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Unformatted text preview: neering design of the truss as a nonlinear problem, under the assumption that members can have different cross‐sectional areas (i.e., without the restriction that all members must have the same cross‐sectional area). Use Excel Solver to identify the optimal (i.e., least cost) design. Review of Pertinent Engineering Principles Principle of Virtual Work for Linear Elastic Systems Consider an elastic system acted on by a set of external forces Q1 ,Q2 , ,Q j , ,Qr as shown in Figure 3. Prior to the application of these forces, let a virtual unit force P 1 be placed at a given point and in a given direction for which the deflection is desired. Q2 Q1 Qj Qr P 1 Figure 3. Elastic Body with Virtual and External Loading As the set of external forces is gradually applied to the elastic system increasing from zero to full value and thus causing deformations in the structure, the virtual unit force simply rides along during the deformation. Let the displacements at the points of application of the external forces in the directions of the respective forces be denoted by 1 , 2...
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