Analysis Of Beams

Strength of Materials, Beams, Shear Force, Bending Moment, Shear Stress, Bending Stress, Slope, Deflection

What you'll learn

Understand the Types of Beams, Supports & Loadings

Calculate and Plot the Axial Force, Shear Force & Bending Moment for various cross-sections along a beam’s length

Calculate the maximum induced Bending Stress in a beam to check whether it is below the material's permissible normal stress limits

Calculate the maximum induced Shear Stress in a beam to check whether it is below the material's permissible shear stress limits

Find the Slope and Deflection equations for any cross section along a beam’s length, and check that the maximum deflection is less than the permissible limits

Requirements

Basic Integral and Differential Calculus

Engineering Statics (Mechanics)

Description

This course on Analysis of Beams, consisting of 50 lecture videos and spanning about 4 hours and 24 minutes in total, is designed for learners with little knowledge of Statics, and is aimed at a beginner to an intermediate level of understanding.Beams cover a vast portion of the basic Strength / Mechanics of Materials course, and is a prerequisite to many advanced subjects of undergraduate studies. The core principles of Beams, and Strength of Materials in general, apply to many disciplines viz., Mech E, Prod or Mfg E, Civil E, Aeronautical E, and Architectural Engineering, to name a few.In this course, you shall first learn how to calculate the internal resisting forces and moments developed within any cross-section along the beam’s length, in response to the applied loads and applied moments; and then plot the corresponding values in the form of diagrams. From this, you shall be able to calculate the maximum bending and shear stresses induced that may be responsible for failure, if the permissible stress limits of the beam material are exceeded. Failure may also happen due to excessive deformations, hence you shall also learn how to calculate the slopes and transverse deformations (called deflections).The information obtained through the bending and shear stresses, and slopes and deflections, is useful for the design and analysis of structures, ensuring safety and stability.A number of examples shall be solved for various beam types and loadings, starting with the most basic to reasonably complex ones. To make the subject simple to understand, the course does not delve much into the rigorous derivation aspects of underlying formulas, but more attention shall be given for the actual usage of the formulas in solving a given problem instead.A small but sufficient number of practice examples shall be listed at the end of every core topic. While it is advised to take notes during the lectures, yet, apart from the lecture videos, electronic documents of the whiteboard material used shall also be appended for ready reference.

Overview

Section 1: Introduction

Lecture 1 Introduction to Beams

Section 2: Axial Force, Shear Force and Bending Moment in Beams

Lecture 2 Solved Problem - 1 (Direct Approach): SS Beam with inclined load at the Centre

Lecture 3 Relation between Rate of Loading, Shear Force and Bending Moment at a Section

Lecture 4 Cantilever Beam - Point load at the tip

Lecture 5 Cantilever Beam - Uniformly Distributed Load (UDL) over the entire length

Lecture 6 Cantilever Beam - Point Load at the tip & UDL over the entire length

Lecture 7 Cantilever Beam - Uniformly Varying Load (UVL) over the entire length

Lecture 8 Cantilever Beam - Concentrated Moment at the tip

Lecture 9 Cantilever Beam - Solved Problem-2 (Combined Loadings)

Lecture 10 Cantilever Beam - Solved Problem-3 (Combined Loadings)

Lecture 11 Cantilever Beam - Practice Problems - 1-3 (Combined Loadings)

Lecture 12 Simply Supported Beam - Central Point Load

Lecture 13 Simply Supported Beam - Eccentric Point Load

Lecture 14 Simply Supported Beam - Uniformly Distributed Load (UDL) over the entire length

Lecture 15 Simply Supported Beam - Uniformly Varying Load (UVL) over the entire length

Lecture 16 Simply Supported Beam - Central Concentrated Moment

Lecture 17 Simply Supported Beam - Symmetrical Triangular Load over the entire length

Lecture 18 Simply Supported Beam - Solved Problem-4 (Combined Loadings)

Lecture 19 Simply Supported Beam - Solved Problem-5 (Combined Loadings)

Lecture 20 Simply Supported Beam - Practice Problems - 4-6 (Combined Loadings)

Lecture 21 Special Beam Applications - Beams with AF/SF/BM Release

Lecture 22 Special Beam Applications - Solved Problem-6 (Internal Hinge)

Lecture 23 Special Beam Applications - Solved Problem-7 (Internal Hinge)

Lecture 24 Special Beam Applications - Practice Problem-7 (Internal Hinge)

Section 3: Bending Stress in Beams (Theory of Pure Bending or Flexure)

Lecture 25 Equation of Pure Bending with Assumptions

Lecture 26 Calculation of Area Moment of Inertia for Basic Planar Shapes about the N.A.

Lecture 27 Computation of Area Moment of Inertia for Complex Cross-Section Shapes

Lecture 28 Bending Stress in Beams - Solved Problem-8

Lecture 29 Bending Stress in Beams - Solved Problem-9

Lecture 30 Bending Stress in Beams - Solved Problem-10

Lecture 31 Bending Stress in Beams - Practice Problems - 8-10

Lecture 32 Bending Stress in Beams - Flitched or Composite Beams

Lecture 33 Flitched or Composite Beams - Solved Problem-11

Lecture 34 Flitched or Composite Beams - Solved Problem-12

Lecture 35 Flitched or Composite Beams - Solved Problem-13

Lecture 36 Flitched or Composite Beams - Practice Problems - 11-13

Section 4: Shear Stress in Beams

Lecture 37 Shear Stress in Beams - Shear Stress Formula

Lecture 38 Shear Stress Distribution for a Rectangular Section

Lecture 39 Shear Stress Distribution for a Circular Section

Lecture 40 Shear Stress Distribution for a Triangular Section

Lecture 41 Shear Stress in Beams - Solved Problems - 14-16

Lecture 42 Shear Stress in Beams - Practice Problems - 14-16

Section 5: Slope and Deflection in Beams

Lecture 43 Slope & Deflection in Beams - An Introduction

Lecture 44 Methods to find Beam Deflections

Lecture 45 Relation between Rate of Loading, Shear Force, B. Moment, Slope and Deflection

Lecture 46 Solved Problem - 17 (Double Integration Method, Cantilever Beam)

Lecture 47 Solved Problem - 18 (Double Integration Method, Simply Supported Beam)

Lecture 48 Solved Problem - 19 (Macaulay’s method)

Lecture 49 Solved Problem - 20 (Macaulay’s method)

Lecture 50 Practice Problems - 17-20 (Macaulay’s method)

"Analysis of Beams" is a major part of the "Strength / Mechanics of Materials" course, and is aimed at the undergraduate students of mechanical / civil / production / manufacturing / aeronautical / architectural engineering students. The level of understanding is beginner to intermediate.