Shear center
Introduction
In resistance of materials, the shear center, also called center of torsion, center of shear or center of shear stresses (CEC), is a point located in the plane of the cross section of a prismatic piece such as a beam or a column such that any shear stress passing through it will not produce a torsional moment in the cross section of the piece, that is, every shear stress generates a torsional moment given by the distance of the shear stress to the shear center. It is usually denoted by (y, z).
When there is an axis of symmetry the shear center is located on it. In pieces with two axes of symmetry, the center of shear coincides with the center of gravity of the section and in that case the bending and torsion are uncoupled and a beam or column can have bending without torsion and torsion without bending. However, in mechanical prisms, beams or columns with asymmetries in their cross section, it is necessary to determine the shear center to correctly determine the stresses.
Definition of shear center
Contenido
Si usamos la coordenada x para medir distancias a lo largo del eje de una pieza prismática y las coordenadas (y, z) para las coordenadas de cualquier punto sobre una sección transversal. El centro de cortantes es el punto definido por las coordenadas (y, z) dadas por:.
Donde son los momentos de área y el producto de inercia. Y donde son los productos de inercia sectoriales definidos como:.
Y es la función auxiliar del alabeo unitario.
Es importante señalar que:.
Thin section profiles
For thin section profiles it can be simplified by calculating the auxiliary unit warping function simply as the sectional area with respect to the center of gravity as:.
where:.
If a system of axes is taken parallel to the principal axes of inertia, I = 0 and therefore the equations of the center of shear stress are simply:
A simpler calculation can be obtained by considering arbitrary shear stresses T, T and the irrotational tangential stress fields given by the Collignon-Zhuravski formula for both directions. For this field of tangential stresses, the effective torsional moment M of the same field is calculated with respect to a suitable point and then calculate: