ch11_彎曲應(yīng)力-習(xí)題

1、2021-6-15max2/6ZMMWbh3210 1061200.05 0.1MPa3/12ZEIEbhMM933200 100.05 0.183.310 1012m例例11-3-12021-6-15m4mkNq210020020010082qL豎放豎放maxmaxZMW2286qLbh6MPa橫放橫放maxmaxZMW2286qLhb12MPaMZZ例例11-3-22021-6-15BAl = 3mq=60kN/mxC1mMxm67.5kN8/2ql 30zy180120K1.1.C C 截面上截面上K K點正應(yīng)力點正應(yīng)力2.2.C C 截面上最大正應(yīng)力截面上最大正應(yīng)力3.3.全梁上最大正

2、應(yīng)力全梁上最大正應(yīng)力4.4.已知已知E E=200GPa=200GPa，C C 截面的曲率半徑截面的曲率半徑 FSx90kN90kNmkN605 . 0160190CMkN90AyFkN90ByF4533Zm10832. 51218. 012. 012bhIMPa7 .61Pa107 .6110832. 510)302180(10606533ZKCKIyM解：解：例例11-3-32021-6-15BAl = 3mq=60kN/mxC1mMxm67.5kN8/2ql 30zy180120K FSx90kN90kN2. 2. C C 截面最大正應(yīng)力截面最大正應(yīng)力C C 截面彎矩截面彎矩mkN60C

3、MC C 截面慣性矩截面慣性矩45Zm10832. 5IMPa55.92Pa1055.9210832. 510218010606533ZmaxmaxIyMCC例例11-3-32021-6-15BAl = 3mq=60kN/mxC1mMxm67.5kN8/2ql 30zy180120K FSx90kN90kN3. 3. 全梁最大正應(yīng)力全梁最大正應(yīng)力最大彎矩最大彎矩mkN5 .67maxM截面慣性矩截面慣性矩45m10832. 5zIMPa17.104Pa1017.10410832. 5102180105 .676533ZmaxmaxmaxIyM例例11-3-32021-6-15BAl = 3mq

4、=60kN/mxC1mMxm67.5kN8/2ql 30zy180120K FSx90kN90kN4. 4. C C 截面曲率半徑截面曲率半徑 C C 截面彎矩截面彎矩mkN60CMC C 截面慣性矩截面慣性矩45Zm10832. 5Im4 .194106010832. 510200359CZCMEIEIM1例例11-3-32021-6-15例例11-3-42021-6-15例例11-3-4 0AM05 . 2162132BFkN36BF 0yF01632BAFFkN12AF2021-6-15例例11-3-4mm2 .531601402001601201601401002001601y2323

5、)2 .53120()160140(12160140)2 .53100()200160(12200160zI47mm109 . 2mm8 .1462 .532002y2021-6-15例例11-3-4zCCIyM176109 . 22 .531012MPa22zCCIyM276109 . 28 .1461012MPa74.602021-6-15例例11-3-4zBBIyM276109 . 28 .146108MPa50.40zBBIyM176109 . 22 .53108MPa67.142021-6-15例例11-3-4zBBIyM2MPa50.40zBBIyM1MPa67.14zCCIyM1

6、MPa22zCCIyM2MPa74.602021-6-1516281448解：解：CzyAS1082628) 514(108141628ASyzCcm13ZWzCzCy單位：單位：cm426200cm3max262001748(2813)zZIWcmy32116 2816 28 (14 13) 123218 1018 10 (19 13) 12 zI 5max61.2 1068.651748 10ZMMPaW5max1.2 10MNmMPa70+例例11-3-52021-6-15m5 . 0m2mkNq30ABkNFA9 .46kNFB1 .28159 .311 .28kNkNm3.7513.

