# Solution to Problem 437 | Relationship Between Load, Shear, and Moment

**Problem 437**

Cantilever beam loaded as shown in Fig. P-437.

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 437**

**To draw the Shear Diagram**

- V
_{A}= -1000 lb - V
_{B}= V_{A}+ Area in load diagram

V_{B}= -1000 + 0 = -1000 lb

V_{B2}= V_{B}+ 500 = -1000 + 500

V_{B2}= -500 lb - V
_{C}= V_{B2}+ Area in load diagram

V_{C}= -500 + 0 = -500 lb - V
_{D}= V_{C}+ Area in load diagram

V_{D}= -500 - 400(4) = -2100 lb

**To draw the Moment Diagram**

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

M_{B}= 0 - 1000(2) = -2000 lb·ft - M
_{C}= M_{B}+ Area in shear diagram

M_{C}= -2000 - 500(2) = -3000 lb·ft - M
_{D}= M_{C}+ Area in shear diagram

M_{D}= -3000 - ½ (500 + 2100)(4)

M_{D}= -8200 lb·ft

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