Tutorial Sheet 1

Tutorial Sheet 1 - Imperial College of Science, Technology...

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Sheet 1 Page 1 Imperial College of Science, Technology & Medicine Department of Aeronautics Second Year Structural Mechanics and Dynamics II Tutorial Sheet 1 Section a – Theory Development 1. The principle of virtual work can be applied in two forms: a) Where the strains ε are real strains and the stresses σ are virtual stresses. ε σ = V dV r R The strains ε arise from the displacements r . Differentiating r with respect to the coordinates x and y gives the strains ε . Similarly, integrating the strains gives the displacements. They are two representations of the same real quantity, the deflection of the structure. The virtual stresses σ are the stresses that are in equilibrium with the virtual load R . Again, they represent the same quantity, the non-real virtual loads applied to the structure. V is the volume of the structure. It is important to note that the real quantities and the virtual quantities are not related, apart from the fact that they act upon the same geometry.
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Tutorial Sheet 1 - Imperial College of Science, Technology...

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