The Design of Modern Steel Bridges - TEDI

114 The Design of Modern Steel Bridges
Figure 5.9 Buckling of plates subjected to in-plane shear.
deflected form. The critical value of the shear stress can be expressed as
tcr ¼ kp2 E
12ð1 m 2 Þ
t
b
2
ð5:24aÞ
where the buckling coefficient k is given approximately by
k ¼ 5:35 þ 4ðb=aÞ 2
ð5:24bÞ
It should be noted that b in the above equations is always the smaller side of
the plate.
5.4.1.4 Plates subjected to a combination of stresses
A rectangular plate with simply supported edges and subjected to a
combination of stresses shown in Fig. 5.10 may be assumed to reach a state
of elastic critical buckling when the following condition is attained:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s1
s1cr
2
þ s2
s2cr
2
þ sB
sBcr
2
þ t
tcr
2
¼ 1 ð5:25Þ
In the above equation s 1, s 2, s B and t are the individual stress components
and s 1cr, s 2cr, s Bcr and t cr are the magnitudes of these individual stress
components that acting alone on the plate will cause elastic critical buckling;
the values of s 1cr, etc. have been derived in the preceding sections for various
plate aspect ratios /¼a/b and slenderness ratios b/t. Equation (5.25) is an
approximate, lower-bound, simple and umbrella-type relationship that covers
reasonably satisfactorily theoretical solutions for many specific stress patterns
and plate geometries obtained by research[5, 6] using various theoretical