The Design of Modern Steel Bridges - TEDI

126 The Design of Modern Steel Bridges
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accurate measure of the plate slenderness is the parameter (b/t) ðsy=EÞ,
which indicates that plates with identical dimensions but of higher yield stresses
are effectively more slender, in the sense that the ratio of their ultimate strength
to yield strength is more reduced.
The effects of initial imperfections and residual stress on the strength of
plated structures were highlighted by the Merrison Inquiry[7] into the failure of
several box girder bridges in the early 1970s. Extensive theoretical and experimental
investigations also took place at Imperial College, London, and elsewhere.
The theoretical methods were based on the elastic large-deflection
equations first suggested by Von Karman for describing the buckling behaviour
of plates. Non-linearity in the material behaviour during/after yielding was
dealt with by adopting:
(1) an ideal elastic/perfectly plastic behaviour, i.e. Hooke’s law of proportionality
between stress and strain up to yielding, and no strain-hardening
in the post-yielding stage
(2) a criterion for stresses to cause yielding; Hencky–Mises’ criterion is used
for this purpose, according to which yielding occurs when an equivalent
stress se reaches the yield stress sy of the material, se being given by the
following formula for a two-dimensional stress field
se ¼½s 2 1 þ s2 2
s1s2 þ 3t 2 Š 1=2
(3) a relationship between stresses and strains during yielding; the flow rules
due to Prandtl–Reuss are used for this purpose, which are based on the
two assumptions that no permanent change of volume occurs and the rate
of change of plastic strain is proportional to the derivatives
qse=qs1, qse=qs2 and qse=qt
The magnitude of the initial out-of-plane imperfections in the plates was
quantified from physical surveys of levels and patterns of imperfections in real
structures, and was also related to the construction tolerance specified in the
specification for steelwork construction. Thus the fabrication tolerance is
given by
¼ G
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sy
250 245
where G is the gauge length over which the geometric imperfection was measuredandisgivenbytwicethesmallerdimensionboftheplate.Theinitialinperfection
assumed for the design strength of the plate is 1.25 and is thus given by
d ¼ b
200
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sy
245
s y being the specified yield stress of the plate in N/mm 2 . The pattern of the
initial inperfection is assumed to be sinusoidal in both directions, and the
number of half-waves in each direction was varied to obtain the worst results