Compute deflections and solve indeterminate structures.
Principle of virtual work: external virtual work equals internal. The unit-load method finds deflection Δ=∫(m M/EI)dx. Castigliano's theorem and Maxwell-Betti reciprocity. Useful for deflections of beams, frames and trusses (Δ=Σ nNL/AE).
Truss joint deflection is found by unit load on the joint and summing nNL/AE.
Virtual work and energy methods calculate deflections and solve indeterminate structures using energy principles, which is practical and widely taught.
Compute deflections and solve indeterminate structures.
Virtual work and energy methods calculate deflections and solve indeterminate structures using energy principles, which is practical and widely taught.
Apply a unit load at the point where the deflection is needed, and integrate the product of the internal forces to find the displacement.
The partial derivative of the strain energy with respect to a force gives the displacement at that force, which helps solve redundant forces.
Typical applications include finding the deflection at the tip of a cantilever under load, checking the redundant reaction in a propped beam and estimating the displacement of a truss joint under a load.
Study "Matrix stiffness method" first (topic 47 of 112 in Civil & Structural). It covers the groundwork this topic builds on.
Virtual force systems. Strain energy. Reciprocal deflections.
Truss joint deflection is found by unit load on the joint and summing nNL/AE.
The next topic is "Plastic analysis", which builds directly on this one.
It is classed as Intermediate in Civil & Structural (topic 48 of 112). It is an intermediate topic. Work through the beginner topics in Civil & Structural first.
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