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1344_Mechanics Homework Mechanics of Materials Solution

1344_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: 11.48 For the state of stress shown in Fig. a, determine the stresses in an element PROBLEM 11.48 oriented as shown in Fig. b. Compare the strain energy density in the given state first by using Fig. a and then by using Fig. 1:. Equating the two results obtained, 0 show that __ /‘ M chr‘s LCM. 1:. Y ’Z. SOLUTION | 1 2. 6' 3 _L __ £2421) 12/01 U = :TE(5}'+5§'*2‘1’5¢3' +26 7151' ' ZE 3:: 12.12%? 2 E lEC) Emmi": 2 - 2E G 2047)) *11.49 A vibration isolation support is made by bonding a rod A, of radius Rb and a tube B, of inner radius R1 to a hollow rubber cylinder. Denoting by G the modulus of rigidity of the rubber, determine the strain energy of the hollow rubber cylinder for the loading shown. PROBLEM 11.49 SOLUTION 1: Ho. +‘5R=O —"r(2an)+Q= o _ (3). Z" lewL U = 3% = gag—W I VQ‘ oiV Q‘ L 2‘ analv' U=SUJV =3’"‘GL‘ VE=W§OSK #3.“pr 1. L pt ,1 r. ‘ L R; . -51: 2‘ '7 qgeL-t SD SRI él-flgw 2 til-"GI; go (finr‘fii')lx "" ”—F'IOV‘I-R“ 4 ...
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