This document provides an overview of stresses and strains in rock mechanics. It discusses key topics such as:
- The Cauchy stress principle which defines stress as a force per unit area.
- Representing the state of stress at a point using stress tensors and describing normal stresses, shear stresses, and principal stresses.
- Transforming stresses between coordinate systems using stress transformation laws.
- Relating stresses on inclined planes to the stress tensor components.
- Equilibrium conditions for stresses and the symmetry of the stress tensor.
- Decomposing stresses into hydrostatic and deviatoric components and defining octahedral stresses.
The document also outlines strain analysis concepts such as deformation and strain
This document discusses calculating displacement of joints in a truss due to changes in member length from temperature changes and fabrication errors. It provides an equation to calculate displacement as the sum of the product of internal forces and length changes. As an example, it calculates the vertical displacement of joint H in a sample truss due to increased temperatures in two members and fabrication errors in shortening one member and elongating another. The total calculated displacement is 1.92 mm.
Numerical Simulation of Pile using PLAXISDr. Naveen BP
This document summarizes field tests and numerical simulations conducted by Naveen B.P. on various geotechnical structures. It describes field load tests on single piles under vertical and lateral loads. It also discusses numerical modeling of pile load tests in PLAXIS and compares the results to field data. Additionally, it examines soil nailing analysis, lateral monitoring of secant pile walls, and a comparison of FLAC 3D and PLAXIS 3D for laterally loaded pile analysis. The document provides details of field experience with various pile load tests and numerical modeling techniques for evaluating pile behavior.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
The document discusses beams, which are horizontal structural members that support applied loads. It defines applied and reactive forces, and describes different types of supports including roller, hinge, and fixed supports. It then defines and describes different types of beams, including cantilever, simply supported, overhanging, fixed, and continuous beams. It also discusses types of loads, including concentrated and distributed loads, and how beams experience both bending and shear forces from loads.
This document discusses stress and strain concepts including:
1. Definitions of normal stress, normal strain, Poisson's ratio, shear stress, and shear strain. It also discusses tensile testing and stress-strain curves.
2. Stress-strain curves are shown for ductile and brittle materials. An example curve for low-carbon steel is described.
3. True stress and true strain are defined based on instantaneous cross-sectional area and gage length. Different regions of stress-strain curves are identified.
The document discusses plate bending theory and the stress-strain hypothesis. Some key points:
1) Plate bending theory studies the behavior of thin, flat plates under external loads and is based on the assumption that plates are very thin compared to their other dimensions and undergo small deformations.
2) The stress-strain hypothesis relates the stress in a plate to the strain it undergoes, assuming stress is proportional to strain via the modulus of elasticity. It also assumes normal stress is proportional to curvature and shear stress is proportional to the rate of change of curvature.
3) The stress-strain hypothesis allows derivation of equations relating external loads on a plate to resulting deformations and stresses, using the principle of virtual work
Structural engineering i- Dr. Iftekhar Anam
Structural Stability and Determinacy,Axial Force, Shear Force and Bending Moment Diagram of Frames,Axial Force, Shear Force and Bending Moment Diagram of Multi-Storied Frames,Influence Lines of Beams using Müller-Breslau’s Principle,Influence Lines of Plate Girders and Trusses,Maximum ‘Support Reaction’ due to Wheel Loads,Maximum ‘Shear Force’ due to Wheel Loads,Calculation of Wind Load,Seismic Vibration and Structural Response
http://www.uap-bd.edu/ce/anam/
Principle of virtual work and unit load methodMahdi Damghani
The document summarizes the principle of virtual work (PVW) which is a fundamental tool in analytical mechanics. It defines virtual work as the work done by a real force moving through an arbitrary virtual displacement. The PVW states that if a particle is in equilibrium, the total virtual work done by the applied forces equals zero. Examples are provided to demonstrate how PVW can be used to determine unknown internal forces and slopes by equating the virtual work of external and internal forces.
This document discusses calculating displacement of joints in a truss due to changes in member length from temperature changes and fabrication errors. It provides an equation to calculate displacement as the sum of the product of internal forces and length changes. As an example, it calculates the vertical displacement of joint H in a sample truss due to increased temperatures in two members and fabrication errors in shortening one member and elongating another. The total calculated displacement is 1.92 mm.
Numerical Simulation of Pile using PLAXISDr. Naveen BP
This document summarizes field tests and numerical simulations conducted by Naveen B.P. on various geotechnical structures. It describes field load tests on single piles under vertical and lateral loads. It also discusses numerical modeling of pile load tests in PLAXIS and compares the results to field data. Additionally, it examines soil nailing analysis, lateral monitoring of secant pile walls, and a comparison of FLAC 3D and PLAXIS 3D for laterally loaded pile analysis. The document provides details of field experience with various pile load tests and numerical modeling techniques for evaluating pile behavior.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
The document discusses beams, which are horizontal structural members that support applied loads. It defines applied and reactive forces, and describes different types of supports including roller, hinge, and fixed supports. It then defines and describes different types of beams, including cantilever, simply supported, overhanging, fixed, and continuous beams. It also discusses types of loads, including concentrated and distributed loads, and how beams experience both bending and shear forces from loads.
This document discusses stress and strain concepts including:
1. Definitions of normal stress, normal strain, Poisson's ratio, shear stress, and shear strain. It also discusses tensile testing and stress-strain curves.
2. Stress-strain curves are shown for ductile and brittle materials. An example curve for low-carbon steel is described.
3. True stress and true strain are defined based on instantaneous cross-sectional area and gage length. Different regions of stress-strain curves are identified.
The document discusses plate bending theory and the stress-strain hypothesis. Some key points:
1) Plate bending theory studies the behavior of thin, flat plates under external loads and is based on the assumption that plates are very thin compared to their other dimensions and undergo small deformations.
2) The stress-strain hypothesis relates the stress in a plate to the strain it undergoes, assuming stress is proportional to strain via the modulus of elasticity. It also assumes normal stress is proportional to curvature and shear stress is proportional to the rate of change of curvature.
3) The stress-strain hypothesis allows derivation of equations relating external loads on a plate to resulting deformations and stresses, using the principle of virtual work
Structural engineering i- Dr. Iftekhar Anam
Structural Stability and Determinacy,Axial Force, Shear Force and Bending Moment Diagram of Frames,Axial Force, Shear Force and Bending Moment Diagram of Multi-Storied Frames,Influence Lines of Beams using Müller-Breslau’s Principle,Influence Lines of Plate Girders and Trusses,Maximum ‘Support Reaction’ due to Wheel Loads,Maximum ‘Shear Force’ due to Wheel Loads,Calculation of Wind Load,Seismic Vibration and Structural Response
http://www.uap-bd.edu/ce/anam/
Principle of virtual work and unit load methodMahdi Damghani
The document summarizes the principle of virtual work (PVW) which is a fundamental tool in analytical mechanics. It defines virtual work as the work done by a real force moving through an arbitrary virtual displacement. The PVW states that if a particle is in equilibrium, the total virtual work done by the applied forces equals zero. Examples are provided to demonstrate how PVW can be used to determine unknown internal forces and slopes by equating the virtual work of external and internal forces.
The document discusses shear force and bending moment in beams. It defines key terms like shear force, bending moment, and types of loads, supports and beams. It provides examples of different loading conditions and how to calculate and draw the shear force and bending moment diagrams for beams subjected to point loads, uniformly distributed loads, uniformly varying loads, couples and overhanging beams. The diagrams show the variations in shear force and bending moment, including locations of maximum and points of contraflexure where bending moment changes sign.
This document discusses stress distribution in soil due to various types of loading. It begins by introducing key concepts like how applied loads are transferred through the soil mass, creating stresses that decrease in magnitude but increase in area with depth. The factors that affect stress distribution, like loading size/shape, soil type, and footing rigidity are also covered. The document then examines specific load types - point loads, line loads, rectangular/triangular strip loads, and circular loads - providing the equations to calculate vertical stress increases below each. Several examples demonstrate calculating stress increases below compound load arrangements. The summary provides an overview of the key topics and calculations presented in the document.
