Review 2
Fall 08
1. A pressurized steel tank is constructed with a helical weld that makes an angle
α
= 60
o
with the longitudinal axis (see figure). The tank has radius
r
and wall thickness
t
and is
subjected to an internal pressure
p
. An electrical resistance strain gage placed along the
weld measure the extensional strain in the weld direction
0
ε
. The Young’s modulus and
Poisson’s ratio for the tank material (steel) are given as
E
and
ν
, respectively.
(a) Find expressions for longitudinal (axial) strain
a
ε
, circumferential (hoop) strain
h
ε
and
shear strain
ah
γ
in terms of
E
,
ν
,
p
,
r
and
t
.
(b) Using the strain transformation (formula or Mohr’s circle), find an expression for the
strain along weld direction, in terms of
E
,
ν
,
p
,
r
and
t
.
(c) Equating the expression obtained in part (b) to the measured strain
0
ε
, find internal
pressure
p
in terms
E
,
ν
,
r
,
t
and
0
ε
.
(d) If
a
h
ε
ε
5
=
, find Poisson’s ratio
ν
(
use expressions obtained in part a
)
.
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 Spring '11
 staff
 Force, Shear Stress, Second moment of area, maximum shear stress, resistance strain gage, steel beam ABCD

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