Question

A weight of 18,000 lb is supported on a rectangular base plate that is 9 in. wide and 2 ft long. the base plate rests on a concrete slab. determine the stress that the base plate exerts on the concrete slab. express your answer in units of (a) lb/in.2 and (b) lb/ft2. (precision of 1 for (a) and of 1000 for (b))

Answer 1

The stress that the base plate exerts on the concrete slab is 4,636,800 lb/ft² and 668,467,200 lb/in².

Step-by-step explanation:

To determine the stress that the base plate exerts on the concrete slab, we need to calculate the pressure exerted by the weight on the base plate. Pressure is equal to force divided by area.

(a) First, we convert the weight of 18,000 lb to force by using the acceleration due to gravity, which is approximately 32.2 ft/s^2. So the force is 18,000 lb * 32.2 ft/s^2 = 579,600 lb⋅ft/s^2.

The area of the base plate is 9 in. * 2 ft = 18 in² * 1/144 ft²/in² = 0.125 ft². Now we can calculate the stress by dividing the force by the area: Stress = 579,600 lb⋅ft/s^2 / 0.125 ft² = 4,636,800 lb/ft².

(b) To convert to lb/in², we multiply the stress by 144, because there are 144 in² in 1 ft²: Stress = 4,636,800 lb/ft² * 144 in²/ft² = 668,467,200 lb/in² (rounded to 1 decimal place).

Answer 2

We want to find the area of the plate in square inches and square feet.
1) Here we need inches. The area is 9in * 24in =216 in.^2., since 1ft = 12in. 18,000lb / 216 in.^2 = 83lb/in.^2
2) Here we need feet. With 12 in = 1 ft, 9in = .75ft. The area is .75ft * 2ft = 1.5 ft.^2
18,000lb / 1.5 ft.^2 = 12,000lb/ft.^2