This document summarizes stress distribution in soil due to concentrated and uniform loads. It presents Westergaard and Boussinesq equations to calculate vertical stress below a concentrated load. It also discusses the approximate and elastic theory methods to calculate vertical stress below a uniform load on circular and rectangular areas using influence coefficients. Several examples are provided to illustrate calculating vertical stress at different depths and locations below concentrated and uniform loads.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This document provides information about the Strength of Materials CIE 102 course for first year B.E. degree students. It includes a list of 10 topics that will be covered in the course, such as simple stress and strain, shearing force and bending moment, and stability of columns. It also lists several reference books for the course and provides an overview of concepts that will be discussed in the first chapter, including stress, strain, stress-strain diagrams, and ductile vs brittle materials.
The unconfined compression test is a type of unconsolidated-undrained test used for clay specimens. It involves compressing a cylindrical clay sample axially without lateral confinement. The major principal stress is the axial stress, while the minor principal stresses are zero. This allows measuring the unconfined compressive strength, sensitivity, shear strength parameters, and cohesion of cohesive soils. The test procedure involves extruding and trimming a soil specimen, measuring it, and compressing it at a controlled strain rate between loading plates while recording the load and stress. Parameters are calculated based on the failure load and specimen dimensions.
Geotechnical Engineering-II [Lec #6: Stress Distribution in Soil]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
1. The presentation covered design for torsion in structural members, including definitions, effects of torsion such as rotation and warping, and methods for calculating torsional stresses.
2. Equations were presented for calculating torsional moments in circular and rectangular beams under different loading cases.
3. Two theories for analyzing reinforced concrete members under torsion were discussed: skew bending theory and space truss analogy theory. Limitations on torsional reinforcement in concrete were also reviewed.
The document discusses shear strength of soils. It defines shear strength as the soil's resistance to shearing stresses and deformation from particle displacement. Shear strength depends on cohesion between particles and frictional resistance, as modeled by the Mohr-Coulomb failure criterion. Laboratory tests like direct shear and triaxial shear tests are used to determine the shear strength parameters (c, φ) that describe a soil's failure envelope.
Geotechnical Engineering-II [Lec #25: Coulomb EP Theory - Numericals]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Mohr circle mohr circle anaysisand applicationShivam Jain
Mohr's circle is a graphical representation used to analyze the state of stress at a point. It relates the normal and shear stresses acting on planes of all orientations passing through that point. The document discusses how to construct Mohr's circle through an example and how it can be used to analyze principal stresses, maximum shear stress, and normal and shear stresses on any given plane. Applications of Mohr's circle include analyzing brittle and ductile deformation, the effects of pore pressure, and detecting stability in structures like bridges, dams, and slopes.
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.
The document discusses soil mechanics topics related to consolidation and settlement. It covers three types of settlement (immediate, primary consolidation, and secondary consolidation). It also explains the fundamental concept of consolidation using a piston-spring model and describes how a one-dimensional consolidation test (oedometer test) is conducted in the laboratory to determine soil compressibility.
Principle of Virtual Work in structural analysisMahdi Damghani
The document provides an overview of the principle of virtual work (PVW) for structural analysis. Some key points:
1) PVW is based on the concept of work and energy methods. It states that for a structure in equilibrium under applied forces, the total virtual work done by these forces due to a small arbitrary displacement is zero.
2) PVW can be used to determine unknown internal forces or displacements in statically indeterminate structures by applying virtual displacements or forces.
3) Examples demonstrate using PVW to calculate the bending moment at a point in a beam and the force in a member of an indeterminate truss by equating the external virtual work to internal virtual work.
1. The document discusses stress distribution in soils due to different types of loading, including point loads, line loads, triangular loads, strip loads, rectangular loads, and circular loads.
2. Several methods for estimating stress distribution are presented, including Boussinesq's method, Westergaard's method, and the use of influence factor charts and bulbs of pressure charts.
