Question

The safe loadof a wooden beam supported at both ends varies jointly as the width, w, the square of the depthd, and inversely as the length A wooden beam 7 inwide, 10 indeepand 19 ft long holds up 4422 What load would a beam inwide. 5 indeep and long of the same material support? (Round off your answer to the nearest pound )

Answer 1

L = k(wd^2/ l)

L = load

L1= 4422 lb

w = width

w1= 7 in

d = depth

d1= 10 in

l = lenght

l1= 19 ft

L2=

w2= 5in

d2=5in

l2= 11ft

First solve the constant with values 1

L1= k [(w1) (d1)^2 / l1]

4422= k [(7) (10)^2 / 19]

k = 4422 / [(7) (10)^2 / 19]

k= 120 lb/ft in^3

Replace with values 2

L2= k [(w2) (d2)^2 / l2]

L2= 120 [(5) (5)^2 / 11]

L2= 1363.63 LB