应力和应变分析强度理论

1、chapter7 3 32 21 1 fl/2l/2fl/2l/2s213afzyzyfsyxzafwt34st2 zzxwm 1 1 t1wt t3wt zyfszyzzxwm 3 3 pdyzp 42dpf da 442pdddpaf lp yfnfnd 0 0 yf20lpld 2 2pd plddpl dsin20 xyzxyaeaxyaeaeaea0sin)sind(cos)sind( cos)cosd( sin)cosd(d0 aaaaafyyxxxyn 2cos2sin22sin2cos22xyyxxyyxyx 0cos)sind(sin)sind( sin)cosd(cos)c

2、osd(d0 aaaaafyyxxxytyx 9 90 0 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx 02cos2sin2 2dd xyyx 02tan2xyxy 90900 00 0 2 22 22 22 2sincosxyyxyx 2 22 22 22 2xyyxyx )(minmax 2 22 22 22 22 22 22 2cossinsincosxyyxxyyxyx 02sin2cos2 2dd xyyxxyyx 2 22 21 1 tan 90901 11 1 2 22 22 2cossinxyyx 2 22 22 2xyyx )(mi

3、nmaxxyyx 2 22 21 1 tanyxxy 2 22 20 0tan1 10 02 21 12 2 tantan 4,2220101 a ala5 50 00 07 70 0 xyyx ,429. 10)70(50222tan0 yxxy 027.5117.5xa a mpampa)(minmax9 96 62 26 62 22 22 22 2xyyxyx mpa,mpa9 96 60 02 26 63 32 21 1 n3030efmpa3 .58 )60sin()50()60cos(2604026040 2sin2cos2230 xyyxyxmpa3 .18)60cos()50(

4、 )60sin(260402cos2sin230 xyyx1 16 60 04 40 05 50 02 22 22 20 0 )(tanyxxy 022.5115.5 mpa7 .60mpa7 .80)2(222minmaxxyxyx mpa7 .60 0 mp7 .80321 1 yxxy 2 22 20 0tan090227004513545 2 22 22 22 2xyyxyx)(minmax 1 cossin sincos 2 22 22 22 22 22 22 2xyyxxyyxyx 2 22 22 22 22 22 2xyyxyx )()(),(0 02 2yxc 2 22 22

5、2xyyxr )( xyd xyo xy xa y yxd2 22 22 2xyyxr )(d xyo xa y yxd2 22 21 12 21 1yxoboaoboaoboc )()(2 22 22 22 22 2xyyxadcacd )(2 2yx d xyo xa y yxdfxya )22cos(0 ceoccfocof 2 22 22 22 20 00 0sinsincoscoscdcdoc 2 22 22 22 2sincosxyyxyx 2 22 22 22 22 22 20 00 0sincoscossin)sin(cdcdcefeo 2 22 22 2cossinxyyxa

6、b a1 12 22 21 11 12 22 2 max)(xyyxyxcaocoa2 22 22 21 11 12 22 2 min)(xyyxyxcbocob 2d xyo xa y yxdfb1a1d xyo xa y yxd 2a1b1yxxycada 2 22 20 0)(tanyxxy 2 22 20 0tan()022arctanxyxy d xyo xa y yxd 2a1b1g1g2max)( 2 22 21 12 2xyyxcgmin)( 2 22 22 22 2xyyxcg2 22 21 1 minmax acb(-1,-0.2)dd(-0.4,0.2)adc bd120

7、15152709z250kn1.6m2mabc+200kn50kn+80knm250kn1.6m2mabczimy 4633mm1088 1227011112300120 zimm135 aydisfzz*s 3 32560002560005 57 71501501515120120mm).(* zas12015152709zmpa5 .122 azcayim mpa.*s6 66 64 4 disfzzaa a cab(122.5 , 64.6)d(0 , - 64.6)a1 a2mpa27mpa1502211 oaoa 4520 5 .220 mpa mpa22 27 70 01 15 5

8、0 03 31 1 5 522220 0. a12015152709zmpa5 .136 bzcbyim 0 b mm150 byb 0,mpa5 .136321 b(136.5 , 0)d(0 , 0) 1 3 1 2 2 2 1 1 2 3 3 2 1 a 1o 2bc 3 1 2 1 2 3 a 1o 2bc 31 1 max a 1o 2bc 3)(2131max mpa20 z 40mpaxyz20mpa20mpa20mpampampampa mpa2020202020204040 yxyxyx a1a2 o c 1 3mpamax3 36 6 yoxyoyxxyoyx sindco

