Stepped Bar Strain Energy Solution: Mechanics of Materials

________________________________________________________________________
PROBLEM (12.6) The stepped bar seen in Fig. P12.6 consists of a square cross section with sides a
and a circular cross section of diameter d. The bar is subjected to a tensile force P. Determine the ratio of
d/a so that the strain energy in both parts is the same.
SOLUTION
Axial strain energy Use Eq. (12. 2), circular Part:
22 2
22
2
22( )
4
CPL PL PL
d
AE d E
E
ππ
== =
U
Square Part:
22 2
22
(2)
22 4
SPL P L PL
U
AE a E a E
== =
Requirement::
22
22
2
;4
CS PL PL
UU
dE aE
π
==
8d
a
π
=
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