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

ExAmpLE 13.11
A unidirectional T-300 graphite–epoxy composite material is loaded with stresses
σ x = 60 ksi, σ y = 10 ksi, and τ xy = 5 ksi in the principal material directions. The graphite
fibers are aligned in the x direction. Determine the normal and shear strains in the
principal material directions.
SolutioN
The material properties from Table 3.1 are E x = 19,200 ksi, E y = 1,500 ksi, G xy = 950 ksi, and
ν xy = 0.25. The minor Poisson’s ratio is
Ey
1,500 ksi
vyx
= vxy
= (0.25) = 0.0195
E 19,200 ksi
The normal strain in the direction of the fibers is
x
x
σ x
σ y 60 ksi
10 ksi
e x = − vyx
= − (0.0195)
E E 19,200 ksi 1,500 ksi
y
−6
= 2,995 × 10 in./in.
Ans.
The normal strain perpendicular to the fibers is
σ y σ x 10 ksi
60 ksi
e y = − vxy
= − (0.25)
E E 1,500 ksi 19,200 ksi
y
x
−6
= 5,886 × 10 in./in.
Ans.
and the shear strain is calculated
τ xy 5ksi
− 6
γ xy = = = 5,263 × 10 rad
Ans.
G 950 ksi
xy
mecmovies
ExAmpLE
m13.6 The strain rosette shown was used to obtain the
following normal strain data at a point on the free surface of
an aluminum [E = 70 GPa; ν = 0.33] plate: ε a = 770 µε,
ε b = 1,180 µε, ε c = −350 µε.
c
y
b
(a) Determine the stress components σ x , σ y , and τ xy at the point.
(b) Determine the principal stresses at the point.
(c) Show the principal stresses in an appropriate sketch.
45°
45°
a
x
ExERcISE
m13.6 Principal Stresses from Rosette Data. A strain rosette
was used to obtain normal strain data at a point on the free surface
of a steel [E = 200 GPa; ν = 0.32] plate. Determine the normal
strains, the shear strain, and the principal stresses in the x–y plane.
y
c 90°
a
FIGURE m13.6
45°
b
x
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