1. When a force is applied to a body, it causes the body to deform or change shape. This deformation is called strain. Direct stress is calculated as the applied force divided by the cross-sectional area.
2. Materials deform both elastically and plastically when stressed. Elastic deformation is reversible but plastic deformation causes a permanent change in shape. Hooke's law describes the linear elastic behavior of many materials, where stress is directly proportional to strain up to the elastic limit.
3. Thermal expansion and contraction can induce stress in materials as temperature changes unless deformation is unconstrained. The total strain is the sum of strain due to stress and strain due to temperature changes.
This document provides an overview of topics related to simple stresses and strains, including:
- Types of stresses and strains such as tensile, compressive, direct stress, and direct strain.
- Hooke's law and how stress is proportional to strain below the material's yield point.
- Stress-strain diagrams and key points such as the elastic region, yield point, and fracture point.
- Definitions of terms like working stress, factor of safety, Poisson's ratio, and elastic moduli.
- Examples of problems calculating stresses, strains, extensions, and deformations of simple structural members under various loads.
This document provides information about shear stress and shear force in structural elements like beams. It defines shear stress and explains how to calculate it. It discusses the distribution of shear stress across different cross section shapes, including rectangular, circular, T-sections, and wide flange sections. It also describes how shear stress affects steel and concrete materials and what reinforcement is used to address problems caused by shear stresses.
The document discusses various types of loading on structural members including pure bending, eccentric axial loading, and transverse loading. It covers bending deformations, strain and stress due to bending, section properties, and examples of bending stresses in composite and reinforced concrete beams. Plastic deformations in members made of elastic-plastic materials are also examined.
The document discusses Deepak's academic and professional background, including an MBA from IE Business School in Spain and experience founding perfectbazaar.com. It also provides an overview of the topics to be covered in the Strength of Materials course, such as stresses, strains, Hooke's law, and analysis of bars with varying cross-sections. The grading policy and syllabus are outlined which divide the course into 5 units covering various strength of materials concepts.
1. The document discusses various types of mechanical loading and stresses including tensile, compressive, shear, bending, and torsional stresses.
2. It describes different types of strains and properties of materials like elasticity, plasticity, ductility. Hooke's law and relationships between stress and strain are explained.
3. Methods for analyzing stresses in machine components subjected to combinations of loads are presented, including principal stresses, Mohr's circle, and thermal stresses. Bending stresses and shear stresses are analyzed for beams under different support conditions.
1. When a force is applied to a body, it causes the body to deform or change shape. This deformation is called strain. Direct stress is calculated as the applied force divided by the cross-sectional area.
2. Materials deform both elastically and plastically when stressed. Elastic deformation is reversible but plastic deformation causes a permanent change in shape. Hooke's law describes the linear elastic behavior of many materials, where stress is directly proportional to strain up to the elastic limit.
3. Thermal expansion and contraction can induce stress in materials as temperature changes unless deformation is unconstrained. The total strain is the sum of strain due to stress and strain due to temperature changes.
This document provides an overview of topics related to simple stresses and strains, including:
- Types of stresses and strains such as tensile, compressive, direct stress, and direct strain.
- Hooke's law and how stress is proportional to strain below the material's yield point.
- Stress-strain diagrams and key points such as the elastic region, yield point, and fracture point.
- Definitions of terms like working stress, factor of safety, Poisson's ratio, and elastic moduli.
- Examples of problems calculating stresses, strains, extensions, and deformations of simple structural members under various loads.
This document provides information about shear stress and shear force in structural elements like beams. It defines shear stress and explains how to calculate it. It discusses the distribution of shear stress across different cross section shapes, including rectangular, circular, T-sections, and wide flange sections. It also describes how shear stress affects steel and concrete materials and what reinforcement is used to address problems caused by shear stresses.
The document discusses various types of loading on structural members including pure bending, eccentric axial loading, and transverse loading. It covers bending deformations, strain and stress due to bending, section properties, and examples of bending stresses in composite and reinforced concrete beams. Plastic deformations in members made of elastic-plastic materials are also examined.
The document discusses Deepak's academic and professional background, including an MBA from IE Business School in Spain and experience founding perfectbazaar.com. It also provides an overview of the topics to be covered in the Strength of Materials course, such as stresses, strains, Hooke's law, and analysis of bars with varying cross-sections. The grading policy and syllabus are outlined which divide the course into 5 units covering various strength of materials concepts.
1. The document discusses various types of mechanical loading and stresses including tensile, compressive, shear, bending, and torsional stresses.
2. It describes different types of strains and properties of materials like elasticity, plasticity, ductility. Hooke's law and relationships between stress and strain are explained.
3. Methods for analyzing stresses in machine components subjected to combinations of loads are presented, including principal stresses, Mohr's circle, and thermal stresses. Bending stresses and shear stresses are analyzed for beams under different support conditions.
This document outlines an introduction to strength of materials course taught by Dr. Dawood S. Atrushi. The course covers topics such as simple stress and strain, shear force and bending moment diagrams, stresses in beams, and torsion. It discusses how strength of materials relates to other areas of mechanics and engineering. The course aims to help students understand how different forces affect structural components and materials, and analyze stresses and deformations. SI units and concepts like stress, internal forces, and free-body diagrams are also introduced.
This document discusses key concepts in strength of materials including stress, strain, true stress and strain, stress-strain curves, tensile and compressive stress, lateral and volumetric strain, Poisson's ratio, Young's modulus, modulus of rigidity, ductile and brittle materials. Some key points covered are:
- True stress is calculated based on the instantaneous area during loading while engineering stress uses the original area.
- Stress-strain curves relate the stress and strain in a material.
- Ductile materials exhibit a large percentage of elongation before failure while brittle materials break suddenly with little yielding.