3. Factors that influence stress distribution include the size and shape of the loading area, load magnitude and type, soil type, depth, and distance from the load. Stress decreases with depth and distance from the load.
Geotechnical Engineering-II [Lec #19: General Bearing Capacity Equation]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This document discusses deflection in simply supported beams. A simply supported beam is supported at both ends but not fixed, allowing it to move vertically but not horizontally. The theoretical deflection of a simply supported beam under a center load can be calculated using the Euler-Bernoulli beam equation, which takes into account the load, length, modulus of elasticity, and moment of inertia. The document compares theoretical deflection values calculated from the equation to practical deflection values measured in experiments.
This document provides information about soil compressibility and consolidation. It discusses the different types of soil settlement that can occur when stress is applied, including immediate elastic settlement, primary consolidation settlement, and secondary consolidation settlement. It describes how consolidation settlement occurs as water is expelled from saturated soils under increased stress levels. Graphs are presented showing typical relationships between void ratio, effective stress, and compression index that help explain consolidation concepts. The role of overconsolidation ratio and preconsolidation stress are defined in relation to soil compressibility. Methods for estimating settlement magnitudes, such as using Casagrande's approach, are also summarized.
1. The document provides examples of calculating consolidation parameters such as void ratio, coefficient of consolidation, and primary consolidation settlement from given soil testing data.
2. Parameters like initial void ratio, applied pressure, and thickness of soil layers are used to determine the change in stress and void ratio to then calculate settlement.
3. Several methods are presented to calculate the average effective stress and stress change at different points to then determine the consolidation settlement under different boundary conditions, stress histories, and soil properties.
1. The document introduces the concepts of stress and strain in rheology, the science of deformation and flow of materials. It discusses how stress is quantified by factors like force and pressure.
2. The lecture defines stress as a dynamic quantity expressing force magnitude, and strain as a kinematic quantity expressing media deformation. It explains how to describe an object's complete stress state in 3D and determine if stress will cause failure.
3. Key concepts covered include surface forces vs. body forces, tractions as normalized forces, and using the Cauchy stress tensor to represent the full stress state at a point and find stress on any plane.
This document provides an overview of geomechanics concepts for petroleum engineers. It discusses stress and strain theory, elasticity, homogeneous and heterogeneous stress fields, principal stresses, and the Mohr circle construction. It also covers rock deformation mechanisms including cataclasis and intracrystalline plasticity. Key concepts are defined such as normal and shear stress, elastic moduli like Young's modulus and Poisson's ratio, elastic stress-strain equations, and strain measures including conventional, quadratic, and natural strain.
The document discusses shear force and bending moment in beams. It defines key terms like shear force, bending moment, and types of loads, supports and beams. It provides examples of different loading conditions and how to calculate and draw the shear force and bending moment diagrams for beams subjected to point loads, uniformly distributed loads, uniformly varying loads, couples and overhanging beams. The diagrams show the variations in shear force and bending moment, including locations of maximum and points of contraflexure where bending moment changes sign.
This document discusses stress distribution in soil due to various types of loading. It begins by introducing key concepts like how applied loads are transferred through the soil mass, creating stresses that decrease in magnitude but increase in area with depth. The factors that affect stress distribution, like loading size/shape, soil type, and footing rigidity are also covered. The document then examines specific load types - point loads, line loads, rectangular/triangular strip loads, and circular loads - providing the equations to calculate vertical stress increases below each. Several examples demonstrate calculating stress increases below compound load arrangements. The summary provides an overview of the key topics and calculations presented in the document.
This document summarizes stress distribution in soil due to concentrated and uniform loads. It presents Westergaard and Boussinesq equations to calculate vertical stress below a concentrated load. It also discusses the approximate and elastic theory methods to calculate vertical stress below a uniform load on circular and rectangular areas using influence coefficients. Several examples are provided to illustrate calculating vertical stress at different depths and locations below concentrated and uniform loads.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This document provides information about the Strength of Materials CIE 102 course for first year B.E. degree students. It includes a list of 10 topics that will be covered in the course, such as simple stress and strain, shearing force and bending moment, and stability of columns. It also lists several reference books for the course and provides an overview of concepts that will be discussed in the first chapter, including stress, strain, stress-strain diagrams, and ductile vs brittle materials.
