Mechanical Engineering Chapter 3 Stress And Deformation Analysis Part 2

ͷʹǤ ݐܽ݊ߠ ൌ͸ȀͳʹൌͲǤͷǣߠ ൌʹ͸Ǥ͸ι

ܣ

௫ൌʹܣ௬ൌʹͶͲͲൌ ܥ௫







஺ೣ

ͷ͵Ǥ 



ሺሻ

ߪൌ

ி೓

஺൅ெ

ௌൌଷ଴ଵே

ହ଴ሺଶ଴ሻ௠௠మ൅ሺସଷ଴ேሻሺସ଴଴௠௠ሻ

ሺଶ଴ሻሺହ଴ሻమȀ଺௠௠య

௧ൌට଺ሺସଵ଴଻ሻ

ଶ଴ ൌ ͵ͷǤͳǢ݄ ൌ ͵͸Ǣܣ ൌ ݐ݄ ൌ͹ʹͲଶ

ܵൌ

௧௛మ

଺ൌଶ଴ሺଷ଺ሻమ

଺ൌͶ͵ʹͲଷ

ͺൈͳͲǣ

ܣ

ൌʹǤͻ͸ଶǢܵ൅͹Ǥͺͳଷ

ሾͳͷǦͻሿ

ͳʹͲͲ ൌ ୷

ܸ

ሺሻ

ܯ

ሺήሻ

ܴ஺ൌ ʹ͸ͺ͵

ͳʹͲͲ

െ͸ͲͲ

Ͳ

ߠܤ ܥ

ͺ

ͶͺͲͲή ൌ ͷ͹͸ͲͲή

ͶͲͲ

ܣ

ܤ ܥ

ܨ௫

͵Ͳͳ

ͷͲ͵ͷι

32

 ݄ ൌͳͺǢݐ ൌ ʹͲǢܵ ൌʹͲሺͳͺሻଶȀ͸ൌͳͲͺͲଷǢܣൌͳͺሺʹͲሻൌ͵͸Ͳଶ

࣌

࡯ൌଷ଴ଵ୒

ଷ଺଴୫୫మ൅ଶଵହ଴଴୒ή୫୫

ଵ଴଼଴୫୫యൌ૛૙Ǥૠ૝ۻ۾܉۽ܓ

ͷͶǤ ͸ൈʹൈͳͶ

ൗ Ǣ

 ͳͷǦͳͶ

 





ǣߪ ൌ െிೣ

஺൅ெ

ௌ

ͷͷǤ ͵ǦͳͻǢܯ ൌͺ͹ͷήǢܨ௫ൌ ͵ͷǤͲ

ܣൌͷǤͲ

ሺʹǤͶሻൌͳʹǤͲ

ͷ͸Ǥ ܤܥ ൌξͷͲଶ൅͸Ͳଶൌ ͹ͺǤͳ

 ܥܨ ൌ ʹǤͷȀݏ݅݊ߠ ൌ ͵ͻǤͲͷ

ܤܨ ൌͳͳ͹Ǥͳͷ

ܯ

Ͳ

ʹͲͲͲ ܨ௬ൌ ͶͲͲͲ

͵Ͳι

െʹͲͲͲ Ͷ ʹ ʹ Ͷ

ܣ

ܤ

ͷǤͲ

ͷͲ ʹͷ



୷

ൌͳͳͷʹ

ܨ௫

33

ܣൌͶǤͷͻ

ଶǢܵ௫ൌ ͹Ǥ͵͸ଷ





ǣ

஻ೣ

ͷ͹Ǥ ܣ ൌ ܾଶǢܵ ൌ ܾଷȀ͸

ߪൌെ

ி

஺െெ

ௌൌି଺଴

௕మെଶସ଴

௕యȀ଺

଺଴

ͷͺǤ ͵ǦͶʹǣ

 ܤെܥ͵ͻ͵͹ͷή

͹ͺǤ

ͳ

͵ͻǤͲͷ

ܯ

ሺήሻͲ

ܤܥܨܨ௬ൌ

ͳͳͷʹ

ͶͶͻͺ͸

ܤ௬ൌ ͷ͹͸

Ͷ ͸Ͳ

ܾ

ʹʹͷ ͷͲͲ ܴଶ

ʹͲͲ ʹʹͷ

ܯ ൌ͵ͻ͵͹ͷή

ܣ

ܤ ܥ

34

͹ͷ

͹ͷ

ܯܯ

ܣ

ൌ͹ͷଶൌͷ͸ʹͷଶ

ܵൌ͹ͷ

ଷȀ͸ൌ͹Ͳ͵ͳ͵ଷ

ͷͻǤ ͵ǦͶ͵ǣܯ ൌ ൌͻ͵͹ͷͲή

ൌ

ିହ଴଴୒

ହ଺ଶହ୫୫మെଽଷ଻ହ଴୒ή୫୫

଻଴ଷଵଷ୫୫మ

͸ͲǤ ͵ǦͶ͹ǣ



ǢVൌʹͷͲͲͲ

 



