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Pause now for a moment and reflect on how shape is used to modify the ways in which materials behave. A material has a modulus and a strength, but it can be made stiffer and stronger when loaded in bending or twisting by shaping it into an I-beam or a hollow tube. It can be made less stiff by flattening it into a leaf or winding it, in the form of wire, into a helix. Thinned shapes help dissipate heat; cellular shapes help conserve it. There are shapes to maximize electrical capacitance, to conserve magnetic field, shapes that control optical reflection, diffraction and refraction, shapes to reflect a sound, and shapes to absorb it. Shape is even used to change the way a material feels, making it smooth or rough, slippery, or grippy. And of course, it is shape that distinguishes the Venus de Milo from the marble block from which she was carved. It is a rich subject.
Here we explore one part of it the way shape can be used to increase the mechanical efficiency of a material. Shaped sections carry bending, torsional, and axial-compressive loads more efficiently than solid sections do. By "shaped" we mean that the cross-section is formed to a tube, a box-section, an I-section or the like. By "efficient" we mean that, for a given loading conditions, the section uses as little material as possible. Tubes, boxes and I-sections will be referred to as "simple shapes". Even greater...