7、16 W=77.5cmW=77.5cm3 3 maxWM361.2cmSFM例例11-3-62021-6-15L=4mABq=0.5KN/m8 . 0DdMPa12M(+)281qL解：解：2max81qLM31.0 10 N m)1 (3243DWzmaxMmD113. 0,226. 0mD 2max81qLMzW)1 (3243D4.0qKNm例例11-3-72021-6-15 zIyMmaxmaxmaxMzW,kN5 .62,m16. 0,m267. 0,1302Fbammd.MPa60mm1601d？ zWMmaxmax例例11-3-82021-6-15MPa5 .41Pa105 .4

8、116. 0322675 .62326331maxdFaWMzBBMPa4 .46Pa104 .4613. 0321605 .62326332maxdFbWMzCCF Fa aF Fb b解：解： 例例11-3-82021-6-15m1m2ABmkNq12m3kNF25CDB B截面截面302003017061139z36.3MPamaxB82.8MPamaxBmaxC44MPaM75.12mkN 24M=24,maxt,maxcB截面,maxt,maxcM=12.7533724 1061 10403 1033724 10139 10403 1061139zC截面C C截面截面33712.75

9、 10139 10403 10+-+例例11-3-92021-6-15 ccttmax,max, MPa,60,MPa30ct例例11-3-12021-6-15mm522012020808020120102080cy462323m1064. 728120201212020422080122080zIz1yz52解：解：例例11-3-12021-6-15 ttMPa2 .27Pa102 .271064. 710521046633max, ccMPa1 .46Pa101 .461064. 710881046633max,kN.m5 .2kN.m4例例11-3-1 ttMPa8 .28Pa108 .

10、281064. 71088105 . 26633max,2021-6-15maxMzWMPa,140kN,7 . 61F,kN502Fm,5 . 9l zWMmaxmax例例11-3-12021-6-15 zWMmaxmax 33663maxcm962m109621014045 . 910)507 . 6(MWz解：解：3cm962zWkg/m6 .67q例例11-3-12021-6-15例例11-3-12021-6-15例例11-3-12021-6-15IyMBB1MPa101 .2648101666MPa4 .29zBIyMB2MPa101 .2614210166687.0MPa43.5M

11、PaMPa101 .26142108662IyMCC例例11-3-12021-6-15mm240mm400m3kN85bhlF例例11-12021-6-15mm240mm400m3kN85bhlFmaxmax127.585kN m kNSMF4933mm1028. 11240024012bhIz例例11-12021-6-15zaBaIyM92MPa.191028. 1200105 .1279649mm1028. 1zIMPa96. 9zcBcIyMMPa0dMPa96. 9e92MPa.19f例例11-12021-6-15fa49mm1028. 1zI*SzcezF SI b2401028.

12、1150)240100(1085930996MPa. 0maxdS32FA33MPa. 14002402108533例例11-12021-6-15 21maxmax6bhlFWMz SF FM Fl 3.75kNN375061015010010692721 lbhF bhFAFS2/32/32max kN01N100003/101501001023/2662 bhF Fl100505050z解：解：例例11-2021-6-15 gZZSbhFbbhhbFbISF 341233323*g 3.825kNN382541034. 010150100343663 gbhF 3.75kNkN825. 3

13、kN10kN75. 3minmin iFFFl100505050M FlzSF F例例11-2021-6-15例例11-32021-6-15例例11-32021-6-15mkN6 .19max FaM/maxMW 3636mm1018. 2mm9/106 .19261bhW 32814361hhh mm1059. 2mm1018. 2882363Whmm260 取為mm200,mm1095. 1mm106 . 2434322取為hb例例11-32021-6-15max32SmaxFAMPa2002601098233MPa8 . 2例例11-32021-6-1532S maxFA 2423mm1

14、088. 5mm5 . 2109823432hbhAmm280mm1088. 534344Ahmm210mm2804343hb例例11-32021-6-15FLbhzzzWM2maxmax622bhFL23bhFL max 23bhFL LbhF32例例11-2021-6-15zWMmaxmax622hbFL223bhFL LbhF322FLbhzAFs23max bhLbh232232 Lh2bLFsmaxAFs 422dbh hbd2例例11-2021-6-152021-6-152021-6-152021-6-15kN66AFkN44BFkN66SF解解 求出支反力求出支反力D截面的剪力截

