Answer:
a) 60000 psi
b) 1.11*10^6 psi
c) 112000 psi
d) 30.5%
e) 30%
Explanation:
The yield strength is the load applied when yielding behind divided by the section.
yield strength = Fyield / A
A = π/4 * D^2
A = 0.5 in^2
ys = Fy * A
y2 = 30000 * 0.5 = 60000 psi
The modulus of elasticity (E) is a material property that is related to the object property of stiffness (k).
k = E * L0 / A
And the stiffness is related to change of length:
Δx = F / k
Then:
Δx = F * A / (E * L0)
E = F * A / (Δx * L0)
When yielding began (approximately the end of the proportional peroid) the force was of 30000 lb and the change of length was
Δx = L - L0 = 1.8075 - 1.8 = 0.0075
Then:
E = 30000 * 0.5 / (0.0075 * 1.8) = 1.11*10^6 psi
Tensile strength is the strees at which the material breaks.
The maximum load was 56050 lb, so:
ts = 56050 / 0.5 = 112000 psi
The percent elongation is calculated as:
e = 100 * (L / L0)
e = 100 * (2.35 / 1.8 - 1) = 30.5 %
If it necked with and area of 0.35 in^2 the precent reduction in area was:
100 * (1 - A / A0)
100 * (1 - 0.35 / 0.5) = 30%
