ch11_弯曲应力-习题

1、2022-4-8max2/6ZMMWbh3210 1061200.05 0.1MPa3/12ZEIEbhMM933200 100.05 0.183.310 1012m例例11-3-12022-4-8m4mkNq210020020010082qL竖放竖放maxmaxZMW2286qLbh6MPa横放横放maxmaxZMW2286qLhb12MPaMZZ例例11-3-22022-4-8BAl = 3mq=60kN/mxC1mMxm67.5kN8/2ql 30zy180120K1.1.C C 截面上截面上K K点正应力点正应力2.2.C C 截面上最大正应力截面上最大正应力3.3.全梁上最大正应力全

2、梁上最大正应力4.4.已知已知E E=200GPa=200GPa，C C 截面的曲率半径截面的曲率半径 FSx90kN90kNmkN605 . 0160190CMkN90AyFkN90ByF4533Zm10832. 51218. 012. 012bhIMPa7 .61Pa107 .6110832. 510)302180(10606533ZKCKIyM解：解：例例11-3-32022-4-8BAl = 3mq=60kN/mxC1mMxm67.5kN8/2ql 30zy180120K FSx90kN90kN2. 2. C C 截面最大正应力截面最大正应力C C 截面弯矩截面弯矩mkN60CMC C

3、 截面惯性矩截面惯性矩45Zm10832. 5IMPa55.92Pa1055.9210832. 510218010606533ZmaxmaxIyMCC例例11-3-32022-4-8BAl = 3mq=60kN/mxC1mMxm67.5kN8/2ql 30zy180120K FSx90kN90kN3. 3. 全梁最大正应力全梁最大正应力最大弯矩最大弯矩mkN5 .67maxM截面惯性矩截面惯性矩45m10832. 5zIMPa17.104Pa1017.10410832. 5102180105 .676533ZmaxmaxmaxIyM例例11-3-32022-4-8BAl = 3mq=60kN/

4、mxC1mMxm67.5kN8/2ql 30zy180120K FSx90kN90kN4. 4. C C 截面曲率半径截面曲率半径 C C 截面弯矩截面弯矩mkN60CMC C 截面惯性矩截面惯性矩45Zm10832. 5Im4 .194106010832. 510200359CZCMEIEIM1例例11-3-32022-4-8例例11-3-42022-4-8例例11-3-4 0AM05 . 2162132BFkN36BF 0yF01632BAFFkN12AF2022-4-8例例11-3-4mm2 .531601402001601201601401002001601y2323)2 .53120

5、()160140(12160140)2 .53100()200160(12200160zI47mm109 . 2mm8 .1462 .532002y2022-4-8例例11-3-4zCCIyM176109 . 22 .531012MPa22zCCIyM276109 . 28 .1461012MPa74.602022-4-8例例11-3-4zBBIyM276109 . 28 .146108MPa50.40zBBIyM176109 . 22 .53108MPa67.142022-4-8例例11-3-4zBBIyM2MPa50.40zBBIyM1MPa67.14zCCIyM1MPa22zCCIyM2

6、MPa74.602022-4-816281448解：解：CzyAS1082628) 514(108141628ASyzCcm13ZWzCzCy单位：单位：cm426200cm3max262001748(2813)zZIWcmy32116 2816 28 (14 13) 123218 1018 10 (19 13) 12 zI 5max61.2 1068.651748 10ZMMPaW5max1.2 10MNmMPa70+例例11-3-52022-4-8m5 . 0m2mkNq30ABkNFA9 .46kNFB1 .28159 .311 .28kNkNm3.7513.16 W=77.5cmW=7

