The Design of Modern Steel Bridges - TEDI

Figure 5.8 Buckling of plate under edge bending.
edges of dimension b, i.e. stresses caused by equal and opposite applied
in-plane bending moments on these edges (Fig. 5.8). By taking a sufficient
number of terms from a double Fourier series expression for the deflected shape
of the plate, it can be shown[5] that instability occurs when the magnitude of
the applied stress reaches a critical value
sBx cr ¼ kp2 E
12ð1 m 2 Þ
t
b
2
ð5:22Þ
where the buckling coefficient k depends to a small extent upon the aspect ratio
a ¼ a/b of the plate. For a > 0.5, the minimum and maximum values of k are
23.9 (for a ¼ 0.67) and 25.6 (for a ¼ 0.5 and 1.0); for a < 0.5, k is larger. For
the sake of simplicity k may be taken to be 24 irrespective of a, leading to
sBx cr ¼ 24p2 E
12ð1 m 2 Þ
t
b
2
¼ 21:7E t
b
5.4.1.3 Plates subjected to in-plane shear
Rolled Beam and Plate Girder Design 113
2
, taking m ¼ 0:3 ð5:23Þ
Consider a rectangular plate with larger side a, smaller side b and thickness t,
with all the edges simply supported and subjected to in-plane shear stresses t
as shown in Fig. 5.9.
When the applied shear stress reaches a critical value the plate buckles; the
buckling pattern appears in a pronounced form if there are no or little in-plane
restraints on the edges. Diagonal buckles appear in elongated shapes along the
direction of principal tension 1–1, i.e. several ripples forming across the
direction of principal compression 2–2. Closed-form solutions of the St Venant
equation are not available, but numerical solutions have been obtained[5] by
the energy method by taking several terms of a Fourier series expression of the