# Solution to Problem 632 | Moment Diagrams by Parts

**Problem 632**

For the beam loaded as shown in Fig. P-632, compute the value of (Area_{AB}) barred(X)_{A}. From this result, is the tangent drawn to the elastic curve at B directed up or down to the right? (Hint: Refer to the deviation equations and rules of sign.)

**Solution 632**

$3R_1 + 200(1) = 800(2)(2)$

$R_1 = 1000 \, \text{N}$

$\Sigma M_A = 0$

$3R_2 = 200(4) + 800(2)(1)$

$R_1 = 800 \, \text{N}$

$(Area_{AB}) \, \bar{X}_A = \frac{1}{2}(2)(2000)(\frac{4}{3}) + \frac{1}{2}(1)(800)(\frac{7}{3}) - \frac{1}{3}(2)(1600)(\frac{3}{2}) - \frac{1}{2}(1)(400)(\frac{7}{3}) - \frac{1}{2}(1)(200)(\frac{8}{3})$

$(Area_{AB}) \, \bar{X}_A = 1\,266.67 \, \text{N}\cdot\text{m}^3$ *answer*

The value of (Area_{AB}) barred(X)_{A} is positive, therefore point A is above the tangent through B, thus **the tangent through B is upward to the right**. See the approximate elastic curve shown above and refer to the rules of sign for more information.