The unconfined compression test is a type of unconsolidated-undrained test used for clay specimens. It involves compressing a cylindrical clay sample axially without lateral confinement. The major principal stress is the axial stress, while the minor principal stresses are zero. This allows measuring the unconfined compressive strength, sensitivity, shear strength parameters, and cohesion of cohesive soils. The test procedure involves extruding and trimming a soil specimen, measuring it, and compressing it at a controlled strain rate between loading plates while recording the load and stress. Parameters are calculated based on the failure load and specimen dimensions.
Geotechnical Engineering-II [Lec #6: Stress Distribution in Soil]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
1. The presentation covered design for torsion in structural members, including definitions, effects of torsion such as rotation and warping, and methods for calculating torsional stresses.
2. Equations were presented for calculating torsional moments in circular and rectangular beams under different loading cases.
3. Two theories for analyzing reinforced concrete members under torsion were discussed: skew bending theory and space truss analogy theory. Limitations on torsional reinforcement in concrete were also reviewed.
The document discusses shear strength of soils. It defines shear strength as the soil's resistance to shearing stresses and deformation from particle displacement. Shear strength depends on cohesion between particles and frictional resistance, as modeled by the Mohr-Coulomb failure criterion. Laboratory tests like direct shear and triaxial shear tests are used to determine the shear strength parameters (c, φ) that describe a soil's failure envelope.
Geotechnical Engineering-II [Lec #25: Coulomb EP Theory - Numericals]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Mohr circle mohr circle anaysisand applicationShivam Jain
Mohr's circle is a graphical representation used to analyze the state of stress at a point. It relates the normal and shear stresses acting on planes of all orientations passing through that point. The document discusses how to construct Mohr's circle through an example and how it can be used to analyze principal stresses, maximum shear stress, and normal and shear stresses on any given plane. Applications of Mohr's circle include analyzing brittle and ductile deformation, the effects of pore pressure, and detecting stability in structures like bridges, dams, and slopes.
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.
The document discusses soil mechanics topics related to consolidation and settlement. It covers three types of settlement (immediate, primary consolidation, and secondary consolidation). It also explains the fundamental concept of consolidation using a piston-spring model and describes how a one-dimensional consolidation test (oedometer test) is conducted in the laboratory to determine soil compressibility.
Principle of Virtual Work in structural analysisMahdi Damghani
The document provides an overview of the principle of virtual work (PVW) for structural analysis. Some key points:
1) PVW is based on the concept of work and energy methods. It states that for a structure in equilibrium under applied forces, the total virtual work done by these forces due to a small arbitrary displacement is zero.
2) PVW can be used to determine unknown internal forces or displacements in statically indeterminate structures by applying virtual displacements or forces.
3) Examples demonstrate using PVW to calculate the bending moment at a point in a beam and the force in a member of an indeterminate truss by equating the external virtual work to internal virtual work.
1. The document discusses stress distribution in soils due to different types of loading, including point loads, line loads, triangular loads, strip loads, rectangular loads, and circular loads.
2. Several methods for estimating stress distribution are presented, including Boussinesq's method, Westergaard's method, and the use of influence factor charts and bulbs of pressure charts.
3. Factors that influence stress distribution include the size and shape of the loading area, load magnitude and type, soil type, depth, and distance from the load. Stress decreases with depth and distance from the load.
Geotechnical Engineering-II [Lec #19: General Bearing Capacity Equation]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This document discusses deflection in simply supported beams. A simply supported beam is supported at both ends but not fixed, allowing it to move vertically but not horizontally. The theoretical deflection of a simply supported beam under a center load can be calculated using the Euler-Bernoulli beam equation, which takes into account the load, length, modulus of elasticity, and moment of inertia. The document compares theoretical deflection values calculated from the equation to practical deflection values measured in experiments.
