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

pRoBLEmS
p13.31 An 8 mm thick brass [E = 83 GPa; ν = 0.33] plate is
subjected to biaxial stress with σ x = 180 MPa and σ y = 65 MPa. The
plate dimensions are b = 350 mm and h = 175 mm. (See Figure
P13.31.) Determine
σ y
y
(a) the change in length of edges AB and AD.
(b) the change in length of diagonal AC.
(c) the change in thickness of the plate.
O
x
σ x
h
D
A
FIGURE p13.31
p13.32 A 0.75 in. thick polymer [E = 470,000 psi; ν = 0.37]
casting is subjected to biaxial stresses σ x = 2,500 psi and σ y =
8,300 psi, acting in the directions shown in Figure P13.32. The
dimensions of the casting are b = 12.0 in. and h = 8.0 in. Determine
(a) the change in length of edges AB and AD.
(b) the change in length of diagonal AC.
(c) the change in thickness of the plate.
b
σ y
B
C
σ x
z
σ z
FIGURE p13.35/36
FIGURE p13.33
p13.34 A thin steel [E = 30,000 ksi; ν = 0.3] plate in a state of
plane stress has dimensions of 8 in. in the x direction and 4 in. in
the y direction. The plate increases in length in the x direction by
0.0015 in. and decreases in the y direction by 0.00028 in. Compute
the normal stresses σ x and σ y that produced these deformations.
Assume that τ xy = 0.
p13.35 A thin aluminum [E = 10,000 ksi; G = 3,800 ksi] plate
is subjected to biaxial stress (Figure P13.35/36). The strains measured
in the plate are e x = 810 me and e z = 1,350 me. Determine σ x
and σ z .
y
σ x
x
D
σ y
C
p13.36 A thin stainless steel plate [E = 190 GPa; G = 86 GPa] plate
is subjected to biaxial stress (Figure P13.35/36). The strains measured
in the plate are e x = 275 me and e z = 1,150 me. Determine σ x and σ z .
h
A
B
σ x
p13.37 The thin brass [E = 16,700 ksi; ν = 0.307] bar shown in
Figure P13.37/38 is subjected to a normal stress σ x = 19 ksi. A
strain gage is mounted on the bar at an orientation of θ = 25° as
shown in the figure. What normal strain reading would be expected
from the strain gage at the specified stress?
FIGURE p13.32
b
σ x
y
θ
n
x
σ x
p13.33 A 100 mm by 100 mm square plate with a circle inscribed
is subjected to normal stresses σ x = 200 MPa and σ y = 90 MPa,
acting as shown in Figure P13.33. The plate material has an elastic
modulus E = 70 GPa and a Poisson’s ratio ν = 0.33. Assuming
plane stress, determine the major and minor axes of the ellipse
formed after deformation of the plate.
FIGURE p13.37/38
p13.38 A strain gage is mounted on a thin brass [E = 12,000 ksi;
ν = 0.33] bar at an angle of θ = 35° as shown in Figure P13.37/38.
If the strain gage records a normal strain e n = 470 me, what is the
magnitude of the normal stress σ x ?
580