A review of the problem of the shear centre(s)

The problem of defining and determinating the shear centre is present in the literature since the first decades of this century. It soon interlaced with the definition of the twist centre and their ways became unextricable in the following decades. A number of researchers dealt with this subject meeting with variable issues, yet in the authors' opinion it seems of some interest to run through it again. In this paper a general survey of the literature is performed and the two definitions of the shear centre (here named kinematic and energetic) are compared. It is remarked how the energetic definition for the shear centre makes it coincide with a suitably chosen twist centre. An example is given to show that the two definitions generally fail to provide the same place even for simple cross sections. It is shown that the two definitions provide the same place, using standard approximate formulæ, in the case of thin-walled mono-connected sections with regularly varying thickness and two-connected sections with constant thickness. As a new result, it will be shown that the two definitions of shear centre do not provide the same place for thin-walled sections with connection higher than two even in the trivial case of uniform thickness; an example is given.