Reaction moment in cantilever beam

[gladius999]

Hi guys,

I'm wondering how the wall of the cantilever beam (a beam fixed at one end at a wall) can exert a reaction moment? Is this done by the wall pushing back on the cantilever beam away from its centroidal axis?

Also is the reaction moment always applied to the centroidal axis of the cantilever beam? If i took a chop at the y plane at a point in the beam does only the centroidal axis contain a moment? Or do other points along the beam in the y-axis have a moment too?

At the plane of the intersection between the wall and the beam, do I always take moments around the centroidal axis when there is a load? i.e. always take that point as the pivot?

Thanks

 

[Studiot]

Well firstly the word cantilever refers to projecting part that has no support at the free end.

The reactions are a property of the support arrangement, not the fact that there is a cantilever projection.

At the support there may be zero moment because the cantilevered or projecting section is 'balanced' by a projection in the other direction exerting equal but opposite moment.

The fixed end of the cantilever may be built in or encastre, in which case the moment is generated as a couple between toe and heel forces as the fixed end jams in its mounting.
You can regard this suport condition as a clamping action.

The fixed end may be bolted down either onto a horizontal support in which case the back end exerts an uplift force and the front or toe end a downward force. The reaction provide a couple.

These vertical couple providing forces are in addition to the vertcal support force reaction.

Finally the projection may be bolted to a vertical wall, in which case the moment is provided by horizontal forces forming a couple between the lower reaction resisting pressure on the wall and the upper reaction resisting pull out from the wall.