Instructor : Asst.Prof.Dr.Turgut AKYÜREK

e-mail :

Office: L-A18

Office Telephone: 2331303

Lecture Hours : Thursday 17:00 – 20:00 @ Balgat

Office Hours : Wednesday 10:20 – 11:10. Appointments are accepted.

Web site :

Course Description: 

  • The course covers the following topics; analysis of stress, strain and material properties, problems in elasticity, failure criteria, bending of beams, torsion of prismatic bars, numerical method, application of energy methods, and plastic behavior of materials.
  • The course will begin with a thorough explanation to solving mechanical problems, by presenting the theory of stress and strain.  These basics will be used to derive generalized elastic constitutive relations in materials with anisotropic and time-dependent properties.  Prediction of failure of materials will be covered in sections dealing with yielding, failure criteria, and fatigue.
  • These components will provide a basis for elasticity solutions assuming either plane stress or strain.  Finally, these solution techniques will be applied to the stress analysis of curved beams, beams on elastic foundations, asymmetric beams, torsion of prismatic elements, and thick-walled cylinders.  

Course Objective: Aims of this course are:

  • To provide a thorough understanding of advanced topics concerning the response of materials and structural elements to applied forces of deformation.    
  • To give a firm foundation to advanced design topics while providing the foundations to finite element solutions to more complex problems.

Method of Instruction: 

The instruction for ME 526 will consist of three one-hour lectures each week.  These lectures will introduce the analytical techniques and advanced mechanics concepts that were described above.  The theories will be reinforced through regular homework assignments and exams. 

Course Material: Text Book is “Advanced Mechanics of Materials and Applied Elasticity”,  5th Edition, Ugural, A. C. and S. K. Fenster.  2012.  Prentice Hall.  704 pp, ISBN-10 0-13-707920, ISBN-13 978-0-13-707920-9. 



There will be 1 mid-term examination, 1 final examination, 5 quizzes and 5 homework. 

Notes and Assignments: 

Course notes and assignments, along with additional information, will be placed on a course web page in PDF format for the student to download. Homework will be due at the beginning of the lecture on the due date, which will be shown on all homework assignments.  No late assignments will be accepted.  Missing assignments will be given a grade of zero.

All electronic material will be in pdf format.  


According to the university regulations, students must attend at least 70 % of the lecture hours. Otherwise, the student gets NA (Not attended) from the course. Valid excuses are exempt from computation of these percentages. 

Apart from the university regulations, it is of student’s benefit to attend all of the lecture hours. 


Overall final grade will be over 1000 points. Weight of each grading item will be as below.

Progress and retention will be evaluated with homework assignments and exams.  Homework will be assigned regularly to reinforce concepts covered in lecture.  A Mid-Term Exam will be given to assess the understanding of the general elasticity components.  A Final Exam will be assigned to assess the ability to utilize the different analysis methods presented in the course.   

The course grade will compromise a weighted average of all assignments.  The specific distribution will be: 


Item Weight


Homework (5x40)


Quiz (5x40)


Mid-Term Exam


Final Exam





All the announcements, including the examination dates, will be posted on the course web site.


Reference Books:

  1. Advanced Strength and Applied Stress Analysis, Richard G. Budynas, 2nd Edition, McGraw Hill, 1999, ISBN: 978–0–07–008985–3.
  2. Mechanics of Materials, Craig, R.R, 3rd Edition, John Wiley & Sons, 2011, ISBN: 978-0-470-48181-3 

Tentative weekly course schedule:






