Question 2.39:
A solid bronze sphere ( E = 110 GPa,
ν
=
3
1
, r = 150 mm) is subjected to hydrostatic
pressure p so that its volume is reduced by 0.5 %. Determine(a) the pressure p, and(b) the
strain energy U in the sphere.( Note: Volume of a sphere
r
V
3
3
4
×
×
=
p
)
Solution
:
The “dilatation” e, or the change in volume per unit volume,
10
5
.
0
2

×

=
∆
=
V
V
e
………….
.(The negative sign indicates the
reduction of the volume)
The Bulk modulus of elasticity,
)
2
1
(
3
n

=
E
k
10
110
)
3
2

1
(
3
10
110
3
3
×
=
×
=
∴
k
MPa
(a) TO FIND p:
By definition, the dilatation of the sphere is,
k
p
e

=
MPa
p
550
)
10
5
.
0
(
10
110

2
3
=
×

×
×
=
∴

(b)TO FIND U
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 Fall '09
 Law
 Strain, Energy density, strain energy, Strain Energy density, solid bronze sphere

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