Buckling Calculators

Buckling of Rectangular Plate

In this calculation, a rectangular plate with dimensions a × b and thickness s, fixed at edges is considered. A pair of opposite edges is subjected to a load σ_x determined by compressive stresses. Based on the results of calculations, the minimum critical load on adjacent edges, given by compressive stress σ_y, corresponding to the first form of the loss of stability is determined.

For the calculation, the elastic modulus E and Poisson's ratio ν of the plate should be specified.

Buckling of rectangular plate

Elastic stability of rectangular

INITIAL DATA

а - Edge length with stress σ_y;

b - Edge length with stress σ_x;

s - Plate thickness;

E - Young's modulus;

ν - Poisson's ratio;

σ_x - Given compression or tension stress on edge "b".

RESULTS DATA

σ_y - Critical stress of buckling on edge "a".

Metric Imperial

Edge length (a)

Edge length (b)

Plate thickness (s)

Young's modulus (Е)

Poisson's ratio (ν)

Given stress (σ_x)

Critical stress (σ_y)

BASIC FORMULAS

Critical stresses σ_x and σ_y are determined by parametric equations of the form:

σ_x + (a²/b²)*σ_y = 1.1EF;

F - coefficients, depending on the dimensions of rectangle.

INITIAL DATA

а - Edge length with stress σ_y;

b - Edge length with stress σ_x;

s - Plate thickness;

E - Young's modulus;

ν - Poisson's ratio;

σ_x - Given compression or tension stress on edge "b".

RESULTS DATA

σ_y - Critical stress of buckling on edge "a".

MATERIALS PROPERTIES

Material	Young’s modulus Pa (psi)	Poisson’s ratio
Steel	1.86÷2.1×10¹¹ (2.7÷3.05×10⁷)	0.25÷0.33
Cast iron	0.78÷1.47×10¹¹ (1.1÷2.1×10⁷)	0.23÷0.27
Copper	1.0÷1.3×10¹¹ (1.45÷1.9×10⁷)	0.34
Tin bronze	0.74÷1.22×10¹¹ (1.1÷1.8×10⁷)	0.32÷0.35
Brass	0.98÷1.08×10¹¹ (1.4÷1.6×10⁷)	0.32÷0.34
Aluminum alloy	0.7×10¹¹ (1.0×10⁷)	0.33
Magnesium alloy	0.4÷0.44×10¹¹ (5.8÷6.4×10⁶)	0.34
Nickel	2.5×10¹¹ (3.6×10⁷)	0.33
Titanium	1.16×10¹¹ (1.7×10⁷)	0.32
Lead	0.15÷0.2×10¹¹ (2.2÷2.9×10⁶)	0.42
Zinc	0.78×10¹¹ (1.1×10⁷)	0.27
Glass	4.9÷5.9×10¹⁰ (7.1÷8.5×10⁶)	0.24÷0.27
Concrete	1.48÷2.25×10¹⁰ (2.1÷3.3×10⁶)	0.16÷0.18
Wood (along the grain)	8.8÷15.7×10¹⁰ (12.8÷22.8×10⁶)	-
Wood (across the grain)	3.9÷9.8×10¹⁰ (5.7÷14.2×10⁶)	-
Nylon	1.03×10¹⁰ (1.5×10⁶)	-

OTHER CALCULATORS

AREA MOMENTS OF INERTIA

BEAM CALCULATORS

TORSION OF BARS

CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

SHAFT CONNECTIONS

BEARINGS

DRIVES

FATIGUE

HEAT TRANSFER