What are the impact loads and stresses produced by different components in machine design?
Analysis of Impact Loads and Stresses
Machine design involves analyzing and comparing the impact loads and stresses produced by different components. In this question, we are given four different loads produced by various components. Let's go through each case:
a. Load on 1-inch diameter steel rod:
Load (W) = 10 lbs
Length (L) = 12 inches
Assuming the load is applied at the end of the rod. To calculate the stress, we use the formula for stress (σ):
σ = F / A
Where:
F = Force applied (load)
A = Cross-sectional area of the rod
The cross-sectional area (A) of the rod is given by:
A = π * (d/2)^2
where d is the diameter of the rod.
In this case:
d = 1 inch = 1/12 feet (since 1 foot = 12 inches)
So,
A = π * (1/24)^2
A ≈ 0.00136 square feet
Now, calculating the stress (σ):
σ = 10 lbs / 0.00136 sq. ft
≈ 7352 psi (pounds per square inch)
b. Load on 1-inch diameter steel rod with height (h) of 5 inches:
Load (W) = 10 lbs
Length (L) = 6 inches (assuming the height is the length of the rod)
Assuming the load is applied at the end of the rod. We'll use the same formula for stress (σ) and the same cross-sectional area (A) since it's the same rod as in case a.
σ = 10 lbs / 0.00136 sq. ft
≈ 7352 psi
c. Load on 11-inch diameter steel rod:
Load (W) = 10 lbs
Length (L) = 12 inches (assuming the load is applied at the end of the rod)
Using the same formula for stress (σ), we calculate the cross-sectional area (A) for this larger diameter rod:
d = 11 inches = 11/12 feet
A = π * (11/24)^2
≈ 0.1269 square feet
Now, calculating the stress (σ):
σ = 10 lbs / 0.1269 sq. ft
≈ 78.85 psi
d. Load on 12-inch V-shaped steel rod:
Load (W) = 10 lbs
Length (L) = 12 inches (assuming the load is applied at the top end of the V-shape)
Since this is a V-shaped rod, the cross-sectional area will be different. To simplify the analysis, let's assume the V-shape forms a right-angled triangle with sides of 6 inches and 12 inches. The area (A) of a right-angled triangle is given by:
A = 0.5 * base * height
A = 0.5 * 6 inches * 12 inches
A = 0.25 square feet
Now, calculating the stress (σ):
σ = 10 lbs / 0.25 sq. ft
= 40 psi
In summary, the stresses produced by the different loads are as follows:
a. 1-inch dia. steel rod (L=12"): 7352 psi
b. 1-inch dia. steel rod (L=6"): 7352 psi
c. 11-inch dia. steel rod (L=12"): 78.85 psi
d. 12-inch V-shaped steel rod (L=12"): 40 psi
Please note that these stress values are based on simplified assumptions, and in a real-world scenario, there might be other factors and considerations that need to be taken into account for an accurate analysis.