Thick Cylinders and Spheres
Thick cylinders need Lame’s equations:,, with A,B from inner/outer pressures.
Level
Intermediate
Topic tags
Thick cylinders and spheres, Som, Rk Bansal Som
Useful for
GATE favourite, Interview ask
Source
Strength of Materials
What you'll learn in this topic
- Use thick-wall theory when is not large (radial stress matters).
- BC: at , at .
- Internal pressure only: max at inner surface.
- Compound cylinders: interference creates residual compressive hoop in the liner.
Key Formulas
Important equations & their meanings
Worked Examples
Step-by-step solved problems
- 1.Lame — inner hoop
Common Mistakes
Avoid these errors in exams & interviews
- Applying pd/(2t) to a clearly thick wall.
- Wrong signs on boundary pressures when solving for A,B.
- Reporting outer hoop as maximum under internal pressure.
Practice Questions
Strengthen your concepts with questions
9+
Practice Questions
Interview Questions
Most asked interview problems
8
Interview Questions
GATE Questions
Previous year GATE questions
1
GATE Questions
Applications in real world
Beams
Frames and structural members
Shafts
Torsion and combined loading
Pressure vessels
Hoop and longitudinal stress
Machine frames
Stiffness and strength checks
Visual concept
Problem
Model
Compute
Verify
Model the physics, compute, then verify against limits.
Recommended Book
Strength of Materials
RK Bansal
Read: Syllabus unit
Related Topics
What should I learn next?
Nearby topics on your path
University exams
Important Topic
Industry relevance
High
Concept difficulty
Medium
Average time
18 min
See how this topic connects to real mechanical engineering careers
Learn from engineers who use this concept in their daily work.
Introduction
- Lame’s equations and boundary conditions
- Internal / external pressure cases
- Compound cylinders (shrink fit)
- Thick spheres (outline)
Concept: Lame’s equations
Constants and follow from pressures at the inner and outer radii , :
Hoop stress is largest at and decreases toward the outside.
Fundamentals: reading stresses and design implications
Concept: compound cylinders and thick spheres
Exam mistakes to avoid
- Wrong signs on boundary pressures when solving for .
- Reporting outer hoop as maximum under internal pressure.
- Forgetting residual stresses in compound-cylinder working-stress checks.