Course Description

Develops the concepts of stress and strain in three dimensions for design analysis. Material behavior is accounted for in the constitutive modeling of solids including metals, ceramics, and composites by generalized Hooke's law, nonlinear elastomers such as rubber or soft biological tissue by nonlinear elasticity and polymers by viscoelasticity. Linear elasticity is developed and applied to curved beams, torsion of a rod, pressurized thick-walled cylinders, etc. Equilibrium deformation analysis by energy methods (the foundation of the finite element method) is developed and applied to plates, etc.


Advanced Strength and Applied Elasticity, Fourth Edition


Text Book Advanced Strength and Applied Elasticity, Fourth Edition  by Ansel C. Ugural (Author), Saul K. Fenster (Author)

ANSEL C. UGURAL, Ph.D., is Research Professor at New Jersey Institute of Technology. He has held various faculty and administrative positions at Fairleigh Dickinson University, and he taught at the University of Wisconsin. Ugural has considerable industrial experience in both full-time and consulting capacities. A member of several professional societies, he is the author of the books Mechanics of Materials, Stresses in Plates and Shells, and Mechanical Design: An Integrated Approach.

SAUL K. FENSTER, Ph.D., is Professor at New Jersey Institute of Technology, where he served as a president for over two decades. In addition to experience in industry, he has held varied positions at Fairleigh Dickinson University and taught at the City University of New York. Fenster, a Fellow of the American Society of Mechanical Engineers and the American Society for Engineering Education, is co-author of a text on mechanics.



Statics, Strength, Machine Design


Prof Dr Bülent Ekici      

Room: MC 570

email: bulent.ekici@marmara.edu.tr

Tel: 0216-3480292 561

Office Hours 

To be announced.


Lecture Contents

1. Analysis of Stress.

Introduction. Scope of Treatment. Definition of Stress. Components of Stress: Stress Tensor. Some Special Cases of Stress. Internal Force-Resultant and Stress Relations. Stresses on Inclined Planes in an Axially Loaded Member. Variation of Stress within a Body. Two-Dimensional Stress at a Point. Principal Stresses and Maximum Shear Stress in Two Dimensions. Mohr's Circle for Two-Dimensional Stress. Three-Dimensional Stress at a Point. Principal Stresses in Three Dimensions. Normal and Shear Stresses on an Oblique Plane. Mohr's Circle for Three-Dimensional Stress. Boundary Conditions in Terms of Surface Forces.

2. Strain and Stress-Strain Relations.

Introduction. Deformation. Strain Defined. Equations of Compatibility. State of Strain at a Point. Engineering Materials. Stress-Strain Diagrams. Hooke's Law and Poisson's Ratio. Generalized Hooke's Law. Measurement of Strain: Bonded Strain Gages. Strain Energy. Strain Energy in Common Structural Member. Components of Strain Energy. Saint-Venant's Principle.

3. Two-Dimensional Problems in Elasticity.

Introduction. Fundamental Principles of Analysis. Part A-Formulation and Methods of Solution. Plane Strain Problems. Plane Stress Problems. Airy's Stress Function. Solution of Elasticity Problems. Thermal Stresses. Basic Relations in Polar Coordinates. Part B-Stress Concentrations. Stresses Due to Concentrated Loads. Stress Distribution near Concentrated Load Acting on a Beam. Stress Concentration Factors. NEUBER'S DIAGRAM. Contact Stresses.

4. Failure Criteria.

Introduction. Failure. Failure by Yielding. Failure by Fracture. Yield and Fracture Criteria. Maximum Shearing Stress Theory. Maximum Distortion Energy Theory. Octahedral Shearing Stress Theory. Comparison of the Yielding Theories. Maximum Principal Stress Theory. Mohr's Theory. Coulomb-Mohr Theory. Introductory Fracture Mechanics. Failure Criteria for Metal Fatigue. Fatigue Life under Combined Loading. Impact or Dynamic Loads. Dynamic and Thermal Effects.

5. Bending of Beams.

Introduction. Part A-Exact Solutions. Pure Bending of Beams of Symmetrical Cross Section. Pure Bending of Beams of Asymmetrical Cross Section. Bending of a Cantilever of Narrow Section. Bending of a Simply Supported, Narrow Beam. Part B-Approximate Solutions. Elementary Theory of Bending. Bending and Shearing Stresses. Effect of Transverse Normal Stress. Composite Beams. Shear Center. Statically Indeterminate Systems. Energy Method for Deflections. Part C-Curved Beams. Exact Solution. Tangential Stress. Winkler's Theory. Combined Tangential and Normal Stresses.