Analysis of Stress











1.1 Introduction

1.2 Scope of Treatment

1.3 Analysis and Design

1.4 Conditions of Equilibrium

1.5 Definition and Components of Stress

1.6 Internal Force-Resultant and Stress Relations

1.7 Stresses on Inclined Sections

1.8 Variation of Stress within a Body

1.9 Plane-Stress Transformation

1.10 Principal Stresses and Maximum In-Plane Shear Stress

1.11 Mohr’s Circle for Two-Dimensional Stress

1.12 Three-Dimensional Stress Transformation

1.13 Principal Stresses in Three Dimensions

1.14 Normal and Shear Stresses on an Oblique Plane

1.15 Mohr’s Circles in Three Dimensions


Strain and Material Properties










2.1 Introduction (HW 1, Quiz 1)

2.2 Deformation

2.3 Strain Defined

2.4 Equations of Compatibility

2.5 State of Strain at a Point

2.6 Engineering Materials

2.7 Stress-Strain Diagrams

2.8 Elastic versus Plastic Behavior

2.9 Hooke’s Law and Poisson’s Ratio

2.10 Generalized Hooke’s Law

2.11 Hooke’s Law for Orthotropic Materials

2.12 Measurement of Strain: Strain Rosettes

2.13 Strain Energy

2.14 Strain Energy in Common Structural Members

215 Components of Strain Energy

2.16 Saint-Venant’s Principle


Problems in Elasticity









3.1 Introduction (HW 2, Quiz 2)

3.2 Fundamental Principles of Analysis

Part A – Formulations and Methods of Solutions

3.3 Plain Strain Problems

3.4 Plain Stress Problems

3.5 Comparison of Two-Dimensional Isotropic Problems

3.6 Airy’s Stress Function

3.7 Solution of Elasticity Problems

3.8 Thermal Stresses

3.9 Basic Relations in Polar Coordinates

3.10 Stresses Due to Concentrated Loads

3.11 Stress Distribution Near Concentrated Loads

3.12 Stress Concentration Factors 


Failure Criteria





4.1 Introduction (HW 3, Quiz 3)

4.2 Failure

4.3 Failure by Yielding

4.4 Failure by Fracture

4.5 Yield and Fracture Criteria

4.6 Maximum Shearing Stress Theory

4.7 Maximum Distortion Energy Theory

4.8 Octahedral Shearing Stress Theory

4.9 Comparison of Yielding Theories

4.10 Maximum Principal Stress Theory

4.11 Mohr’s Theory

4.12 Coulomb-Mohr Theory

4.13 Fracture Mechanics

4.14 Fracture Toughness

4.15 Failure Criteria for Metal Fatigue

4.16 Impact or Dynamic Loads

4.17 Dynamic and Thermal Effects


Bending of Beams












5.1 Introduction (Midterm Exam)

5.2 Pure Bending of Beams of Symmetrical Cross Section

5.3 Pure Bending of Beams of Asymmetrical Cross Section

5.4 Bending of a Cantilever of Narrow Section

5.5 Bending of Simply Supported Narrow Beam

Part B – Approximate Solutions

5.6 Elementary Theory of Bending

5.7 Normal and Shear Stresses

5.9 Composite Beams

5.10 Shear Center

5.11 Statically Indeterminate Systems

5.12 Energy Methods for Deflections

Part C – Curved Beams

5.13 Elasticity Theory

5.14 Curved Beam Formula

5.15 Comparison of the Results of Various Theories

5.16 Combined Tangential and Normal Stresses


Torsion of Prismatic Bars



6.1 Introduction (HW 4, Quiz 4)

6.2 Elementary Theory of Torsion of 

6.3 Stresses on Inclined Planes

6.4 General Solution of the Torsion Problem

6.5 Prandtl’s Stress Function

6.6 Prandtl’s Membrane Analogy

6.7 Torsion of Narrow Rectangular Cross Section

6.8 Torsion of Multiply Connected Thin Walled Sections

6.9 Fluid Flow Analogy and Stress Concentration

6.10 Torsion of Restrained Thin-Walled Members of Open Cross Section


Numerical Methods










Part A – Finite Difference Method

7.1 Introduction

7.2 Finite Differences

7.3 Finite Difference Equations

7.4 Curved Boundaries

7.5 Boundary Conditions

Part B – Finite Element Method

7.6 Fundamentals

7.7 The Bar Element

7.8 Arbitrarily Oriented Bar Element

7.9 Axial Force Equation

7.10 Force Displacement Relations for a truss

7.11 Beam Element

7.12 Properties of Two-Dimensional Elements

7.13 General Formulation of the Finite Element Method

7.14 Triangular Finite Element

7.15 Case Studies in Plane Stress

7.16 Computational Tools


Applications of Energy Methods


10.1 Introduction (HW 5, Quiz 5)

10.2 Work Done in Deformation

10.3 Reciprocity Theorem

10.4 Castigliano’s Theorem

10.5 Unit- or Dummy-Load Method

10.6 Crotti-Engesser Theorem

10.7 Statically Indeterminate Systems

10.8 Prınciple of Virtual Work

10.9 Principle of Minimum Potential Energy

10.10 Deflections of Trigonometric Series

10.11 Rayleigh-Ritz Method


Plastic Behavior of Materials



12.1 Introduction

12.2 Plastic Deformation

12.3 Idealized Stress-Strain Diagrams

12.4 Instability in Simple Tension

12.5 Plastic Axial Deformation and Residual Stress

12.6 Plastic Deflection of Beams

12.7 Analysis of Perfectly Plastic Beams

12.8 Collapse Load of Structures: Limit Design

12.9 Elastic-Plastic Torsion of Circular Shafts

12.10 Plastic Torsion: Membrane Analogy

12.11 Elastic Plastic Stresses in Rotating Discs

12.12 Plastic Stress-Strain Relations

12.13 Plastic Stress-Strain Increment Relations

12.14 Stresses in Perfectly Plastic Thick Walled Cylinders