A prismatic bar has length L = 2m and a circular cross-section with diameter d = 50 mm. A tensile load is applied which causes thhe bar to extend by ∂ = 1.4 mm.
a) Find the normal strain.
b)If the elastic modulus is 200 GPa, find the applied aal tensile load P.
I got part a) to equal 0.14 (200*10^9 * ((1.4*10^-3)/2)
Thank you for your help
To find part a) the normal strain, you correctly used the formula:
ε = ∂ / L
where ε represents the strain and ∂ represents the change in length.
To calculate the normal strain, you substituted the given values:
ε = (1.4 * 10^-3) / 2
which correctly gives:
ε = 0.7 * 10^-3
So the normal strain is 0.7 * 10^-3.
Now let's move on to part b) which asks to find the applied axial tensile load P.
To find the applied tensile load P, we need to use Hooke's law, which states that the stress (σ) is directly proportional to the strain (ε) for an elastic material. The formula is:
σ = E * ε
where σ represents the stress, E represents the elastic modulus, and ε represents the strain.
We have the strain (0.7 * 10^-3) and the elastic modulus (200 GPa), but we need to convert the diameter from millimeters to meters before substituting values into the formula.
The formula for the cross-sectional area (A) of a circular cross-section is:
A = π * (d / 2)^2
where A represents the cross-sectional area and d represents the diameter.
Substituting the given diameter (50 mm):
A = π * (50 / 2)^2
A = π * 25^2
A = 625π mm^2
So the cross-sectional area is 625π mm^2.
Now, we need to convert the cross-sectional area to square meters by dividing it by 1,000,000:
A = 625π / 1,000,000
A ≈ 0.001964 m^2 (approximated to 4 decimal places)
Now that we have the cross-sectional area, we can substitute into Hooke's law:
σ = E * ε
σ = (200 * 10^9 Pa) * (0.7 * 10^-3)
σ = 140 * 10^6 Pa (or N/m^2)
Now, the tensile load (P) can be calculated using the equation:
P = σ * A
P = (140 * 10^6 Pa) * (0.001964 m^2)
P = 275,968 N (or Newtons)
Therefore, the applied axial tensile load is 275,968 Newtons.
I hope this explanation helps you understand how to calculate the normal strain and the applied axial tensile load for a prismatic bar with the given values. Let me know if you have any further questions!