ch01-03 stress & strain & properties

01 Solutions 46060 5/6/10 2:43 PM Page 55
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1–82. The three steel wires are used to support the
load. If the wires have an allowable tensile stress of
s allow = 165 MPa, determine the required diameter of each
wire if the applied load is P = 6 kN.
A
C
The force in wire BD is equal to the applied load; ie, F BD = P = 6 kN. Analysing
the equilibrium of joint B by referring to its FBD, Fig. a,
45
B
30
: + ©F x = 0; F BC cos 30° - F AB cos 45° = 0
+ c ©F y = 0; F BC sin 30° + F AB sin 45° - 6 = 0
Solving Eqs. (1) and (2),
F AB = 5.379 kN F BC = 4.392 kN
For wire BD,
s allow = F BD
; 165(10 6 ) = 6(103 )
p
A BD
4 d BD 2
d BD = 0.006804 m = 6.804 mm
Use d BD = 7.00 mm
For wire AB,
s allow = F AB
; 165(10 6 ) = 5.379(103 )
p
A AB
4 d AB 2
d AB = 0.006443 m = 6.443 mm
Use d AB = 6.50 mm
For wire BC,
s allow = F BC
; 165(10 6 ) = 4.392(103 )
p
A BC
4 d BC 2
d BC = 0.005822 m = 5.822 mm
d BC = 6.00 mm
(1)
(2)
Ans.
Ans.
Ans.
D
P
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