Stress Thin Walled Tube

Overview

Engineering reference data for Stress Thin Walled Tube in electrical engineering.

Key Formulas

Ohm's Law

$V = IR$

Voltage = Current × Resistance.

Power

$P = VI = I^2R = V^2/R$

Electrical power.

Energy

$E = Pt$

Energy = Power × Time.

Variables

Assumptions & Applicability

The thin-walled equations apply when the wall thickness is less than 1/20 of the tube or cylinder diameter ($t < d/20$). For thicker walls, more complex thick-walled cylinder theory (Lamé equations) should be used.

Stress Analysis

Hoop (Circumferential) Stress

The hoop stress acts circumferentially around the cylinder, perpendicular to both the axis and the radius of the wall. This stress is typically the controlling design factor, as it is twice the longitudinal stress.

Longitudinal (Axial) Stress

For a cylinder closed at both ends, internal pressure creates a force along the cylinder axis. The longitudinal stress acts parallel to the cylinder's central axis.

Worked Example

Given: A thin-walled tube with:

• Internal diameter: $d = 0.3\ \text{m}$
• Wall thickness: $t = 0.001\ \text{m}$
• Internal pressure: $p = 1000\ \text{kPa}$ (10 bar)

Hoop Stress Calculation:

$\sigma_h = \frac{p \cdot d}{2t} = \frac{(1000\ \text{kPa})(0.3\ \text{m})}{2(0.001\ \text{m})} = 150{,}000\ \text{kPa} = 150\ \text{MPa}$

Longitudinal Stress Calculation:

$\sigma_l = \frac{p \cdot d}{4t} = \frac{(1000\ \text{kPa})(0.3\ \text{m})}{4(0.001\ \text{m})} = 75{,}000\ \text{kPa} = 75\ \text{MPa}$

Note: Typical maximum allowable stress for carbon steel pipes is below 135 MPa. The hoop stress in this example (150 MPa) exceeds this limit, indicating that the wall thickness should be increased for safe operation with carbon steel.

References

• Original Source