Energy stored in deformed material; used in impact and deflection methods.
Stored elastic energy per volume is σ²/(2E); for a bar U=P²L/(2AE), for bending U=∫M²/(2EI)dx. Castigliano's theorem gives deflection as ∂U/∂P. Impact loads produce stresses sqrt-proportional to drop energy.
A weight dropped suddenly on a spring causes twice the static deflection.
Strain energy links stress and deformation to energy, which helps calculate deflections and impact responses that are hard to get otherwise.
Energy stored in deformed material; used in impact and deflection methods.
Strain energy links stress and deformation to energy, which helps calculate deflections and impact responses that are hard to get otherwise.
For a linear material, the energy is half the force times the displacement, or one half of stress times strain times volume.
A falling load converts potential energy into strain energy, and the stress rises far above the static value, so impact is much more severe.
Typical applications include estimating the deflection of a beam by the energy method, calculating how much energy a bolt absorbs during a sudden load and checking the impact force on a rope from a falling mass.
Study "Buckling of columns" first (topic 65 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Energy methods avoid solving ODEs. Resilience and toughness. Impact factor 1+√(1+2h/δst).
A weight dropped suddenly on a spring causes twice the static deflection.
The next topic is "Stress concentration", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 66 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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