Are you a civil, mechanical, or aerospace engineering student struggling to understand the relationship between shear stress and shear strain ? If so, this guide is for you.
In this article, we’ll cover the essential topics from your lecture:
- ✅ Shear stress
- ✅ Direct shear & pin connections (single/double shear)
- ✅ Shear strain
- ✅ Shear modulus
- ✅ Normal vs. shear stress in axially loaded members
We'll also help you find free downloadable handwritten notes in PDF format that explain these concepts clearly and concisely—perfect for GATE, ESE, SSC JE , and other competitive exams or university preparation.
📘 Lecture Summary: Shear Stress and Shear Strain
🔹 a) Shear Stress (τ)
Shear stress occurs when forces are applied parallel or tangential to the surface of a material.
Formula :
Where:
- = shear stress (in Pa or MPa)
- = shear force
- = cross-sectional area over which the force is applied
Shear stress causes sliding or tearing deformation within the material.
🔹 b) Direct Shear and Single/Double Shear in Pins
➤ Direct Shear
Occurs when forces act directly across a single plane, e.g., in bolts, pins, or rivets.
➤ Single Shear
One shear plane exists. The pin or bolt resists the load through one cross-section.
➤ Double Shear
Two shear planes exist. The same load is resisted by two cross-sections, reducing the shear stress per area.
Example : In a clevis joint or fork connection.
🔹 c) Shear Strain (γ)
Shear strain measures how much a material deforms under shear stress.
Definition :
It is the ratio of the lateral displacement to the original length perpendicular to the force.
Units: Dimensionless (radians)
🔹 d) Shear Modulus (G)
Also known as the modulus of rigidity , it defines the material’s resistance to shear deformation.
Formula :
Typical values:
- Steel: ~75 GPa
- Aluminum: ~25 GPa
- Rubber: ~0.1 GPa
This modulus helps in predicting how materials behave under torsion or shear loading.
🔹 e) Normal and Shear Components of Stress in Axially Loaded Members
When a member is subjected to axial loading (tensile or compressive), the stresses can be resolved into:
- Normal stress (σ) — acts perpendicular to the inclined plane
- Shear stress (τ) — acts parallel to the inclined plane
Using stress transformation equations , we can calculate both components based on the angle of the inclined section.
This concept is crucial in understanding failure theories like Maximum Shear Stress Theory (Tresca Criterion) .
📝 Why These Topics Are Important
Understanding shear stress and strain is vital for:
- Designing joints, fasteners, and connectors
- Predicting failure modes in beams and columns
- Solving problems in solid mechanics , machine design , and structural analysis
These topics are heavily tested in:
- GATE (Mechanical/Civil)
- ESE (Engineering Services Exam)
- PSUs Recruitment Exams
- University Semester Exams
📥 Download Free Handwritten Notes PDF
📥 Download Shear Stress and Shear Strain Handwritten Notes PDF
📁 File Size: ~1 MB
📌 Format: PDF
📄 Pages: 16
📘 Content Includes:
- Clear diagrams and derivations
- Solved numerical examples
- Comparison of direct shear and double shear
- Relationship between shear stress-strain and shear modulus
- Derivation of normal and shear stress on inclined sections
⚠️ Note: This link is an example. You can search for “Shear Stress and Strain Handwritten Notes PDF” on platforms like:
- Google Drive engineering groups
- Made Easy / ACE Academy Notes
- Unacademy or BYJU'S Exam Prep
🔗 Related Resources
- Fundamentals and Applications (3rd Edition) – Free PDF Book Download
📢 Final Thoughts
Whether you're preparing for an exam or working on a project, mastering shear stress and shear strain will improve your understanding of structural behavior and mechanical design.
Use the notes and explanation above to strengthen your foundation in engineering mechanics .
📚 Don’t forget to share these notes with classmates or fellow engineers who might benefit from them!
📝 Disclaimer: All downloadable files are hosted on third-party servers or shared via open-access platforms. We do not host or upload any files directly.
0 Comments