7、7.5cm3 3 maxWM361.2cmSFM例例11-3-62022-4-8L=4mABq=0.5KN/m8 . 0DdMPa12M(+)281qL解：解：2max81qLM31.0 10 N m)1 (3243DWzmaxMmD113. 0,226. 0mD 2max81qLMzW)1 (3243D4.0qKNm例例11-3-72022-4-8 zIyMmaxmaxmaxMzW,kN5 .62,m16. 0,m267. 0,1302Fbammd.MPa60mm1601d？ zWMmaxmax例例11-3-82022-4-8MPa5 .41Pa105 .4116. 0322675 .623

8、26331maxdFaWMzBBMPa4 .46Pa104 .4613. 0321605 .62326332maxdFbWMzCCF Fa aF Fb b解：解： 例例11-3-82022-4-8m1m2ABmkNq12m3kNF25CDB 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 10139 10403 10+-+

9、例例11-3-92022-4-8 ccttmax,max, MPa,60,MPa30ct例例11-3-12022-4-8mm522012020808020120102080cy462323m1064. 728120201212020422080122080zIz1yz52解：解：例例11-3-12022-4-8 ttMPa2 .27Pa102 .271064. 710521046633max, ccMPa1 .46Pa101 .461064. 710881046633max,kN.m5 .2kN.m4例例11-3-1 ttMPa8 .28Pa108 .281064. 71088105 . 26

10、633max,2022-4-8maxMzWMPa,140kN,7 . 61F,kN502Fm,5 . 9l zWMmaxmax例例11-3-12022-4-8 zWMmaxmax 33663maxcm962m109621014045 . 910)507 . 6(MWz解：解：3cm962zWkg/m6 .67q例例11-3-12022-4-8例例11-3-12022-4-8例例11-3-12022-4-8IyMBB1MPa101 .2648101666MPa4 .29zBIyMB2MPa101 .2614210166687.0MPa43.5MPaMPa101 .26142108662IyMCC

11、例例11-3-12022-4-8mm240mm400m3kN85bhlF例例11-12022-4-8mm240mm400m3kN85bhlFmaxmax127.585kN m kNSMF4933mm1028. 11240024012bhIz例例11-12022-4-8zaBaIyM92MPa.191028. 1200105 .1279649mm1028. 1zIMPa96. 9zcBcIyMMPa0dMPa96. 9e92MPa.19f例例11-12022-4-8fa49mm1028. 1zI*SzcezF SI b2401028. 1150)240100(1085930996MPa. 0ma

12、xdS32FA33MPa. 14002402108533例例11-12022-4-8 21maxmax6bhlFWMz SF FM Fl 3.75kNN375061015010010692721 lbhF bhFAFS2/32/32max kN01N100003/101501001023/2662 bhF Fl100505050z解：解：例例11-2022-4-8 gZZSbhFbbhhbFbISF 341233323*g 3.825kNN382541034. 010150100343663 gbhF 3.75kNkN825. 3kN10kN75. 3minmin iFFFl100505050

13、M FlzSF F例例11-2022-4-8例例11-32022-4-8例例11-32022-4-8mkN6 .19max FaM/maxMW 3636mm1018. 2mm9/106 .19261bhW 32814361hhh mm1059. 2mm1018. 2882363Whmm260 取为mm200,mm1095. 1mm106 . 2434322取为hb例例11-32022-4-8max32SmaxFAMPa2002601098233MPa8 . 2例例11-32022-4-832S maxFA 2423mm1088. 5mm5 . 2109823432hbhAmm280mm1088

14、. 534344Ahmm210mm2804343hb例例11-32022-4-8FLbhzzzWM2maxmax622bhFL23bhFL max 23bhFL LbhF32例例11-2022-4-8zWMmaxmax622hbFL223bhFL LbhF322FLbhzAFs23max bhLbh232232 Lh2bLFsmaxAFs 422dbh hbd2例例11-2022-4-82022-4-82022-4-82022-4-8kN66AFkN44BFkN66SF解解 求出支反力求出支反力D截面的剪力截面的剪力0.6m0.4mADF=110 kNBDFBFA2201010yzC10347

