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

p12.46 Figure P12.46 shows Mohr’s circle for a point in a physical
object that is subjected to plane stress.
(a) Determine the stresses σ x , σ y , and τ xy , and show them on a
stress element.
(b) Determine the stresses σ n , σ t , and τ nt , and show them on a
stress element that is properly rotated with respect to the x–y
element. The sketch must include the magnitude of the angle
between the x and n axes and an indication of the direction of
rotation (i.e., either clockwise or counterclockwise).
τ
x
p12.48–p12.51 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
P12.48–P12.51.
(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.
(c) Show these stresses in an appropriate sketch (e.g., see Figure
12.15 or Figure 12.16).
(d) Determine the absolute maximum shear stress at the point.
18 ksi
18 ksi
12 ksi
30 ksi
t
C
σ
36 ksi
6 ksi
n
FIGURE p12.48
FIGURE p12.49
y
65 MPa
45 MPa
1 grid square = 10 MPa
FIGURE p12.46
p12.47 Figure P12.47 shows Mohr’s circle for a point in a physical
object that is subjected to plane stress.
(a) Determine the stresses σ x , σ y , and τ xy , and show them on a
stress element.
(b) Determine the stresses σ n , σ t , and τ nt , and show them on a
stress element that is properly rotated with respect to the x–y
element. The sketch must include the magnitude of the angle
between the x and n axes and an indication of the direction of
rotation (i.e., either clockwise or counterclockwise).
y
τ
τ
t
FIGURE p12.50
24 MPa
35 MPa
25 MPa
FIGURE p12.51
p12.52–p12.55 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
P12.52–P12.55.
(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.
(c) Show these stresses in an appropriate sketch (e.g., see Figure
12.15 or Figure 12.16).
(d) Determine the absolute maximum shear stress at the point.
C
σ
8.4 MPa
126 MPa
x
44.8 MPa
66 MPa
n
60.5 MPa
96 MPa
1 grid square = 3 MPa
τ
FIGURE p12.47
FIGURE p12.52
FIGURE p12.53
530