Introduction to Mechanics: Free Body Diagrams, Equilibrium, and Force Analysis, Lecture notes of Mechanics

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ESO202A-204:ESO202A-204:

Mechanics of Solids Mechanics of Solids

Introduction Introduction

S.Kamle S.Kamle

Aerospace Engg. Department Aerospace Engg. Department

Outline of Today’s lectureOutline of Today’s lecture

About the courseAbout the course

Review of physics concepts- Force,Review of physics concepts- Force,

Moment, vectors Moment, vectors

Introduction to Mechanics- FreeIntroduction to Mechanics- Free

Body Diagram Body Diagram

About ESO202A-ESO204About ESO202A-ESO

The course is being developed as a webThe course is being developed as a web

based course. All Home Work sheets, based course. All Home Work sheets,

Quiz / Exam. solutions will be posted on Quiz / Exam. solutions will be posted on

Brihaspati. Brihaspati.

Course content available on-line at Course content available on-line at

Brihaspati: Brihaspati:

http://brihaspati.nmeict.in/brihaspati/servlet/b http://brihaspati.nmeict.in/brihaspati/servlet/b

You can login As guest (The password isYou can login As guest (The password is

also guest). also guest).

Course ContentsCourse Contents

Free body diagram, Modeling ofFree body diagram, Modeling of

supports, Conditions for equilibrium, supports, Conditions for equilibrium,

friction. friction.

Force-deformation relationship andForce-deformation relationship and

geometric compatibility (for small geometric compatibility (for small

deformations) with illustrations deformations) with illustrations

through simple problems on axially through simple problems on axially

loaded members and thin-walled loaded members and thin-walled

pressure vessels pressure vessels

Course ContentsCourse Contents

 (^) Discussion of experimental results on 1-D stress-Discussion of experimental results on 1-D stress- strain curve, Concepts of isotropy, orthotropy, strain curve, Concepts of isotropy, orthotropy, anisotropy, Generalized Hooke's law (without and anisotropy, Generalized Hooke's law (without and with thermal strains), Complete equations of with thermal strains), Complete equations of elasticity, elasticity,  (^) Torsion of circular shafts and thin-walled tubesTorsion of circular shafts and thin-walled tubes (plastic analysis and rectangular shafts not to be (plastic analysis and rectangular shafts not to be discussed). discussed).  (^) Bending of beams with symmetric cross sectionBending of beams with symmetric cross section (Normal and shear stresses) (shear center and (Normal and shear stresses) (shear center and plastic analysis not to be discussed). plastic analysis not to be discussed).

Course ContentsCourse Contents

Combined stresses, Yield criteria.Combined stresses, Yield criteria.

Deflection due to bending,Deflection due to bending,

Integration of the moment-curvature Integration of the moment-curvature

relationship for simple boundary relationship for simple boundary

conditions, Superposition principle conditions, Superposition principle

(singularity functions not to be (singularity functions not to be

used). used).

BooksBooks

 Text BookText Book

S.H.Crandall, N.C.Dahl and T.J.Lardner,S.H.Crandall, N.C.Dahl and T.J.Lardner,

"An introduction to the mechanics of "An introduction to the mechanics of

solids", second edition with SI units, solids", second edition with SI units,

McGraw Hill 1978 McGraw Hill 1978

Reference Books Reference Books

Shames I.H., "Engineering MechanicsShames I.H., "Engineering Mechanics

Statics and Dynamics", Prentice Hall of Statics and Dynamics", Prentice Hall of

India, 1996 India, 1996

Popov E.G. "Engineering mechanics ofPopov E.G. "Engineering mechanics of

soilds", Prentice Hall of India, 1993 soilds", Prentice Hall of India, 1993

Grade Break-upGrade Break-up

Method Of evaluation Weightage

Mid. Sem. Exam.15 Feb 30%

End Sem. Exam.18 April 40%

Quiz(best 3 of 4 quizzes) 15%

Home Work 8%

Attendance 7%

Vector AnalysisVector Analysis

 (^) Vectors have aVectors have a starting point at one starting point at one end (tail) and an end (tail) and an arrow at the opposite arrow at the opposite end (head). The tail is end (head). The tail is located at the point of located at the point of origin. origin.  (^) Component vectorsComponent vectors can be determined by can be determined by plotting them on a plotting them on a rectangular coordinate rectangular coordinate system system

Addition of vectorsAddition of vectors

When twoWhen two or more vectors are added theyor more vectors are added they

yield the sum or resultant vector. yield the sum or resultant vector.

Vector operationsVector operations

Dot ProductDot Product

Projection of a vectorProjection of a vector

Cross ProductCross Product