Chapter 43 Problem 10RBC The strength S of a rectangular bea

Chapter 4.3, Problem 10RBC

The strength S of a rectangular beam varies directly with its width W and the square of its thickness T, and inversely with length L. A beam that is 4 inches wide, 4 inches thick, and 50 inches long can support a load of 600pounds. determine how much a similar beam that is 2 inches wide, 2 inches thick, and 50 inches long can support?

Solution

From given data

S=kWT²/L

k= constant of proportionality

S=600,W=4 ,T=4 and L=50

Therefore

600= k*4*4²/50

k=468.75

Now we again the same formula

S=kWT²/L

S=468.75*2*2²/50

    =468.75*2*4/50

   = 75 pounds