sm8 124

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PROBLEM (*8.124) A steel shaft of radius r is loaded by a torque T, as shown in Fig. P8.124. A
strain gage is placed at point A measures the strain
φ
ε
at an angle of
φ
to the axis of the shaft. What
is the value of the torque T ?
Given: r = 2 in., G = 11.5 x 106 psi ,
φ
ε
= 500
μ
,
φ
= 25o
*SOLUTION
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3
2xy
xy xy
Tc Jc r
JG
c
τ
π
τγ
=
===
25 00 o
xy xy
σσ εε θφ == == ==
Mohr’s circle for strain:
τ
A
x
y
1()
2
avg x y
εεε
0
=
+= 1
2
x
y
R
γ
=
1
sin2 sin2
2
avg xy
R
φ
ε
εθγ =+ = θ
2
φ
x’
ε
2
γ
y
O
A
’
x
R
sin2 sin2
22
xy Tc
GGJ
τ
φ
φ ==
This gives
2
sin2
GJ
T
φ
ε
c
φ
=
Substitute the given data:
63 6
(11.5 10 )(2) (500 10 )
(2)sin50o
T
π
−
××
=94.3 .kip in
=
⋅