Mechanics Of Materials: Fundamentals

Exploring Structural Mechanics, Stresses and Strains, Axially Loaded Members, Stresses in Beams, Mohr’s Circle.

What you'll learn

Practical Stress & Strain Analysis: Calculate stress, grasp Hooke's Law, and understand materials. Essential for real-world engineering challenges!

Engineer for Real-Life Scenarios: Analyze axially loaded members, thermal effects, and strain energy. Gain hands-on skills for structural projects!

Applied Beam Behavior Analysis: Master pure & non-uniform bending, shear stresses in beams. Practical insights for early-career engineers!

Practical Strain Energy Applications: Calculate strain energy in nonuniform bars & displacements caused by single loads. Enhance your structural understanding.

Critical Stress and Strain Analysis: Explore principal stresses & maximum shear stresses, master Mohr’s circle for plane stress. Ensure material safety.

Understanding Allowable Stresses: Grasp allowable stresses & loads, making informed decisions for safe & reliable structure designs.

Real-World Case Studies: Dive into practical stress analysis case studies for engineering problem-solving. Gain valuable insights for your career.

Requirements

To begin your journey, a basic understanding of mathematics and fundamental knowledge of statics will suffice. I'll provide explanations for these fundamentals whenever necessary.

Description

Welcome to Mechanics of Materials: Exploring Structural Mechanics!In this course, we delve into the fascinating world of stress and strain analysis in three-dimensional elastic bodies. Gain a profound understanding of how different materials behave under load and how these analyses relate to the real-life performance of structural members.Through engaging lectures, we'll cover essential topics such as tension, compression, shear stress, elasticity, plasticity, and creep. You'll learn to calculate stresses and strains in various materials and analyze axially loaded members, thermal effects, and strain energy in nonuniform bars. Master the art of beam analysis, including pure bending, non-uniform bending, and longitudinal strains in beams made of linearly elastic materials.Moreover, we'll explore critical stress analysis, investigating principal stresses, maximum shear stresses, and harnessing Mohr's circle for plane stress to ensure the utmost material safety. By the end of this course, you'll be well-equipped to tackle real-world engineering challenges with confidence, making informed decisions for robust structural designs. Join us on this enriching journey into Mechanics of Materials and unlock the secrets of structural mechanics!Course Contents:Behavior & Mechanical Properties of Materials:Introduction to Mechanics of MaterialsNormal Stress and StrainMechanical Properties of MaterialsElasticity, Plasticity, and CreepLinear Elasticity, Hooke’s Law, and Poisson’s Ratio Shear Stress and StrainAllowable Stresses and Allowable Loads Axially Loaded Members:Changes in Lengths of Axially Loaded MembersThermal Effects Strain Energy-1 (Nonuniform Bars) Strain Energy-2 (Displacements Caused by a Single Load) Stresses in Beams:Pure Bending and Non-uniform Bending Curvature of a Beam, Longitudinal Strains in Beams Normal Stresses in Beams (Linearly Elastic Materials) Shear Stresses in BeamsAnalysis of Stress and Strain:Principal Stresses  Maximum Shear StressesMohr’s Circle for Plane Stress

Overview

Section 1: Introduction & Normal Stress and Strain & Mechanical Properties of Materials

Lecture 1 Introduction

Lecture 2 2-Normal stress and strain

Lecture 3 3- Examples-Normal stress and strain

Lecture 4 3-1 Exercise 1- Circular Post

Lecture 5 3-2 Exercise 2- Brake Pedal

Lecture 6 3-3 Exercise 3- Circular Tube with strain gage

Lecture 7 3-4 Exercise 4- Car on inclined track

Lecture 8 4- Mechanical properties of materials

Lecture 9 5-Stress-strain diagram- Part 1/2

Lecture 10 6-Stress-strain diagram- Part 2/2

Section 2: Material Behavior & Properties

Lecture 11 7- Elasticity

Lecture 12 8- Creep and Relaxation

Lecture 13 9-Linear Elasticity and Hooks Law

Lecture 14 10-Poissions Ratio

Lecture 15 11- Example-Linear elasticity-Poisson's-Hooks

Lecture 16 11-1 Exercise on stress-strain of steel

Lecture 17 11-2 Exercise on permanent set of a bar

Lecture 18 11-3 Exercise on Aluminum bar in tension

Lecture 19 11-4 Exercise on Modulus of elasticity of brass specimen

Section 3: Assignment on Material Behavior and Properties

Lecture 20 Assignment-1

Lecture 21 11-5 Assignment 1-problem 1 (solution of problem-1 in Exam-1)

Lecture 22 11-6 Assignment 1-problem 2 (solution of problem-2 in Exam-1)

Lecture 23 11-7 Assignment 1-problem 3 (solution of problem-3 in Exam-1)

Section 4: Shear stress and strain

Lecture 24 12-shear stress-1-Concept

Lecture 25 13-shear stress-2-Shear Stresses on Perpendicular Planes-sign convention

Lecture 26 14-shear stress-3-Hooks Law in Shear

Lecture 27 15-shear stress-4-example-1-Shear stress in a plate

Lecture 28 16-shear stress-5-example-2-Bearing and shear stresses in pins and bolts

Lecture 29 17- shear stress-6-example-3-shear stresses & strains in elastomeric bearing pad

Lecture 30 17-1-Exercises-Shear stress and strain-Hollow box

Lecture 31 17-2 Exercises-Shear stress and strain-Cable sling

Section 5: Allowable stress and allowable loads (Axial loads)