This document provides information about soil compressibility and consolidation. It discusses the different types of soil settlement that can occur when stress is applied, including immediate elastic settlement, primary consolidation settlement, and secondary consolidation settlement. It describes how consolidation settlement occurs as water is expelled from saturated soils under increased stress levels. Graphs are presented showing typical relationships between void ratio, effective stress, and compression index that help explain consolidation concepts. The role of overconsolidation ratio and preconsolidation stress are defined in relation to soil compressibility. Methods for estimating settlement magnitudes, such as using Casagrande's approach, are also summarized.
1. The document provides examples of calculating consolidation parameters such as void ratio, coefficient of consolidation, and primary consolidation settlement from given soil testing data.
2. Parameters like initial void ratio, applied pressure, and thickness of soil layers are used to determine the change in stress and void ratio to then calculate settlement.
3. Several methods are presented to calculate the average effective stress and stress change at different points to then determine the consolidation settlement under different boundary conditions, stress histories, and soil properties.
1. The document introduces the concepts of stress and strain in rheology, the science of deformation and flow of materials. It discusses how stress is quantified by factors like force and pressure.
2. The lecture defines stress as a dynamic quantity expressing force magnitude, and strain as a kinematic quantity expressing media deformation. It explains how to describe an object's complete stress state in 3D and determine if stress will cause failure.
3. Key concepts covered include surface forces vs. body forces, tractions as normalized forces, and using the Cauchy stress tensor to represent the full stress state at a point and find stress on any plane.
This document provides an overview of geomechanics concepts for petroleum engineers. It discusses stress and strain theory, elasticity, homogeneous and heterogeneous stress fields, principal stresses, and the Mohr circle construction. It also covers rock deformation mechanisms including cataclasis and intracrystalline plasticity. Key concepts are defined such as normal and shear stress, elastic moduli like Young's modulus and Poisson's ratio, elastic stress-strain equations, and strain measures including conventional, quadratic, and natural strain.
This section discusses three-dimensional stress and strain. It introduces the traction vector and its components, which are represented by the stress tensor. Cauchy's law relates the traction vector on a surface to the stress tensor and the surface normal. The stress tensor transforms between coordinate systems according to the tensor transformation rule. Stresses can be resolved into normal and shear components on any plane through a point.
This document summarizes the key concepts from a seminar on structural vibration analysis using finite element methods. It introduces common sources and types of vibration, including free vibration from impacts and forced vibration from repetitive external forces. It also describes using finite element analysis to model structural vibration, including modeling structures as mass-spring-damper systems and discretizing continuous structures into finite elements to analyze their vibration modes and frequencies.
1. This module discusses stress, strain, and material behavior concepts in 3 dimensions. It defines stress as internal forces acting on an internal plane and strain as the deformation of an object.
2. Materials can be isotropic, requiring only 2 elastic constants, orthotropic requiring 9 constants, or fully anisotropic requiring 21 constants. Isotropic materials like metals have properties that do not depend on direction, while orthotropic materials like composites have some directional dependence.
3. Hooke's law relates stress and strain linearly through compliance or stiffness matrices. These matrices are symmetric for conservative materials, reducing the independent constants needed to describe the material.
The document discusses stress and strain in materials subjected to forces or loads. It defines normal stress as the distribution of force over the area on which it acts. Normal stress is calculated as force divided by cross-sectional area. For a straight bar undergoing axial loading, if the normal stress is uniform over the cross section, it corresponds to an axial force acting through the centroid of the cross section. The magnitude of the uniform normal stress in an axially loaded, prismatic bar is equal to the applied load divided by the cross-sectional area.
1) The document discusses stress and strain analysis, defining stress at a point, stress tensors, equations of equilibrium, different states of stress including uniaxial, biaxial, and triaxial stresses.
2) It introduces Mohr's circle as a graphical method to determine stresses on any plane passing through a point using the known normal and shear stresses.
