ESDU 09013:2009

INTRODUCTION

This Data Item provides a method of calculating the initial
buckling stress of a flat isosceles triangular plate of uniform
thickness subjected to

(a) a uniform compression f = f_c
along the base reacted by compressive stress along the two equal
edges of the plate (see Sketch 2.1a), or

(b) a uniform compression f = f_s
along the base reacted by shear stress q along the two
equal edges of the plate (see Sketch 2.1b).

The Item also provides a method of calculating the critical
total buckling stress, f_cr, of a flat isosceles
triangular plate of uniform thickness subjected to

(c) a uniform compression f = f_c +
f_s along the base of the triangular plate
reacted by a combination of compression f_c and
shear q along the two equal edges (see Sketch 2.1c).

The boundary conditions considered are either all three edges
clamped (fixed in rotation and out-of-plane displacement) or all
three edges simply-supported (free to rotate, fixed in out-of-plane
displacement).

The data given in this Item are obtained by FEA (Derivation 3)*
for loading cases (a) and (b) above and from the interaction
formula, Equation (2.1), for the combined case (c). The shear
stress is taken as positive for the load directions shown in Sketch
2.1.

The curves in Figures 1 to 4 are applicable only to plates of
isotropic material and have been calculated for v = 0.3. Results
for materials with other Poisson's ratios can be obtained by
multiplying the values given by the curves by
(1-0.3²)/(1-v²).

Figure 1 presents curves of K_c versus
h/a for uniform compression f =
f_c along the base reacted by compressive stress
f_c along the two equal edges of the plate (as
in Sketch 2.1a).

Figure 2 presents curves of K_s versus
h/a for uniform compression f =
f_s along the base reacted by shear stress
q along the two equal edges of the plate (as in Sketch
2.1b).

Figures 3 and 4 presents curves of K
versus f_c/f  for combined uniform
compression f = f_c +
f_s along the base reacted by a combination of
uniform compression f_c and shear stress
q along the two equal edges (as in Sketch 2.1c) for plates
with simply-supported and clamped edge cases respectively.

It may be observed that the value of K_c is
consistently low in comparison with K_S : this
is because the former corresponds to a state of biaxial compression
whereas the latter condition implies a biaxial stress state in
which the transverse stress component is tensile.

* The present Data Item supersedes ESDU STRUCT 02.04.06 in which
a theoretical solution based on an approximate mode of buckling
(Derivations 1 and 2) was found to be insufficiently accurate, and
this has now been replaced by a finite element analyis.