# Solution to Problem 426 | Relationship Between Load, Shear, and Moment

**Problem 426**

Cantilever beam acted upon by a uniformly distributed load and a couple as shown in Fig. P-426.

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. (Note to instructor: Problems 403 to 420 may also be assigned for solution by semi-graphical method describes in this article.)

**Solution 426**

**To draw the Shear Diagram**

- V
_{A}= 0 - V
_{B}= VA + Area in load diagram

V_{B}= 0 - 5(2)

V_{B}= -10 kN - V
_{C}= V_{B}+ Area in load diagram

V_{C}= -10 + 0

V_{C}= -10 kN - V
_{D}= V_{C}+ Area in load diagram

V_{D}= -10 + 0

V_{D}= -10 kN

**To draw the Moment Diagram**

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

M_{B}= 0 - ½(2)(10)

M_{B}= -10 kN·m - M
_{C}= M_{B}+ Area in shear diagram

M_{C}= -10 - 10(2)

M_{C}= -30 kN·m

M_{C2}= -30 + M = -30 + 60 = 30 kN·m - M
_{D}= M_{C2}+ Area in shear diagram

M_{D}= 30 - 10(1)

M_{D}= 20 kN·m

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