hw6sol

# hw6sol - ME 363 1(a Homework#6 σ fm Κ ε n 1 = ε n 1 =...

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Unformatted text preview: ME 363 1. (a) Homework #6 σ fm Κ ε n +1 = ε n +1 = ε = ln 1.22 Αo 0.5 = 0.713 = 2 ln Α 0.35 45,000 ( 0.1713) 0.713 1.22 = 34, 240 psi ⎡⎛ ⎣⎝ σ d = σ fm ⎢⎜ 1 + μ ⎞ Αo 2 ⎤ +α ln α ⎟ Α1 3 ⎥ ⎠ ⎦ ⎡ ⎛ 0.1 ⎞ 0.52 2 ⎤ = 34, 240 ⎢ ⎜ 1 + + ( 0.1) ⎥ ⎟ ln 2 ⎣ ⎝ 0.1 ⎠ 0.35 3 ⎦ ⎛ ⎞ 12 0 π × = 0.1 ⎟ α= ⎜ 2 180 ⎝ ⎠ = 34, 240 × 1.49 = 51,133 psi Fd = A f × σ d = (b) π 4 ( 0.35) 2 × 51,133 = 4,920 lbs P= Fd × V 4920 × 2 = = 17.9 Hp 550 550 2. UTS = 600 MPa = 87,000 psi l = 2 ( 23.5 + 2 ) + 2 = 13 in Pmax = 0.7 (UTS ) × t × l 5 × 13 32 = 123,731 lbs ( = 549kN ) = 0.7 (87,000 ) × 3. (a) Ri ⎛ RY ⎞ ⎛ RY = 4 ⎜ i ⎟ - 3⎜ i Rf ⎝ ET ⎠ ⎝ ET 3 3 ⎞ ⎟ +1 ⎠ ⎛ 10 × 120 ⎞ ⎛ 10 × 120 ⎞ = 4⎜ ⎟ - 3⎜ ⎟ +1 3 3 ⎝ 70 × 10 × 2 ⎠ ⎝ 70 × 10 × 2 ⎠ = 4 ( 0.0085) - 3 ( 0.0085) + 1 3 = 0.975 Rf = Ri 10 = = 10.26 0.975 0.975 ∴ D f = 2 × R f = 20.52 mm (b) R f = 20 Ri ⎛ RY ⎞ ⎛ RY ⎞ = 4 ⎜ i ⎟ - 3⎜ i ⎟ + 1 20 ⎝ ET ⎠ ⎝ ET ⎠ ⎛ R × 120 ⎞ ⎛ Ri × 120 ⎞ Ri 4⎜ i 3 +1 = 0 ⎟ - 3⎜ ⎟− 70 × 10 × 2 ⎠ 70 × 103 × 2 ⎠ 20 ⎝ ⎝ 19.5 Ri = 3 3 (c) 50 −1 T r 20 50 = −1 2 r ∴ r = 4.5 = Rf 4. (a) UTS = 320 MPa = 46, 410 psi 1 ⎛ 12 ⎞ Fmax = π × 9 × × 46, 410 ⎜ − 0.7 ⎟ 8 ⎝9 ⎠ = 103,883lbs (b) 103,883 = 415,534lbs 0.25 415,532 Pressure = = 8, 400 psi π (122 − 92 ) 4 Force = ...
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