Pipes and Shells Calculators

Tube Under Linearly Distributed Uniform Load

In this calculation, a tube with a mean diameter D, length L, and wall thickness t is considered. The tube is under the influence of a load P, uniformly distributed along the generatrix and acting perpendicular to the axis. The ends of the tube are simply supported. For the calculation, the elastic modulus E and Poisson's ratio ν of the tube should be specified.

As a result of calculation, the maximum membrane stress σ₁ and the maximum bending stress σ₂ are determined. The total deformation X is also calculated, which is the deflection of the deformed tube from the cylindrical surface. When calculating the deformation, the total flexure of the loaded tube is not taken into account.

Calculation of tube under uniform load

Tube under uniform load

INITIAL DATA

D - Mean tube diameter;

L - Tube length;

t - Tube wall thickness;

p - Uniform load, distributed over entire length L;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

σ₁ - Maximum membrane stress;

σ₂ - Maximum bending stress;

Х - Deflection of the tube wall in the load direction.

Metric Imperial

Diameter (D)

Length (L)

Wall thickness (t)

Load (P)

Young's modulus (E)

Poisson's ratio (ν)

Membrane stress (σ₁)

Bending stress (σ₂)

Deflection (Х)

BASIC FORMULAS

Maximum membrane stress:

σ₁ = 0.5*((12(1 - ν²))^0.125*P*(D/2)^0.75*L^-0.5*t^-1.25);

Maximum bending stress:

σ₂ = 1.2*[1/((12(1 - ν²))^0.125]*P*(D/2)^0.25*L^0.5*t^-1.75);

Tube deflection in radial direction:

X = 0.03*((12(1 - ν²))^0.625*P*(D/2)^0.75*L^1.5*t^-2.25) / E.

INITIAL DATA

D - Mean tube diameter;

L - Tube length;

t - Tube wall thickness;

p - Uniform load, distributed over entire length L;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

σ₁ - Maximum membrane stress;

σ₂ - Maximum bending stress;

Х - Deflection of the tube wall in the load direction.

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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