Beam/Frame/Truss Deflection Methods (Theory)

[S.E.]

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?

 

[nilesh_pat]

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.