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Buckling Calculators







Buckling of Curved Beam

In this calculation, curved beams with a radius of curvature D/2, central bending angle α and a moment of inertia of the cross section Ix are considered. Calculations are performed for arches with hinged (scheme II) and fixed (scheme III) ends. Also, a closed ring is calculated as a special case.

As a result of calculations, a critical uniformly distributed load q is determined, the excess of which causes a loss of stability in the first form.

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

Buckling of circular arches
Buckling of arches under loads

INITIAL DATA

D - Arch diameter;


Ix - Moment of inertia of the arch cross-section;


α - Arch bending angle (see at figure);


E - Young's modulus.

RESULTS DATA

q - Critical uniform radial load of buckling.

Curvature diameter (D)

Moment of inertia (Ix)

Angle (α)

Young's modulus (E)

Scheme # 1

Scheme # 2

Scheme # 3

Critical load (q)

BASIC FORMULAS

Critical pressure for ring:

q = 3E*Ix / (D/2)3;

Critical pressure for arch with hinged ends:

q = [E*Ix / (D/2)3]*[(2π / α)2 - 1];

Critical pressure for arch with fixed ends:

q = [E*Ix / (D/2)3]*[K2 - 1];

K*tan(α/2)*cot(Kα/2) = 1.

INITIAL DATA

D - Arch diameter;


Ix - Moment of inertia of the arch cross-section;


α - Arch bending angle (see at figure);


E - Young's modulus.

RESULTS DATA

q - Critical uniform radial load of buckling.

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