15、140102022-4-832max,mm101061)2/10310103(2zSMPa4 .30101152201010611066423max,SmaxzzdISF中性轴以下两块腹板对中性轴的面积矩中性轴以下两块腹板对中性轴的面积矩MPa5 .2610115210104621066423SzzadISF32mm10462)2/140(10310140zSa点以下一块腹板对中性轴的面积矩点以下一块腹板对中性轴的面积矩a点处的切应力为点处的切应力为y220a1010zC10347140102022-4-833mm1042)2/150(10310150zSMPa1 .2410115210104

16、21066433SzzdISFd点处的水平剪应力为点处的水平剪应力为d点以右部分腹板对中性轴的面积矩点以右部分腹板对中性轴的面积矩y220d1010zC1034714010yCzFSDdmaxa2022-4-8 例例 跨度为跨度为6m的简支钢梁，是由的简支钢梁，是由32a号工字钢在其中间号工字钢在其中间区段焊上两块区段焊上两块 100 10 3000mm的钢板制成。材料均的钢板制成。材料均为为Q235钢，其钢，其 =170MPa， =100MPa。试校核该。试校核该梁的强度。梁的强度。kN80AFkN70BF解解 计算反力得计算反力得F1F2 50kN 50kN 50kNCABFB1.5 m1

17、.5 mFA1.5 m 1.5 mzy9.510010320102022-4-8FS(kN)xM(kNmm)x80203070120150105F1F2 50kN 50kN 50kNCABFB1.5 m1.5 mFA1.5 m 1.5 mzy9.51001032010kN80max,SFmkN150maxM2022-4-8mkN150maxM)2102320(101001210100 2105 .11075234zI44mm1016522最大弯矩为最大弯矩为334maxmm1097210)2/320(1016522yIWzzMPa3 .154109721015036maxmax,zEWMF1F

18、2 50kN 40 kN 60kNCABFB1.5 m1.5 mFA1.5 m 1.5 mzy9.51001032010E2022-4-8MPa4 .173102 .6921012036max,zCCWMMPa7 .306 .2745 . 910803max,maxmaxzzdISmkN120CMC截面弯矩为截面弯矩为FS(kN)xM(kNmm)x80203070120150105F1F2 50kN 50kN 50kNCABFB1.5 m1.5 mFA1.5 m 1.5 mzy9.51001032010但未超过但未超过的的5%，还是，还是允许的。允许的。2022-4-8mkN28/2maxqq

19、lMkN22/max,SqqlFyz20100100101802404545解：解：33)202240()452180(12112240180zI44mm1014736334maxmm1012281201014736yIWzz2022-4-8kN/m14. 6q1010122810236maxmaxqWMzyz20100100101802404545kN22/max,SqqlF33max,mm108462100100452)220100(20180zSMPa78. 0101473690108461014. 62433max,maxS,maxzzbISF33mm10396)220100(2018

20、0zSMPa367. 0101473690103961014. 62433maxS,zzbISF2022-4-82022-4-8z(a)z1(b)MM1cSS2022-4-8每排铆钉承受的剪力等于一每排铆钉承受的剪力等于一根钢轨在距离为纵向间距根钢轨在距离为纵向间距 S的两个横截面上压（拉）力的两个横截面上压（拉）力之差。之差。1TTTSTT1sQT2 Q2022-4-8STT1sQT2 QTb s*m axzzQSbI*maxzS为一根钢轨的横截面为一根钢轨的横截面面积对中性轴的静矩面积对中性轴的静矩*64max.640zA cSm2022-4-8STT1sQT2 QbsT bISzzQ*max ZI为整个横截面对中性轴为整个横截面对中性轴的惯性矩的惯性矩212().ZZA CII441.334 10 m*max1222ZZsQTQbSSI17.86KN2022-4-8STT1sQT2 Q*max1222ZZsQTQbSSI17.86KN铆钉的剪应力为铆钉的剪应力为 256.94QMPad铆