Skip to content
EngineeringHulk

EngineeringHulk

Free Educational Notes

  • Home
  • Automobile
    • Module 1
      • Clutch
      • Propellar Shaft & Axle
      • Transmission
    • Module 2
      • Braking System
      • Final Drive and Differential
      • Steering System
    • Module 3
      • Suspension System
      • Wheels & Tyres
    • Module 4
      • Automotive Electrical System
    • Module 5
      • Body Engineering
    • Module 6
      • Recent trends in Automobiles
  • IT
  • general
  • Manufacturing
  • Renewable Energy
    • Energy from Biomass
    • Energy from the ocean
    • Geothermal Energy
    • Hydrogen Energy
    • Introduction to Energy Sources
    • Solar Energy
    • Wind Energy
  • Thermodynamics
  • Contact us
  • Toggle search form
  • cisce.org
    CISCE – cisce.org general
  • Types of Pumps
    Types of Pumps – All Types and Subtypes with Description Manufacturing Engineering
  • wheels and tyres
    Wheels and Tyres in Automobile Engineering Automobile Engineering
  • Punjab School Education Board - (PSEB)
    pstet – Punjab State Teacher Eligibility Test general
  • MBBS full form
    MBBS full form – Bachelor of Medicine & Bachelor of Surgery general
  • Leave letter for school
    Leave letter for school general
  • master cylinder in hydraulic braking system
    Brake Master Cylinder – Detailed Working Principle Automobile Engineering
  • DNC - engineering hulk
    What is Direct Numerical Control (DNC) Manufacturing Engineering
  • Mansa Musa
    Mansa Musa – Life & Influence of the Richest King in History general
  • first law of thermodynamics
    LIMITATIONS OF THE FIRST LAW OF THERMODYNAMICS Thermodynamics
  • blackboard keiser
    Blackboard Keiser general
  • Strain Formula
    Strain Formula – Definition, Types, and Applications general
  • What is co prime number
    What is co prime number? general
  • GEOPRESSURIZED HOT DRY ROCK
    GEO-PRESSURIZED HOT DRY ROCK – Energy from Rocks Geothermal Energy
  • VSEPR theory.
    VSEPR theory general
Shear Modulus

Shear modulus – Definition, Formula, Applications & Examples

Posted on April 28, 2023April 28, 2023 By Admin

Table of Contents

  • Definition of Shear Modulus
  • The formula for Shear Modulus
  • Significance of Shear Modulus:
  • Factors Affecting Shear Modulus:
  • Importance and Application of Shear Modulus
  • Shear modulus Examples:

Shear Modulus: Understanding its Definition, Formula, and Importance

The shear modulus is a fundamental physical property that describes a material’s ability to resist deformation in response to applied shear stress. It is also known as the modulus of rigidity, and it is an essential parameter for characterizing the mechanical behavior of solid materials. 

Shear Modulus
Shear Modulus

Definition of Shear Modulus

Shear modulus is defined as the ratio of shear stress to the corresponding shear strain in a material. In simple terms, it is a measure of a material’s resistance to deformation when subjected to an external force. It is denoted by the symbol G and expressed in units of pascals (Pa).

The formula for Shear Modulus

The formula for calculating shear modulus is given by:

G = τ/γ

G =  (F/A)/(Δx/l)

G =  Fl/AΔx

where G is the shear modulus, τ is the applied shear stress, and γ is the resulting shear strain.

where G is the shear modulus, F is the applied force, A is the cross-sectional area of the specimen, Δx is the displacement of the specimen, and l is the length of the specimen.

The unit of shear modulus

The unit of shear modulus is the pascal (Pa), which is equivalent to one newton per square meter (N/m²). The Pascal is a derived unit in the International System of Units (SI), and it is used to express the amount of stress required to produce a given amount of deformation.

Other units that can be used to express shear modulus include pounds per square inch (psi) and gigapascals (GPa). To convert from psi to Pa, you can use the conversion factor 1 psi = 6,894.76 Pa. To convert from GPa to Pa, you can use the conversion factor 1 GPa = 10^9 Pa.

Significance of Shear Modulus:

The shear modulus is a measure of the stiffness of a material when subjected to shear stress. It is an important material property that is used in the design of structural components, such as beams, shafts, and springs. The shear modulus is also used to calculate the shear strain in a material when subjected to shear stress.

The shear modulus is important in the study of elasticity, as it relates to the deformation of a material under shear stress. The shear modulus is related to Young’s modulus, which describes the material’s ability to withstand deformation under tensile or compressive stress.

