A stairwell is supported by two circular steel rods at one end. The other end supported above. The two steel rods are subjected to a total load of 12,800lbs. The rods are 24 ft long and E=30*10^6 psi. Select the rod based on the following specs. The rod deformation should not exceed 0.375 inches and the allowable tensile stress is 10,844 psi?

I calculated reqd diameter of sqrt 1.64in^2/0.7854 = 1.45in diameter with choice of 2inch rod. Am I going right or do I need to recheck

To calculate the required diameter of the rod, you are on the right track. The formula to calculate the required diameter is as follows:

d = sqrt((4 * F * L) / (pi * d^2 * E))

First, let's convert the load from pounds to pascal, as the units should be consistent:

F = 12,800 lbs = 12,800 * 4.44822 N = 56,857.6 N

Now, let's rearrange the formula to solve for the diameter:

d^3 = (4 * F * L) / (pi * E * 0.375)
d^3 = (4 * 56,857.6 * 24) / (pi * 30,000,000 * 0.375)
d^3 = 643,356.48 / 3,534,294.15
d^3 = 0.182
d = (0.182)^(1/3)
d ≈ 0.577 inch

It seems that you made an error in the calculation, resulting in a different diameter. Therefore, rechecking your calculations is advised.

Based on the given specifications, the required diameter of the rod is approximately 0.577 inches. However, since the closest available option is a 2-inch rod, you may need to choose the nearest available size that meets the requirements.

To determine if you have calculated the required diameter correctly, let's go through the calculation and compare the results.

First, we need to determine the maximum tensile stress in the rod. The formula for the stress in a rod under tension is:

Stress = Load / (pi * (diameter/2)^2)

Given that the load is 12,800 lbs and the allowable tensile stress is 10,844 psi, we can rearrange the formula to solve for the diameter:

diameter = 2 * sqrt(Load / (pi * Allowable stress))

Substituting the values into the formula:

diameter = 2 * sqrt(12,800 / (pi * 10,844))

Using a calculator, the calculated diameter comes out to be approximately 1.617 inches. It seems like the difference in your calculation is due to not using the correct decimal point in the value of 1.64 square inches.

Therefore, it seems that you need to recheck your calculation and make sure you are using the correct decimal point value for the required area.