A large chandelier weighing 1500lbs. is suspended from the roof of a theater lobby. The steel pipe from which it hangs is 20ft long. Determine the size of the pipe necessary to carry chandelier safely. Use A36 steel. What is the resulting elongation of the pipe?
I calculated reqd A=54.3in^2 to get diameter of 8.31in and elongation of 216inches. Am I doing it right?
I believe you are way off. Your tensile stress would be only 27 psi and the elongation 90% with you numbers.
Too little stress; too much strain.
The yield strength of A36 steel is 36,000 psi. Your stress is over 1000 times less than that.
You must know what the formulas are for stress and strain. You must be using wrong units or making a large computation error.
Do they specify a factor of safety? You will need one. Four might ne reasonable
To determine the size of the pipe necessary to carry the chandelier safely, you need to consider two factors: the weight of the chandelier and the maximum allowable stress on the pipe material.
First, let's calculate the required cross-sectional area of the pipe. The chandelier weighs 1500 lbs, so the force acting on the pipe is 1500 lbs. Since the chandelier is hanging vertically, this force is equivalent to the weight of the chandelier. We can use the formula F = A * σ, where F is the force, A is the cross-sectional area of the pipe, and σ is the stress on the pipe material.
Assuming A36 steel is being used, the allowable stress is typically around 36,000 psi. Rearranging the formula to solve for A, we have A = F / σ. Plugging in the values, A = 1500 lbs / 36,000 psi.
Now, let's convert the force from pounds to pounds-force (lbf) to take into account the Earth's gravitational acceleration. Since the weight of an object is equal to its mass multiplied by gravitational acceleration (g ≈ 32.2 ft/s^2), we have F = 1500 lbs * 32.2 ft/s^2.
To determine the size (diameter) of the pipe, we can use the formula A = π * r^2, where A is the cross-sectional area of the pipe and r is the radius of the pipe. Rearranging the formula to solve for r, we have r = sqrt(A / π).
Plugging in the value of A, we can calculate the required diameter of the pipe by multiplying r by 2.
Once you have the diameter of the pipe, you can calculate its elongation using the formula δ = (F * L) / (E * A), where δ is the resulting elongation, F is the force, L is the length of the pipe, E is the modulus of elasticity of the steel material, and A is the cross-sectional area of the pipe.
Now, let's plug in the values and calculate whether your calculations are correct.
F = 1500 lbs * 32.2 ft/s^2 = 48,300 lbf
A = (48,300 lbf) / (36,000 psi) = 1.34 in^2
d = 2 * sqrt(1.34 in^2 / π) ≈ 1.72 in
Assuming you have the correct diameter (8.31 in), it seems there may have been an error in your calculations. Please recheck your calculations to determine the correct diameter and elongation of the pipe.