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

p13.39 A thin brass [E = 100 GPa; G = 39 GPa] plate is subjected
to biaxial stress as shown in Figure P13.39/40. The normal
stress in the y direction is known to be σ y = 160 MPa. The strain
gage measures a normal strain of 920 me at an orientation of θ = 35°
in the indicated direction. What is the magnitude of σ x that acts on
the plate?
y
b
c
60° 60°
a
x
FIGURE p13.42
σ y
θ
y
x
σ x
p13.43 On the free surface of a steel [E = 207 GPa; ν = 0.29]
component, a strain rosette located at point A in Figure P13.43 was
used to obtain the following normal strain data: e a = 133 me, e b =
–92 me, and e c = –319 me. If θ = 50°, determine the stresses σ n , σ t ,
and τ nt that act at point A.
t
y
n
FIGURE p13.39/40
θ
P
x
p13.40 A thin brass [E = 14,500 ksi; G = 5,500 ksi] plate is
subjected to biaxial stress (Figure P13.39/40). The normal stress in
the x direction is known to be twice as large as the normal stress in
the y direction. The strain gage measures a normal strain of 775 µε
at an orientation of θ = 50° in the indicated direction. Determine the
magnitudes of the normal stresses σ x and σ y acting on the plate.
p13.41 On the free surface of an aluminum [E = 10,000 ksi; ν =
0.33] component, the strain rosette shown in Figure P13.41 was
used to obtain the following normal strain data: ε a = 440 µε, ε b =
550 µε, and ε c = 870 µε. Determine
(a) the normal stress σ x .
(b) the normal stress σ y .
(c) the shear stress τ xy .
A
FIGURE p13.43
p13.44–p13.46 The strain components e x , e y , and γ xy are
given for a point on the free surface of a machine component. Determine
the stresses σ x , σ y , and τ xy at the point.
c
60°
60°
A
y
a
60°
b
x
y
c
Problem ε x ε y γ xy E ν
P13.44 680 µε −320 µε −840 µrad 16,500 ksi 0.33
45°
45°
b
x
P13.45 −1,120 µε −890 µε 1,300 µrad 207 GPa 0.30
P13.46 1,500 µε 2,100 µε 950 µrad 28,000 ksi 0.12
a
FIGURE p13.41
p13.42 On the free surface of an aluminum [E = 70 GPa; ν =
0.35] component, the strain rosette shown in Figure P13.42 was
used to obtain the following normal strain data: ε a = –300 µε, ε b =
735 µε, and ε c = 410 µε. Determine
(a) the normal stress σ x .
(b) the normal stress σ y .
(c) the shear stress τ xy .
p13.47–p13.49 The strain rosettes shown in Figures P13.47–
P13.49 were used to obtain normal strain data at a point on the free
surface of a machine component. In each of Problems P13.47–
P13.49, determine
(a) the stress components σ x , σ y , and τ xy at the point.
(b) the principal stresses and the maximum in-plane shear stress
at the point; show these stresses on an appropriate sketch that
indicates the orientation of the principal planes and the planes
of maximum in-plane shear stress.
(c) the magnitude of the absolute maximum shear stress at the
point.
581