Answer:
a. Maximum Load = Force = 27085.09 N
b. Maximum Energy = 3.440 Joules
Step-by-step explanation:
Given
Rod diameter = ½in = 0.5in
Length = 5in
Young's modulus = 15.5Msi
By applying the 0.2% offset rule,
The maximum load the rod can hold before it gets to breaking point is given as follows by taking the strain as 0.2%
Young Modulus = Stress/Strain ------- Make Stress the Subject of Formula
Stress = Strain * Young Modulus
Stress = 0.2% * 15.5
Stress = 0.002 * 15.5
Stress = 0.031Msi
Calculating the area of the rod
Area = πr² or πd²/4
Area, A = 22/7 * 0.5^4 / 4
A = 22/7 * 0.25 / 4
A = 5.5/28
A = 0.1964in²
The maximum load that the rod would take before it starts to permanently elongate is given by
Force = Stress * Atea
Force = 0.031Msi * 0.1964in²
Force = 31Ksi * 0.1964in²
Force = 6.089Ksi in²
Force = 6.089 * 1000lbf
Force = 6089 lbf
1 lbf = 4.4482N
So, Force = 6089 * 4.4482N
Force = 27085.09 N
b.
Using Strain to Energy Formula
U = V×σ²/2·E
Where V = Volume
V = Length * Area
V = 5 in * 0.1964in²
V = 0.982in³
σ = Stress = 0.031Msi
= 0.031 * 1000Ksi
= 31Ksi
= 31 * 1000psi
= 31000psi
E = Young Modulus = 15.5Msi
= 15.5 * 1000Ksi
= 15.5 * 1000 * 1000psi
= 15500000psi
So,
Energy = 0.982 * 31000²/ ( 2 * 15500000)
Energy = 943,702,000/31000000
Energy = 30.442in³psi
------- Converted to ftlbf
Energy = 2.537 ftlbf
-------- Converted to Joules
Energy = 3.440 Joules