- Properties like Young's modulus, shear modulus, and Poisson's ratio describe a material's elastic properties
ppt about simple stress and strains. use full for B.E. in 3 semester. all content of chapter are covered in this ppt. i hope this is useful fore some peoples.if you like then plz click lick.
Loads can be tensile (pulling) or compressive (pushing) forces. Common types of loads include dead loads from structural weight, live loads from moving objects, impact loads from vibrations, and cyclic loads from repeated forces. When loads are applied, they cause stress in materials. Stress is the internal resisting force per unit area. Stresses can be tensile (pulling), compressive (pushing), or shear (tangential). Corresponding strains are the changes in dimensions from stresses. Hooke's law states that within the elastic limit, stress is proportional to strain by a constant modulus of elasticity.
The document discusses stress and strain under axial loading. It covers topics such as normal strain, stress-strain diagrams, Hooke's law, elastic and plastic behavior, fatigue, deformations under axial loading, static indeterminacy, thermal stresses, Poisson's ratio, generalized Hooke's law, shear strain, relations among elastic properties, composite materials, stress concentrations, and examples.
This document provides information about a Mechanics of Materials course, including:
- The instructor's name and credentials.
- An overview of course contents including stresses, strains, torsion, bending, centroids, and beam deflection methods.
- An introduction to mechanics of materials and the objectives to analyze stresses, strains, and displacements in structures.
- Key terms like stress, strain, axial force, normal force, shear force, deformation, prismatic and non-prismatic bars are defined.
- The stress-strain diagram is discussed and key points like the elastic region, proportional limit, yield point, strain hardening, ultimate stress, and necking are explained.
Lecture 9 shear force and bending moment in beamsDeepak Agarwal
The document discusses stresses in beams. It covers topics like shear force and bending moment diagrams, bending stresses, shear stresses, deflection, and torsion. Beams are structural members subjected to transverse forces that induce bending. Stresses and strains are created within beams when loaded. Shear forces and bending moments allow determining these internal stresses and maintaining equilibrium. Formulas are provided for calculating shear forces and bending moments in different beam configurations like cantilevers, simply supported beams, and beams with various load types.
This document provides an introduction and overview of mechanics of materials. It defines key terms like stress, strain, normal stress, shear stress, factor of safety, and allowable stress. It also gives examples of calculating stresses in structural members subjected to various loads. The document is an introductory reading for a mechanics of materials course that will analyze the relationship between external forces and internal stresses and strains in structural elements.
The document discusses bending stresses in beams. It describes how bending stresses are developed in beams to resist bending moments and shearing forces. The theory of pure bending is introduced, where only bending stresses are considered without the effect of shear. Equations for calculating bending stresses are derived based on the beam's moment of inertia, bending moment, and distance from the neutral axis. Several beam cross-section examples are provided to demonstrate how to calculate the maximum bending stress and section modulus.
This document discusses torsional stress and its effects on beams and circular shafts. It makes the following key points:
1. Torsional stress is the shear stress developed in a material subjected to a twisting torque, and is highest at the outermost parts of the material furthest from the central axis.
2. Cracks form under torsional stress and initially appear at the middle of the longest side of a beam, then the shortest side, before circulating around the beam's periphery.
3. Failure of brittle materials under pure torsion occurs along planes inclined to the beam axis, not perpendicular, due to elastic theory principles.
The document provides an overview of mechanics of materials concepts related to torsion, including:
- Torsion causes shearing stresses that vary linearly from zero at the center to a maximum at the surface for circular shafts.
- Torsion can cause both shearing stresses and normal stresses depending on the orientation of the material element.
- Ductile materials fail in shear while brittle materials fail in tension when subjected to torsion.
- The angle of twist is proportional to the applied torque, material properties, and shaft length based on elastic torsion formulas.
- Stress concentrations can occur due to geometric discontinuities and influence the maximum shearing stress.
Strength of Materials, Lecture - 1.
Introduction + Recommended Books
Mehran University of Engineering and Technology.
Department of Mechanical Engineering.
1. The document defines static load, failure, material strength properties including yield strength and ultimate strength in tension and compression.
2. It describes ductile materials as deforming significantly before fracturing, while brittle materials yield very little before fracturing and have similar yield and ultimate strengths.
3. The maximum shear stress theory and distortion energy theory are introduced as failure theories used in design based on yield strength and ultimate strength respectively. Safety factors are used to avoid failure based on these theories.
- The document defines concepts related to forces, stress, strain and elasticity. It also discusses shear force, bending moment, and torsion.
- Examples are provided for drawing shear force and bending moment diagrams for cantilever beams and simply supported beams under different loading conditions like point loads, uniformly distributed loads.
- The key steps involve calculating reactions, determining shear force and bending moment values at different points, and plotting them on diagrams to understand their variations along the beam.
The document discusses different types of stresses and strains experienced by materials. It defines normal stress as stress perpendicular to the resisting area, with tensile and compressive stresses elongating and shortening materials. Combined stress includes shear and torsional stresses from parallel forces. Strain is defined as the change in dimension due to an applied force. The stress-strain diagram is then explained, showing the material's behavior from the proportional limit through yielding and strain hardening until ultimate failure. Key points on the curve include the proportionality limit, elastic limit, yield points, and ultimate stress.
This document provides information about shear stresses and shear force in structures. It includes:
- Definitions of shear force and shear stress. Shear force is an unbalanced force parallel to a cross-section, and shear stress develops to resist the shear force.
- Explanations of horizontal and vertical shear stresses that develop in beams due to bending moments. Shear stress is highest at the neutral axis and reduces towards the top and bottom of the beam cross-section.
- Derivations of formulas for calculating shear stress across different beam cross-sections. Shear stress is directly proportional to the shear force and beam geometry.
