Shear centre (S.C.), GATE & ESE , Strength of materials (SOM) , Mechanical Engineering

Introduction to shear centre 

    We already know that ,

• Beams are subjected to simple bending (i.e. both shear force & bending moment ) under transverse shear load (TSL).
• Beams are subjected to simple bending and twisting under  transverse shear load.
• But some cross section are subjected to simple bending and twisting even under  transverse shear load also . e.g. cross section which are not symmetric about horizontal centroidal axis (HCA) and vertical centroidal axis (VCA) like channel , angular  , T cross section.
• Hence to avoid twisting of these cross section line of action of shear load should pass through the shear centre .
• Therefore the shear centre location is important in these types of cross section.
• These cross section are straight under bending but weak under twisting under T.S.L. 

Shear centre location of different cross sections

     P = Load

     S = Shear centre

     C = Centroid

     e = eccentricity

Shear centre 

1. S.C. is the point through which line of action of shear load should pass through so that the beam is subjected to only simple bending. (i.e. without any twisting )
2. S.C. is known as centre of twist or centre of flexure.
3. S.C. location depends only on shape of cross section . (i.e. independent of shear load magnitude )
4. S.C.location is important in the cross section which are not symmetric about both HCA and VCA.
5. Variation of shear force per unit length is known as shear flow.
6. Horizontal shear stress (i.e. in flange ) varies linearly but transverse shear stress varies parabolically.
7. Shear centre will coincide with centre of cross section which is symmetric about both HCA and VCA .
8. Shear centre lies on the centroidal axis about which the cross section is symmetric e.g. channel and T section.
9. When cross section is made of two rectangles then shear centre lies on the intersection of their centroidal axis.