15、面的剪力0.6m0.4mADF=110 kNBDFBFA2201010yzC10347140102021-6-1532max,mm101061)2/10310103(2zSMPa4 .30101152201010611066423max,SmaxzzdISF中性軸以下兩塊腹板對中性軸的面積矩中性軸以下兩塊腹板對中性軸的面積矩MPa5 .2610115210104621066423SzzadISF32mm10462)2/140(10310140zSa點以下一塊腹板對中性軸的面積矩點以下一塊腹板對中性軸的面積矩a點處的切應(yīng)力為點處的切應(yīng)力為y220a1010zC10347140102021-6-1

16、533mm1042)2/150(10310150zSMPa1 .241011521010421066433SzzdISFd點處的水平剪應(yīng)力為點處的水平剪應(yīng)力為d點以右部分腹板對中性軸的面積矩點以右部分腹板對中性軸的面積矩y220d1010zC1034714010yCzFSDdmaxa2021-6-15 例例 跨度為跨度為6m的簡支鋼梁，是由的簡支鋼梁，是由32a號工字鋼在其中間號工字鋼在其中間區(qū)段焊上兩塊區(qū)段焊上兩塊 100 10 3000mm的鋼板制成。材料均的鋼板制成。材料均為為Q235鋼，其鋼，其 =170MPa， =100MPa。試校核該。試校核該梁的強(qiáng)度。梁的強(qiáng)度。kN80AFkN7

17、0BF解解 計算反力得計算反力得F1F2 50kN 50kN 50kNCABFB1.5 m1.5 mFA1.5 m 1.5 mzy9.510010320102021-6-15FS(kN)xM(kNmm)x80203070120150105F1F2 50kN 50kN 50kNCABFB1.5 m1.5 mFA1.5 m 1.5 mzy9.51001032010kN80max,SFmkN150maxM2021-6-15mkN150maxM)2102320(101001210100 2105 .11075234zI44mm1016522最大彎矩為最大彎矩為334maxmm1097210)2/320

18、(1016522yIWzzMPa3 .154109721015036maxmax,zEWMF1F2 50kN 40 kN 60kNCABFB1.5 m1.5 mFA1.5 m 1.5 mzy9.51001032010E2021-6-15MPa4 .173102 .6921012036max,zCCWMMPa7 .306 .2745 . 910803max,maxmaxzzdISmkN120CMC截面彎矩為截面彎矩為FS(kN)xM(kNmm)x80203070120150105F1F2 50kN 50kN 50kNCABFB1.5 m1.5 mFA1.5 m 1.5 mzy9.51001032

19、010但未超過但未超過的的5%，還是，還是允許的。允許的。2021-6-15mkN28/2maxqqlMkN22/max,SqqlFyz20100100101802404545解：解：33)202240()452180(12112240180zI44mm1014736334maxmm1012281201014736yIWzz2021-6-15kN/m14. 6q1010122810236maxmaxqWMzyz20100100101802404545kN22/max,SqqlF33max,mm108462100100452)220100(20180zSMPa78. 01014736901084

20、61014. 62433max,maxS,maxzzbISF33mm10396)220100(20180zSMPa367. 0101473690103961014. 62433maxS,zzbISF2021-6-152021-6-15z(a)z1(b)MM1cSS2021-6-15每排鉚釘承受的剪力等于一每排鉚釘承受的剪力等于一根鋼軌在距離為縱向間距根鋼軌在距離為縱向間距 S的兩個橫截面上壓（拉）力的兩個橫截面上壓（拉）力之差。之差。1TTTSTT1sQT2 Q2021-6-15STT1sQT2 QTb s*m axzzQSbI*maxzS為一根鋼軌的橫截面為一根鋼軌的橫截面面積對中性軸的靜矩面積對中性軸的靜矩*64max.640zA cSm2021-6-15STT1sQT2 QbsT bISzzQ*max ZI為整個橫截面對中性軸為整個橫截面對中性軸的慣性矩的慣性矩212().ZZA CII441.334 10 m*max1222ZZsQTQbSSI17.86KN2021-6-15STT1sQT2 Q*max1222ZZsQTQbSSI17.86KN鉚釘?shù)募魬?yīng)力為鉚釘?shù)募魬?yīng)力為 256.94QM