- Examples of calculating maximum and average shear stresses for various cross-sections
1. The document discusses structures, loads, stresses, strains and material properties related to mechanics of materials.
2. It defines key terms like stress, strain, elastic modulus and explains stress-strain relationships. Common stress types like tensile, compressive, shear and their effects are described.
3. Examples of different structures like cylinders, spheres, arches, towers and bridges are provided to illustrate stress distributions and effects of loads. Material properties of common materials are also listed.
This document provides information about the Solid Mechanics course ME 302 taught by Dr. Nirmal Baran Hui at NIT Durgapur in West Bengal, India. It lists four required textbooks for the course and provides a detailed syllabus covering topics like stress, strain, elasticity, bending, deflection, columns, torsion, pressure vessels, combined loadings, springs, and failure theories. The document also includes examples of lecture content on stress analysis, stresses on oblique planes, and material subjected to pure shear.
This document discusses the basics of strength of materials. It defines solid mechanics as the branch of mechanics dealing with the behavior of solid materials under external forces or internal forces caused by temperature changes, phase changes, or other agents. It describes several key mechanical properties of materials including ductility, hardness, impact resistance, plasticity, fracture toughness, elasticity, endurance strength, creep resistance, and more. It also defines stress, strain, and explains Hooke's law relating stress and strain within a material's elastic limit according to its modulus of elasticity.
The document discusses stress and strain in engineering structures. It defines load, stress, strain and different types of each. Stress is the internal resisting force per unit area within a loaded component. Strain is the ratio of dimensional change to original dimension of a loaded body. Loads can be tensile, compressive or shear. Hooke's law states stress is proportional to strain within the elastic limit. The elastic modulus defines this proportionality. A tensile test measures the stress-strain curve, identifying elastic limit and other failure points. Multi-axial stress-strain relationships follow Poisson's ratio definitions.
This document provides an overview of simple stress and strain concepts. It defines load, stress, strain, Hooke's law, elastic moduli, stress-strain curves, and analyses of bars with varying cross-sections, tapered sections, and composite sections. Key points include: load is defined as external forces on a structure; stress is the internal resisting force per unit area; strain is the ratio of dimensional change to original dimension; Hooke's law states stress is proportional to strain within the elastic limit; and stress-strain curves from tensile tests show elastic and plastic deformation regions.
This document outlines an introduction to strength of materials course taught by Dr. Dawood S. Atrushi. The course covers topics such as simple stress and strain, shear force and bending moment diagrams, stresses in beams, and torsion. It discusses how strength of materials relates to other areas of mechanics and engineering. The course aims to help students understand how different forces affect structural components and materials, and analyze stresses and deformations. SI units and concepts like stress, internal forces, and free-body diagrams are also introduced.
This document discusses key concepts in strength of materials including stress, strain, true stress and strain, stress-strain curves, tensile and compressive stress, lateral and volumetric strain, Poisson's ratio, Young's modulus, modulus of rigidity, ductile and brittle materials. Some key points covered are:
- True stress is calculated based on the instantaneous area during loading while engineering stress uses the original area.
- Stress-strain curves relate the stress and strain in a material.
- Ductile materials exhibit a large percentage of elongation before failure while brittle materials break suddenly with little yielding.
- Properties like Young's modulus, shear modulus, and Poisson's ratio describe a material's elastic properties
ppt about simple stress and strains. use full for B.E. in 3 semester. all content of chapter are covered in this ppt. i hope this is useful fore some peoples.if you like then plz click lick.
Loads can be tensile (pulling) or compressive (pushing) forces. Common types of loads include dead loads from structural weight, live loads from moving objects, impact loads from vibrations, and cyclic loads from repeated forces. When loads are applied, they cause stress in materials. Stress is the internal resisting force per unit area. Stresses can be tensile (pulling), compressive (pushing), or shear (tangential). Corresponding strains are the changes in dimensions from stresses. Hooke's law states that within the elastic limit, stress is proportional to strain by a constant modulus of elasticity.
The document discusses stress and strain under axial loading. It covers topics such as normal strain, stress-strain diagrams, Hooke's law, elastic and plastic behavior, fatigue, deformations under axial loading, static indeterminacy, thermal stresses, Poisson's ratio, generalized Hooke's law, shear strain, relations among elastic properties, composite materials, stress concentrations, and examples.
This document provides information about a Mechanics of Materials course, including:
- The instructor's name and credentials.
- An overview of course contents including stresses, strains, torsion, bending, centroids, and beam deflection methods.
- An introduction to mechanics of materials and the objectives to analyze stresses, strains, and displacements in structures.
- Key terms like stress, strain, axial force, normal force, shear force, deformation, prismatic and non-prismatic bars are defined.
- The stress-strain diagram is discussed and key points like the elastic region, proportional limit, yield point, strain hardening, ultimate stress, and necking are explained.
Lecture 9 shear force and bending moment in beamsDeepak Agarwal
The document discusses stresses in beams. It covers topics like shear force and bending moment diagrams, bending stresses, shear stresses, deflection, and torsion. Beams are structural members subjected to transverse forces that induce bending. Stresses and strains are created within beams when loaded. Shear forces and bending moments allow determining these internal stresses and maintaining equilibrium. Formulas are provided for calculating shear forces and bending moments in different beam configurations like cantilevers, simply supported beams, and beams with various load types.
This document provides an introduction and overview of mechanics of materials. It defines key terms like stress, strain, normal stress, shear stress, factor of safety, and allowable stress. It also gives examples of calculating stresses in structural members subjected to various loads. The document is an introductory reading for a mechanics of materials course that will analyze the relationship between external forces and internal stresses and strains in structural elements.
