Selection of Shapes
So far we have learned how the combination of material properties can be used to develop a material index for the selection of a suitable material for a given application under different loading conditions.
Similarly, the cross-sectional shape of a part can be used to enhance the load bearing capacity. An engineering material confirms to a modulus and strength, but it can be made stiffer and stronger when loaded under bending or twisting by shaping it into an I-beam or a hollow tube, respectively.
It can be made less stiff by flattening it into a leaf or winding it, in the form of a wire, or into a helix. ‘Shaped’ sections (i.e. cross-section formed to a tube, a box section, an I-section or the like) carry bending, torsional, and axial compressive loads more ‘efficiently’ (i.e. for a given loading conditions, the section uses as little material as possible) than solid sections.
The efficiency can be enhanced by introducing sandwich panels of the same or different materials. But when choosing shapes one has to be careful so the basic functional requirement is not violated.
Shape Factor (φ)
Shape Factor is a dimensionless number that characterizes the efficiency of the shape, regardless of its scale, for a given mode of loading, e.g. bending, torsion, twisting, etc.
The four primary shape factors of our consideration are,
All the shape factors are defined equal to 1 for a solid cylinder i.e. our reference cross sectional shape is circular. Shape Factor of all other cross section will be evaluated w.r.t this one.