Thin Cylinders and Spheres
Closed thin cylinders under internal pressure develop hoop and longitudinal membrane stresses.
Level
Intermediate
Topic tags
Thin cylinders and spheres, Som, Rk Bansal Som
Useful for
GATE favourite, Interview ask
Source
Strength of Materials
What you'll learn in this topic
- Thin-wall: typically ; neglect radial stress.
- Closed cylinder: , .
- With joint efficiency: (as applicable).
- for closed cylinder (with ).
Key Formulas
Important equations & their meanings
Worked Examples
Step-by-step solved problems
- 1.Closed thin cylinder
- 2.Thin sphere
Common Mistakes
Avoid these errors in exams & interviews
- Using pd/(2t) for a **sphere**.
- Confusing radius and diameter in pd/2t.
- Ignoring η when the problem states joint efficiency.
Practice Questions
Strengthen your concepts with questions
10+
Practice Questions
Interview Questions
Most asked interview problems
8
Interview Questions
GATE Questions
Previous year GATE questions
2
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
22 min
See how this topic connects to real mechanical engineering careers
Learn from engineers who use this concept in their daily work.
Introduction
- Hoop and longitudinal stresses
- Spheres and joint efficiency
- Dimensional change / volumetric strain
- Pressure plus torque (brief)
Concept: equilibrium of a thin cylinder
Fundamentals: spheres, joints, and strain
(or the form specified for longitudinal vs circumferential joints).
Diameter strain ; volumetric strain of contents/capacity
Concept: wire winding and combined loads
Exam mistakes to avoid
- Confusing radius and diameter in .
- Ignoring when the problem states joint efficiency.
- Applying thin formulas when is small (need thick-wall theory).