Answer:
(a) 1.90 kpsi
(b) 0.40 kpsi
(c) 0.61 in.
(d) 0.009
(a) 8 MPa
(b) 1.30 cm⁴
(c) 2.04 cm⁴
(d) 62.2 MPa
Explanation:
(a) σ = M/Z, where M = 1770 lbf·in and Z = 0.943 in³.
1770/0.943 = 1876.988 lbf/in² = 1.90 kpsi
(b) σ = F/A, where F = 9440 lbf and A = 23.8 in².
9440 /23.8 = 396.639 lbf/in² = 0.4 kpsi
(c) y = Fl³/(3EI)
F = 270 lbf
l = 31.5 in.
E = 30 Mpsi
I = 0.154 in.⁴
y = 270×31.5³/(3×30×10⁶×0.154) = 0.61 in.
(d) θ = Tl/(GJ), where T = 9740 lbf·in, l = 9.85 in. G = 11.3 Mpsi, and d = 1.00 in.
J = π·d⁴/32 = π/32 in.⁴
∴ θ = 9740 × 9.85 /(11.3 × 10⁶× π/32) = 0.009
(a) σ = F/wt, where F = 1 kN, w = 25 mm, and t = 5 mm
∴ σ = 1000/(0.025 × 0.005) = 8 MPa
(b) I = bh³/12, where b = 10 mm and h = 25 mm.
10×25³/12 = 1.30 cm⁴
(c) I = π·d⁴/64 where d = 25.4 mm.
I = π × 25.4⁴/64 = 2.04 cm⁴
(d) τ = 16×T/(π×d³), where T = 25 N·m, and d = 12.7 mm.
16×25/(π×0.0127³) = 62.2 MPa.
