Solution to Problem 418 | Shear and Moment Diagrams | Strength of Materials Review at MATHalino

Problem 418
Cantilever beam loaded as shown in Fig. P-418.

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Write shear and moment equations for the beams in the following problems. In each problem, let x be the distance measured from left end of the beam. Also, draw shear and moment diagrams, specifying values at all change of loading positions and at points of zero shear. Neglect the mass of the beam in each problem.

Solution 418

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Segment AB:
$V_{AB} = -20 \, \text{kN}$

$M_{AB} = -20x \, \text{kN}\cdot\text{m}$

Segment BC:
$V_{BC} = -20 \, \text{kN}$

$M_{BC} = -20x + 80 \, \text{kN}\cdot\text{m}$

To draw the Shear Diagram:

V_AB and V_BC are equal and constant at -20 kN.

To draw the Moment Diagram:

M_AB = -20x is linear; when x = 0, M_AB = 0; when x = 4 m, M_AB = -80 kN·m.
M_BC = -20x + 80 is also linear; when x = 4 m, M_BC = 0; when x = 6 m, M_BC = -40 kN·m

Solution to Problem 418 | Shear and Moment Diagrams

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