The document discusses bending stresses in beams. It describes how bending stresses are developed in beams to resist bending moments and shearing forces. The theory of pure bending is introduced, where only bending stresses are considered without the effect of shear. Equations for calculating bending stresses are derived based on the beam's moment of inertia, bending moment, and distance from the neutral axis. Several beam cross-section examples are provided to demonstrate how to calculate the maximum bending stress and section modulus.
This document discusses torsional stress and its effects on beams and circular shafts. It makes the following key points:
1. Torsional stress is the shear stress developed in a material subjected to a twisting torque, and is highest at the outermost parts of the material furthest from the central axis.
2. Cracks form under torsional stress and initially appear at the middle of the longest side of a beam, then the shortest side, before circulating around the beam's periphery.
3. Failure of brittle materials under pure torsion occurs along planes inclined to the beam axis, not perpendicular, due to elastic theory principles.
The document provides an overview of mechanics of materials concepts related to torsion, including:
- Torsion causes shearing stresses that vary linearly from zero at the center to a maximum at the surface for circular shafts.
- Torsion can cause both shearing stresses and normal stresses depending on the orientation of the material element.
- Ductile materials fail in shear while brittle materials fail in tension when subjected to torsion.
- The angle of twist is proportional to the applied torque, material properties, and shaft length based on elastic torsion formulas.
- Stress concentrations can occur due to geometric discontinuities and influence the maximum shearing stress.
Strength of Materials, Lecture - 1.
Introduction + Recommended Books
Mehran University of Engineering and Technology.
Department of Mechanical Engineering.
1. The document defines static load, failure, material strength properties including yield strength and ultimate strength in tension and compression.
2. It describes ductile materials as deforming significantly before fracturing, while brittle materials yield very little before fracturing and have similar yield and ultimate strengths.
3. The maximum shear stress theory and distortion energy theory are introduced as failure theories used in design based on yield strength and ultimate strength respectively. Safety factors are used to avoid failure based on these theories.
- The document defines concepts related to forces, stress, strain and elasticity. It also discusses shear force, bending moment, and torsion.
- Examples are provided for drawing shear force and bending moment diagrams for cantilever beams and simply supported beams under different loading conditions like point loads, uniformly distributed loads.
- The key steps involve calculating reactions, determining shear force and bending moment values at different points, and plotting them on diagrams to understand their variations along the beam.
The document discusses different types of stresses and strains experienced by materials. It defines normal stress as stress perpendicular to the resisting area, with tensile and compressive stresses elongating and shortening materials. Combined stress includes shear and torsional stresses from parallel forces. Strain is defined as the change in dimension due to an applied force. The stress-strain diagram is then explained, showing the material's behavior from the proportional limit through yielding and strain hardening until ultimate failure. Key points on the curve include the proportionality limit, elastic limit, yield points, and ultimate stress.
This document provides information about shear stresses and shear force in structures. It includes:
- Definitions of shear force and shear stress. Shear force is an unbalanced force parallel to a cross-section, and shear stress develops to resist the shear force.
- Explanations of horizontal and vertical shear stresses that develop in beams due to bending moments. Shear stress is highest at the neutral axis and reduces towards the top and bottom of the beam cross-section.
- Derivations of formulas for calculating shear stress across different beam cross-sections. Shear stress is directly proportional to the shear force and beam geometry.
- Examples of calculating maximum and average shear stresses for various cross-sections
1. The document discusses structures, loads, stresses, strains and material properties related to mechanics of materials.
2. It defines key terms like stress, strain, elastic modulus and explains stress-strain relationships. Common stress types like tensile, compressive, shear and their effects are described.
3. Examples of different structures like cylinders, spheres, arches, towers and bridges are provided to illustrate stress distributions and effects of loads. Material properties of common materials are also listed.
This document provides information about the Solid Mechanics course ME 302 taught by Dr. Nirmal Baran Hui at NIT Durgapur in West Bengal, India. It lists four required textbooks for the course and provides a detailed syllabus covering topics like stress, strain, elasticity, bending, deflection, columns, torsion, pressure vessels, combined loadings, springs, and failure theories. The document also includes examples of lecture content on stress analysis, stresses on oblique planes, and material subjected to pure shear.
This document discusses the basics of strength of materials. It defines solid mechanics as the branch of mechanics dealing with the behavior of solid materials under external forces or internal forces caused by temperature changes, phase changes, or other agents. It describes several key mechanical properties of materials including ductility, hardness, impact resistance, plasticity, fracture toughness, elasticity, endurance strength, creep resistance, and more. It also defines stress, strain, and explains Hooke's law relating stress and strain within a material's elastic limit according to its modulus of elasticity.
The document discusses stress and strain in engineering structures. It defines load, stress, strain and different types of each. Stress is the internal resisting force per unit area within a loaded component. Strain is the ratio of dimensional change to original dimension of a loaded body. Loads can be tensile, compressive or shear. Hooke's law states stress is proportional to strain within the elastic limit. The elastic modulus defines this proportionality. A tensile test measures the stress-strain curve, identifying elastic limit and other failure points. Multi-axial stress-strain relationships follow Poisson's ratio definitions.
This document provides an overview of simple stress and strain concepts. It defines load, stress, strain, Hooke's law, elastic moduli, stress-strain curves, and analyses of bars with varying cross-sections, tapered sections, and composite sections. Key points include: load is defined as external forces on a structure; stress is the internal resisting force per unit area; strain is the ratio of dimensional change to original dimension; Hooke's law states stress is proportional to strain within the elastic limit; and stress-strain curves from tensile tests show elastic and plastic deformation regions.
1. The document defines key terms related to loads, stresses, strains, and elastic behavior of materials. It describes different types of loads, stresses, strains and their relationships based on Hooke's law.
2. Formulas are provided for calculating tensile stress, compressive stress, shear stress, elastic modulus, and deformation of tapered and composite bars.
