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Shear and moment

The shear force $V$ and the bending moment $M$ vary along a beam and are linked: the moment is the area under the shear diagram. Where the shear force changes sign (or is zero), the moment has an extreme value. The diagrams show where the beam is most stressed.

\dfrac{dM}{dx} = V

relation between shear and moment

Symbols

$V$	shear force	N
$M$	bending moment	Nm
$x$	position along the beam	m

Example

The shear force changes sign right under a point load.

That is where the bending moment is largest.

Find the moment maximum where the shear force diagram crosses zero.

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Part of Statics and Dynamics: Bending of beams.