiǎn)化結(jié)構(gòu)EFEF(b)G0-0.5-0.5CBCFCGCDDB0.30.40.20.1-201000-5-5-1.5-2-1-0.50.58.5-2-1-5.5-4.5E0F-1-1 (d)解：（1）計(jì)算分配系數(shù)：**S3i34EI3EI,S4i42.5EI2EI,CBCB4CGCG5S4i44EI4EI,Si4EIEICFCF4CDCD4S3EICBS0.3CBssS3EI2EI4EIEICBCGCFCD2EISCGS0.2CGssS3EI2EI4EIEICBCGCFCD4EISCFS0.4CFssS3EI2EI4EIEICBCGCFCDSEICDS0.1CDssS3EI2EI4EIEICBCGCFCD（2）計(jì)算固端彎矩：AB桿段剪力和彎矩是靜定的，利用截面法將外伸段從B處切開(kāi)，讓剪力直接通過(guò)感謝閱讀BE桿傳給地基，而彎矩暴露成為BC段的外力偶矩，將在遠(yuǎn)端C引起固端彎矩。感謝閱讀MF20kNmMFmql220104228210kNmBCCB8MFMFPl2.545kNmCDDC22MFMF0CGGC（3）分配與傳遞，計(jì)算如圖所示。（4）疊加固端彎矩和分配彎矩或傳遞彎矩，得各桿端的最后彎矩，作彎矩圖如圖所示。精品文檔放心下載9-3e利用力矩分配法計(jì)算剛架，并畫其彎矩圖。**36kN·m36kN·m48.555.542.25q=24kN/m18kNq=24kN/m18kN10818AA37.5BCDBC18kN·m42.25題9-3eEI=常數(shù)mM圖6(kNm)EFEF21.134.5m6m1m18.75(a)(b)(c)BABEBCCBCF1/31/31/30.50.5(-36)(-18)00-727236363618-18-36-366663-0.75-1.5-1.50.250.250.2542.2542.25-48.50018-183-0.750.13(d)-18.7521.13解：（1）計(jì)算分配系數(shù)：剛結(jié)點(diǎn)：S3EI2EI,S4EI2EI,S4EI2EIBA4.53BC63BE631BABCBE3剛結(jié)點(diǎn)：S4EI2EI,S4EI2EICB63CF630.5CBCF（2）計(jì)算固端彎矩：CD桿段剪力和彎矩是靜定的，利用截面法將外伸段從B處切開(kāi)，讓剪力直接通過(guò)謝謝閱讀CF桿傳給地基，而彎矩暴露成為作用于剛結(jié)點(diǎn)B的外力偶矩，將在遠(yuǎn)端C不引起固端彎矩。精品文檔放心下載ql2172kNmql2172kNmMF2462MF2462BC1212BC1212無(wú)荷載桿無(wú)固端彎矩。（3）分配與傳遞，計(jì)算如圖所示。**（4）疊加固端彎矩和分配彎矩或傳遞彎矩，得各桿端的最后彎矩，作彎矩圖如圖所示。謝謝閱讀9-3h利用力矩分配法計(jì)算剛架，并畫其彎矩圖。q=30kN/m53.3140.0580kN13.3813.3760ABCD26.6880EI=常數(shù)m題9-3h4M圖EF(kNm)(b)13.344m4m2m2m·(a)BABCCBCFCD0.50.50.3640.3640.272-4040000-6010.9221.8421.8416.32-12.73-25.46-25.46-12.732.324.634.633.47-0.58-1.16-1.16-0.580.210.210.16-53.3113.38-13.3813.3726.68-40.05010.92(c)2.320.1013.34解：（1）計(jì)算分配系數(shù)：剛結(jié)點(diǎn)：S 4EIEI,S 4EIEI,感謝閱讀BA 4 BC 42EIEI0.5BABC剛結(jié)點(diǎn)：S3EI3EI,S4EIEI,S4EIEICD44CF4CB4EI0.364CFCB3EIEIEI43EI40.272CD3EIEIEI4（2）計(jì)算固端彎矩：**ql21ql2140kNmMF304240kNmMF3042BA1212AB1212MF3Pl380460kNmCD1616MFMFMF0BCCBCF無(wú)荷載桿無(wú)固端彎矩。（3）分配與傳遞，計(jì)算如圖所示。（4）疊加固端彎矩和分配彎矩或傳遞彎矩，得各桿端的最后彎矩，作彎矩圖如圖所示。