Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

P12.35 (a) 25.6 MPa
(b) 23.1° clockwise from x axis
P12.37 σ y = −117.5 psi
P12.49
18 ksi
y
P12.39 τ xy = −19.98 ksi, σ p1 = 27.0 ksi,
σ p2 = −37.0 ksi, σ p3 = 0
P12.41 (a) max. τ xy = 116.1 MPa
(b) σ p1 = 175.0 MPa,
σ p2 = –125.0 MPa
P12.43
30 ksi
y
10.00 ksi
25.00 ksi
15.00 ksi
6 ksi
30.59 ksi
30 ksi
Abs max
shear stress
39.35° 12.00 ksi
42.59 ksi
x
30.59 ksi
18.59 ksi
10 ksi
Abs max
shear stress
25.00 ksi
P12.45
15 ksi
18.43°
35.00 ksi
x
P12.51
25 MPa
y
45 MPa
24.01°
22.50 MPa
33.63 MPa
x
Abs max
shear stress
25.00 MPa
30 MPa
20 MPa
P12.47 36 MPa
y
y
x
9 MPa
26.57°
57.0°
15.00 MPa
40.00 MPa
12 MPa
n
t
6 MPa
18 MPa
30 MPa
25.00 MPa
x
10.00 MPa
Abs max
shear stress
33.63 MPa
56.13 MPa
P12.53 (b) σ p1 = 178.7 MPa, σ p2 = 43.3 MPa,
τ max = 67.7 MPa, θ p = −38.6° (to σ p2 )
(d) τ abs max = 89.3 MPa
P12.55 (b) σ p1 = −659 psi, σ p2 = −2,540 psi,
τ max = 941 psi, θ p = −23.1° (to σ p1 )
(d) τ abs max = 1,270 psi
P12.57 (b) σ p1 = 141.4 MPa, σ p2 = −47.4 MPa,
τ max = 94.4 MPa, θ p = −24.9° (to σ p1 )
(c) σ n = −34.5 MPa, τ nt = –47.6 MPa
(d) τ abs max = 94.4 MPa
P12.59 (b) σ p1 = 4,830 psi, σ p2 = –6,860 psi,
τ max = 5,850 psi, θ p = 14.87° (to σ p1 )
(c) σ n = –2,690 psi, τ nt = −5,600 psi
(d) τ abs max = 5,850 psi
11.13 MPa
P12.61 (a) σ = −19.00 ksi, τ = 11.18 ksi (arrow points to
the right)
(b) σ x = −24.0 ksi, σ y = −14.00 ksi,
τ xy = 10.00 ksi
(c) τ abs max = 15.09 ksi
842