Vpr statics derivation of beam hinging

[dahoa]

For a beam above between two columns and bars are yield and hinging.. the formula to get the probable shear or vpr (from statics) is

V= M(+) + M(-) /ln
I guess it is derived from V * ln = M(+) + M(-)
First of all. Why is the shear only present when it is hinging and not before (I'm talking of the shear in hinging (plastic rotation) and not the gravity loads which I'm aware has its own shear diagram)

Now what would happen if the beam is part of cantilever where one side is free (not on any support).. how do you make the statics derivation of V?

 

[PhanthomJay]

I am unsure of what you are asking, but for a cantilever subject to a moment couple at the free end, there is no shear anywhere in the beam.

 

[dahoa]

I am unsure of what you are asking, but for a cantilever subject to a moment couple at the free end, there is no shear anywhere in the beam.

But for a point load at the free end.. there can be shear at the cantilever right?

 

[PhanthomJay]

But for a point load at the free end.. there can be shear at the cantilever right?

Oh sure, if you apply a point load Q acting down at the free end, then from sum of forces = 0 in vertical direction, for equilibrium, there must be a vertical load Q acting up at the fixed end, and the internal shear force is then Q constant along the full length of the cantilever.