Four thin-walled sections, each with a thickness of t, are shown in Fig 2. The length along the mid-line of each thin wall is y = 2tr. Each section is subjected to pure torques, and all four sections have equal beam lengths L and shear moduli G. Determine which of the following shapes would achieve the highest torsional rigidity by calculating and comparing the torsion constant J for each of them.
2TY
0.5TY
(d)
(a)
(b)
(c)
Fig 2