Factors Affecting Shear Modulus:

The shear modulus of a material depends on various factors, including the material’s composition, structure, and temperature. Some materials, such as metals, have a higher shear modulus than others, such as plastics.

The crystalline structure of a material also affects its shear modulus. Materials with a regular, ordered structure, such as metals, have a higher shear modulus than materials with an amorphous, disordered structure, such as glass.

The temperature of a material also affects its shear modulus. As the temperature increases, the shear modulus of a material decreases. This is due to the increased mobility of the atoms in the material, which reduces its stiffness.

Importance and Application of Shear Modulus

Shear modulus is a critical material property that affects the behavior of materials in many applications. Some of the key areas where shear modulus plays a crucial role are:

1. Structural Engineering: In structural engineering, the shear modulus is used to calculate the shear deformation of beams, columns, and other structural elements. It is essential for designing structures that can withstand the stresses and strains of their intended use.

2. Material Science: In material science, the shear modulus is used to compare the mechanical properties of different materials. It is an important parameter for characterizing the strength and stiffness of materials, and it is often used in material testing and research.

3. Manufacturing: In manufacturing, the shear modulus is used to determine the optimal parameters for shaping and forming materials. By understanding the shear modulus of a material, manufacturers can choose the appropriate tools and techniques for shaping and processing the material.

4. Aerospace: In aerospace applications, the shear modulus is critical for designing components that can withstand the high stresses and strains of flight. It is used to determine the strength and stiffness of materials for use in aircraft structures, engines, and other critical components.

let’s consider an example to illustrate the use of this formula.

Shear modulus Examples:

Question 1. A rectangular block of steel is subjected to a shear stress of 200 MPa. The corresponding shear strain is 0.002. Calculate the shear modulus of the steel.

Solution:

Using the formula above, we can calculate the shear modulus of the steel as follows:

G = τ/γ

G = 200 MPa / 0.002

G = 100,000 MPa

Therefore, the shear modulus of the steel block is 100,000 MPa.

In this example, we have shown how to calculate shear modulus using the relevant formula. It is important to note that the value of shear modulus varies for different materials and can be affected by factors such as temperature, pressure, and composition. Shear modulus is an important property in the study of material science and is used to characterize the behavior of materials under shear stress.

Question 2. Consider a rectangular block made of steel with dimensions of 10 cm x 20 cm x 30 cm. The block is subjected to a shear stress of 200 MPa. Calculate the shear modulus of the steel block.

Solution:

The shear modulus of a material is defined as the ratio of shear stress to shear strain. Therefore, we need to calculate the shear strain in the block to determine the shear modulus. Let us assume that the block is sheared in the x-y plane, as shown in the figure below:

In this case, the shear strain (γ) can be calculated using the formula:

γ = tan θ

where θ is the angle of deformation. In the given figure, θ can be calculated as:

θ = L/h = 20/10 = 2

Therefore, the shear strain can be calculated as:

γ = tan θ = tan 2 = 1.10

Now, we can calculate the shear modulus (G) using the formula:

G = τ/γ

where τ is the shear stress. In this case, τ = 200 MPa. Substituting the values, we get:

G = 200/1.10 = 181.82 MPa

Therefore, the shear modulus of the steel block is 181.82 MPa.

Also, read the spring constant

general

Post navigation

Previous Post: Spring constant – Definition, Unit, Formula & Applications
Next Post: Mechanical Properties of Materials

Related Posts

  • The Enigma of Kohlrausch’s Law and its Contentious History
    Kohlrausch law general
  • Lami's theorem
    Lami’s theorem general
  • Strain Formula
    Strain Formula – Definition, Types, and Applications general
  • BMW configurator
    BMW Configurator: Customizing Your Dream Car general
  • power transistor in power electronics
    Power transistor in power electronics general
  • The White Teak Company
    The White Teak Company general
  • TunerCult
    TunerCult – Your One-Stop-Shop for Car Enthusiasts general
  • Introversion
    Introvert meaning in Hindi general
  • vernier caliper diagram
    Vernier caliper – Diagram, Definition, Types, Uses general
  • Methods to prevent corrosion
    Methods to prevent corrosion – Detailed Overview general
  • ELEMENTARY EDUCATION DIPLOMA (D.El.Ed.)
    d el ed full form general
  • SIM full form
    SIM full form general
  • How to Vote India
    How to Vote India general
  • how many countries in the world
    how many countries in the world? general
  • Cutting plier
    Cutting Plier – Types in detail general

Categories

  • Automobile Engineering (31)
    • Module 1 (12)
      • Clutch (3)
      • Propellar Shaft & Axle (2)
      • Transmission (7)
    • Module 2 (10)
      • Braking System (5)
      • Final Drive and Differential (2)
      • Steering System (3)
    • Module 3 (2)
      • Suspension System (1)
      • Wheels & Tyres (1)
    • Module 4 (6)
      • Automotive Electrical System (6)
  • Computer Engineering (32)
  • Electrical Engineering (6)
  • general (214)
  • Manufacturing Engineering (51)
  • News (1)
  • Renewable sources of Energy (25)
    • Energy from Biomass (6)
    • Geothermal Energy (6)
    • Solar Energy (1)
    • Wind Energy (3)
  • Thermodynamics (8)
  • Universities and Colleges (21)
  • Advantages and disadvantages of Biogas
  • Advantages, disadvantages & application of geothermal energy
  • Magma geothermal energy source
  • Prospects of geothermal energy in India
  • Analysis of Aerodynamic forces acting on windmill blades
  • Basic components of wind energy Turbine
  • Design considerations of horizontal and vertical axis wind machines
  • GEO-PRESSURIZED HOT DRY ROCK – Energy from Rocks
  • SOURCE OF GEOTHERMAL ENERGY
  • Hydrothermal Energy Sources/Resources
  • Biogas generation plants
  • Biomass conversion technologies Noted
  • Biomass Energy – Defenition, Benefits & Working
  • Filling a Biogas Digester for Starting
  • Constructional details of Biogas generation Plant
  • BBA Aviation Course, Fees, Syllabus, Jobs & Scope
  • Top State Universities in Delhi: Ranking, Types, Fees
  • What is UGC (University Grants Commission)?
  • Automobile Clutch | Types | Working | Pros | Cons | Uses
  • Automobile Clutch Friction Materials
  • Sliding mesh Gear Box
  • Constant Mesh Gear Box
  • Synchromesh Gear Box
  • Overdrive in Automobile
  • Hydrodynamic Torque Converter
  • Troubleshooting and remedies of the Transmission system
  • Propeller shafts and universal joints
  • Types of axles in Automobile Engineering
  • Types of Final drive
  • Rear Differential – Construction, Working, Types & Features
  • Mechanical Brakes – Types, working, advantages & disadvantages
  • Hydraulic Brake System – Construction & Working
  • Brake Master Cylinder – Detailed Working Principle
  • Introduction to antilock braking system (ABS)
  • Requirements of Brake System in Automobiles
  • Steering Geometry in Automobile Engineering
  • What is Oversteer and Understeer in Automobile Engineering
  • Cornering power in Automobile
  • Suspension System in Automobile Engineering
  • Wheels and Tyres in Automobile Engineering
  • Starting system in Automobile Engineering
  • Bendix Drive in Automobile Engineering
  • Dynamo – Definition, Construction, & Working
  • Alternator in Automobile Engineering
  • Lead Acid Battery – Construction, Working, Advantages
  • Battery Charging – Methods, Advantages, & Disadvantages
  • Material Removal Techniques in Manufacturing Process
  • What is Computer Numerical Control (CNC)?
  • What is Direct Numerical Control (DNC)
  • Numerical Control (NC) Procedure
  • Numerical Control (NC) Motion Control Systems
  • Mechanical properties of metals
  • Heat-treatment of steel
  • what is Annealing? How it Works
  • What is the hot working and cold working of steel?
  • What are the Materials and Alloys used in Workshop?
  • MAT Entrance Exam 2022 – Everything you need
  • PES University Campus, Fees, Admission, Courses
  • SEBI Grade A Result 2022 – Direct PDF Download
  • Components of the internal combustion engine (IC Engine)
  • LIMITATIONS OF THE FIRST LAW OF THERMODYNAMICS
  • The Law of Conservation of Energy: Everything You Need to Know
  • Ultrasonic Machining
  • The vapor compression refrigeration cycle
  • A Refrigeration cycle operates between a condenser temperature of + 27
  • Types of solar panels – Detailed Article 2023
  • Best courses after computer engineering
  • Gram seed – Rate, Production, Types, Harvesting
  • Types of ovules – Location, Components, Types, fun facts
  • Development of Dicot Embryo
  • Boiler Classification: Types, Components & Applications
  • Application of Zener diode – Advantages, Disadvantages
  • Role of Individuals in the Conservation of natural resources
  • Relationship between linear velocity and angular velocity
  • S.I unit of conductivity
  • Issues In the Design Of The Code Generator
  • Domains of AI (Artificial Intelligence)
  • Cymose Inflorescence
  • Top 10 Engineering Colleges in Hyderabad
  • Charlotte Engineering Early College
  • ISBM College of Engineering Pune
  • Tetravalency: Exploring the Unique Properties of Carbon
  • Dijkstra’s Algorithm – A Detailed Information
  • Microprogramming
  • Floyd Algorithm
  • Operating System Functions
  • Classifications Of DBMS (Database Management System)
  • Types of CSS (Cascading Style Sheet)
  • Diploma in Civil Engineering?
  • What is plain cement concrete (PCC) in foundation construction?
  • Toughest Exam In India
  • Basic School Teaching Course- BSTC
  • pstet – Punjab State Teacher Eligibility Test
  • National Institute of Technology- NIT
  • Intrusion Prevention Systems – (IPS)