Ǣܯ ൌ ͳͳͺͳͳήǢߪ ൌܯȀܵǢܵ ൌ ெ

ఙൌଵଵ଼ଵଵ୪ୠή୧୬

ଶହ଴଴଴୪ୠȀ୧୬మൌͲǤͶ͹ʹଷ

ଷȀ͵ʹǢܦ ൌ ඥ͵ʹܵȀߨ

యൌඥ͵ʹሺͲǤͶ͹ʹሻȀߨ

యൌͳǤ͸ͻǣܦ ൌ ͳǤ͹ͷ



StressConcentrations

ǣܭ௧ͳͺ

ǡǡ

Ǥ

͸ͳǤ ܦȀ݀ ൌ ͻȀ͸ ൌ ͳǤͷͲ

36

͸͵Ǥ ሾǦ͸͵ሿǣ݀Ȁݓ ൌ ͲǤ͹ʹȀͳǤͶͲൌͲǤͷͳ

ܭ

௧ൌʹǤͳͷሾͳͺǦͶሿ

͸ͶǤ ܪȀ݄ ൌ ͳǤͷͲȀͲǤͺͲൌ ͳǤͺ͹ͷ

͸ͷǤ ܦȀ݀ ൌ ͶʹȀ͵Ͳ ൌ ͳǤͶͲ

͸͸Ǥ ܦȀ݀ ൌ ʹǤͲͲȀͳǤʹͷൌͳǤ͸Ͳ

͸͹ǤܦȀ݀ൌʹǤͲͲȀͳǤʹͷൌͳǤ͸Ͳ࣌࢓ࢇ࢞ ൌଶǤଶଷሺଶ଼଴଴ሻ୪ୠή୧୬

஠ሺଵǤଶହሻయȀଷଶ୧୬మൌ ૜૛૞૟૝ܘܛܑ

͸ͺǤ ݀Ȁݓ ൌ ͳǤ͵ͺȀʹǤͲͲ ൌ ͲǤ͸ͻ՜ ܭ௧ൌͳǤ͵ͺ

࣌

࢓ࢇ࢞ ൌܭ

௧ߪ௡௢௠ ൌ௄೟଺ெௐ

ሺ௪యିௗయሻ௧ൌሺଵǤଷ଼ሻሺ଺ሻሺଵଶ଴଴଴ሻሺଶǤ଴଴ሻ

ሾሺଶǤ଴଴ሻయିሺଵǤଷ଼ሻయሿ଴Ǥ଻ହ ൌ૝ૢ૜૛૜ܘܛܑ

ܭ௧ൌʹǤͳͲ [From Appendix A18-

ܭ௧ൌʹǤ͵Ͳ [From Appendix A18-1]

