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For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment.
(a)
Since the loading of the cantilever beam is uniformly varying load so the total load on the beam is area under the loading diagram and is acting at the distance L/3 from the point B.
Draw the free body diagram of the beam showing the reactions at point B.
Since the beam is in the static equilibrium, so it follows all the equilibrium equations.
Apply vertical force equilibrium equation.
Apply the moment equilibrium equation about point B.
Consider a section x-x at the distance x from the free end A.
Evaluate the total load up to the section x-x.
Draw the loading diagram upto the section x-x.
The shear force varies parabolicaly from the point A to B.
Evaluate the shear force at point A.
Evaluate the shear force at point B.
Draw the shear force diagram as follows.
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