Baseplate Stress Calculation: How Much Pressure Can It Handle?

What is the stress exerted by a 24,000 lb weight supported on a rectangular baseplate that is 9-in wide and 2-ft long resting on a concrete slab?

Calculate the stress that the baseplate exerts on the concrete slab.

Stress Calculation:

To determine the stress that the baseplate exerts on the concrete slab, we can use the formula for stress:
Stress (σ) = Force (F) / Area (A)

First, let's convert the weight of 24,000 lb to force in pounds by multiplying by the acceleration due to gravity (g) which is approximately 32.2 ft/s^2:
F = 24,000 lb * 32.2 ft/s² = 772,800 lb

Next, let's convert the width of the baseplate from inches to feet:
Width (w) = 9 in / 12 = 0.75 ft

The length of the baseplate is given as 2 ft. Now, we can calculate the area of the rectangular baseplate:
Area (A) = Length (L) * Width (W) = 2 ft * 0.75 ft = 1.5 ft²

Finally, we can plug the values of force and area into the stress formula to calculate the stress exerted by the baseplate on the concrete slab:
Stress (σ) = Force (F) / Area (A) = 772,800 lb / 1.5 ft² ≈ 515,200 lb/ft²