Buckling of Cantilever Beam

Buckling of Cantilever Beam

In this calculation, a cantilever beam of length L and rectangular cross-section with dimensions H × b is considered. Following the calculations, the minimum critical load F of the first form of stability loss, applied to the free end of the beam and acting in the direction of dimension H is determined.

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

Buckling of Cantilever Beam

calculation of Buckling of Cantilever Beam

INITIAL DATA

L - Beam length;

H - Height of the cross-section;

b - Width of the cross-section;

E - Young's modulus.

ν - Poisson's ratio.

RESULTS DATA

F - Critical load of buckling.

Metric Imperial

Beam length (L)

Height (H)

Width (b)

Young's modulus (E)

Poisson's ratio (ν)

Critical buckling load (F)

BASIC FORMULAS

Critical load:

F = [(0.67bH³(EG - 0.63bEG/H)^0.5) / l²]*[1 - H(E / (G(1 - 0.63b/H)))/4l];

G - Shear modulus.

INITIAL DATA

L - Beam length;

d - Height of the cross-section;

b - Width of the cross-section;

E - Young's modulus.

ν - Poisson's ratio.

RESULTS DATA

F - Critical 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