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Unformatted text preview: Sec_2.7.qxd 9/25/08 11:42 AM Page 205 205 SECTION 2.7 Strain Energy Solution 2.7-8 Rigid bar supported by springs
(c) FORCES IN THE SPRINGS
F1 F3 3W
10 3kd kd W
10 3k k2 1.5k k3 k W ; ; 600 N k U 5kd2 kd2
(a) STRAIN ENERGY U OF ALL SPRINGS
2a 2 3kd
b + 2a
10k 8.0 mm F1 3W
10 180 N F2 3W
20 90 N F3 W
10 2 5kd2 ; Work done by the weight W equals Wd
2 Strain energy of the springs equals 5k
5kd2 and d W
10k 2 ; NOTE: W Problem 2.7-9 A slightly tapered bar AB of rectangular cross
section and length L is acted upon by a force P (see figure). The
width of the bar varies uniformly from b2 at end A to b1 at end B.
The thickness t is constant.
(a) Determine the strain energy U of the bar.
(b) Determine the elongation of the bar by equating the
strain energy to the work done by the force P. 60 N
2F1 7500 N/mm W2
; 2.4 J d (b) DISPLACEMENT Wd
10k 2.4 N # m For a spring: U 2 7.5 N/mm 5k a downward displacement of rigid bar ... 3W
20 (d) NUMERICAL VALUES k1 U 1.5kd ; ; ; ; 2F2 F3 A 600 N (Check) B b2 L b1
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11