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1319_Mechanics Homework Mechanics of Materials Solution

1319_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: PROBLEM 11 14 11.14 The steel rods AB and BC are made ofa steel for which the yield strength is ' a, = 300 MPa and the modulus of elasticity is E = 200 GPa. Determine the maximum strain energy that can be acquired by the assembly without causing any permanent defonnation when the length a of rod AB is (a) 2 m, (b) 4m. SOLUTION A“, = @209)": 78.54 m‘ = 78.5.4 #0“ m‘ am An: = ECG-Y 9 7613.317‘immt =' 28.174 V10“ ma" P = 6m...“ = (3002:0‘)(2s.27qud‘) - = 8. 4822 X103 N 1 EL U 2 QEA (0.) a=2m L—aré-Z= 4w- U _ (8.4822xto‘)‘(23 + (3.4322xros)‘(4) “ (z\(2ooxto*) 78.59MB“) (2)0200 no? )(28527‘! x IO") = 4.5203 + gamma. = 30.0 N‘IM = 30.0 J ~— 00‘ ael-im L—m’G-H=2M U _ (3.4s22~t&3‘(4> + gsflszauto‘ 3‘00 ' meow IO‘XTS-S‘Oxio“ ) (2)9100 my Mam-2w (0") = $1906 + {2.7233 = 21.4 N-m = 2H J' -- 11.]5 Rod AB is made ofa steel for which the yield strength is a, = 65 ksi and the PROBLEM “-15 modulus ofelasticity is E = 29 x 10‘ psi; rod BC is made of an alumiuum alloy for which a, = 40 ksi and E =10.6 x lO‘psi. Determine the maximum strain energythat can be acquired by the composite rodABC without causing permanem deformation. ' SOLUTION A“ = £30m? = 0. use; M 5: 290m ksn‘ A“ , :5 (as? =- o.zsz7‘t in‘ E“ = Joeoo ks.‘ 0.6-in. diameter ?.1' = ”SYA :‘PN each iDQP+ 0.4411. diameter AB: Pm =(65360J2566) = 8.167? 2:... Ba: Ba - (40)(o.-2821‘H = meme kc,» U52 Smaller Vail}? P: 8.167? kI'P-S : (3.1e77)1(22) + £2. me? am (ZlCZqOOOXO-ms‘“) (21(Ioé003(o.2827'-H 256.3 no“ + %7.5xlo'5 =- ' - 729 I‘M-2n. Ll t__i ...
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