8 is the gravitational acceleration the lefthand side

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Unformatted text preview: s force balance. The tensions have given limits, Tjmin ≤ tj ≤ Tjmax , with Tjmin ≤ 0 and Tjmax ≥ 0, for j = 1, . . . , m. (For example, if bar j is a cable, then it can only apply a nonnegative tension, so Tjmin = 0, and we interpret Tjmax as the maximum tension the cable can carry.) The first p nodes, i = 1, . . . , p, are free, while the remaining n − p nodes, i = p + 1, . . . , n, are anchored (i.e., attached to a foundation). We will refer to the external forces on the free nodes as load forces, and external forces at the anchor nodes as anchor forces. The anchor forces are unconstrained. (More accurately, the foundations at these points are engineered to withstand any total force that the bars attached to it can deliver.) We will assume that the load forces are just dead weight, i.e., have the form f (i) = 0 −wi , where wi ≥ 0 is the weight supported at node i. 121 i = 1, . . . , p, The set of weights w ∈ Rp is supportable if there exists a set of tensions t ∈ Rm and anchor forces + f (p+1) , . . ....
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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 Berkeley.

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