Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 137

4.7.6 Beam webs in shear and bending

Where the design moment M Ed and shear V Ed are both high, the beam must be
designed against combined shear and bending. For stocky webs, when the shear
force is less than half the plastic resistance V pl , Rd , EC3 allows the effect of the
shear on the moment resistance to be neglected. When V Ed > 0.5 V pl , Rd , EC3
requires the bending resistance to be determined using a reduced yield strength

f yr = ( 1 − ρ) f yw (4.95)

for the shear area, where

2 V Ed
V pl , Rd − 1

2

ρ = . (4.96)

Theinteractioncurvebetweenthedesignshearforce V Ed anddesignmoment M Ed
isshowninFigure4.30.Theseequationsarelessconservativethanthevon-Mises
yield condition (see Section 1.3.1)

f yr + 3 τ Ed = f y .

(4.97)

Equations 4.95 and 4.96 may be used conservatively for the well-known propor-
tioningmethodofdesign,forwhichonlytheflangesareusedtoresistthemoment
and the web to resist the shear force, and which is equivalent to using a reduced
yield strength f yr = 0 in equation 4.95 for the web.

1.0

0.8

0.6

0.5

0.4

0.2

0.7

0 0

0.2 0.4 0.6 0.8 1.0

M v,Ed / M pl,Rd

Figure 4.30 Section resistances of beams under bending and shear.