sm12 28

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PROBLEM (12.28) Calculate the strain-energy density and its components at the point depicted in
Fig. P12.28 in a loaded member.
Given: E = 30 x 106 psi ,
ν
= 0.3
SOLUTION
From Fig. P12.28:
1300
p
si
σ
= and 2700
p
si
σ
=
−
We have
66
30 10 11.5 10
2(1 0.3)
Gp
×
==×
+si
Apply Eqs.(12.17), (12.19), and (12.20) with 30:
σ
=
422
06
10 [3 7 2(0.3)(21)]
2(30 10 )
U=++
×
43
118 10 . .in lb in
−
=× ⋅
42
06
12(0.3)
10 (3 7)
6(30 10 )
v
U− =−
×
43
3.5 10 . .in lb in
−
=× ⋅
422
06
10 (3 7 3 7)
6(11.5 10 )
d
U=++×
×
43
114.5 10 . .in lb in
−
=× ⋅
Check:
UU
00 0vd
U=+ 43 118 10 . .in lb in
−
=× ⋅
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