Recent Posts

  • Avogadro’s Number: Unlocking the Secrets of the Atomic World
  • Newton’s Second Law: The Foundation of Classical Mechanics
  • Photosynthesis Equation
  • The Volume of a Cone – Formula, Derivation, Application
  • Niche Definition – Importance, Strategy, and more
  • Kinematic Equations – Types, Formula, and Application
  • Mansa Musa – Life & Influence of the Richest King in History
  • Plant cell – Diagram, Working, Types & more
  • Greater than sign (>) with examples
  • Distance Formula – Details, Definition, & Derivation
  • Silver sport transmission – Features, Function, & Location
  • BMW Configurator: Customizing Your Dream Car
  • Mercedes Steering Wheels: Design, and Functionality
  • S 580 Mercedes Sedan: Price, Specifications, & Features
  • 2023 Toyota Camry configurations
  • Startup adjectives – Definition, Importance, & Examples
  • A Guide to Craigslist Wilmington, NC: Unveiling the Details
  • Dinar Recaps: Benefits, Importance, & Risk
  • Mastering Trixie Tongue Tricks: A Comprehensive Guide
  • AARP Games: A Guide to Fun & Brain-Stimulating Entertainment
  • Octordle, or Wordle8: A Fascinating Word Puzzle Game
  • Satyendra Nath Bose: The Father of Bose-Einstein Statistics
  • PM Kisan Yojana – Application Process, Eligibility, Features
  • Shala Darpan: Meaning, features, Registration
  • EPFO (Employee Provident Fund Organization) – Schemes
  • Mental Age Test – Example, Purpose, and Benefits
  • Earth Day – History, Mission, Significance, & Themes
  • IQ Test – Types, Significance, Purpose, & More
  • Personality Tests – Guide to finding your Personality
  • Bubble letters – Meaning, Characteristics, and Uses
  • Mandela Effect – Examples, Impact, & Significance
  • Night Cloaked Deck – Game Strategy, In-depth Explanation
  • Lake Xochimilco: Mexico City’s UNESCO World Heritage Site
  • How to buy Anesthesia Machines – Step by Step
  • Wall Street Institute – Fees, Eligibility, Admission
  • Angel 65 keyboard – Perfect Balance of Style & Functionality
  • Ana Mercedes Hoyos – Death, Art, life, Awards
  • Classification of food – Based on different factors
  • Classification of surveying
  • Structure and function of the ecosystem – In Details 2023
  • Cuevana – Guide to the Popular Online Streaming Platform
  • Omtech Laser – Uses, Materials, Laser Engraving Applications
  • TCS Xplore – Features, Benefits, Courses & Website
  • Red Rocks community college – Fees, Admission, Location
  • Estrella mountain community college
  • University of Georgia – Admission, Location, Fees, & More
  • University of Miami – Fees, Admission, Location & More
  • The University of Idaho – Fees, Admission, Location, & More
  • Walden University – Admission, Fees, and More
  • Southern New Hampshire University (SNHU)
  • Capella University – Fees, Admission, Location, & More
  • Grand Canyon University – Fees, Admission, Location & More
  • Century College – Fees, Admission, Location & More
  • Maryland Lacrosse – Location, Fees, Admission & More
  • Tidewater community college
  • Middle Georgia state university – Fees, Admission, Location
  • Alcorn state university – Fees, Admission, Location & More
  • Emporia State University – Fees, Admission, Courses & more
  • Webber International University – Fees, Admission, Location
  • Rasmussen College – Fees, Location, Admission & More
  • Florida Career College – Admission, Location, Fees & More
  • Columbia Southern University-Adress, fees, Admission & more
  • Athens state university – Location, Financial Aid, Programs
  • Laser etching machine – Parts, Working, Advantages
  • Injection molding machine – Types, Working, Advantages
  • Waterjet machine – Types, Working & Benefits
  • Laser cutting machine – Types, Working, Advantages
  • PLA filament – Types, Properties, Advantages & Disadvantages
  • Laser engraver – Working, Advantages, & Disadvantages
