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Unformatted text preview: Sec_2.7.qxd 9/25/08 11:42 AM Page 209 209 SECTION 2.7 Strain Energy (c) STRAIN ENERGY U1 IS NOT EQUAL TO
P1(2 s) P1s
(This quantity is greater than U1.)
For d U1 2s: Pd
area under a straight line from O to B, which
is larger than U1.
is not equal to the strain energy because
the force-displacement relation is not linear. 2(k1 + k2)s2 area under line OAB. Problem 2.7-12 A bungee cord that behaves linearly
elastically has an unstressed length L0 760 mm and a
stiffness k 140 N/m.The cord is attached to two pegs, distance b 380 mm apart, and pulled at its midpoint by a
force P 80 N (see figure). A b B (a) How much strain energy U is stored in the cord?
(b) What is the displacement C of the point where the
load is applied?
(c) Compare the strain energy U with the quantity
(Note: The elongation of the cord is not small compared
to its original length.) C
P Solution 2.7-12 Bungee cord subjected to a load P.
DIMENSIONS BEFORE THE LOAD P IS APPLIED 1
2 From triangle ACD:
d b2 329.09 mm DIMENSIONS AFTER THE LOAD P IS APPLIED L0
b 760 mm L0
2 380 mm 380 mm
k 140 N/m Let L1 distance CD
stretched length of bungee cord (1) ...
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- Fall '11