ENGINEERING 5312:Mechanics of Solids II


Instructor†††††††††††††††††† Dr. Seshu Adluri†††††††††††††††††††† Teaching Assist: Mr. B.C. Mondal (assgnmt)

E-mail†††††††††††††††††††††††††††††††††††††††††††††† E-mail††††††††††††† ††† bm6080@

Phone†††††††††††††††††††††††† 864-3800†††††††††††††††††††††††††††††††† Phone††††††††††††††††††††††††

Office Location††††††††† EN-3022††††††††††††††††††††††††††††††††† Office Location†† EN 4030

Office Hours†††††††††††††† Monday 10:00-11:50 a.m.†††† Office Hours††††††††††††††



CALENDAR ENTRY: †††††††††††††††


Begins with an introduction to earlier concepts then considers strain transformation; deflections of beams and shafts, energy methods; failure theories; buckling of columns and the inelastic behaviour of beams.††




The course gives an insight into the bending and axial deformation characteristics of mechanical and structural components such as beams, columns, etc. Continuing from the earlier course on the stress/strain response of structural elements, this course will seek to introduce the theory and application of several important principles for the failure of materials, estimation of deformations, use of energy methods, etc. Emphasis will be on the basic requirements of satisfying force equilibrium, compatibility of deformation, and material behaviour. The laboratory experiments give a physical introduction to the behaviour of elements when subjected to loads that deform them.


PREREQUISITES:†††††††††††††††††††† ENGI 4312


COREQUISITES:†††††††††††††††††††††† ENGI 1010


SCHEDULE:††††††††††††††††††††††††††††† LECTURE: MWF 12:00-12:50 pm†††† †† Room: EN4035

††††††††††††††††††††††† ††††††††††††††††††††††† TUTORIAL: Monday 4:00-4:50††† ††††††† Room: EN1054


CREDIT VALUE:†††††††††††††††††††††† 3 credits




††††††††††† Text book

         Mechanics of Materials by R.C. Hibbeler, Prentice-Hall


REFERENCES:As discussed in class from time to time




1. Combined Loads (quick review) and Stress Transformation

1.1 Plane Stress Transformation

1.2 General Equations for Stress Transformation

1.3 Principal Stresses and Max. In-Plane Shear Stress

1.4 Mohrís Circle for Stresses

1.5 Absolute Max. Shear Stress

2. Strain Transformation

2.1 Plane Strain (Review)

2.2 Equations of Plane Strain Transformation (over view)

2.2.1 Principal strains (over view)

2.2.2 Maximum in-plane shear strain (over view)

2.3 Mohr's Circle for Plane Strain (over view)

2.4 Absolute Maximum Shear Strain (over view)

2.5 Strain Gauge Rosettes

2.6 Material Property Relationships

2.7 Theories of Failure

2.7.1 Ductile materials

2.7.2 Brittle materials

2.8 Inelastic Bending and Residual Stresses (optional)

3. Deflection of Beams and Shafts

3.1 Elastic Curve

3.2 Slope and Displacement of Statically Determinate Beams and Shafts

3.2.1 Integration method

3.2.1 Discontinuity functions

3.2.1 Moment-Area method

3.2.1 Method of superposition

3.3 Slope and Displacement of Statically Indeterminate Beams and Shafts

3.3.1 Integration method

3.3.1 Moment-Area method

3.3.1 Method of superposition

4. Buckling of Columns

4.1 Critical Load

4.1.1 Ideal column with pin supports

4.1.2 Fixed and pinned supports

4.2 Secant Formula (optional)

5. Energy Methods

5.1 External Work and Strain Energy

5.1.1 Work of a force

5.1.2 Work of a couple

5.1.3 Strain energy

5.2 Strain Energy for Different Loadings

5.2.1 Axial load

5.2.2 Bending moment

5.2.3 Transverse shear

5.2.3 Torsional moment

5.3 Conservation of Energy

5.4 Impact Loading

5.5 Virtual Work

5.6 Castigliano's Theorem (optional)

The topics above may be supplemented with other topics. The optional topics above may be covered depending upon the interest and time available.All topics that are covered will be part of the examination.




