EAS3434 Aero Struc I Ch04_PartA (2018 10 09).pptx

EAS3434 Aero Struc I Ch04_PartA (2018 10 09).pptx - Chap 4...

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Chap. 4: Energy method for statically determinate structures (5 hrs) External work, principle of virtual work and their applications Strain energy, Castigliano's theorem and their applications Impact loading 1
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2 4. Learning Outcomes At the end of this chapter, we should be able to:- solve for displacement and forces in statically determinate trusses, beams, and frames using the virtual work method. solve for displacement of trusses, beams, and frames using the energy method. explain a method to estimate impact energy absorbed by a structure.
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3 4. External work Recall from the Dynamics class, that external work is done when an external force (or moment) applied to an object causes displacement. External work for a particle Imagine that a particle A moves virtually to A’, the work done by force F is or
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4 4. External work External work for a rigid body For a couple moment that causes rotation of theta radian, the work done is given by Rewrite as a pure moment:
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5 4. Virtual work Virtual work for a particle Imagine that a particle A moves to A’ due to many forces: (R is the resultant force) If the particle is in equilibrium, then the resultant R is zero, hence the virtual work due to the virtual displacement is also zero.
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6 4. Virtual work Virtual work for a rigid body External forces induce internal forces for all particles in the body.
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