Answer:
0.6727
-0.02017
Explanation:
diameter = 15.7
l = 178
E =elastic modulus = 67.1 Gpa
poisson ratio = 0.34
p = force = 49100N
first we calculate the area of the cross section
[tex]A=\frac{\pi }{4} d^{2}[/tex]
[tex]A=\frac{\pi }{4} (15.7)^{2} \\A = \frac{774.683}{4} \\[/tex]
A = 193.6mm²
1. Change in directon of the applied stress
[tex]= \frac{pl}{AE}[/tex]
= 49100*178/193.6*67.1*10³
= [tex]=\frac{8739800}{12990560}[/tex]
δl = 0.6727 mm
2. change in diameter of the specimen
equation for poisson distribution =
m = -(δd/d) / (δl/l)
0.34 = (δd/15.7) / (0.6727/178)
0.34 = (-δd * 178) / 15.7 * 0.6727
0.34 = -178δd / 10.56139
we cross multiply
10.56139*0.34 =-178δd
3.5908726 = -178δd
δd = 3.5908726/-178
δd = -0.02017 mm
the change in dimeter has a negative sign. it decreases
