Question

1. 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

a)
`83.3\ lb/in^2`

b)
`12000\ lb/ft^2`

Explanation:

Given : 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.

To find : Determine the stress that the base plate exerts on the concrete slab. Express your answer in units of (a) lb/in². and (b) lb/ft².

Solution :

a) A rectangular base plate that is 9 in. wide and 2 ft long.

Converting ft into inches,

1 feet = 12 inch

2 feet = 2×12= 24 inch

The area of the rectangular base is
`A=l* b`

`A_1=24* 9`

`A_1=216\ in^2`

The weight is W=18,000 lb.

The stress that the base plate exerts on the concrete slab is given by,

`S=(W)/(A_1)`

`S=(18000\ lb)/(216\ in^2)`

`S=83.3\ lb/in^2`

b) A rectangular base plate that is 9 in. wide and 2 ft long.

Converting inches into ft,

1 inch =
`(1)/(12)\ ft`

9 feet =
`(9)/(12)=0.75\ ft`

The area of the rectangular base is
`A=l* b`

`A_2=2* 0.75`

`A_2=1.5\ ft^2`

The weight is W=18,000 lb.

The stress that the base plate exerts on the concrete slab is given by,

`S=(W)/(A_2)`

`S=(18000\ lb)/(1.5\ ft^2)`

`S=12000\ lb/ft^2`