12. Simple Bending Moment and Shear Force Diagrams
Let us apply a Concentrated Load on a simply supported beam and see how
the beam behaves
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Now let us cut the beam in to three imaginary parts and examine the
internal response of the beam
It is obvious that none of the 3 parts are in rotational equilibrium, for example if
we take the element of the beam it will rotate as below:
To establish rotational equilibrium, the beam has to develop internal moments as
shown below>
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These internal moments which establish rotational equilibrium for the
elements of the beam are the Bending Moments in the Beam.
One objective of this chapter is to determine the internal Bending Moment
along the length of the beam for various simple loadings on the beam.
Every beam, in a building , bridge or any other construction is subjected to
the internal Bending moment. And one of the objectives of design is to make
the beam adequate to sustain the expected Bending Moments on it.
Shear in Beams
Let us load a simply supported beam
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The above phenomenon is called shear in Beams.
In order to satisfy vertical equilibrium the beam should develop internal forces
as shown below
Putting the above ideas of Bending Moment and Shear
together we get the following behavior
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