ܭ௧ൌͳǤͶ͵ [From Appendix A18-



ܣ

ܤ

ത

Ƭܥܦ

ത

െͳͺǤ͹ͷ

ʹͲ ܴ

஼

ൌ͹Ǥͷ

 ʹǤͷ

R

B

= 20.0

kN

ProblemsofaGeneralNature

͸ͻǤ ȭܯ

஼

ൌͲ ൌ ͳʹǤͷሺͶǤͲ݉ሻെܴ

஻

ሺʹǤͷሻ

ܴ

஻

ൌሺͳʹǤͷሻሺͶǤͲሻȀʹǤͷൌ ʹͲǤͲ ՛

ܣܤ

ത

ൌܣ

஺஻

ሺʹͲ݉݉ሻ

ଶ

ൌͶͲͲ

ଶ



 Ȃ

ത

ଶగ஽

మ

గ஽

మ

గሺ଼Ǥ଴௠௠ሻ

మ

ଶ

஺

ೞ

ଵ଴଴Ǥହ୫୫

మ

 ܥܦ

ത

ǣܤǣߪ

஻

ൌܯȀܵൌ

ଵ଼Ǥ଻ହൈଵ଴

ల

୒ή୫୫

ଵଷଷଷ୫୫

య

ൌ ૚૝૙૟૜ۻ۾܉܄܍ܚܡܐܑ܏ܐ

 ܥܦ

ത

ߪ

஻

൏ͶͲͲ

ଵ଼Ǥ଻ହൈଵ଴

ల

୒ή୫୫

૜

ʹͲ

38

͹ͲǤ 



ܮȀʹܮȀʹ

݄

௫

ൌ ʹͲ൅ͲǤͳݔݔ ൑ ʹͲͲ

ܲ

ͶͲ ͶͲ

ͶͲ

39

ܣ

ܤܥ ܦ ܧܨܩ

ܣ

ܤܥ ܦ ܧ ܨ ܩ

ܴ

ଵ

ൌͺͷ͹ ܴ

ଶ

ൌ͸Ͷ͵

͹ʹǤ ߪ ൌ

௄

೟

ெ

ௌ



ሺሻ



Ǣܯ

஼

ൌ ͷͳͶ͵ή

ଶ

ሺଵǤଶ଴ሻሺସǤ଴ሻ

మ

ଷ

ଷǤଶ଴୧୬

య

ሺሻ



ͳǤͷͲ

ܯ

஽

ൌ ͵ͺͷ͹ήǢ݀Ȁݓ ൌ

ଵǤହ଴

ସǤ଴଴

ൌ ͲǤ͵͹ͷ

ଷǤ଴ଷ

ሺሻ



ʹǤͷͲ

ଶǤହ଴

ଶǤସଵଽ

ሺሻ



ǣܪ ൌ ͶǤͲͲǡ݄ ൌʹǤͺͲǡݎ ൌ ͲǤͳͷ

ଵǤହ଻



ͳͶͲ ͳͲͲ ͳͲͲ ͳͶͲ

ʹܲ

ݎൌ͵

ܣ

ܤܥܦ

ܧ

ͳʹ ʹͶ ͵͸ Ͷͺ ݐൌͺ

ܲ

͹͵Ǥ ߪ ൌ௄೟ெ

ௌ

ܯ

஻ൌʹܲܮ

ଷ

ܯ

஼ൌʹܲܮ

ଷ

ܲ

41

ܯܸ

ͲͲ

െʹ͸Ͳ

ʹ͸Ͳ

ʹͲͲ

Ͳ

Ͳ

ܣ

ܧ

͹ͶǤ ܯ ൌܨሺͷʹ൅ʹͷȀʹሻൌሺʹͷͲͲܰሻሺ͸ͶǤͷ݉݉ሻൌ ͳ͸ͳʹͷͲή

ߪൌ

௄೟ெ

ௌ೙೐೟ Ǣܵ௡௘௧ ൌ൫௪యିௗయ൯ሺ௧ሻ

଺௪ 

͹͹Ǥ 





 ǣܵ ൌ ௧௛మ

଺ൌሺ଴Ǥ଻ହሻሺଶǤ଴଴ሻమ

଺ൌͲǤͷͲଷ

ௌൌଵǤଶହሺଷଵଶ଴ሻ

଴Ǥଷ଻଼ ൌ૚૙૜૛૙ܘܛܑ

76

ܯ

ሺήሻ

Ͳ

ܥ

ܧ

ܣ

ܤ

ܧ

ܤ

െͲǤͶͷ െͳǤʹ

െͳǤͷ͹ͷ

ܥ



௥

ௗൌଶ

ସହ ൌͲǤͲͶͶ

ܭ

௧

ൌʹǤͲͷ

ܯ

ܸ

ʹͺͲͲ

ܦ

43

LugJoints

͹ͻǤ 

 ǣ͵Ǧ͸ͻǢ݀ ൌͺǤͲǡݓ ൌ ʹͲǤͲ

 ݓ ൌ݀ȀͲǤͶͲ ൌ ͺǤͲȀͲǤͶͲ ൌ ʹͲǤͲ

 ൌ݀௛௢௟௘ ൌ݀௣௜௡ሺͳǤͲͲʹሻൌͺǤͲͳ͸

 Ͷ͵ͶͲͺͲͲǡݏ௨ൌ ͳͶͷͲ

ߪ

ௗൌ௦ೠ

ேൌଵସହ଴ெ௉௔

ହൌʹͻͲ

݀ൌ

