COURSE UNIT TITLE

: THEORY OF ELASTICITY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
CIE 5003 THEORY OF ELASTICITY ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR BINNUR GÖREN KIRAL

Offered to

STRUCTURAL ENGINEERING
Structural Engineering
STRUCTURAL ENGINEERING

Course Objective

The aim of this course is to introduce the student to the analysis of linear elastic solids under mechanical and thermal loads. The primary intention is to provide for students the essential fundamental knowledge of the theory of elasticity together with a compilation of solutions of special problems that are important in engineering practice and design. The topics presented in this course will also provide the foundation for pursuing other solid mechanics courses such as theory of plates and shells, elastic stability, composite structures and fracture mechanics.

Learning Outcomes of the Course Unit

1   To define an elasticity problem
2   To determine/explain the main concepts in elasticity such as plane stress, plain strain, equations of equilibrium, boundary conditions, compatibility equations and stress function
3   To compare advantages and disadvantages of different solution strategies
4   To select the best solution method to solve an elasticity problem
5   To discuss the results of a solution and compare them with those of elementary level

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Introduction: Introduction, Stress, Components of stress, Components of strain, Hooke's Law, Index notation
2 Plane stress and plane strain: Plane stress, Plane strain, Stress at a point, Strain at a point, Differential equations of equilibrium, Boundary conditions, Compatibility equations, Stress function
3 Two-dimensional problems in rectangular coordinates: Solution by polynomials. Saint-Venant's Principle, Determination of displacements (1st Assignment)
4 Two-dimensional problems in rectangular coordinates: Bending of a beam by uniform load, Other cases of continuously loaded beams, Bending of a cantilever loaded at the end (1st Assignment is submitted)
5 Two-dimensional problems in polar coordinates: General equations in polar coordinates, Stress distribution symmetrical about an axis, Pure bending of curved bars, Strain components in polar coordinates (2nd Assignment)
6 Two-dimensional problems in polar coordinates: Displacements for symmetrical stress distributions, Rotating disks, Bending of a curved bar by a force at the end, The effect of circular holes on stress distributions in plates (2nd Assignment is submitted)
7 Two-dimensional problems in polar coordinates: Concentrated force at a point of a straight boundary, Any vertical loading of a straight boundary, Stresses in a circular disk, Other cases
8 1st Mid-Term Examination
9 Bending of Bars: Bending of a cantilever, Stress function, Circular cross section, Elliptic cross section, Rectangular cross section
10 Torsion: Torsion of straight bars, Elliptic cross section, Membrane analogy, Torsion of a bar of narrow rectangular cross section (3rd Assignment)
11 Torsion: Torsion of rectangular bars, Solution of torsional problems by energy method, Torsion of hollow shafts, Torsion of thin tubes (3rd Assignment is submitted)
12 Analysis of stress and strain in three dimensions: Introduction, Principal stresses, Determination of the principal stresses, Stress invariants, Determination of the maximum shearing stress, Strain at a point, Principal axes of strain, Rotation (4th Assignment)
13 Elementary problems of elasticity in three dimensions: Uniform stress, Stretching of a prismatic bar by its own weight, Twist of circular shafts of constant cross section
14 Elementary problems of elasticity in three dimensions: Pure bending of prismatical bars, Pure bending of plates (4th Assignment is submitted)

Recomended or Required Reading

1. S.P. Timoshenko, J.N. Goodier, Theory of Elasticity. McGraw-Hill, 3rd Edition, Singapore, 1984.
2. M.H. Sadd, Elasticity: Theory, Applications, and Numerics, Elsevier Academic Press, 2005.
3. A.C. Ugural, S. K. Fenster, Advanced Strength and Applied Elasticity, Prentice Hall, 2003.

Planned Learning Activities and Teaching Methods

Lecturing (theoretical), assignments

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

binnur.goren@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparation before/after weekly lectures 13 3 39
Preparing Individual Assignments 4 10 40
Preparation for Final Exam 1 30 30
Preparation for Mid-term Exam 1 25 25
Midterm 1 4 4
Final 1 4 4
TOTAL WORKLOAD (hours) 181

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.144345
LO.24545
LO.344
LO.4454
LO.54445

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