Elasticity of Steel Rod: Stress, Strain and Elongation Calculations

[woolleyd.2011]

a structural steel rod has a radius of .5 inches and length of 32 in. 4000 lb force stretches along its length. modulus of elasticity is 29 x 10^6 psi.


Need to figure out stress on rod, the elongation of rod due to force, and strain on rod due to force

Homework Equations

The Attempt at a Solution

 

[PhanthomJay]

Forum rules require that you show some attempt at your work before we can be of assistance. What are the relevant equations for stress, elongation, and strain?

 

[Mene]

To begin, we can use the formula for stress, which is force divided by cross-sectional area. In this case, the force is given as 4000 lbs, and the cross-sectional area can be calculated using the formula for the area of a circle (πr^2). Plugging in the given radius of 0.5 inches, we get a cross-sectional area of 0.1963 square inches. Therefore, the stress on the steel rod is 4000 lbs/0.1963 in^2, which is approximately 20,385 psi (pounds per square inch).

Next, we can calculate the elongation of the steel rod using the formula for strain, which is change in length divided by original length. In this case, the change in length is equal to the force applied (4000 lbs) divided by the modulus of elasticity (29 x 10^6 psi). This gives us an elongation of 0.0001379 inches.

Finally, we can calculate the strain on the steel rod using the formula for strain, which is change in length divided by original length. In this case, the change in length is equal to the elongation we just calculated (0.0001379 inches) divided by the original length of the rod (32 inches). This gives us a strain of 4.31 x 10^-6, which is a very small amount.

In conclusion, the stress, elongation, and strain on the steel rod can be calculated using the given information and formulas. These calculations are important for understanding the behavior and limitations of the steel rod in a structural setting. It is important for scientists and engineers to consider these factors when designing and using steel rods in various applications.