ch01-03 stress & strain & properties

03 Solutions 46060 5/7/10 8:45 AM Page 17
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•3–21. The stress–strain diagram for a polyester resin
is given in the figure. If the rigid beam is supported by a
strut AB and post CD, both made from this material, and
subjected to a load of P = 80 kN, determine the angle
of tilt of the beam when the load is applied.The diameter of
the strut is 40 mm and the diameter of the post is 80 mm.
2 m
B
P
A
C
From the stress–strain diagram,
0.75 m
0.75 m
0.5 m
D
E = 32.2(10)6
0.01
Thus,
s AB = F AB
= 40(103 )
p
= 31.83 MPa
A AB (0.04)2
e AB = s AB
E = 31.83(106 )
3.22(10 9 = 0.009885 mm>mm
)
s CD = F CD
= 40(103 )
p
= 7.958 MPa
A CD (0.08)2
e CD = s CD
E = 7.958(106 )
3.22(10 9 = 0.002471 mm>mm
)
d AB = e AB L AB = 0.009885(2000) = 19.771 mm
d CD = e CD L CD = 0.002471(500) = 1.236 mm
Angle of tilt a:
= 3.22(10 9 ) Pa
4
4
s (MPa)
100
95
80
70
60
50
40
32.2
20
0
0
compression
tension
0.01 0.02 0.03 0.04
P (mm/mm)
tan a = 18.535
1500 ; a = 0.708°
Ans.
17