ඥʹͲ͸Ǥͻ݉݉ଶȀͲǤ͹ͷൌͳ͸Ǥ͸

44

 ǣ݀ ൌͳͺሾʹሿ 

ǣݓൌ

ௗ

ൌ

ଵ଼

ൌ ͶͷǤͲǢݐ ൌ ͲǤͷ݀ ൌ ͻǤͲ

ி

ଶ଴଴଴଴ே

గሺଵ଼௠௠ሻ

మ

Ȁଶ

߬

ௗ

ൌ

ௌ௦

ೠ

ே

ൌ

଴Ǥ଻ହ௦

ೠ

ହ

ൌ

଴Ǥ଻ହሺଵସହ଴ெ௉௔ሻ

ହ

ൌ ʹͳ͹Ǥͷ ൐ ͵ͻǤ͵

 ൌ݀

௛௢௟௘

ൌ݀

௣௜௡

ሺͳǤͲͲʹሻൌ ͳͺǤͲሺͳǤͲͲʹሻൌͳͺǤͲ͵͸



CurvedBeams

ͺͳǤ ͵͸ǣݏ

௬

ൌ͵͸ ൌ ʹͶͺȂ





ߪ

଴

ൌ

ெሺோି௥

బ

ሻ

஺௥

బ

ሺோ

೎

ିோሻ

ߪ

௜

ൌ

ெሺோି௥

೔

ሻ

஺௥

೔

ሺ௥

೎

ିோሻ



௠௠

మ

ିଵǤଽ଺ଶ

45

ݎ

௢

ݎ

௖



ͳʹͲ

ͺʹǤ ǣ 



ͳʹͲ





 ͳͲʹͲǢݏ

௬

ൌ͵ͷʹ

ܣܵܨൌ͸݈݊

ሺݎ

௢

Ȁݎ

௜

ሻൌͶ݈݊ሺ͵ʹȀʹʹሻൌͳǤͶͻͺ͹

 ܴ ൌ ܣȀܣܵܨ ൌ ͶͲȀͳǤͶͻͺ͹ൌ ʹ͸Ǥ͸ͺͺ

 ͺͳǤ

ఙ

೔

ିଶଽ଻Ǥ଺୑୔ୟ

ܰ

௢

ൌ

௦

೤

ఙ

೚

ൌ

ଷହଶெ௉௔

ଶଷଵǤ଼ெ௉௔

ൌͳǤͷʹ

ͺ͵Ǥ   ͵Ǧͺ͵

ǣ཰Ǧཱ



ܦ

ଵ

ൌ ͳͲ

཰

݀ൌ F

46

ܣܵܨ

ଶൌʹߨൣݎ

௖െሺݎ௖ଶെܦ

ଶ

 ܣܵܨ ൌ͵ǤͻͻͲ͵െͳǤͶʹͳͺ ൌ ʹǤͷ͸ͺͷ

ܴൌ

஺

஺ௌி ൌହ଴Ǥଶ଺ହ௠௠మ

ଶǤହ଺଼ହ௠௠ ൌͳͻǤͷ͸ͻ

 ሾͺͳሿ

ࡺ

࢏ൌ௦೤

ఙ೔ൌିଷହଶ୑୔ୟ

ିହସ଴Ǥଷ୑୔ୟ ൌ૙Ǥ૟૞૚

ࡲ

ࢇ࢒࢒ ൌଵଶହ଴ଽ୒ή୫୫

଼଴୫୫ ൌ ૚૞૟Ǥ૝ۼ





ͺͶǤ



  



Ǥ



 ǣ͵ͷ͸ǤͲǦ͸ǡݏ௬ൌ ʹͲ͹

݀

Ͷͺ

ʹǤͺ͹ͷൌ



ͳ

ʹǤͶ͸ͻൌ



ʹ

=ro

ͺͳǤ    ͵Ǧͺͷ

 ǣͷ͵ǦǢݏ௬ൌ ͵ͷ

ܯൌܨή݀ൌ

ሺʹ͵ͲሻሺͶͺሻൌെͳͳͲͶͲήሺሻ

49

ߪ

௜ൌெሺோି௥೔ሻ

஺௥೔ሺ௥೎ିோሻൌଷଵǤହହଷிሺଷǤଽ଺ଽሻ

ሺହ଻ሻሺହሻሺଵǤହ଼ଷሻൌͲǤʹ͹͹͸ܨ௜

ࡲ

࢏ൌଵଷସǤ଺଻୒Ȁ୫୫మ

଴Ǥଶ଻଻଺୫୫మൌ૝ૡ૞Ǥ૚ۼ

ߪ

௢ൌெሺோି௥೚ሻ

஺௥೚ሺ௥೎ିோሻൌଷଵǤହହଷிሺିଵ଴Ǥ଴ଷ଴଻ሻ

ሺହ଻ሻሺଵଽሻሺଵǤହ଼ଷሻൌͲǤͳͺͶ͸ܨ௢

ܮ݁ݐߪ

௢ൌ௦ೠ೎

ଷൌെଶ଺ଽ୑୔ୟ

ଷൌെͺͻǤ͸͹Ȁଶ

ࡲ

࢕ൌି଼ଽǤ଺଻୒Ȁ୫୫మ

ି଴Ǥଵ଼ସ଺୫୫మൌ૝ૡ૞Ǥૠۼ

ܨ௢ൎܨ

௜ǡǦ

Ǥ

ͳǣ

ܣ

ଵൌ͵ήͺൌʹͶଶ

ଶൌ͵ήͳͳൌ͵͵ଶ

ܣൌܣ

ଵ൅ܣଶൌ ͷ͹ଶ

ݎ௢ൌݎ

௜൅ͳͶൌͷ൅ͳͶൌͳͻ

ሺݎ௖െܴሻൌ ͳͲǤͷͷ͵െͺǤͻ͸ͻ ൌ ͳǤͷͺ͵

ܣ