3. The principles of superposition and self-weight induced stresses in cantilever beams are also summarized.
Strength of Materials also called mechanics of materials, is a subject which deals with behavior of solid objects subjected to stresses and strains.
The Strength of Materials is subject, which refers to various methods for calculating the stresses and strains in structural members such as beams, columns and shafts. The methods employed to predict the response of structure under loading.
The document defines key terms related to stress and strain in engineering structures:
1. Load is defined as external forces acting on a structure from service conditions. Common loads are tension and compression. Tension applies a direct pull while compression applies a direct push.
2. Stress is the internal resisting force per unit area within a material when an external force is applied. Strain is the ratio of dimensional change in a material to its original dimension under an applied force.
3. There are different types of stress, including normal stress (perpendicular to the area) and shear stress. Normal stress is further divided into tensile stress (tends to increase length) and compressive stress (tends to decrease length
- Stress is defined as the resistance force acting per unit cross-section area of a body. It is calculated as the applied load divided by the cross-sectional area.
- The main types of stress are normal stress, shear stress, tensile stress, and compressive stress. Tensile stress results from pulling forces, while compressive stress is from pushing forces.
- Shear stress acts tangentially across a surface. Elasticity refers to a material's ability to deform under stress but return to its original shape when the stress is removed, as described by Hooke's law.
This document discusses different types of stresses:
1. Stress is defined as the internal resisting force per unit area within a material subjected to an external force. Different types of stresses include normal stress, shear stress, tensile stress, compressive stress, bending shear stress, and torsional shear stress.
2. Tensile stress acts normal to the area and pulls on the area, while compressive stress pushes on the area. Shear stress induces a tendency for a material to shear off across a resisting section when subjected to opposing tangential forces.
3. Bending shear stress results when a beam experiences loading, producing compressive stress on the top fibers and tensile stress on the bottom fibers that varies linearly
This document provides information on stress, strain, elasticity, Hooke's law, and other fundamental concepts in strength of materials. Some key points:
- Stress is defined as the internal resisting force per unit area within a material when subjected to external forces. It is proportional to applied load and inversely proportional to cross-sectional area.
- Strain is the ratio of deformation to original dimension of a material. There are different types including tensile, compressive, and shear strains.
- Hooke's law states that within the elastic limit, stress is proportional to strain. The proportionality constant is known as modulus of elasticity.
- Materials behave elastically and return to their original shape when
This document provides an overview of fundamental mechanical engineering concepts including stress, strain, Hooke's law, stress-strain diagrams, elastic constants, and mechanical properties. It defines stress as force per unit area and strain as the deformation of a material from stress. Hooke's law states that stress is directly proportional to strain within the elastic limit. Stress-strain diagrams are presented for ductile and brittle materials. Key elastic constants like Young's modulus, shear modulus, and Poisson's ratio are defined along with their relationships. Mechanical properties of materials like elasticity, plasticity, ductility, strength, brittleness, toughness, hardness, and stiffness are also summarized.
This document provides an overview of fundamental mechanical engineering concepts including stress, strain, Hooke's law, stress-strain diagrams, and elastic properties of materials. Key points include:
- Stress is defined as force per unit area. Normal stress acts perpendicular to the area while shear stress acts tangentially.
- Strain is the deformation from applied stress. Tensile and compressive strains refer to changes in length while shear and volumetric strains refer to other types of deformations.
- Hooke's law states that stress is directly proportional to strain within the elastic limit. The modulus of elasticity is the constant of proportionality.
- Stress-strain diagrams graphically show the relationship between stress and strain
This document is a presentation on stress and strain analysis given by Mr. Oduor Wafulah. It defines stress and strain, discusses related terminology, and outlines the different types of stress and strain. It also covers Hooke's law, which states that stress is proportional to strain, and stress-strain diagrams. Factors like elasticity, elastic limits, and modulus of elasticity are examined in relation to the stress-strain relationship. Beams theory and the theories of Timoshenko and torsion are also briefly introduced.
Basic mechanical engineering (BMET-101/102) unit 5 part-1 simple stress and ...Varun Pratap Singh
Download Link: https://sites.google.com/view/varunpratapsingh/teaching-engagements
UNIT-5
Stress and Strain Analysis Simple stress and strain: Introduction, Normal shear stresses, Stress-strain diagrams for ductile and brittle materials, Elastic constants, One dimensional loading of members of varying cross section, Strain energy, Thermal stresses.
Compound stress and strains: Introduction, State of plane stress, Principal stress and strain, Mohr’s circle for stress and strain.
Pure Bending of Beams: Introduction, Simple bending theory, Stress in beams of different cross sections.
Torsion: Introduction, Torsion of Shafts of circular section, Torque and Twist, Shear stress due to Torque.
1) Materials deform when stressed, returning to original shape within the elastic limit. Beyond this, deformation is permanent.
2) Hooke's law describes the linear relationship between stress and strain within the elastic limit. The slope is Young's modulus, a measure of stiffness.
3) Poisson's ratio defines the lateral contraction that occurs when a material is stretched. Most materials contract laterally to some degree.
Machine elements are basic mechanical components that are combined to form machines. They experience various stresses from forces like loads, temperature changes, and vibrations. Stresses produce strains in the elements. The relationship between stress and strain is linear within the elastic limit according to Hooke's law. Different types of stresses like tensile, compressive, shear, and bearing are discussed along with the corresponding strains. Material properties important for design like modulus of elasticity, Poisson's ratio, and stress-strain diagrams are also introduced. Factors to consider for selecting appropriate materials and factors of safety for machine elements are outlined.
