Beam/Frame/Truss Deflection Methods (Theory)

In summary, the Virtual Work method, Euler-Bernoulli Beam Equation, and Castigliano's theorem can all be used to solve for deflections in structural members. However, the Virtual Work method is applicable in most situations and can be used as the primary method for solving for displacements. The other methods may be necessary in specific cases where the structure and load conditions require their use.
  • #1
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Homework Statement



No specific problem.

Homework Equations



1/ρ=M(x)/EI
Internal Work = External Work
δ = ∂U/∂P

The Attempt at a Solution



N/A


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So I have a question about solving for deflections in various structural members, frames and trusses.

So far, I find myself utilizing Virtual Work method to solve for displacements exclusively. I keep trying to discover situations where I would have to use the Euler-Bernoulli Beam Equation or Castigliano's method because Virtual Work is inapplicable but I have yet to do so.

Is there a situation where Virtual Work can not be utilized to solve for displacements but the others can be? Or can I safely stick to my most comfortable method in every case?
 
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  • #2
The Virtual Work method is applicable in any situation where the displacement of the structure can be determined by a summation of the external forces and moments applied to each member. The Euler-Bernoulli Beam Equation is an equation that describes the deflection of a beam under the application of a concentrated load, distributed load, or a combination of both. Castigliano's theorem states that the change in the potential energy of a system due to the application of a set of loads is equal to the negative of the sum of the products of the displacements of the members caused by the loads and the components of the force applied at the corresponding points. This theorem can be used to solve for the deflection of members due to a given load.
 

1. What are the different types of deflection methods for beams, frames, and trusses?

The three main types of deflection methods for beams, frames, and trusses are the moment area method, the conjugate beam method, and the virtual work method.

2. How do these methods differ from each other?

The moment area method is based on the area under the bending moment diagram, the conjugate beam method involves replacing the real beam with a hypothetical beam, and the virtual work method uses the principle of virtual work to determine deflections.

3. Which method is the most accurate for calculating deflections?

The virtual work method is considered the most accurate method for calculating deflections because it takes into account all forces acting on the structure and does not make any assumptions about the shape of the deflected structure.

4. Can these methods be used for all types of beams, frames, and trusses?

Yes, these methods can be used for all types of beams, frames, and trusses as long as the structure is linear elastic and the material properties are known.

5. Are there any limitations to using these deflection methods?

One limitation of these deflection methods is that they assume the structure is perfectly rigid and does not take into account the effects of deformation on the stiffness of the structure. Additionally, these methods may not be accurate for structures with complex geometries or irregular loading conditions.

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