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

30.0 ksi
2,250 psi
a
5.5 ksi
680 psi
σ
150 MPa
17.5 ksi
950 psi
τ
45°
FIGURE p12.54
p12.56–p12.59 Consider a point in a structural member that
is subjected to plane stress. Normal and shear stresses acting on
horizontal and vertical planes at the point are shown in Figures
P12.56–P12.59.
(a) Draw Mohr’s circle for this state of stress.
(b) Determine the principal stresses and the maximum in-plane
shear stress acting at the point, and show these stresses in an
appropriate sketch (e.g., see Figure 12.15 or Figure 12.16).
(c) Determine the normal and shear stresses on the indicated
plane, and show these stresses in an appropriate sketch.
(d) Determine the absolute maximum shear stress at the point.
4
9.4 ksi
FIGURE p12.56
FIGURE p12.58
5
5
2
5.7 ksi
42 MPa
3.8 ksi
20 MPa
28 MPa
FIGURE p12.55
14 MPa
p12.60 At a point in a stressed body, the principal stresses are
oriented as shown in Figure P12.60. Use Mohr’s circle to determine
(a) the stresses on plane a–a.
(b) the stresses on the horizontal and vertical planes at the point.
(c) the absolute maximum shear stress at the point.
50°
FIGURE p12.57
FIGURE p12.59
860 psi
72 MPa
108 MPa
1,460 psi
50° 2,150 psi
θ p
1
θp
tan
2
( )
–1 3
=
4
FIGURE p12.60
p12.61 At a point in a stressed body, the principal stresses are
oriented as shown in Figure P12.61. Use Mohr’s circle to determine
(a) the stresses on plane a–a.
(b) the stresses on the horizontal and vertical planes at the point.
(c) the absolute maximum shear stress at the point.
x
x
a
p12.62 A solid 1.50 in. diameter shaft is subjected to a torque
T = 330 lb ⋅ ft and an axial load P acting as shown in Figure
P12.62/63. If the largest tensile normal stress in the shaft must be
limited to 12,000 psi, what is the largest load P that can be applied
to the shaft?
z
1
θ p= tan –1 ( 2)
2
FIGURE p12.61
y
A
FIGURE p12.62/63
θ p
H
p12.63 A solid 20 mm diameter shaft is subjected to an axial
load P = 30 kN and a torque T acting as shown in Figure P12.62/63.
If the largest shear stress in the shaft must be limited to 90 MPa,
what is the largest torque T that can be applied to the shaft?
a
σ
τ
7.82 ksi
(1)
45°
30 MPa
T
B
a
30.18 ksi
P
x
531