This document discusses key concepts in strength of materials and engineering basics. It defines stress as the force per unit area on a material, and strain as the deformation or change in shape of a material under stress. The document outlines different types of stresses like tensile, compressive, and shear stress and the corresponding strains. It also discusses stress-strain curves and elastic properties like Young's modulus and Poisson's ratio. Finally, it covers topics like types of beams, loads, mechanical properties and more.
This document discusses key concepts in strength of materials and engineering basics. It defines stress as the force per unit area on a material, and strain as the deformation or change in shape of a material under stress. The document outlines different types of stresses like tensile, compressive, and shear stress and the corresponding strains. It also discusses stress-strain curves and elastic properties like Young's modulus and Poisson's ratio. Finally, it covers types of beams, loads, and mechanical properties of materials.
- Stress is the internal resisting force per unit area caused by external forces. It is measured in units of pressure like Pa or MPa. Strain is the deformation per original length and is dimensionless.
- Hooke's law states that deformation is directly proportional to applied force. The constant of proportionality is the modulus of elasticity E. A graph of stress vs strain results in a straight line with slope E.
- Materials have a maximum stress level before breaking called the ultimate tensile stress. Shear stress is caused by sideways forces and measured as force per unit area. Shear strain is the ratio of deformation to original height for small angles. The modulus of rigidity G defines the relationship between shear
The document discusses stress and strain in materials. It introduces the key concepts of normal stress, shear stress, bearing stress, and thermal stress. Normal stress acts perpendicular to a cross-section, shear stress acts tangentially, and bearing stress occurs at contact points. The relationships between stress, strain, elastic modulus, and Poisson's ratio are explained. Methods for calculating stress and strain in axial loading, torsion, bending and combined loading are presented through examples. The stress-strain diagram is discussed to show material properties like yield strength and ductility.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapte...University of Maribor
Slides from talk presenting:
Aleš Zamuda: Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapter and Networking.
Presentation at IcETRAN 2024 session:
"Inter-Society Networking Panel GRSS/MTT-S/CIS
Panel Session: Promoting Connection and Cooperation"
IEEE Slovenia GRSS
IEEE Serbia and Montenegro MTT-S
IEEE Slovenia CIS
11TH INTERNATIONAL CONFERENCE ON ELECTRICAL, ELECTRONIC AND COMPUTING ENGINEERING
3-6 June 2024, Niš, Serbia
2. 1.1 LOAD
Load is defined as the set of external forces
acting on a mechanism or engineering structure
which arise from service conditions in which the
components work
Common loads in engineering applications are
tension and compression
Tension:- Direct pull. Eg:Force present in lifting
hoist
Compression:- Direct push. Eg:- Force acting on
the pillar of a building
Sign convention followed: Tensile forces are
positive and compressive negative
3. 1.1.1TYPES OF LOAD
There are a number of different ways in which
load can be applied to a member. Typical loading
types are:
A) Dead/ Static load- Non fluctuating forces
generally caused by gravity
B) Live load- Load due to dynamic effect. Load
exerted by a lorry on a bridge
C) Impact load or shock load- Due to sudden
blows
D) Fatigue or fluctuating or alternating loads:
Magnitude and sign of the forces changing with
time
4. 1.2 STRESS
When a material is subjected to an external force,
a resisting force is set up within the component,
this internal resistance force per unit area is
called stress. SI unit is N/m²(Pa). 1kPa=1000Pa,
1MPa=10^6 Pa, 1 Gpa=10^9Pa, 1 Terra
Pascal=10^12 Pa
In engineering applications, we use the
the original cross section area of the specimen
and it is known as conventional stress or
Engineering stress
5. 1.3 STRAIN
When a body is subjected to some external force,
there is some change of dimension of the body. The
ratio of change of dimension of the body to its original
dimension is known as strain
Strain is a dimensionless quantity
Strain may be:- a) Tensile strain b) Compressive
strain c) Volumetric strain d) Shear strain
Tensile strain- Ratio of increase in length to original
length of the body when it is subjected to a pull force
Compressive strain- Ratio of decrease in length to
original length of the body when it is subjected to a
push force
Volumetric strain- Ratio of change of volume of the
body to the original volume
Shear strain-Strain due to shear stress
7. 1.4.1TYPES OF DIRECT
STRESS
Direct stress may be normal stress or shear
stress
Normal stress (σ) is the stress which acts in
direction perpendicular to the area. Normal stress
is further classified into tensile stress
Tensile stress is the stress induced in a body,
when it is subjected to two equal and opposite
pulls (tensile forces) as a result of which there is a
tendency in increase in length
It acts normal to the area and pulls on the area
8. 1.4.1 TYPES OF DIRECT STRESS
(Tensile stress)
Consider a bar subjected to a tensile force P at its
ends. Let
A= Cross sectional area of the body
L=Original length of the body
dL= Increase in length of the body due to its pull
P
σ= Stress induced in the body
e= Tensile strain
Consider a section X-X which divides the body into
two halves
9. 1.4.1 TYPES OF DIRECT STRESS
(Tensile stress)
The left part of the section x-x, will be in
equilibrium if P=R (Resisting force). Similarly the