Lecture 32 18-allowable stress and allowable loads

Lecture 33 19-allowable stress and allowable load example

Lecture 34 20- Design for axial loads and direct shear example

Lecture 35 20-1-Exercises on axial load and shear

Lecture 36 20-2-Exercises on axial load and shear

Lecture 37 21-axial loads stiffness

Lecture 38 22-axial loads stiffness-example

Section 6: Thermal effects

Lecture 39 23-Themal effects

Lecture 40 24- Thermal stress example-Prismatic bar under different temperatures

Lecture 41 24-1-Exercises on thermal effects-Railroad track

Lecture 42 24-2-Exercises on thermal effects-Steel rod

Section 7: Assignment on Axial loads & Thermal effects

Lecture 43 24-3 Assignment problem # 1: Design for axial loads for steel base plate

Lecture 44 24-4 Assignment problem # 2: Thermal effect on plastic bar

Section 8: Strain Energy

Lecture 45 25-strain energy-1

Lecture 46 26-strain energy-2-elastic and inelastic strain energy

Lecture 47 27-strain energy-3-linearly elastic behavior

Lecture 48 28-strain energy-4-comments on strain energy

Lecture 49 29-strain energy-5-non uniform bars

Lecture 50 30-strain energy-6-example-non uniform bars

Lecture 51 31-strain energy-7-disp from single load

Lecture 52 32- strain energy-8-example disp from single load

Lecture 53 32-1 Strain energy exercises

Lecture 54 32-2 Strain energy exercises

Lecture 55 32-3 Strain energy exercises

Section 9: Curvature and longitudinal strain in Beams

Lecture 56 33-beams-1-Pure Bending and nonuniform bending

Lecture 57 34-beams-2-Curvature of a Beam

Lecture 58 35- beams-3-Longitudinal Strains in beams

Lecture 59 35-1 Exercises on longitudinal strains in beams

Lecture 60 35-2 Exercises on longitudinal strains in beams

Section 10: Normal stress and strain

Lecture 61 36-Normal stress in beams-1-Resultant of the normal stresses

Lecture 62 37-Normal stress in beams-2-Location of neutral Axis

Lecture 63 38-Normal stress in beams-3- Moment-Curvature Relationship

Lecture 64 39-Normal stress in beams-4-Flexure Formula

Lecture 65 40-Normal stress in beams-5-Maximum Stresses at a Cross Section

Lecture 66 41-Normal stress in beams-6-Doubly Symmetric Shapes

Lecture 67 42- Normal stress in beams-7-Example

Lecture 68 42-1 exercises on beams-A thin strip of Copper

Lecture 69 42-2 exercises on beams- Highway bridge

Section 11: Shear stress in beams

Lecture 70 43-Shear stresses in beams-1-Vertical and Horizontal Shear Stresses

Lecture 71 44-Shear stresses in beams-2-Shear formula

Lecture 72 45- Shear stresses in beams-3- Example-Metal beam

Lecture 73 45-1 Exercises on shear stresses on beams-Cantiever wood beam

Lecture 74 45-2 Exercises on shear stresses on beams-Laminated wood beam

Lecture 75 45-3 Assignment-3-Laminated plastic beam

Lecture 76 45-4 Assignment-3-Simply supported wood beam

Section 12: Plane stress element

Lecture 77 46-Analysis of stress and strain-planes stress-sign convention

Lecture 78 47-Analysis of stress and strain- stresses on inclined sections

Lecture 79 48-Analysis of stress and strain-transformation equations

Lecture 80 49- Analysis of stress and strain-transformation equations-example

Lecture 81 49-1 Exercises on Plane stress element

Lecture 82 49-2 Exercises on Plane stress element

Section 13: Principal stress

Lecture 83 50-Principal stress-1 variation with angle

Lecture 84 51-Principal stress-2-principal angles

Lecture 85 52-Principal stress-3-principal stress equations

Lecture 86 53-special cases-1

Lecture 87 54-max shear stress

Lecture 88 55-Example part-1

Lecture 89 56-Example part-2

Lecture 90 57- Example 3 maximum shear stress

Lecture 91 57-1 Assignment 4 on Principal stresses and maximum shear stresses-problem 1

Lecture 92 57-2 asignment 4 on Principal stresses and maximum shear stresses-problem 2

Section 14: Mohr Circle-Graphical Technique for Stress Visualization

Lecture 93 58-Mohr circle-1- Introduction

Lecture 94 59-Mohr circle-2- Equation of Mohr circle

Lecture 95 60-Mohr circle-3- Representation of Mohr circle

Lecture 96 61-Mohr circle-4- Construction of Mohr circle

Lecture 97 62-Mohr circle-5- stress on inclined element of Mohr circle

Lecture 98 63-Mohr circle-6- Principal stress of Mohr circle

Lecture 99 64-Mohr circle-7- Max shear stresses of Mohr circle

Lecture 100 65-Mohr circle-8- Example on Mohr circle

Lecture 101 65-Mohr circle-9-Excercise1

Lecture 102 65-Mohr circle-10-Excercise 2

Lecture 103 65-Mohr circle-11-Excercise 3

Aspiring Engineers: Those who aim to pursue a career in engineering and want to strengthen their knowledge of mechanics of materials.,Engineering Students: Undergraduate and graduate students studying engineering disciplines, seeking to solidify their understanding of structural mechanics.,Early-Career Professionals: Engineers in the early stages of their careers looking to enhance their expertise in stress and strain analysis for practical applications.,Materials Science Enthusiasts: Individuals interested in understanding the behavior of materials under various loads and exploring their mechanical properties.,Construction and Civil Engineering Professionals: Those working in construction or civil engineering fields, aiming to apply stress analysis principles to optimize structural integrity.,Mechanical and Aerospace Engineers: Professionals in the mechanical and aerospace industries seeking to expand their knowledge in mechanics for improved design and analysis.,Self-Learners and Enthusiasts: Anyone with a curiosity for the mechanics of materials, eager to explore real-world case studies and develop problem-solving skills.