Solution to Problem 426 | Relationship Between Load, Shear, and Moment | Strength of Materials Review at MATHalino

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

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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

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426-load-shear-and-moments-diagrams-cantilever-beam.gif

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

Tags:

shear and moment diagrams

moment load

Uniformly Distributed Load

cantilever beam

relationship between load shear and moment

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