3) Mohr's circle construction procedure is outlined, showing how to determine principal stresses and planes, and maximum shear stresses and planes.
This document provides an overview of basic engineering theory concepts covered in 8 chapters:
1) Mechanics of Materials: Stress and Strain
2) Hooke's Law
3) Failure Criteria
4) Beams
5) Buckling
6) Dynamics
7) Fluid Mechanics
8) Heat Transfer
Each chapter introduces fundamental concepts and equations within the topic area.
This document gives the class notes of Unit 3 Compound stresses. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document discusses stress and strain analysis. It defines stress at a point and introduces the stress tensor. The stress tensor is symmetric. Principal stresses are the maximum and minimum normal stresses. Mohr's circle can be used to determine stresses on any plane through a point by graphically representing the transformation of stresses between planes. The principal planes contain no shear stress and maximum shear stress planes are 45 degrees from principal planes.
This document provides an overview of the theory of elasticity. It discusses three key topics:
1) Stress and strain analysis including three-dimensional stress and strain, stress-strain transformations, stress invariants, and equilibrium and compatibility equations.
2) Two-dimensional problems involving solutions in Cartesian and polar coordinates, as well as beam bending problems.
3) Energy principles, variational methods, and numerical methods for solving elasticity problems.
This document provides an introduction to the theory of plates, which are structural elements that are thin and flat. It defines what is meant by a thin plate and discusses different plate classifications based on thickness. The document derives the basic equations that describe plate behavior by taking advantage of the plate's thin, planar character. It also discusses three-dimensional considerations like stress components, equilibrium, strain and displacement for putting the plate theory into context.
This document discusses stresses and strains, including traction vectors, stress components, stress tensors, and principal stresses. It defines key terms like traction vector, stress components, Cauchy stress tensor, principal axes, and principal stress. It also covers how to determine principal stresses through solving a system of linear homogeneous equations involving the stress tensor components and direction cosines of a unit vector. Coordinate transformation of stress tensors is explained using transformation matrices.
This document discusses the physical state of the lithosphere, including stresses, strains, heat flow, gravity, isostasy, and rock rheology. Specifically, it covers stress and strain in the lithosphere, including lithostatic stress, deviatoric stress, and principal stresses and strains. It also discusses heat flow through conduction and convection, and concepts of isostasy and compensation of topography through density differences. Finally, it examines rock rheology, including fundamentals of rheology, viscosity of the mantle and crust, and elastic versus plastic behavior.
This document provides an overview of chapter 3 from a textbook on load and stress analysis. The chapter covers topics such as equilibrium and free-body diagrams, shear force and bending moments in beams, stress, Mohr's circle for plane stress, and other structural analysis concepts. It introduces key equations and definitions for analyzing loads and stresses. The summary focuses on the high-level purpose and scope of the chapter content.
This document presents the development of a state space equation approach to obtain the three-dimensional solution for thick orthotropic plates with symmetric clamped-free edges. The state space method allows for an exact solution that satisfies all equations of elasticity and accounts for all elastic constants. The system matrix, which is a key part of the state space solution, is derived for symmetric clamped-free boundary conditions. Modal expansions are used to develop sixth-order differential equations governing the transverse displacement, whose solutions provide the stresses and displacements across the plate thickness.
This chapter discusses stress and strain in materials subjected to tension or compression. It defines stress as the load applied over the cross-sectional area. Strain is defined as the change in length over the original length. Hooke's law states that stress is proportional to strain for elastic materials. Young's modulus is the constant of proportionality between stress and strain. The chapter also discusses stress and strain calculations for materials with non-uniform cross-sections, as well as examples of stress and strain problems.
This document provides an introduction to beams and beam mechanics. It discusses different types of beams and supports, how to calculate beam reactions and internal forces like shear force and bending moment, shear force and bending moment diagrams, theories of bending and deflection, and methods for analyzing statically determinate beams including the direct method, moment area method, and Macaulay's method. The key objectives are determining the internal forces in beams, establishing procedures to calculate shear force and bending moment, and analyzing beam deflection.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
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
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.
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.