In-plane bending of beams - The Behaviour and Design of Steel Structures to EC3 - page 168

5.4.3 Shear centre

The shear stresses τ v induced by the vertical shear force V z exert a torque equal
to ∫ 0 τ v t ρ d s about the centroid C of the thin-walled cross-section, as shown in
Figure 5.15, and are therefore statically equivalent to a vertical shear force V z
which acts at a distance y 0 from the centroid equal to

E

y 0 = 1
V z

τ v t ρ d s . (5.24)

0

Similarly, the shear stresses τ h induced by the horizontal shear force V y are
staticallyequivalenttoahorizontalshearforce V y whichactsatadistance z 0 from
the centroid equal to

E

z 0 =− 1
V y

τ h t ρ d s .

(5.25)

0

Thecoordinates y 0 , z 0 definethepositionoftheshearcentreSofthecross-section,
through which the resultant of the bending shear stresses must act. When any
applied load does not act through the shear centre, as shown in Figure 5.16,
then it induces another set of shear stresses in the section which are additional
to those caused by the changes in the bending normal stresses described above
(seeequations5.16and5.23).Theseadditionalshearstressesarestaticallyequiv-
alent to the torque exerted by the eccentric applied load about the shear centre.
They can be calculated as shown in Sections 10.2.1.4 and 10.3.1.2.

s

δ s

O

t

v t δ s

y

C

E

V

z

y 0

z

Figure 5.15 Moment of shear stress τ v about centroid.