2.4-1 - PI'DIJIBm 2.4-1 The assembly shown in the figure...

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Unformatted text preview: PI'DIJIBm 2.4-1 The assembly shown in the figure consists of a brass eore {diameter d1 = 1125 in.) surrounded by a steel shell {inner diameter 112 = 0.23 in., wter diameter 113 = 13.35 in.). A load P compresses the core and shell, which have length L = 4.0 in. The moduli of elasticity of the brass and steel are Es = 15 X 105 psi and E3 = 31:! D-C ll)“E psi, respectively. {a} What load P will compress the assembly by 0.1133 i11.‘? (b) Ifthe allowable stress in the steel is ‘22 ksi and the allowable stress in the brass is 16 ksi, what is the allowable compressive load Pm”? (Suggestion: Use fl1e equations derived in Example 2—5.} Steel shell Brass eore Substitute numerical values: 11311, + E1111 = 1311 x 11:15 psi}[fl.fl34fi-t1 111.11 + {15 x 11::‘3 11511101149119 in?) Steel shell =1.11s 1-: 10511:. Brass core [1 m3 _ . ll]. P= 1.116 >1 1051b (—) i i 4.1:: in. d1 = 13311111 4— 111 {b} ALlflWABLE Loan ”3 arJ=22 1:51 n'b=lfi 151 Use Eqs. (2—12a and b) of Example 2—5. F t l: 111 = 0.25111. sb=1s x 1116 psi Dr 5 a“ PE [1' =n.2s'. s=:11:1>-<1115 ' =—‘ P=EA+EA " d; m , p51 U; 11,111+sta1, .1 (1-1 111g 11' =o.ss'. 11=— — =n.1134e1'.2 221' '1’ m ‘ 401% ‘13) m P, = {1.11M 11:15 1b1(—5’_)= 1101111: 3ft X 11:15 ps1 L = «LG in. Ab. = $11] = H.04909 i11.2 For brass: _i P _ E A U!“ {a}DECREASE]I~ILEI~IGTH{E=fl.m3in.} Ub—Eafis'i'EaAh ’_( iA“+E" ”E Use . 2—13 ofEx lei—5. 1611' Eq { i “m” P,=1:1.11s>-< 11:15 1b1(—5’_)= 1s911 lb FL 15 x 106 ps1 s=— or E, A, + E5 11;, Steel governs. Pm = 13E") lb 4— P = (E, A3 + Eb ski?) ...
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