# Shear Centre: Thin and Thick Shells

By BYJU'S Exam Prep

Updated on: September 25th, 2023

In civil engineering, structures are designed based on the external load acting on them. These loads should act in such a way internal reactions nullify the effect of external load. To nullify the effect, these loads should act on a particular point for a particular cross-section. The shear centre can also be defined in the same contrast. The shear centre is the point on which, if the load acts, there will not be any twisting on that section.

Many points can be defined similarly to the shear centre in a structural member. These points can be centroid, point of contra flexure, point of inflexion, etc. This article contains basic notes on the “Shear centre” topic of the “Strength of Materials” subject.

Table of content

## What is Shear Centre?

The shear centre is defined as the point about which the external load must be applied to produce no twisting moment across the cross-section of the structural member. Loads must be applied at a particular point in the cross-section, called the shear centre if the beam is to bend without twisting.

The shear centre of the cross-section may differ from the centroid of the cross-section. And the distribution of the shear stress across the section depends on the geometry of the section and other cross-sectional parameters. The resultant of the shear stress for a particular cross-section acts on the point of the shear centre of the section. For a doubly symmetric cross-section, the shear centre and centroid of the section will coincide. The transverse load will result in a bending moment and twisting moment for a beam if it is not applied at the shear centre, but if it is applied on the shear centre, then it will only cause a bending moment to the cross-section.

## Location of Shear Centre

The shear centre for a member is the point at which, if the load is applied, it will cause no twisting to the centre. the location of the shear centre can be found by equating the moment due to external force to the total resisting moment for a particular section. Here a general expression for a section is explained below with the help of the following diagram.

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