Answer:
Final Length = 11.992 in
Final Diameter = 6.001 in
Explanation:
First we calculate the cross-sectional area:
Area = A = πr² = π(3 in)² = 28.3 in²
Now, we calculate the stress:
Stress = Compressive Load/Area
Stress = - 150 kips/28.3 in²
Stress = -5.3 ksi
Now,
Modulus of Elasticity = Stress/Longitudinal Strain
8000 ksi = -5.3 ksi/Longitudinal Strain
Longitudinal Strain = -6.63 x 10⁻⁴
but,
Longitudinal Strain = (Final Length - Initial Length)/Initial Length
-6.63 x 10⁻⁴ = (Final Length - 12 in)/12 in
Final Length = (-6.63 x 10⁻⁴)(12 in) + 12 in
<u>Final Length = 11.992 in</u>
we know that:
Poisson's Ratio = - Lateral Strain/Longitudinal Strain
0.35 = - Lateral Strain/(- 6.63 x 10⁻⁴)
Lateral Strain = (0.35)(6.63 x 10⁻⁴)
Lateral Strain = 2.32 x 10⁻⁴
but,
Lateral Strain = (Final Diameter - Initial Diameter)/Initial Diameter
2.32 x 10⁻⁴ = (Final Diameter - 6 in)/6 in
Final Diameter = (2.32 x 10⁻⁴)(6 in) + 6 in
<u>Final Diameter = 6.001 in</u>
