The Design of Modern Steel Bridges - TEDI

emains flat until an elastic critical value of the loading is reached. Also, as in
the case of plates, stiffened plates may often have substantial post-buckling
strengths.
5.5.1 Elastic critical buckling of stiffened panels
Two basic methods are available for the analysis of elastic critical buckling of
ideally flat residual-stress-free stiffened plates. In the classical method, either
(i) a differential equation of equilibrium is solved in general terms by assuming
a deflected shape and then the boundary conditions are used to obtain a
characteristic equation for the elastic critical buckling load, or (ii) a Fouriertype
series representation is set up for the possible deformation mode consistent
with the boundary conditions and then an energy or work approach is
applied. The second method, i.e. the numerical or computer-based method, can
tackle the complex problems; in this method a solution is formed in terms of a
discrete number of unknowns located at many points in the stiffened plate.
Thus a large-order matrix equation is formed, whose coefficients are given by
the geometry of the stiffened plate and its loading conditions; the elastic
critical buckling load is the value of the load at which the determinant of the
coefficients is zero. The critical buckling load of a stiffened panel is generally
expressed as
scr ¼ k p2 D
b 2 t
where k is a buckling coefficient that depends on the geometry of the stiffened
plate, the loading pattern and the boundary conditions, plus three relative
rigidities of the stiffener, given by
flexural: g ¼ EIs=bd
torsional: y ¼ GJs =bd
extensional: d ¼ As=bt
Rolled Beam and Plate Girder Design 137
and D is the flexural rigidity of the plate, equal to Et 3 =12ð1 m 2 Þ
b ¼ spacing of the stiffeners
t ¼ thickness of the plate
I s ¼ is the second moment of area of the stiffener cross-section, with the width
of the plate acting with it, about its centroidal plane parallel to the plate
Js ¼ torsional constant of the stiffener cross-section
A s ¼ area of the cross-section.
Many solutions are available for a large range of stiffened panel geometries
and loading types in References [10] and [11] for ‘open’-type stiffener crosssections
(i.e. not ‘closed’- or box-type cross-sections) with negligible torsional
rigidity.