sm12 1

PROBLEM (12.1) A stepped bar of diameters d1 and d2 and length L is subjected to tensile
force P (Fig. P12.1). Calculate the largest amount of strain energy that can be stored in the bar without
causing any yielding.
Given: d1 = 20 mm, d2 = 30 mm, L = 1.2 m, y
σ
= 220 MPa, E = 200 GPa
SOLUTION
0.4 m
A
C
B
P
30 m
m
20 mm
0.8 m
Segment BC
262
(0.02) 314 10
4
Am
π
−
==×
N
66
220 10 (314 10 ) 69.08
yp
PA k σ
−
==× ×=
232
69
(69.08 10 ) (0.4) 15.2
2 2(314 10 )(200 10 )
BC PL
UJ
AE −
×
== =
××
Segment AB
262
69.08 (0.03) 706.5 10
4
PkNA m
π
−
===×
232
69
(69.08 10 ) (0.8) 13.51
2 2(706.5 10 )(200 10 )
AB PL
UJ
AE −
×
== =
××
Total energy
13.51 15.2 28.71UJ=+=
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