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Stress Thick Walled Tube

Reference data and engineering information about stress thick walled tube for electrical applications.

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Overview

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

Key Formulas

Ohm's Law

V=IRV = IR

Voltage = Current × Resistance.

Power

P=VI=I2R=V2/RP = VI = I^2R = V^2/R

Electrical power.

Energy

E=PtE = Pt

Energy = Power × Time.

Variables

SymbolDescriptionUnit
VVVoltageV
IICurrentA
RRResistanceΩ
PPPowerW

Stress Distribution Analysis

Stress Formulas

The stress state in a thick-walled cylinder under internal and external pressure is defined by three principal stresses.

Axial (Longitudinal) Stress: σa=piri2−poro2ro2−ri2\sigma_a = \frac{p_i r_i^2 - p_o r_o^2}{r_o^2 - r_i^2}

Circumferential (Hoop) Stress: σc=piri2−poro2ro2−ri2+ri2ro2(pi−po)r2(ro2−ri2)\sigma_c = \frac{p_i r_i^2 - p_o r_o^2}{r_o^2 - r_i^2} + \frac{r_i^2 r_o^2 (p_i - p_o)}{r^2 (r_o^2 - r_i^2)} where rr is the radius to the point in the wall (ri<r<ror_i < r < r_o). The maximum hoop stress occurs at the inner wall (r=rir = r_i).

Radial Stress: σr=piri2−poro2ro2−ri2−ri2ro2(pi−po)r2(ro2−ri2)\sigma_r = \frac{p_i r_i^2 - p_o r_o^2}{r_o^2 - r_i^2} - \frac{r_i^2 r_o^2 (p_i - p_o)}{r^2 (r_o^2 - r_i^2)} where rr is the radius to the point in the wall. The maximum radial stress (compressive) occurs at the inner wall (r=rir = r_i).

Example Calculation

For a cylinder with an inside diameter of 200 mm (ri=100r_i = 100 mm), outside diameter of 400 mm (ro=200r_o = 200 mm), and an internal gauge pressure of 100 MPa (pi=100p_i = 100 MPa, po=0p_o = 0 MPa), the stresses at the inner wall are calculated as follows.

  • Axial Stress: σa=(100 MPa)(100 mm)2−(0)(200 mm)2(200 mm)2−(100 mm)2=33.3 MPa\sigma_a = \frac{(100 \text{ MPa})(100 \text{ mm})^2 - (0)(200 \text{ mm})^2}{(200 \text{ mm})^2 - (100 \text{ mm})^2} = 33.3 \text{ MPa}

  • Hoop Stress (at r=ri=100r = r_i = 100 mm): σc=33.3 MPa+(100 mm)2(200 mm)2(0−100 MPa)(100 mm)2((200 mm)2−(100 mm)2)=167 MPa\sigma_c = 33.3 \text{ MPa} + \frac{(100 \text{ mm})^2(200 \text{ mm})^2 (0 - 100 \text{ MPa})}{(100 \text{ mm})^2((200 \text{ mm})^2 - (100 \text{ mm})^2)} = 167 \text{ MPa}

  • Radial Stress (at r=ri=100r = r_i = 100 mm): σr=33.3 MPa−(100 mm)2(200 mm)2(0−100 MPa)(100 mm)2((200 mm)2−(100 mm)2)=−100 MPa\sigma_r = 33.3 \text{ MPa} - \frac{(100 \text{ mm})^2(200 \text{ mm})^2 (0 - 100 \text{ MPa})}{(100 \text{ mm})^2((200 \text{ mm})^2 - (100 \text{ mm})^2)} = -100 \text{ MPa}

Additional Considerations

Note: In addition to stress induced by pressure, significant stress can also be introduced into the cylinder wall due to restricted thermal expansion. This must be considered in the total stress analysis for design.

References

Source: engineeringtoolbox.com