Advanced Mechanics of Materials and Applied Elasticity, 6th Edition

Answers to Selected Problems

Chapter 1 Analysis of Stress

1.1. P = 4.27 kN

1.4. P = 32.5 kN, θ = 26.56°

1.6. P_all = 38.3 kN

1.8. σ_x′ = 156 MPa, τ_x′y′ = −131 MPa

1.10. σ_x′ = −13.15 MPa, τ_x′y′ = -15.67 MPa

1.11. F = 67.32 kN/m³

1.14. F_x = F_y = F_z = 0

1.21. (a) σ = 153.3 MPa, σ = 231 MPa

1.31. (a) σ₁ = 121 MPa, σ = −71 MPa, τ_max = 96 MPa

(b) σ₁ = 200 MPa, σ₂ = −50 MPa, τ_τmax = 125 MPa

θp′ = 26.57°, θs′ = 71.57°

1.36. (a) σ_x = 38.68 MPa, σ_x = 12.12 MPa, τ_xy = 7 MPa

(b) σ₁ = 40.41 MPa, σ₂ = 10.39 MPa, θp′ = 13.9°

1.39. P = 3πpr²

1.42. τ_max = 48 MPa, θp″ = 29°

1.43. σ_w = −61.5 MPa, τ_w = 26.3 MPa

1.47. (a) σ = −0.237τ_o, τ = 0.347 τ_o

(b) σ₁ = 3.732τ_o, σ₂ = −0.268τ_o, θp′=15°

1.49. σ₁ = −σ₂ = 51.96 MPa, θp′ = −30°

1.51. σ₁ = 46.17 MPa, σ₂ = 13.83 MPa, ...