**Problem 639**

The downward distributed load and an upward concentrated force act on the cantilever beam in Fig. P-639. Find the amount the free end deflects upward or downward if E = 1.5 × 10^{6} psi and I = 60 in^{4}.

**Solution 639**

$t_{A/C} = \dfrac{1}{EI}(Area_{AB}) \, \bar{X}_A$

$t_{A/C} = \dfrac{1}{(1.5 \times 10^6)(60)}[ \, \frac{1}{2}(6)(5400)(6) - \frac{1}{3}(8)(6400)(6) \, ] \, (12^3)$

$t_{A/C} = -0.09984 \, \text{ in}$

∴ The free end will move by 0.09984 inch downward. *answer*