Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 122

cr

crl

crl

cr cr

d

crl crl

cr

L

Figure 4.23 Simply supported plate under shear and bending.

approximate interaction equation [2, 4, 5, 13]
τ cr
τ cro

2 σ crl

σ crlo

2

+ = 1 (4.39)

in which τ cro is the elastic buckling stress when the plate is in pure shear
(see equations 4.21-4.24) and σ crlo is the elastic buckling stress for pure bending
(see equations 4.35 and 4.36). If the elastic buckling stresses τ cr , σ crl are used in
the Hencky-Von Mises yield criterion (see Section 1.3.1)

3 τ cr + σ crl = f y , (4.40)

itcanshownfromequations4.39and4.40thatthemostsevereloadingcondition
forwhichelasticbucklingandyieldingoccursimultaneouslyisthatofpureshear.
Thus,inanunstiffenedwebofasteelforwhich E = 210000N/mm 2 and ν = 0.3,
yielding will occur before buckling while (see equation 4.25)

f y
235 ≤ 86.4.

d
t

(4.41)

4.5.2 Ultimate strength

4.5.2.1 Unstiffened plates

Stockyunstiffenedwebsinsteelbeamsyieldbeforetheybuckle, andtheirdesign
resistancescanbeestimatedapproximatelybyusingtheHencky-VonMisesyield
criterion (see Section 1.3.1), so that the shear force V w and moment M w in the
web satisfy

V w
dt

2 6 M w

d 2 t

2

= f y .

3 + (4.42)