謝謝閱讀5、9-4b利用對(duì)稱性，采用力矩分配法計(jì)算剛架，并畫其彎矩圖。感謝閱讀q=5kN/m5kN/mECEGG14.7814.78F0.50.5Ei=2i=4G0-26.67-13.333.3325.21i=140kNi=1i=120kN11.6711.67-11.67m-0.4428.6628.665D0.220.22-0.2217.0317.0314.7814.78-25.22Ci=4i=8K33i=3i=3i=31.61.611m51.345CECACKKAB8.511/60.51/38.514m4m4m0-40-40M(kN·m)(b)6.67補(bǔ)充題2013.33-13.3(d)(a)5.841.95-0.97-2.92-1.950.110.04-0.02-0.05-0.0411.6317.03-28.66-51.34A 010 (c)-1.46-0.038.516、9-4d利用對(duì)稱性，采用力矩分配法計(jì)算剛架，并畫其彎矩圖。感謝閱讀**Ai=1Ei=1Bl5Ai=1Ei=1Bl5Ai=1Ei=4i=2i=4i=4..Gi=2i=1i=2H00GGllCi=1Fi=1D(b)(c)ll(a)5ql2ql2ql25ql2ql2ql2ql2488ql288AGAEE482424240.50.50-ql2ql2ql2121224ql2ql2ql2ql2ql22424482424ql2ql25ql2242448G0(d)(e)ql2ql2-ql28(f)824-24ql27、9-9c利用無(wú)剪力分配法計(jì)算剛架，并畫其彎矩圖。謝謝閱讀4kNAGBABAGBi=22kN2kN2kNi=22kNmi=1i=1i=168kNH4kN4kN4kNH4kNCi=2DCDCi=2Dmi=1i=1i=16EFEFEF6m(b)(c)題9-9a(a)**ACAG0.080.92G2kNA2kN-60.0GG-1.68i=4A0.617.07-0.04i=10.0030.037-7.117.114kNHHCi=46kNCCACECHH0.070.070.86-6-180.0i=11.681.6820.64-0.61E0.040.040.53E-4.89-16.2821.17(d)(e)(f)E-18-1.68-0.04-19.72

A7.10 7.117.11 B21.1716.28D4.89C4.8916.2821.17M(kN·m)E19.72F19.72(g)解：（1）由于剛架是對(duì)稱的，因此可將荷載分解為正對(duì)稱和反對(duì)稱兩部分，如上圖（b）、（c）感謝閱讀所示。而正對(duì)稱結(jié)點(diǎn)荷載作用下剛架處于無(wú)彎矩狀態(tài)，原圖的彎矩圖只考慮反對(duì)稱荷載作用。考慮剛架感謝閱讀和荷載的對(duì)稱性，可以取半剛架如(d)所示。由于(d)圖半剛架立柱的剪力是靜定的，每一跨都可以化為感謝閱讀單跨超靜定梁，因此選取如圖(e)所示無(wú)剪力分配法力學(xué)計(jì)算模型。謝謝閱讀SAG3iAG340.92AGSS3ii341AGACAGACSi1ACAC0.08SS3ii341ACAGACAGACSi110.07CACACASSSi3ii134114CACHCECACHCES3i3412C結(jié)點(diǎn)：CHCH0.86CHSSSi3ii134114CACHCECACHCE11Si0.07CECECESSSi3ii134114CACHCECACHCE（2）計(jì)算固端彎矩：MFMFPl26上6kNmACCA22MFMFPl（24）6上+下18kNmCEEC22**MFMF1604120kNmBCCB2（3）彎矩的分配與傳遞計(jì)算過(guò)程如圖（f）所示。結(jié)點(diǎn)的分配次序?yàn)镃→A→C→A精品文檔放心下載（4）繪制彎矩圖如（f）所示。8、利用分層法計(jì)算多層剛架。q=10kN/mq=10kN/mG2EIH2EIIGi=4H6IGHImEIEIEIm0.9i=2.72.72.7m2.72.72.74q=30kN/m44q=30kN/mFDEFFD2EIE26m4mDi=4E6EImEIEIEIm33344A令EI=12BCA6mBC6m4m4m題9-10解：（1）分層：以梁為界選取如圖(b)、(c)所示分層法計(jì)算模型。線剛度：上層各柱打折—9折。