ENGINEERING – MECHANICAL ENGINEERING CALCULATOR
Thick Wall Lame
A precise tool.
What is the Thick Wall Lame & How does it work?
In a thickβwalled cylinder the stress state varies through the wall thickness, unlike thinβwalled assumptions where stresses are uniform. The LamΓ© solution, derived from equilibrium in cylindrical coordinates, provides the radial stress (sigma_r) and hoop (circumferential) stress (sigma_theta) as functions of the radial position (r).
The constants (A) and (B) are obtained from the inner radius (r_i), outer radius (r_o), internal pressure (p_i) and external pressure (p_o):
A = \frac{p_i r_i^{2} – p_o r_o^{2}}{r_o^{2} – r_i^{2}}
A = constant from boundary pressures
B = \frac{r_i^{2} r_o^{2} (p_o – p_i)}{r_o^{2} – r_i^{2}}
B = constant from boundary pressures
With (A) and (B) known, the hoop stress at any radius (r) is given by the LamΓ© expression:
\sigma_{\theta} = A + \frac{B}{r^{2}}
Ο_ΞΈ = hoop stress at radius r
Parameters
Result
β
Frequently Asked Questions
What is the LamΓ© solution used for?
The LamΓ© solution is used to calculate the stress distribution in thick-walled cylinders under internal and external pressure.
How do I determine the constants A and B in the LamΓ© solution?
Constants A and B are determined using the inner radius (r_i), outer radius (r_o), internal pressure (p_i), and external pressure (p_o).
What is the difference between radial stress and hoop stress in a thick-walled cylinder?
Radial stress acts perpendicular to the axis of the cylinder, while hoop stress acts circumferentially around the cylinder.
Can this calculator handle both internal and external pressures?
Yes, the LamΓ© solution can account for both internal pressure (p_i) and external pressure (p_o).
What is the significance of wall thickness in the stress analysis of a cylinder?
Wall thickness affects how stresses vary through the cylinder’s cross-section, unlike thin-walled assumptions where stresses are uniform.
How does the LamΓ© solution differ from thin-walled cylinder assumptions?
The LamΓ© solution accounts for varying stress through the wall thickness, while thin-walled assumptions assume uniform stress distribution.
What are the applications of the LamΓ© solution in engineering?
The LamΓ© solution is used in various engineering fields, including pressure vessel design, mechanical engineering, and structural analysis.
Results are for informational purposes only and do not constitute professional advice.