ch01-03 stress & strain & properties
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01 Solutions 46060 5/6/10 2:43 PM Page 56<br />
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1–83. The three steel wires are used to support the<br />
load. If the wires have an allowable tensile <strong>stress</strong> of<br />
s allow = 165 MPa, and wire AB has a diameter of 6 mm, BC<br />
has a diameter of 5 mm, and BD has a diameter of 7 mm,<br />
determine the greatest force P that can be applied before<br />
one of the wires fails.<br />
A<br />
45<br />
B<br />
30<br />
C<br />
The force in wire BD is equal to the applied load; ie, F BD = P. Analysing the<br />
equilibrium of joint B by referring to its FBD, Fig. a,<br />
: + ©F x = 0; F BC cos 30° - F AB cos 45° = 0<br />
(1)<br />
D<br />
P<br />
+ c ©F y = 0; F BC sin 30° + F AB sin 45° - P = 0<br />
(2)<br />
Solving Eqs. (1) and (2),<br />
F AB = 0.8966 P F BC = 0.7321 P<br />
For wire BD,<br />
s allow = F BD<br />
A BD<br />
; 165(10 6 ) =<br />
For wire AB,<br />
P<br />
p<br />
4 (0.0072 )<br />
P = 6349.94 N = 6.350 kN<br />
s allow = F AB<br />
; 165(10 6 ) = 0.8966 P<br />
p<br />
A AB 4 (0.0062 )<br />
P = 52<strong>03</strong>.42 N = 5.2<strong>03</strong> kN<br />
For wire BC,<br />
s allow = F BC<br />
; 165(10 6 ) = 0.7321 P<br />
p<br />
A BC 4 (0.0052 )<br />
P = 4425.60 N = 4.43 kN (Controls!)<br />
Ans.<br />
56