right part of the section x-x will be in equilibrium if
P=R (Resisting force)
10. 1.4.1 TYPES OF DIRECT STRESS
(Tensile stress)
Tensile stress (σ)= Resisting force/ Cross sectional
area= Applied force/Cross sectional area=P/A
Tensile strain= Increase in length/Original length= dL/L
Compressive stress:- Stress induced in a body, when
subjected to two equal and opposite pushes as a
result of which there is a tendency of decrease in
length of the body
It acts normal to the area and it pushes on the area
In some cases the loading situation is such that the
stress will vary across any given section. In such
cases the stress at any given point is given by
σ= Lt ΔA 0 ΔP/ ΔA= dP/dA= derivative of force w.r.t
area
11. 1.4.1 TYPES OF DIRECT STRESS
(Compressive stress)
Compressive stress=Resisting force/ cross sectional
area= Applied force/ cross sectional area
Compressive strain= Decrease in length/ Original length= -
dL/L
Sign convention for direct stress and strain:- Tensile
stresses and strains are considered positive in sense
producing an increase in length. Compressive stresses
and strains are considered negative in sense producing
decrease in length
12. 1.4.1 TYPES OF DIRECT STRESS
(Shear stress)
Shear stress :- Stress Induced in a body, when
subjected to two equal and opposite forces which
are acting tangentially across the resisting
section as a result of which the body tends to
shear off across that section
Consider a rectangular block of height h, length L
and width unity. Let the bottom face AB of the
block be fixed to the surface as shown. Let P be
the tangential force applied along top face CD of
the block. For the equilibrium of the block, the
surface AB will offer a tangential reaction force R
which is equal in magnitude and opposite in
direction to the applied tangential force P
13. 1.4.1 TYPES OF DIRECT STRESS
(Shear stress)
Consider a section X-X cut parallel to the applied force
which splits rectangle into two parts
For the upper part to be in equilibrium; Applied force
P=Resisting force R
For the lower part to be in equilibrium; Applied force
P=Resisting force R
Hence, shear stress τ= Resisting force/Resisting area=P/L
x 1=P/L
Shear stress is tangential to the area on which it acts
14. 1.4.1 TYPES OF DIRECT STRESS
(Shear stress)
As the face AB is fixed, the rectangular section ABCD
will be distorted to ABC1D1, such that new vertical
face AD1 makes an angle φ with the initial face AD
Angle φ is called shear strain. As φ is very small,
φ=tan φ=DD1/AD=dl/h
Hence shear strain=dl/h
15. 1.5 ELASTICITY & ELASTIC
LIMIT
The property of a body by virtue of which it undergoes
deformation when subjected to an external force and
regains its original configuration (size and shape)
upon the removal of the deforming external force is
called elasticity.
The stress corresponding to the limiting value of
external force upto and within which the deformation
disappears completely upon the removal of external
force is called elastic limit
A material is said to be elastic if it returns to its
original, unloaded dimensions when load is removed.
If the external force is so large that the stress exceeds
the elastic limit, the material loses to some extent its
property of elasticity. If now the force is removed, the
material will not return to its original shape and size
and there will be a residual deformation in the
material
16. 1.6 HOOKE’S LAW & ELASTIC
MODULI
Hooke’s law states that: “ When a body is loaded
within elastic limit, the stress is proportional to
strain developed” or “Within the elastic limit the
ratio of stress applied to strain developed is a
constant”
The constant is known as Modulus of elasticity or
Elastic modulus or Young’s modulus
Mathematically within elastic limit
Stress/Strain=σ/e=E
σ= P/A; e =ΔL/L
E=PL/A Δ L
17. 1.7 HOOKE’S LAW & ELASTIC
MODULI
Young's modulus (E) is generally assumed to be
the same in tension or compression and for most
of engineering applications has a high numerical
value. Typically, E=210 x 10^9 N/m² (=210 GPa)
for steel
Modulus of rigidity, G= τ/φ= Shear stress/ shear
strain
Factor of safety= Ultimate stress/Permissible
stress
In most engineering applications strains donot
often exceed 0.003 so that the assumption that
deformations are small in relation to orinal
dimensions is generally valid
18. 1.8 STRESS-STRAIN CURVE
(TENSILE TEST)
Standard tensile test involves subjecting a
circular bar of uniform cross section to a gradually
increasing tensile load until the failure occurs
Tensile test is carried out to compare the
strengths of various materials
Change in length of a selected gauge length of
bar is recorded by extensometers
A graph is plotted with load vs extension or stress
vs strain
20. 1.8 STRESS-STRAIN CURVE
(TENSILE TEST DIAGRAM)
A Limit of proportionality; It is the point where the
linear nature of the stress strain graph ceases
B Elastic limit; It is the limiting point for the condition
that material behaves elastically, but hooke's law does
not apply . For most practical purposes it can be often
assumed that limit of proportionality and elastic limits
are the same
Beyond the elastic limits, there will be some
permanent deformation or permanent set when the
load is removed
C (Upper Yield point), D (Lower yield point) Points
after which strain increases without correspondingly
high increase in load or stress
E Ultimate or maximum tensile stress; Point where
the necking starts
F Fracture point
21. 1.9 CONSTITUTIVE
RELATIONSHIPS BETWEEN
STRESS & STRAIN
A) 1-Dimensional case (due to pull or push or shear
force)
σ=Ee
B) 2-Dimensional case
Consider a body of length L, width B and height H. Let
the body be subjected to an axial load. Due to this
axial load, there is a deformation along the length of
the body. This strain corresponding to this
deformation is called longitudinal strain.
