立柱的內(nèi)力和應(yīng)力

1、立柱的內(nèi)力和應(yīng)力立柱的內(nèi)力和應(yīng)力ZIyxMAN)(ZWMANmaxmax(min) maxWMMWMYZ2222YZMMM)(maxYYZZWMWMmme50MPaWMANZ66.11)83. 583. 5()3 . 02 . 06503503 . 02 . 010350()(23maxmax)1(MPaAN75. 82 . 01035023max2）（33. 175. 86 .11) 2) 1（mmz5 .5920100206020509020100502060102050142323239 .39820100)105 .40(12201006020)505 .59(1260202050)1

2、05 .59(122050cmIY例例2ttMPaIzMAN2 .322maxcycMPaIzMAN2 .401max立柱不滿足強(qiáng)度要求立柱不滿足強(qiáng)度要求2.2.分析立柱的內(nèi)力和應(yīng)力分析立柱的內(nèi)力和應(yīng)力KNN12mkNPM886. 2105 .4020033.校核強(qiáng)度校核強(qiáng)度MPaEaa2101011021039MPaEbb84104 . 01021039aWPAPbWPAPmmKNP786. 14 .18mmyc551060102070106010102044106 .72mmIzMPaIPAPz8 .16210)8 .37125(10563maxmme5663108 .1621010)10

3、0(10100 xmmx6 .38A、B 二點(diǎn)應(yīng)力最大二點(diǎn)應(yīng)力最大yyzzIzMIyMAN關(guān)于中性軸的概念關(guān)于中性軸的概念 橫截面是否一定存在中性軸橫截面是否一定存在中性軸中性軸是否一定通過橫截面的形心中性軸是否一定通過橫截面的形心橫截面上正應(yīng)力為零的點(diǎn)連成的直線橫截面上正應(yīng)力為零的點(diǎn)連成的直線yPzPIzPzIyPyAPzyazyzay000000、令：yPzPIzPzIyPyAP22yyzZiAIiAI注：）（221yPzPizziyyAP012020）（yPzPizziyyAP12020yPzPizziyy10202zizyiyyPzPPyzPzyziayia22zyazyzay0000

4、00、令：122PyPzzisyir10202zizyiyyPzP例例6 6：短柱的形心為矩形，尺寸為：短柱的形心為矩形，尺寸為b b h h，試確定截試確定截面核心面核心中性軸在坐標(biāo)軸的截距：中性軸在坐標(biāo)軸的截距：zyaha,2PyzPzyziayia22，若中性軸與若中性軸與 AB AB 邊重合：邊重合：ah/6121223hbhbhAIiZz2Pzyyia2yzPaiy262122hhhah/6bcb/6dPzyyia2yzPaiy262122hhhPyzzia2zyPaiz262122bbbdPyzPzyziayia22，AIiZz216464224dddyzPaiy282162ddd

5、2224110544180cmA464410364541280cmIIzyyazayzPaiy2zyPaiz2(1)(2)(3)(4)222729zyyicmAIi2262821cmRAcmRZC49. 8344241756062849. 81028. 6cmIy4421028. 6644021cmIzyazayzPaiy2zyPaiz22228 cmAIiyy22100 cmAIizz(2)(3)(4)(1)1234yazayzPaiy2zyPaiz226 .09 .04 .06 .04 .0mA4333105 .27)4 . 06 . 09 . 04 . 0(121mIz43331048)

6、6 .04 .04 .09 .0(31mIy22132108106 . 01048mAIiyy2221058. 4mAIizz(1)(2)(3)(4)(5)(6)10202zizyiyyPzPFlaSABCFlaSABCFMxzy4321S平面平面yxzMzFMx43211pxWM 1 zzxWM 1 43pxWM 3 pxWM 4 zzxWM 4 F22142122234212313r21213232221）（4r22322422142122234212223134r2243r2231TMWrtWTWM，WWt2圓形截面：22475. 01TMWr223)(4)(trWTWM224)( 3)

7、(trWTWM2231TMWr22475. 01TMWr223)(4)(trWTWM224)( 3)(trWTWM圓形截面或圓形截面或空心圓截面空心圓截面WWt2圓形截面：223)()(WTWMANr224)(75. 0)(WTWMANrzYZrWTMM222223)(4zYZrWTMM22222475. 0)(3NmhPM961NmeWM2002NmlPT160NN31040223)(4)(trWTWMANMPaAN8 .31MPaWM47 總NmM29696200總223)(4)(trWTWMANMPaAN8 .31MPaWM47 總MPaWTt7 .12MPar837 .124)478

8、.31(223WMAP總1tWTkNNmkNTmkNMmkNMzy20,.4.8,.10，TMyMzM總總mkNMMMyz.8 .1222總WMAN總MPa6 .12108010206343MPaWTP201020010463TMyMzWMAP總1tWTM總總223134rWMAN總MPa6 .12108010206343MPaWTP201020010463MPa0 .1362046 .13022例例1414：齒輪軸：齒輪軸ABAB, ,已知軸轉(zhuǎn)速已知軸轉(zhuǎn)速n n =265r/min=265r/min ，輸入輸入功率功率N N =10Kw,=

9、10Kw,D D1 1 =396mm,=396mm,D D2 2 =168mm,=168mm,=20=20。，軸的軸的直徑直徑d d =50mm=50mm， =50MPa=50MPa，試校核軸的強(qiáng)度試校核軸的強(qiáng)度0.080.080.13mNnNTC3612651095499549236111DPzNPNPyz664,182311236122DPyNPNPzy1565,430022NYNYBA3300,1664NZNZBA1630,17500.080.080.13可能危險(xiǎn)截面為可能危險(xiǎn)截面為C C、D DNmMC19313314022NmMD29426413122 MPaWTMDr4370501

10、0361294322223. MPaWTMDr43405010361750294750322224.該軸滿足強(qiáng)度要求該軸滿足強(qiáng)度要求危險(xiǎn)截面：危險(xiǎn)截面：D D 截面截面MPaWM4 .441030620093MPahbT6 .35103030208.0200922MPaAQ67. 110302100032362 MPar6 .866 .3544 .44422223MPa2 .716 .352MPa67. 1 MPar4 .1422 .714042223CRtBCBCBABllyly69612493124912493105 . 6102004450105 .121020102003643 . 0102010843 . 0326 . 0)3 . 0(1020102003646 . 0CCCCRRRREAlRlTEIlRlGIlREIlRCDCDCBCCBCPABCABC3)3 .0(333NRC2 .26CRtBCBCBABllylyMPaRWMCZa0 .201020326 . 093MPaRWTCPa0 . 51020163 . 0932234rNRC2