Problema Solution

The safe load, L, of a wooden beam supported at both ends varies jointly as the width, w, the square of the depth, d, and inversely as the length, l. A wooden beam 8in.

8

in.

wide, 8in.

8

in.

deep, and 11ft

11

ft

long holds up 1946lb

1946

lb

. What load would a beam 9in.

9

in.

wide, 6in.

6

in.

deep and 10ft

10

ft

long of the same material support? (Round off your answer to the nearest pound.)

Answer provided by our tutors

The safe load, L, of a wooden beam supported at both ends varies jointly as the width, w, the square of the depth, d, and inversely as the length, l:

L = C*w*d^2/l, where C is constant

w = 8 in

d = 8 in

l = 11 ft

l = 11*12 in (1 ft = 12 in)

l = 132 in

L = 1946 lb

C*8*8^2/132 = 1946

........

click here to see the equation solved for C

........

C = 32109/64

Now we need to find L for:

w = 9 in

d = 6 in

l = 10 ft

l = 10*12 in

l = 120 in

L = (32109/64)*w*d^2/l

L  = (32109/64)*9*6^2/120

L = 1,355 lb

A wooden beam 9 in wide, 6 in. deep, and 10 ft long holds up 1,355 lb.