Upon successful completion of this course, the student will be able to:

  1. Calculate principal stresses strains and maximum shear stress using equations and Mohrís circle.
  2. Have a basic idea of the plane stress, plane strain and strain gauge calculations.
  3. Describe basic theories of failure for ductile and brittle materials.
  4. Calculate slope and deflection of statically determinate beams and shafts.
  5. Calculate slope and deflection of statically indeterminate beams and shafts.
  6. Compare analytical and experimental values of strains in beams.
  7. Use both measured deflections and theory to determine the Youngís modulus of a given material.
  8. Calculate buckling capacity of elastic columns under axial compression.
  9. Compare analytical and experimental values of buckling loads of columns.
  10. Determine deflections and strains in simple trusses.
  11. Explain the relationship of external work to strain energy.
  12. Use energy methods to determine strain energy and calculate internal forces.
  13. Communicate experimental data, analysis and conclusions in a clear, professional manner.



††††††††††††††††††††††††††††††††††††††††††††††† Approximate Due Dates

Assignments  ††††††††††††††† 10% †††††††††††††††††††††††††† Assignments are due one week from announcement unless otherwise agreed upon

Labs†††††††††††††††††††††††††††††† 5%††††††††††††††††††††††††††††† TBA

Midterm†††††††††††††††††††††† 25%††††††††††††††††††††††††††† Feb 9††

Final exam  ††††††††††††††††† 60%†††††††††††††††††††††††††††

Exam policy: The formula sheet policy is as per the announcement in the class.All or a subset of the preannounced formula sheet will be provided in the exam.It is the same as that from the front flaps of the book.No extra text or notes are permitted in the exam.IPODS, Blackberries, MP3 players, or other electronic storage/retrieval devices are not permitted in the exam.Please see the appropriate guidelines from the University regarding such matters.

Comprehensive examples will be discussed primarily during tutorials. During tutorials, the students may be required to solve the problems in class to gain practice.

Please note that prewritten solutions may or may not be available for the assignments.However, the tutorial immediately following the return of each marked assignment is allotted for discussing the relevant solutions.At that time, if the students ask for it, the problems can be discussed and may even be solved in class.If the students do not raise their need for discussion of the problems, the time will be spent on solving other problems.The same policy holds for midterm exams and quizzes, if any.

The students are expected to solve the assignment problems by themselves in order to reinforce the class instruction.Please refer to copying policy of the University if there is any doubt.Help with the assignment problems can be sought during contact hours and/or tutorial time.

Warning:If the students are unable to draw proper Free Body Diagrams, Bending Moment and Shear Force Diagrams, the relevant questions may be marked zero even if the rest of the solution is partly or wholly correct.The same applies for using and clearly stating the correct units in any given problem.If the student fails in this, the relevant questions may be marked as zero.


Marks going into the final exam

If there are any discrepancies, please talk to Dr. Adluri immediately after the final exam (before leaving the exam hall).

Please note that changes at a later date are not possible.



There will be four laboratory exercises. Each experiment will be set up in the Structures Lab Room EN 1033. Each group will arrange with the Technician to schedule their use of the equipment.†††


Students are expected to demonstrate awareness of, and personal accountability for, safe laboratory conduct.  Appropriate personal protective equipment (PPE) must be worn (e.g. steel-toed shoes, safety glasses, etc.) and safe work practices must be followed as indicated for individual laboratories, materials and equipment.Students will immediately report any concerns regarding safety to the teaching assistant, staff technologist, and professor. 


Lab handouts:

The lab handouts are for general instructions and explanations only.Students are must not simply cut and paste material from the handouts.Students must write the report in their own words.All explanations, calculations, graphs, etc., must be independently done without copying either from the handouts or from another group (present or past).



Students are expected to conduct themselves in all aspects of the course at the highest level of academic integrity. Any student found to commit academic misconduct will be dealt with according to the Faculty and University practices. More information is available at


Students are encouraged to consult the Faculty of Engineering and Applied Science Student Code of Conduct at and Memorial Universityís Code of Student Conduct at



Students who require physical or academic accommodations are encouraged to speak privately to the instructor so that appropriate arrangements can be made to ensure your full participation in the course.All conversations will remain confidential.


The university experience is enriched by the diversity of viewpoints, values, and backgrounds that each class participant possesses.In order for this course to encourage as much insightful and comprehensive discussion among class participants as possible, there is an expectation that dialogue will be collegial and respectful across disciplinary, cultural, and personal boundaries.


STUDENT ASSISTANCE:Student Affairs and Services offers help and support in a variety of areas, both academic and personal.More information can be found at





Lab report general instructions,LAB1, LAB2, LAB3, LAB4




Assign1, Assign2, Assign3, Assign4, Assign5, Assign6, Assign7, Assign8