Bending Moment

OBJECTIVES

There are two objects of an introductory experiment as follows:

1. To comprehend the action of moment of resistance in a beam.

2. To measure the bending moment at a normal section of a loaded beam and to check its agreement with theory.

3. To convert strain readings to force readings.

APPARATUS DESCRIPTION

The experimental beam is in two parts, the shorter beam being (A) and the longer beam (B). At the cut section normal to the beam axis where they join a pair of ball bearing rollers pinned in (B) sits into a semi-circular pocket in (A). To develop the "internal" forces at the section the bearings in the pocket resists shearing, whilst the underslung cantilever resists the bending moment and creates a bending strain which can be converted into bending force.

Figure 1

Two supports, A and B, contain ‘U' brackets with integral ground pins at their top. These create the simply supported nature of the beam and provide variable beam spans as required, up to 900mm. They join to the P4120 Floor (or desk) Mounted Frame by means of a round base and an anchor plate + M8 x 50 socket cap head screw. A 6mm hexagon wrench is used to tighten the M8 socket cap head screws.

Load is applied to the beams by the use of three stirrup shaped load hangers, which can be threaded over the beams, by removing the hanger pin and sliding the hanger over the relevant beam and replacing the hanger.

When the beams are loaded, they need to be brought back to a datum ‘level' position. This is achieved using the thumb screw on the underslung cantilever arrangement. To level the beams a miniature spirit level is provided.

The method of leveling the beams is as follows:

a. Position the spirit level so that it straddles the cut section and is resting on beam A and beam B

b. Adjust the level of the beams by using the thumb screw on the under slung cantilever

S. Atkinson September 2011; March 2012 Page 2 of 5

Integral linear scales are positioned on each beam to allow easy set up of the hangers during testing. A set of

calibrated weights is supplied with the equipment to apply loads to the beams.

THEORY

Figure 2

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 self-weight