6. Torsion of Prismatic Bars.

Introduction. Elementary Theory of Torsion of Circular Bars. General Solution of the Torsion Problem. Prandtl's Stress Function. Prandtl's Membrane Analogy. Torsion of Thin-Walled Members of Open Cross Section. Torsion of Multiply Connected Thin-Walled Sections. Fluid Flow Analogy and Stress Concentration. Torsion of Restrained Thin-Walled Members of Open Cross Section. Curved Circular Bars: Helical Springs.

7. Numerical Methods.

Introduction. Finite Differences. Finite Difference Equations. Curved Boundaries. Boundary Conditions. Finite Element Method. Properties of a Finite Element. Formulation of the Finite Element Method. Triangular Finite Element. Use of Digital Computers.

8. Axisymmetrically Loaded Members.

Introduction. Thick-Walled Cylinders. Maximum Tangential Stress. Application of Failure Theories. Compound Cylinders. Rotating Disks of Constant Thickness. Rotating Disks of Variable Thickness. Rotating Disks of Uniform Stress. Thermal Stresses in Thin Disks. Thermal Stress in Long Circular Cylinders. Finite Element Solution. Formulation of Axisymmetric Element.

9. Beams on Elastic Foundations.

Introduction. General Theory. Infinite Beams. Semi-Infinite Beams. Finite Beams: Classification of Beams. Beams Supported by Equally Spaced Elastic Elements. Simplified Solutions for Relatively Stiff Beams. Solution by Finite Differences. Applications.

10. Energy Methods.

Introduction. Work Done in Deformation. Reciprocity Theorem. Castigliano's Theorem. Unit or Dummy Load Method. Crotti-Engesser Theorem. Statically Indeterminate Systems. Principle of Virtual Work. Principle of Minimum Potential Energy. Application of Trigonometric Series. Rayleigh-Ritz Method.

11. Elastic Stability.

Introduction. Critical Load. Buckling of a Column. End Conditions. Critical Stress in a Column. Allowable Stress. Initially Curved Members Eccentrically Loaded Columns: Secant Formula. Energy Methods Applied to Buckling. Solution by Finite Differences. Finite Difference Solution for Unevenly Spaced Nodes.

12. Plastic Behavior of Materials.

Introduction. Plastic Deformation. True Stress-True Strain Curve in Simple Tension. Instability in Simple Tension. Plastic Deflection of Beams. Analysis of Perfectly Plastic Beams. Collapse Load of Structures. Elastic-Plastic Torsion. Elastic-Plastic Stresses in Rotating Disks. Plastic Stress-Strain Relations. Plastic Stress-Strain Increment Relations. Stresses in Perfectly Plastic Thick-Walled Cylinders.

13. Plates and Shells.

Part A-Bending of Thin Plates.

Basic Assumptions. Strain-Curvature Relations. Stress, Curvature, and Moment Relations. Governing Equations of Plate Deflection. Boundary Conditions. Simply Supported Rectangular Plates. Axisymmetrically Loaded Circular Plates. Deflections of Rectangular Plates by the Strain Energy Method. Finite Element Solution.

Part B-Membrane Stresses in Thin Shells.

Basic Assumptions. Simple Membrane Action. Symmetrically Loaded Shells of Revolution. Some Common Cases of Shells of Revolution. Cylindrical Shells of General Shape.
Appendix A. Indicial Notation.
Appendix B. Solution of the Stress Cubic Equation.
Principal Stresses. Direction Cosines.
Appendix C. Moments of Composite Areas.
Centroid. Moments of Inertia. Parallel-Axis Theorem. Principal Moments of Inertia.
Appendix D. Tables.
Average Properties of Common Engineering Materials. Conversion Factors: SI Units to U.S. Customary Units. SI Unit Prefixes. Deflections and Slopes of Beams.
Answers to Selected Problems.



Grading Policy

Major exam #1                        %30  average of first 6 grade

Major exam #2                        %30  average of last 4 grade

Project                                  %10

Final Exam                              %30


Students are supposed to come to each lecture.


This site was last updated 03/11/15