# Solution to Problem 433 | Relationship Between Load, Shear, and Moment

**Problem 433**

Overhang beam loaded by a force and a couple as shown in Fig. P-433.

Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear.

**Solution 433**

$\Sigma M_C = 0$

$5R_1 + 2(750) = 3000$

$R_1 = 300 \, \text{lb}$

$\Sigma M_A = 0$

$5R_2 + 3000 = 7(750)$

$R_2 = 450 \, \text{lb}$

**To draw the Shear Diagram**

- V
_{A}= R_{1}= 300 lb - V
_{B}= V_{A}+ Area in load diagram

V_{B}= 300 + 0 = 300 lb - V
_{C}= V_{B}+ Area in load diagram

V_{C}= 300 + 0 = 300 lb

V_{C2}= V_{C}+ R_{2}= 300 + 450 = 750 lb - V
_{D}= V_{C2}+ Area in load diagram

V_{D}= 750 + 0 = 750

V_{D2}= V_{D}- 750 = 750 - 750 = 0

**To draw the Moment Diagram**

- M
_{A}= 0 - M
_{B}= V_{A}+ Area in shear diagram

M_{B}= 0 + 300(2) = 600 lb·ft

M_{B2}= V_{B}- 3000

M_{B2}= 600 - 3000 = -2400 lb·ft - M
_{C}= M_{B2}+ Area in shear diagram

M_{C}= -2400 + 300(3) = -1500 lb·ft - M
_{D}= M_{C}+ Area in shear diagram

M_{D}= -1500 + 750(2) = 0