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Suspension. The most efficient building method there is, as long as you have something to hang your structure from.
In the case of teh Brooklyn brdige very massive granite piers on very solid submerged foundations.
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Exploiting tension at the Olympic Games in Munich by Frei Otto. Stocky steel struts (to prevent bukcling!) and massive anchors in the ground keep the suspended roof up. (Many expensive connections!)
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The Bird's nest Olympic stdium. More or less ransom distribution of  loadbearing members ( as ina  bird's nest.)
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Reed architecture. 'Prestressing the arches by sticking them in the sub soil under an outward leaning angle. 'Bundling' to create stiffness and strength..
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Arches can be used in compression (left) or in tension (right) The bridge on the right is probably more 'efficient' than the model on the left. But not often is there enough space to put the arch below the deck.
to eights-five