bv_cvxbook_extra_exercises

# Your method can involve solving several convex

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Unformatted text preview: F2 R r h F1 w The weight of the truss is proportional to the total volume of the bars, which is given by 2π (R2 − r2 ) w2 + h2 This is the cost function in the design problem. The ﬁrst constraint is that the truss should be strong enough to carry the load F1 , i.e., the stress caused by the external force F1 must not exceed a given maximum value. To formulate this constraint, we ﬁrst determine the forces in each bar when the structure is subjected to the vertical load F1 . From the force equilibrium and the geometry of the problem we can determine that the magnitudes of the forces in two bars are equal and given by √ w2 + h2 F1 . 2h 119 The maximum force in each bar is equal to the cross-sectional area times the maximum allowable stress σ (which is a given constant). This gives us the ﬁrst constraint: √ w2 + h2 F1 ≤ σπ (R2 − r2 ). 2h The second constraint is that the truss should be strong enough to carry the load F2 . When F2 is applied, the magnitudes of the forces in two bars are again equal and...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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