# Solution to Problem 630 | Moment Diagrams by Parts

**Problem 630**

For the beam loaded as shown in Fig. P-630, compute the value of (Area_{AB})barred(X)_{A} . From the result determine whether the tangent drawn to the elastic curve at B slopes up or down to the right. (Hint: Refer to the deviation equations and rules of sign.)

**Solution 630**

$4R_1 + 200(2) = \frac{1}{2}(3)(400)(1)$

$R_1 = 50 \, \text{N}$

$\Sigma M_{R1} = 0$

$4R_2 = 200(6) + \frac{1}{2}(3)(400)(3)$

$R_2 = 750 \, \text{N}$

$(Area_{AB}) \, \bar{X}_A = \frac{1}{2}(4)(200)(\frac{8}{3}) - \frac{1}{4}(3)(600)(\frac{17}{5})$

$(Area_{AB}) \, \bar{X}_A = -463.33 \, \text{N}\cdot\text{m}^3$ *answer*

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