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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 crosssectional 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.
 Fall '13
 F.Borrelli
 The Aeneid

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