Buckling Calculators

Buckling of Spherical Segment

In this calculation, a spherical segment with a diameter D, central angle α and wall thickness s is considered. The segment edge is simply supported. Calculations are performed in the range of ratios 800 < D/s < 4000 and 40° < α < 120°. Based on the results of calculations, the minimum uniformly distributed critical load of the first form of stability loss P, acting on the outer surface of the segment is determined.

For the calculation, the elastic modulus E of the segment should be specified.

Buckling of spherical cap

Elastic stability of spherical cap

INITIAL DATA

D - Mean segment diameter;

s - Segment wall thickness;

α - Segment center angle;

E - Young's modulus;

Conditions of calculations:
800 < D/s < 4000;
40° < α < 120°

RESULTS DATA

P - Critical pressure of buckling on the external surface.

Metric Imperial

Sphere diameter (D)

Wall thickness (s)

Angle (α)

Young's modulus (Е)

Critical pressure (P)

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BASIC FORMULAS

Critical pressure P is determined by parametric equations of the form:

P = K*F*E*(s / D)²;

K, F - coefficients, depending on the ratio D/s and angle α.

INITIAL DATA

D - Mean segment diameter;

s - Segment wall thickness;

2α - Segment center angle;

E - Young's modulus;

Conditions of calculations:
800 < D/s < 4000;
40° < α < 120°

RESULTS DATA

P - Critical pressure of buckling on the external surface.

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)	-

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