Mechanics of Materials: The concept of stress and strain

Name: Mechanics of Materials: The concept of stress and strain
Rating: 4.8 (6 reviews)

Materials behavior under loading, Stress, Strain, Stress transformation, Principal stresses, bending stress in beams

Created byProf Dr Farid Khan

Last updated 7/2024

English

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What you'll learn

Demonstrate an understanding of the fundamentals of stress and strain
Ability to estimate deformation, stress and strain and design members under axial loading and torque
Draw shear force and bending moment diagram for beams and to able to design these under different loading scenarios
To introduce basic knowledge and tools of stress, strain and strength
To learn methods for determining the stresses, strains and deflections produced by applied loads
To apply gained knowledge to solve practical problems

Course content

4 sections • 14 lectures • 9h 14m total length

Introduction about mechanics of materials49:56
Explore mechanics of materials, introducing stress and strain, and the behavior of engineering materials under axial loading, torsion, bending, and beam concepts, with Mohr circle and design to prevent failure.
Concept of stress and strain50:08
Explore the concepts of stress and strain, including normal and shear stress, normal and shear strain, and how tensile, compressive, shear, torque, and bending loadings govern material behavior.
General state of stress and strain40:22
Define stress at a point as a nine-component tensor that depends on cutting plane and orientation, expressed in matrix form; distinguish normal and shear stresses in a general state.
Stress-strain plot for a material49:08
Explore coordinate systems, stress-strain concepts, principal stresses, and how a universal testing machine measures ductile and brittle material behavior through stress-strain curves.

Deformation under axial loading41:41
Learn how axial loading causes deformation by linking stress, strain, and elongation via Hooke's law. Derive delta = P L /(E A) and extend to multi-segment rods.
Static Indeterminacy31:07
Learn how to solve statically indeterminate structures by equilibrium and the principle of superposition, replacing redundant reactions with compatible deformations to determine reactions.
Thermal stresses7:33
The lecture uses the principle of superposition to analyze thermal stresses in a statically indeterminate beam, introducing the coefficient of thermal expansion alpha and resulting compressive stress.
Piosson's ratio and generalized Hook's law50:16
Explore Poisson's ratio and generalized Hooke's law linking axial and lateral strains. Understand dilatation and bulk modulus under multiaxial loading in isotropic materials.

Beams classification, loading types and shear force-bending moment53:48
Explore beams as structural members, analyze loads, shear force and bending moment, and apply the section method to draw diagrams for cantilever, simply supported and fixed beams.
Beam bending model39:10
Analyze beam bending and bending stresses, showing compression above the neutral axis and tension below, with sigma equals M y over I and I depending on cross-section.
Shear force, bending moment diagram and bending stress in a beam47:02
Draw the shear force and bending moment diagrams for a cantilever beam under a uniform load and a point load, then compute normal stresses near point B using flexural formula.

General state of stress-review25:13
Explore the general state of stress as a nine-component tensor, distinguishing normal and shear components, and see how coordinate frames and principal stresses inform plane stress analysis.
Transformation of Plane Stress44:48
Explore the transformation of plane stress by deriving the stress transformation equations for sigma_x', sigma_y', and tau_x'y' under rotation theta, using stress elements and Mohr circle to identify principal stresses.
Plane Stress problem: Solving by analytical method24:34
Transform plane stress state to obtain principal stresses and planes, compute maximum shear, and apply the analytical method using sigma_x, sigma_y, and tau_xy.

Requirements

Engineering Statics, basic algebra (not mandatory)

Description

The engineering product (from screw to aircraft, from screw driver to bullet train, from bolt to space rovers, nut to space shuttle) needs to be designed perfectly for their reliable usage during applications. Each and every engineering product, whether small or huge is subjected to several external loads during operation, in order to withstand these loads for that these products mush be designed perfectly while keeping the economical aspect. Stress and strain is the perfect concept that is developed to study the behavior of the material/products when subjected to external loading. This course will describe about the basic concept of stress and strain. How this concept and knowledge is used to determine the analytical models for deformation, deflection, stress, and strain under uni axial load, bi-axial load and tri-axial load will be discussed. Moreover, the stress transformation through analytical tools and graphical methods (Mohr's circle) will also be elaborated in order to equipped the learners with the broad knowledge and understandings from design point of view. Beams which are the basic components of mechanical and civil engineering are also of this course,and shear force diagrams, bending moment diagrams, beams deflection, critical stress determination and beam designing can be easily learnt. Moreover, this course also covers about torsion in shafts and the shear stress produced in shafts and how to use the torsion analytical tools for the designing of shafts etc.

Who this course is for:

Mechanical, Electrical ,Civil, mechatronics, chemical and industrial students and fresh engineers

Mechanics of Materials: The concept of stress and strain

What you'll learn

Explore related topics

Course content

Introduction4 lectures • 3hr 10min

Modeling under axial loading and generalized loading4 lectures • 2hr 11min

Beams3 lectures • 2hr 20min

Transformations of Stress and Strain3 lectures • 1hr 35min

Requirements

Description

Who this course is for: