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103_Mechanics Homework Mechanics of Materials Solution

103_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: 2.53 A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is made of steel (E, = 29 X 106 psi, at; = 6.5 X lO‘°/°F) and portion BC is made of brass (Eh = 15 X lO‘psi, 05,, = 10.4 X 10'°/°F). Knowing that the rod is initially unstressed, determine (a) the normal stresses induced in portions AB and BC by a temperature rise of 65°F, (b) the corresponding deflection of point B. PROBLEM 2.56 2.56 For the rod of Prob. 2.53, determine the maximum allowable temperature change if the stress in the steel portion AB is not to exceed 18 ksi and if the stress in the brass portion CB is not to exceed 7 ksi. SOLUTION AWo-quﬁe 430.052 in egg-ls rev-+30“ . a i . 1.. AB ’ @643 ks: = .-isrto‘psu'_, A“ = 34'- a"; = 11,13 0.25) ' LZRJQ m P = 65A,. = (+18 Kro%)0.2279.) = — 22.07:: x105 16‘ BC: ' -7~:o‘pa;; Am: E ale: = 1312.25? = 3-976! “1‘ L—7wo3X3ﬁ7el) = - 27.333 #103 196. Smaﬂ’ew aJase-JJf'e Value aauerns :- P '—" - 22.0?!) “losﬂb. WWJian JJe +e 'P g -, 3.1.18. pfﬁgg __. _(=2.07m103)(|2\ __§22.099xto")(ls) P E,“ A» EuAei (zexroocmzmy (lexio‘xsam) = — 15.00%:0" in Free + I! elf-Via) Expan 5 {on 8" Midst“) + LRO‘BCAT]= (IZKG-Sxté‘ XAT)+C:5)Cio.qxio"7mi') = (234 wio“)(ATl Té-l-oJ ci'e-Formd-i'm is zen: 87+ 59 ‘ (RS‘lrlO‘XAT )— tamo‘txto'a' = 0 AT = 5\$.G°F ...
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