The Design of Modern Steel Bridges - TEDI

132 The Design of Modern Steel Bridges
in accordance with the Hencky–Mises yield criterion (i.e. equation (5.27) with
tcr replaced by tl given above), and (ii) plastic hinges occur in the flanges,
which together with the yielded zone WXYZ form a plastic mechanism.
Considering the virtual work done in this mechanism and adding the resistance
of the three stages, one obtains the ultimate shear capacity as
Vu ¼ 4Mp
c þ ctwst sin 2 yt þ stbtwðcot yt fÞ sin 2 yt þ t1btw ð5:32Þ
where Mp is the plastic moment of resistance of the flange, c is the distance of
the internal plastic hinge (see Fig. 5.22) in one flange from the corner, and st is
the membrane tensile stress, given by equation (5.27), with tl replacing tcr. The equilibrium condition of the flange between W and X (or between Z
and Y) in Fig. 5.22 leads to
c ¼ 2
rffiffiffiffiffiffiffiffiffi
Mp
; but>j a
sin yt sttw
Putting this expression for c in equation (5.32) leads to the ultimate shear
capacity tu being given by
tu
ty
¼ t1
ty
tu
ty
rffiffiffiffi
pffiffiffiffi
st
þ 5:264 sin yt m
¼ t1
ty
þ 6:928m
f
ty
þðcot yt fÞ sin 2 st
yt
ty
st
þ sin yt cos yt when m5
ty
f2 sin 2 ytst
6:928ty
when m4 f2 sin 2 ytst
6:928ty
ð5:33aÞ
Figure 5.22 Tension-field mechanism of Porter, Rockey and Evans[8].
ð5:33bÞ