Maximum Equivalent Stress at Junction with Shell Calculator

Maximum Equivalent Stress Formula:

\[ f_e = \sqrt{(f_{as})^2 + (f_{cs})^2 + (f_{cc})^2 - (f_{as} \times f_{cs} + f_{as} \times f_{cc} + f_{cc} \times f_{cs})} \]

Maximum Equivalent Stress (f_e):

1. What is Maximum Equivalent Stress at Junction with Shell?

Definition: This calculator determines the maximum equivalent stress at the junction between a shell and coil using the von Mises stress criterion.

Purpose: It helps engineers evaluate whether the combined stresses at the junction meet material yield criteria and safety factors.

2. How Does the Calculator Work?

The calculator uses the von Mises stress formula:

\[ f_e = \sqrt{(f_{as})^2 + (f_{cs})^2 + (f_{cc})^2 - (f_{as} \times f_{cs} + f_{as} \times f_{cc} + f_{cc} \times f_{cs})} \]

Where:

\( f_e \) — Maximum equivalent stress
\( f_{as} \) — Total axial stress in the vessel
\( f_{cs} \) — Total hoop stress in the shell
\( f_{cc} \) — Maximum hoop stress in coil at junction with shell

Explanation: The formula combines the three principal stresses into a single equivalent stress value for comparison with material yield strength.

3. Importance of Stress Calculation

Details: Proper stress evaluation ensures structural integrity, prevents material yielding, and maintains safety margins in pressure vessel design.

4. Using the Calculator

Tips: Enter the three stress components (all positive values). The ±5% indicates typical tolerance in stress measurements. Results are in the same units as inputs.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the stresses?
A: Use consistent units for all inputs (MPa, psi, etc.). The output will be in the same units.

Q2: Why is the equivalent stress important?
A: It allows comparison of multi-axial stress states to uniaxial material properties.

Q3: What does the ±5% tolerance mean?
A: It accounts for typical measurement uncertainties in stress analysis.

Q4: How conservative is this calculation?
A: The von Mises criterion is standard for ductile materials but may need adjustment for brittle materials.

Q5: What safety factor should I apply?
A: Typical safety factors range from 1.5 to 3.0 depending on application and standards.