9、sddyxxop abdxdydxabdxdyxyoyxxppaaxd dopdp cosdcosxppdpx 2coscosdcosd1xxxxopdp apabdxdyxyoyxyppbbyd op sindsinyppdpy d 2sinsindsind2yyyyopdp pbabdxdyxyoyxyppbbxyd op cosdcosyppdpxy cossinsindcosd3xyxyyyopdp 321 cossinsincos22xyyx )sincos(cossin)(222 xyyx 2sin212cos22xyyxyx 2cos212sin22xyyx 22 2 )()(2

10、122minmaxxyyxyx yxxy 02tan 2cos2sin22sin2cos22xyyxxyyxyxxyzzxzyexx eyx ezx xy yzz)(1zyxxe )(1xzyye )(1xyzze gyzyz gxyxy gzxzx zyx,zxyzxy,gyzyz gxyxy gzxzx )(1zyxxe )(1xzyye )(1xyzze gxyxy )(1yxxe )(1xyye )(xyze xyz xy x y yx x y xy yx)(13211e )(11322e )(12133e )(1211e )(1122e )(123e , , , ,123321321

11、3211 dddddd)1(ddd dddddd)1(d)1(d)1(d zyxzyxzyxzyxzyxzyxvvv )(21321e )(13211e )(11322e )(12133e xy 3102 0 3321m mmmm321)(21 ee m m mm321e m m m 1 2 3dxdydz mmmm321211ee )(21321e )(21zyxe mpa301 . 010300233 afaaafzyx z x y)(13211e )(12133e 15.5mpa )30(0.34-10.34)0.34(1 1)1(23221 mpa25.7)(2131max 43321

12、1095. 1)3025 .15(1010034. 021)(e21 mpa303 mpa51521. memea45xyxyx 22minmax)2(2 02tan2xy ee1)(1311 3210450 451 11 empa2 .802121)1(2te11 wmeg 1 3bhzb=50mmh=100mmaaf1f2f2lmpa202 afmpa3023s af a x = 20mpa4 .21mpa4 .41)2(222minmax xyxyxmpa4411. 02 mpa4213. 4311104 . 2)(1 e5312103)( e 4133107 . 1)(1 e020 z

13、yx410 exx5103 xye5103 xze222221eev ()1 1223312v ()222123122331122v edvvvv(a) 1 2 3(b) m m m=( 1+ 2+ 3)/3()()()()()222222bbmmmmmm2m21231223 122126vvv eee ()()()aadavvvv()()bbvvv()()abvvvv)(21321e ()222123122331122v e ()()()2ab123126vvvve ()()() d22212233116vvvve (a) 1 2 3maxnmaxaf maxmaxwmz s aftmaxm

14、ax wt*maxmaxsmax bisfzz eb1 )(13211e )(321 2smax s3131max)(21 31 ()()() 222d1223312s16126vee 2ds126ve )()()(21213232221 )()()(21)(2132322214r313r3212r11r r 阿托阿托莫尔莫尔(o.mohr),18351918o2oo1o3fn22222222c3123t311331c231t1oooofono 231321oooofono t3ct1 （a）dyz（b）mpa904 pdmpa90mpa18021 mpa155 )()()(212132322

15、214r mpa1802 pd 2)(31 2 3 3)()0()0(21222 6 . 0577. 03 （b） （c）70 mpa140 mpa80 mpa（d）50mpa（a）mpa120)0120()120120()1200(212224r 01 mpa12032 mpa120)120(0313r mpa128)140(1103021mpa1402224r313r 1140mpa110mpa2 03 （a） 180mpa-70mpa2 -3140mpa28. 572.9440)23070(2307022minmax mpa72941. mpa2853. mpa502 zmpa2203r

16、 mpa1954r mpa44893r. mpa5 .774r 140 mpa80 mpa（c）70 mpa（d）50mpaff3n23t450106.37mpa0.116700035.7mpa0.1fatw 32397 .35)237. 6(237. 6)2(22222minmax mpa32, 0,mpa39321 1 mpa4 .9410)37. 73 . 088. 1(3 . 011 . 2 )(1722 yxxe xyaa003r7 . 71701701 .183 mpa1 .18310)88. 13 . 037. 7(3 . 011 . 2)(1722 xyye 0,mpa4 .94,mpa1 .183321 mpa1 .183313r 0.42cdab0.421.662.500.42cdab0.421.662.50maxmaxwmz 36maxm10494 mwz