Does the Pivot Exert a Moment Reaction for Equilibrium?

[eurekameh]

I know that the pivot exerts a vertical reaction equal to Cy = w0L / 2 and a horizontal reaction equal to Cx = 0. Does the pivot also exert a moment reaction? My intuition says that it doesn't and that it's actually not in equilibrium because it will rotate about the pivot, but the question is asking for a check of a state of equilibrium. Anyone?

 

[Camille]

Whether it is in equilibrium depends on the type of pivot. If it's a pin support, then there is no bending moment in the pivot but the beam could still be in equilibrium if the moment of the resultant force acting on the left side = moment of the resultant force acting on the right.

If it's a fixed support then there is a moment and the beam would always be in equilibirum (nonuniform distribution of moments on the beam will be equilibrated by the moment in the pivot). But then the answer is always yes, so probably that is not the case.

I think here you have a pin support, so the rotation is allowed, but check the moments on each side to see if it will be stable anyway :)

 

[eurekameh]

Equilibrium worked out after all the math. I have to say that this challenged my intuition because I would think that the beam would start rotating counter-clockwise due to the load on the right of the pivot being larger than the load on the left of the pivot.

 

[Camille]

Yeah, it's not quite intuitive. Here happens to be the critical condition, any more or less load on either side would rotate it. Remember that less force is required on a longer arm and more on the shorter, to produce the same moment :)

 

[asteriatic]

I can confirm that the pivot exerts a moment reaction in addition to the vertical and horizontal reactions. This is because the pivot acts as a point of rotation, and any force applied at this point will create a moment, or rotational force. In order for the pivot to be in a state of equilibrium, the sum of all forces and moments acting on it must be equal to zero. Therefore, the moment reaction from the pivot must also be taken into account in order to accurately assess the state of equilibrium.