  • Plasma cutter – Working, Pros, Cons & Applications
  • Difference between renewable and nonrenewable resources
  • Types of Valves – use with Advantages and Disadvantages
  • Grinder Machine – Working, Types, Applications, Pros & Cons
  • Punching Machine – Working, Types, and Applications
  • Drill Machine – Working, Types, and Application
  • Press machine – Parts, Types detailed information
  • Cutting Plier – Types in detail
  • What is a Clutch? Its Types, Applications & Working
  • Welding Machine – Types, Benefits, Applications
  • What is the moment of force and its SI unit?
  • Difference between soldering and brazing
  • The least count of a vernier bevel protractor
  • Types of Chips in Metal Cutting
  • Volumetric strain – Definition, Significance & Applications
  • Types of Grinding Machines
  • Methods to prevent corrosion – Detailed Overview
  • Vernier bevel protractor – Working, Accuracy & Applications
  • Principal Stress – Types, significance, & Solved Examples
  • Types of Fasteners – Detailed Classification
  • Safar ki Dua – Travel supplication/invocation
  • Law of gearing – Working, Derivation & Solved Examples
  • Young’s modulus of elasticity – with Solved Examples
  • Milling Cutter – Types & Applications
  • Theories of Failure – Detailed Explanation with Derivation
  • Mechanical Properties of Materials
  • Shear modulus – Definition, Formula, Applications & Examples
  • Spring constant – Definition, Unit, Formula & Applications
  • Parallelogram law of forces – Statement & Derivation
  • Hardness test – Types, Characteristics & Applications
  • Types of Hammers and their uses
  • Types of bolts – Detailed Classification with Parts
  • Welding Defects – Types, Causes, Inspection & Prevention
  • Moment of force – Calculation, Types & Application
  • Types of Metals – Ferrous and Non-Ferrous
  • Emery paper – Types, Grades, Uses & Benefits
  • Perpendicular Axis Theorem – Definition & Application
  • Strain Formula – Definition, Types, and Applications
  • Types of Gears – Detailed Explanation with Applications
  • Try square – Types, Grades, Accuracy, & Applications
  • Drill bit – Types, Parts, and different sizes
  • NetSuite CRM – Features, Benefits & Disadvantages
  • TunerCult – Your One-Stop-Shop for Car Enthusiasts
  • Manganato – Your Ultimate Source for Mangalife
  • Types of Pumps – All Types and Subtypes with Description
  • Carnot Cycle – Process, Definition & Applications
  • Venturi meter – Working Principle, Construction,
  • Manometer – Definition, Types & Working Principle
  • Types of Welding – Advantages, disadvantages & Applications
  • Dell Premier – features, advantages, disadvantages
  • C operators – All 7 types with detailed explanations
  • Types of Final drive in automobile engineering
    Types of Final drive Automobile Engineering
  • Dol starter
    Dol starter general
  • Mansa Musa
    Mansa Musa – Life & Influence of the Richest King in History general
  • Photosynthesis equation
    Photosynthesis Equation general
  • biopia
    Byopia/biopia general
  • Vera Gedroits
    Vera Gedroits general
  • Plant cell
    Plant cell – Diagram, Working, Types & more general
  • JEE main exam
    JEE main exam 2023 – Detailed overview general
  • Phoenix Classroom
    Phoenix Classroom – key Features, Advantages, Applications general
  • Charlotte Engineering Early College
    Charlotte Engineering Early College general
  • Plaster of Paris formula
    Plaster of Paris formula general
  • xnxp personality traits
    XNXP Personality Traits – 2021, 2022, 2023 Detailed overview general
  • keep-it-up
    Keep it up meaning in Hindi general
  • fastest century in t20
    The Fastest Century in T20: Record That Continues to Impress general
  • isomers of pentane
    Isomers of pentane general

Privacy Policy

Cookie Policy

About us

Contact us

Careers

Copyright © 2023 EngineeringHulk.

Powered by PressBook News WordPress theme