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Unformatted text preview: Sec_2.4.qxd 146 9/25/08 11:38 AM Page 146 CHAPTER 2 Axially Loaded Members Solution 2.4-14 Bar supported by a collar
FREE-BODY DIAGRAM OF BAR ABC AND COLLAR BD SOLVE SIMULTANEOUSLY EQS. (1) AND (3):
L1A3 + L3A1
L1A3 + L3A1
CHANGES IN LENGTHS (Elongation is positive)
E(L1A3 + L3A1)
ELONGATION OF BAR ABC
AC AB AC SUBSTITUTE NUMERICAL VALUES:
P 40 kN E L1 Fvert 0 RA P 0 (Eq. 1) COMPATIBILITY (distance AD does not change)
AB(bar) BD(collar) 0 (Eq. 2) 125 mm A1 RD 225 mm L3
EQUILIBRIUM OF BAR ABC 250 mm L2 960 mm2 A2 300 mm2 A3 200 GPa 480 mm2 RESULTS: (Elongation is positive.) RA 0.02604 mm BC Substitute into Eq. (2):
EA3 RD AB FORCE-DISPLACEMENT RELATIONS
EA3 0.15000 mm AC 20 kN AB ; 0.176 mm AC (Eq. 3) Problem 2.4-15 A rigid bar AB of length L 66 in. is hinged to a
support at A and supported by two vertical wires attached at points C and
D (see figure). Both wires have the same cross-sectional area (A
0.0272 in.2) and are made of the same material (modulus E 30 106
psi). The wire at C has length h 18 in. and the wire at D has length
twice that amount. The horizontal distances are c 20 in. and d 50 in.
(a) Determine the tensile stresses C and D in the wires due to the
load P 340 lb acting at end B of the bar.
(b) Find the downward displacement B at end B of the bar. 2h
A C D B c
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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