Beam-Bending Moment

Objective

1. To comprehend the action of the moment of resistance within the beam.

2. To measure the bending moment at a normal section of a loaded beam and to compare it with the theoretical value.

Apparatus

Hi-tech HST.1/11 Structures Apparatus

Theory

Consider a beam resting on supports at A and B and supporting a load P. If the beam is cut by a vertical section XX, then for the beam to remain in equilibrium each part must be in equilibrium. Neglecting the selfweight of the beam any extra forces acting on part (A) to preserve equilibrium must be transmitted from part (B) across the section XX, and vice versa. Also, the action of part (A) on part (B) must be equal and opposite to that of (B) and (A)

In the first place these are used for beam as a whole to evaluate the reactions at A and B

For equilibrium of moents take an axis as shown in the section XX to eliminate Qx. Then using the sign convention given for part (A) of the beam

Internal moment Mx = (Ra) (a)

And for part (B) of the beam Mx = (Rb)(b) – P(b-L)

It can easily be proved that