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We study the elastic response of concentrated suspensions of rigid wire frame particles to a step strain. These particles are constructed from infinitely thin, rigid rods of length L. We specifically compare straight rod-like particles to bent and branched wire frames. In dense suspensions, the wire frames are frozen in a disordered state by the topological entanglements between their arms. We present a simple, geometric method to find the scaling of the elastic stress with concentration in these glassy systems. We apply this method to