Local buckling of thin-plate elements - The Behaviour and Design of Steel Structures to EC3 - page 116

4.3.2 Ultimate strength

4.3.2.1 Unstiffened plates

A stocky unstiffened web in an I-section beam in pure shear is shown in
Figure 4.17a. The elastic shear stress distribution in such a section is analysed
in Section 5.10.2. The web behaves elastically in shear until first yield occurs at
τ y = f y / √ 3, and then undergoes increasing plastification until the web is fully
yielded in shear (Figure 4.17b). Because the shear stress distribution at first yield
is nearly uniform, the nominal first yield and fully plastic loads are nearly equal,
andtheshearshapefactorisusuallyverycloseto1.0.Stockyunstiffenedwebsin
steelbeamsreachfirstyieldbeforetheybuckleelastically,sothattheirresistances
are determined by the shear stress τ y , as indicated in Figure 4.18.

Elastic First yield Fully plastic

d

y y

(a) I-section (b) Shear stress distributions

Figure 4.17 Plastification of an I-section web in shear.

1.0

a/d = 0.4
0.6
1.0
1.5
Ultimate strengths
of stiffened plates

Yielding

0.8

0.6

0.4

3

ult /f y 3

Elastic buckling
Ultimate strength of
unstiffened plates

cr /f y
ult /f y

0.2

3

0

0 0.5 1.0 1.5 2.0 2.5 3.0

( ) ( )

2 )

f f

d 12 ( -

Modified plate slenderness

y y

=

t

2

3 3 E

k

cr

Figure 4.18 Ultimate strengths of plates in shear.