杆件应力与强度计算

1、长沙理工大学长沙理工大学蔡明兮蔡明兮20212021年年1111月月2626日星期五日星期五杆件应力与强度计算杆件应力与强度计算PPPPPPPPPPYZdAdAdFNANdAF AdAA AFNP2P/2P/AP)()()(xAxFxNadABCPO30BPNABFNBCF0XFkNPFNAB3020YFkNPFNBC26322ABmm201d4A MpaAFABNABAB1491020110306322BCcm100aA MpaAFBCNBCBC6210100102643.PPk pkPkkPkk p AP 则则，则则 cos/AA，而PF AFp AP cosAP cos cosp 2co

2、s sinp cossin 22sin)cos( 212 F0When1 、达达到到最最大大 maxo45When2 、达达到到最最大大 2 maxo90When3 、0 。即即纵纵截截面面上上无无任任何何应应力力o e p s b上上屈屈服服点点下下屈屈服服点点弹弹性性阶阶段段 屈屈服服阶阶段段强强化化阶阶段段颈颈缩缩阶阶段段o o 残残余余变变形形o o oC300250tWhenoo t b &C300250tWhenoo t b &s b 0 00n bs0nnn5221.93or532. AFN解：解：QFN431kN27 kN45 QFN452111AFN62310

3、1241027 Mpa7238. 1 4m3mQQ2NF1NF111NFA 63101401027 24m10928571 .m105671d2 .mm16d 222AFN4310641045 Mpa7 2 222NFA 6310541045 .22m10 cm10m10Aa12 max maxs AFSPPQ AFS （塑性材料）（塑性材料）（.18060 （脆性材料）（脆性材料）（.10180 为为材材料料的的许许用用拉拉应应力力1 bsbsbsAF bs（塑性材料）（塑性材料）（.15251 （脆性材料）（脆性材料）（.15190 为为材材料料的的许许用用拉拉应应力力1 PP计计算算挤挤

4、压压面面bsbsbsbsAFaabcddhPPmmmm m m tr2 r rtrt tr2m2 dytdxdxtdy)()( G)( 12EGG221u2 dxaa mmdxdx d aa ddxd dxdR max GdxdG AdATAdAdxdG2 AdAdxdG2 A2pdAI令令：pGITdxd pIT pIT pITR maxRIWpP 令令：pWT maxD16DW3P Dd)(43P116DW Dd maxmax pWT5832.aaPPPPPa中性层中性轴dxyyxz dy)(dx ddx yyMM d E yEMMdAy AdAdA NF0 AdAzyM0 AdAyzM

5、M0Iyz 0Sz zEIM1 d A2zdAyIzEIM1 zIMy MzIMymaxmax maxyIWzz 令令zWM maxqL21mkN53q/. m3L qL212qL81zyO120180abc50463zm1032.5812bhImkN943qL81M2 .m050yb. Mpa383IMyzbb. m090yc. Mpa086IMyzcc. m090ya. Mpa086IMyzaa. maxmaxmax zIyMLABPPLPLM maxmkN5375125 .max MWz631016010537 .3cm234 qm4m4Pa40NomNL)qLP2(81q=67.6kg

6、f/m=662.5N/mWz=1090cm3=1.09x10-3m3PL41qL81M2 maxmNP25300 )(max WM631014010091P25300 .kN65.73P kN73Pmm139yc AkN20P mkN10q/ m2m3m1BCD3017020030mkN20 mkN10 46zm10340I .zyY上上Y下下Ycmm139yyc 下下mm61y 上上czBBIyM上上上上 6331034010611020 .Mpa2730. Mpa32c zBBIyM下下下下 63310340101391020 .Mpa9868. Mpa70t zCCIyM上上上上 633

7、1034010611010 .Mpa1415. Mpa70t zCCIyM下下下下 63310340101391010 .Mpa4934. Mpa32c cC51% ）（下下Mpa633. )(1xLFMzyxzo1F2FaLxyzozMYM)(2xaFMyzzIyMyyIzM yyzzIzMIyM maxyyzzWMWMMy SFxdxABmmnnzxhbdx ）（即y dMM xyz 0XF1N2NSdF2NSdF1N 0 yxdx 2N 1AdA 1A1zdAyIdMM 1A1zdAyIdMM*zzSIdMM SdFbdx bdx 1N 1AdA 1A1zdAyIM*zzSIM z*zb

8、ISdxdM zzSbISF*b2h2hyzy1y1dy*zS 1A1dAy112hydyyb )y4h(2b22 )4(222yhIFzSAFS23maxmax max SSFF)97. 095. 0(1AFSmaxzySFzyzzSbISF*yAFS34maxkN200kN200mkN84 m42.0m42.0kN200kN200m66.1MWz 63101601084 36m10525 36zm10534W cm2.24S/Izz mm5.10b zzSbISFmax233102.24105.1010200 Mpa71.78 Mpa100 2242yhIFzS2242yhGIFGzS0dVVbdxVy )( 2hy1bdyVSSdFF SF)(xqdVV Vy ydx21212)4(2hyzSdyyhIbF)31412(2323yyhhIbFzSdxdVb1y )31412(21323yyhhIdxdFzS)()(323zy31y4h12hI2xq b)x(qmaxy qhbqma