Similarly there are deformations along directions
perpendicular to line of application of fore. The strains
corresponding to these deformations are called lateral
strains
23. 1.9 CONSTITUTIVE
RELATIONSHIPS BETWEEN
STRESS & STRAIN
Longitudinal strain is always of opposite sign of
that of lateral strain. Ie if the longitudinal strain is
tensile, lateral strains are compressive and vice
versa
Every longitudinal strain is accompanied by
lateral strains in orthogonal directions
Ratio of lateral strain to longitudinal strain is
called Poisson’s ratio (μ); Mathematically,
μ=-Lateral strain/Longitudinal strain
Consider a rectangular figure ABCD subjected a
stress in σx direction and in σ y direction
24. 1.9 CONSTITUTIVE
RELATIONSHIPS BETWEEN
STRESS & STRAIN
Strain along x direction due to σx= σ x/E
Strain along x direction due to σ y=-μ x σy/E
Total strain in x direction ex= σ x/E - μ x σy/E
Similarly total strain in y direction, ey= σ y/E - μ x
σx/E
In the above equation tensile stresses are
considered as positive and compressive stresses
as negative
C) 3 Dimensional case:-
Consider a 3 D body subjected to 3 orthogonal
normal stresses in x,y and z directions
respectively
25. 1.9 CONSTITUTIVE
RELATIONSHIPS BETWEEN
STRESS & STRAIN
Strain along x direction due to σx= σ x/E
Strain along x direction due to σ y=-μ x σy/E
Strain along x direction due to σ z=-μ x σz/E
Total strain in x direction ex= σ x/E - μ x (σy/E +
σz/E )
Similarly total strain in y direction, ey= σ y/E - μ x
(σxE + σz/E )
Similarly total strain in z direction, ez= σ z/E - μ x
(σxE + σy/E )
26. 1.10 ANALYSIS OF BARS OF
VARYING CROSS SECTION
Consider a bar of different lengths and of different
diameters (and hence of different cross sectional
areas) as shown below. Let this bar be subjected to
an axial load P.
The total change in length will be obtained by adding
the changes in length of individual sections
Total stress in section 1: σ1=E1 x ΔL1/L1
σ1 x L1/E1=ΔL1
σ1=P/A1; Hence ΔL1=PL1/A1E1
Similarly, ΔL2=PL2/A2E2; ΔL3=PL3/A3E3
27. 1.10 ANALYSIS OF BARS OF
VARYING CROSS SECTION
Hence total elongation ΔL=Px (L1/A1E1+L2/A2E2 +
L3/A3E3)
If the Young’s modulus of different sections are the
same, E1=E2=E3=E; Hence ΔL=P/Ex (L1/A1+L2/A2
+ L3/A3)
When a number of loads are acting on a body, the
resulting strain, according to principle of
superposition, will be the algebraic sum of strains
caused by individual loads
While using this principle for an elastic body which is
subjected to a number of direct forces (tensile or
compressive) at different sections along the length of
the body, first the free body diagram of individual
section is drawn. Then the deformation of each
section is calculated and the total deformation is
equal to the algebraic sum of deformations of
individual sections
28. 1.11 ANALYSIS OF UNIFORMLY
TAPERING CIRCULAR ROD
Consider a bar uniformly tapering from a diameter
D1 at one end to a diameter D2 at the other end
Let
P Axial load acting on the bar
L Length of bar
E Young’s modulus of the material
29. 1. 11 ANALYSIS OF UNIFORMLY
TAPERING CIRCULAR ROD
Consider an infinitesimal element of thickness dx, diameter Dx at
a distance x from face with diameter D1.
Deformation of the element d(Δx)= P x dx/ (Ax E)
Ax=π/4 x Dx²; Dx= D1 - (D1 – D2)/L x x
Let (D1-D2)/L=k; Then Dx= D1-kx
d(ΔLx)= 4 x P x dx/(π x (D1-kx)² x E)
Integrating from x=0 to x=L 4PL/(πED1D2)
Let D1-kx=λ; then dx= -(d λ/k)
When x=0, λ=D1; When x=L, λ=D2
31. 1.13 ANALYSIS OF BARS OF
COMPOSITE SECTIONS
A bar, made up of two or more bars of equal
lengths but of different materials rigidly fixed with
each other and behaving as one unit for
elongation and shortening when subjected to
axial loads is called composite bar.
Consider a composite bar as shown below
Let
P Applied load
L Length of bar
A1 Area of cross section of Inner member
A2 Cross sectional area of Outer member
32. 1.13 ANALYSIS OF BARS OF
COMPOSITE SECTIONS
Strain developed in the outer member= Strain
developed in the inner member
σ1/E1 = σ2/E2
Total load (P)= Load in the inner member (P1) +
Load in the outer member (P2)
σ1 x A1 + σ2 x A2= P
Solving above two equations, we get the values
of σ1, σ2 & e1 and e2
33. 1.14 STRESS & ELONGN.
PRODUCED IN A BAR DUE TO ITS
SELF WEIGHT
Consider a bar of length L, area of cross section A
rigidly fixed at one end. Let ρ be the density of the
material. Consider an infinitesimal element of
thickness dy at a distance y from the bottom of the
bar.
The force acting on the element considered= weight
of the portion below it=ρAgy
34. 1.14 STRESS & ELONGN.
PRODUCED IN A BAR DUE TO ITS
SELF WEIGHT
Tensile stress developed= Force acting on the
element/Area of cross section= ρgy.
From the above equation, it is clear that the
maximum stress at the section where y=L, ie at
the fixed end (ρgL) and minimum stress is at the
free end(=0)
Elongation due to self weight
37. 1.16 THERMAL STRESS
Thermal stresses are the stresses induced in a body due
to change in temperature. Thermal stresses are set up in a
body, when the temperature of the body is raised or
lowered and the body is restricted from expanding or
contracting
Consider a body which is heated to a certain temperature
Let
L= Original length of the body
Δ T=Rise in temp
E=Young's modulus
α=Coefficient of linear expansion
dL= Extension of rod due to rise of temp
If the rod is free to expand, Thermal strain developed
et= Δ L/L=α x Δ T
38. 1.16 THERMAL STRESS
The extension of the rod, Δ L= L x α x Δ T
If the body is restricted from expanding freely,
Thermal stress developed is σt/et=E
σt= E x α x Δ T
Stress and strain when the support yields:-
If the supports yield by an amount equal to δ,
then the actual expansion is given by the
difference between the thermal strain and δ
Actual strain, e= (L x α x Δ T – δ)/L
Actual stress= Actual strain x E= (L x α x Δ T –
δ)/L x E