By Hirano K., Imbens G.W., Rubin D.B.
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Additional info for Assessing the effect of an influenza vaccine in an encouragement design
64) together with static and kinematic admissibility ensures a solution that in unique in terms of unique in terms of M F, (see Fig. 10c). the optimal solution may be nonConsidering, for example, two cantilever beams of equal length at right angles (Fig. 12a) in plan view with a hinge (ball-joint) at the intersection of the beams, the displacement field shown in Fig. 12b is kinematically admissible for both beams and hence the only requirement for optimality is that all moments must be statically admissible and negative.
Due to shear strain and curvature are indicated in Figs. 4e. In order to satisfy the boundary condition u = u. + u = 0 at the simple support, the value u = - BL(1 - 2v) was adopted at the righthand end. Then it follws from Fig. 41) v B + / ß 2 + 4 a L(aL/2 + B)]/4aL Check by Differentiation. 42) On t h e b a s i s of F i g s . 4c t h e total volume of t h e beam i s τ3 Φ = aL Then t h e Λ v 4 3. _. 42). 44) PLASTIC DESIGN - SINGLE LOAD AND UNSPECIFIED COST DISTRIBUTION Check for Special Cases.
Of the Prager-Shield Bending Theory and Shear (Rozvany, 197Zg). In optimizing flexural systems (such as beams, frames and grillages) of continuously varying cross-section, most authors assume that the specific cost of the member is a function of the bending moment only. However, the Prager- Shield theory of plastic optimal design can be applied readily to problems in which the specific cost depends on both bending and shear. 12). In the case of parallel chord trusses, the specific cost (volume per unit length) of the chords is governed by the bending moment on the truss (regarded as a single flexural member) and the specific cost of the web members is governed by the shear force.