Bending moment , Physics

Bending moment :

The diagram in created shear forces, but the applied forces also create bending.

442_Bending moment.png

Consider a section x x' at a distance x measured from end B. Then RB creates a moment about x x', which causes a bending effect.

The Bending moment = RB . x

As with shear force, moments causing 1121_Bending moment1.pnghave to be differentiated from moments causing1831_Bending moment2.png. The first case is +ve bending, the second case is -ve bending.

 1121_Bending moment1.png is commonly termed "Sagging"
  1831_Bending moment2.png is commonly termed "Hogging".

Note that as distance x increases, the Bending moment also increases.

Variations in Bending Moment are often shown on a Bending Moment Diagram (BMD).

Considering the beam AB, the BMD is drawn as;

862_Bending moment3.png

Note that in this case, the BMD is all +ve (i.e. the beam is sagging everywhere) and note also that it increases from zero as x increases to the left of B, up to a maximum and then decreases as the effect of RB is reduced by the effect of F , finally becoming zero at A.

(Note that BMD can be treated in the same way by considering distances measured to the right of A - the solutions are exactly the same).

1502_Bending moment4.png

A uniformly distributed load, whilst obeying the same principles, modifies the BMD.

As x increases left of B, RB causes1283_Bending moment6.png, but the distributed load also increases and causes 1054_Bending moment7.png.
The BMD now looks like this.

731_Bending moment5.png

Note: Point loads create BMD's that are triangular. Distributed loads create BMD's that are curved.

Posted Date: 9/14/2012 8:18:33 AM | Location : United States

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