# Solution to Problem 539 | Floor Framing

**Problem 539**

Timbers 12 inches by 12 inches, spaced 3 feet apart on centers, are driven into the ground and act as cantilever beams to back-up the sheet piling of a coffer dam. What is the maximum safe height of water behind the dam if water weighs = 62.5 lb/ft^{3} and ( f_{b} )_{max} = 1200 psi?

**Solution 539**

$w_o = 62.5h \, \text{lb/ft}^2$

$F = \frac{1}{2} w_o h (3) = \frac{3}{2}(62.5h)h$

$F = 93.75h^2 \, \text{lb}$

$M = (\frac{1}{3}h) F = \frac{1}{3}h (93.75h^2)$

$M = 31.25h^3 \, \text{lb}\cdot\text{ft}$

$(\,f_b\,)_{max} = \dfrac{Mc}{I}$

$1200 = \dfrac{31.25h^3(12)(12/2)}{\dfrac{12(12^3)}{12}}$

$h = 9.73 \, \text{ft}$ *answer*

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