Vpr statics derivation of beam hinging

In summary, the formula for calculating the probable shear or Vpr in a beam between two columns and bars is V = (M+) + (M-) / ln, which is derived from V * ln = (M+) + (M-). Shear is only present when the beam is hinging and not before, and this is referring to the shear in hinging or plastic rotation, not the shear from gravity loads. For a cantilever beam with one free end, there is no shear when the beam is subject to a moment couple at the free end. However, if a point load is applied at the free end, there will be shear along the full length of the cantilever.
  • #1
dahoa
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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?
 

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  • #2
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.
 
  • #3
PhanthomJay said:
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?
 
  • #4
dahoa said:
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.
 

1. What is Vpr statics derivation of beam hinging?

The Vpr statics derivation of beam hinging refers to a process in structural engineering where the shear force (V) and the bending moment (M) at the support of a simply supported beam are calculated using static equilibrium equations.

2. Why is Vpr statics derivation important in beam hinging?

The Vpr statics derivation is important because it helps engineers determine the maximum load a beam can withstand at the support before it becomes hinged or fails. This information is crucial in the design and analysis of structural components.

3. How is Vpr calculated in beam hinging?

Vpr is calculated using the following formula: Vpr = Vmax - (Mmax/L). In this formula, Vmax is the maximum shear force, Mmax is the maximum bending moment, and L is the length of the beam.

4. What is the significance of beam hinging in structural design?

Beam hinging plays a crucial role in structural design as it helps engineers determine the stability and strength of a structure. By calculating the maximum load at which a beam will hinge, engineers can ensure that the structure can safely support the intended load without failing.

5. How does Vpr statics derivation differ from other methods of calculating beam hinging?

Vpr statics derivation is a simplified method of calculating beam hinging that uses only static equilibrium equations. Other methods, such as the moment distribution method, use more complex mathematical equations to determine the shear force and bending moment at a beam's support.

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