精品文檔放心下載（2）第二層（頂層）：①求分配系數(shù)：Si2.7GDGD0.403S4iGDSSii2.74GDGDGDGHGDGHG結(jié)點(diǎn)：S4iSi4GHGHGHGH0.597SSii2.74GHGDGHGDGHSi4SHGSHGi0.315S4iHGSii42.76HGHEHFHGHEHF2.7HGHGSiS4iSHESiHEi0.213H結(jié)點(diǎn)：HEHEHESiS4iHGHEHFHGHEHF6HFHFSiHFHF0.472HFSSSiii42.76HGHEHFHGHEHF**Si6IH0.69S4iIHSSii62.7I結(jié)點(diǎn)：IHIHIHIFIHIFS4iSi2.7IFIFIFiIF0.31IFSSi62.7IHIFIHIF②明確傳遞系數(shù)傳遞系數(shù)：兩端固定時(shí)，上層中上下傳1/３，橫傳1/2。謝謝閱讀③求固端彎矩。MGHql21106230kNm,MHG30kNmFGHFMFql21104213.3kNm,MF13.3kNmHIHI1212IH④列表計(jì)算。頂層計(jì)算結(jié)點(diǎn)DGHIFE桿端DGGDGHHGHEHIIHIFFIEH分配系數(shù)0.4030.5970.3150.2130.4720.690.31傳遞系數(shù)1/31/21/21/31/21/21/3固端彎矩-3030-13.313.3分配-2.63-5.26-3.56-7.88-3.9413.1519.489.74-3.23-6.46-2.90與傳遞-1.03-2.05-1.39-3.07-1.540.420.610.300.531.060.48-0.13-0.26-0.18-0.39-0.190.050.080.040.070.130.06-0.03-0.02-0.05最后彎矩4.5413.62-13.6232.48-5.1527.322.36-2.36-0.79-1.72（3）第二層（頂層）：①求分配系數(shù)：**SSii3S4iDASDASiDAi342.70.309DADEDGDADEDGDADASi40.413S4iSDESDEiD結(jié)點(diǎn)：DEDEDESii342.7S4iDADEDGDADEDGDGDGSi2.70.278DGDGDGSSSiii342.7DADEDGDADEDGE結(jié)點(diǎn)：Si4SSEDSiiEDi0.255EDSi4362.7EDEBEFEHEDEBEFEHSi3S4iSSEBSiiEBi0.191EBSi4362.7EDEDEDEBEFEHEDEBEFEHS4iSi6EBEBSSEFSiiEFi0.382S4iEFSi4362.7EFEFEDEBEFEHEDEBEFEHS4iSi2.7EHEHEHEH0.172SSSSiiii4362.7EHEDEBEFEHEDEBEFEHSii6S4iFESSFESiFEi632.70.513FEFCFIFEFCFIFEFESi3S4i0.256SFCFCF結(jié)點(diǎn)：FCFCFCSSiii632.7S4iFEFCFIFEFCFIFIFISi2.7FIFI0.231FISSSFIiii632.7FEFCFEFCFI②明確傳遞系數(shù)傳遞系數(shù)：兩端固定時(shí)，上層柱上下傳1/３，下層柱下傳1/2、橫傳1/2。感謝閱讀③求固端彎矩。MFql2190kNm,MF90kNmDE3062DE1212HGMFql2140kNm,MF40kNmEF3042EF1212IH④列表計(jì)算。**底層計(jì)算結(jié)點(diǎn)AGDEFCIBH桿端ADGDDGDADEEDEHEBEFFEFIFCCFIFBEHE分配系數(shù)0.2780.3090.4130.2550.1720.1910.3820.5130.2310.256傳遞系數(shù)1/31/21/21/21/31/21/21/21/31/2固端彎矩-9090-4040分配-6.38-12.75-8.6-9.55-19.1-9.5526.8029.7839.8019.90-7.81-15.62-6.49-7.80與傳遞-1.54-3.08-2.08-2.31-4.62-2.310.430.480.640.320.601.190.530.59-0.12-0.23-0.16-0.18-0.35-0.180.040.040.040.020.040.090.040.05-0