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Module Code: TRE1262
Module Title: Mechanics of Materials
Semester: 2 (2024-2025)
Credits: 15 & Hours: 102
Co-requisites: Physics for Engineers I & Mathematics for Engineers I
Dear Class,
Welcome everyone to TRE1262 Mechanics of Materials!
My name is Philbert HABIMANA, I am an Assistant Lecturer in the department of Civil, Environmental & Geomatics Engineering (CEGE) delivering a couple of courses including the Design of Reinforced Concrete Structures I, Basics of Reinforced Concrete Design, Civil Engineering Drawing, Engineering Drawing & CAD, Engineering Mechanics, Strength of Materials, Mechanics of Materials, Construction Materials & Technology, Structural Analysis I & II, and Concrete Technology among others.
BRIEF DESCRIPTION
Mechanics of Materials is one of key courses in different engineering fields such as civil engineering and mechanical engineering.
The course aims to develop an understanding of forces systems (including the application of forces on both rigid and deformable bodies and their effects), equilibrium of particles and bodies, truss analysis, mechanical properties of materials, behaviour of different types of materials and geometrical properties of sections.
It introduces stress and strain characteristics and their application in engineering field. In Laboratory, tests, particularly, of tension, compression, shear, etc. are performed to strengthen the theory on mechanical properties of some materials and its behaviour.
Later on, the knowledge gained through this course might help you in selection of materials (i.e. its nature, its size, its geometry, etc.) that might be used in any civil engineering field especially transportation engineering.
Mechanics of Materials is a module offered to Year 1 Undergraduate Students in the department of Civil, Environmental & Geomatics Engineering (CEGE) – Transportation Engineering Option (Nyarugenge Campus). This is a 15 credits course and supposed to be delivered twice a week with a total of 102 contact hours.
The Module intends to develop in the student an ability to understand principles of Mechanics of Materials and instrumental techniques for the practical issues of every life within the engineering field.
- The course aims to provide the basics of Mechanics of Materials as applied to Engineering practice.
- The Mechanics of Materials course delivered here combines the essential of both Engineering Mechanics (Statics & Dynamics) and Strength of Materials previously delivered in the old Civil Engineering program. Therefore, both rigid and deformable bodies are studied taking into account all necessary details.
- This course has three major parts: Statics, dynamics and strength of materials.
- The statics part covers the following topics: Force systems in 1D, 2D & 3D, equilibrium of a particle and equilibrium of a force in 1D, 2D & 3D, truss analysis (both methods of joints & sections), properties of areas (centroid or centre of gravity, first/statical moment of area, second moment of area or moment of inertia, section modulus and radius of gyration), and friction.
- The dynamics part covers the following topics: Rectilinear and curvilinear motions (in kinematics), equation of motion, angular momentum, work and energy, and impulse and momentum (in kinetics).
- The strength of materials part covers the following topics: Mechanical properties of materials, simple stresses and strains, elastic constants, strain energy, geometrical properties of sections, compound stresses and strains, shear force and bending moment, bending stresses in beams, combined direct and bending stresses, deflection of beams, and torsion.
- This course is the pre-requisite for other important courses in any engineering field and particularly in transportation engineering.
Key units to be covered include:
- Statics _ Force systems, equilibrium of a particle and plan truss analysis, properties of areas, and friction.
- Dynamics _ Kinematics and kinetics
- Properties of materials, simple stresses and strains, and strain energy
- Compound stresses and strains
- Equilibrium of beams-Shear force (SF), bending moment (BM), bending and shear stresses, combined direct and bending stresses, deflection, and torsion in members
LEARNING OUTCOMES
- Describe the basic concepts of Mechanics of Materials.
- Demonstrate knowledge and understanding of Engineering Mechanics (statics and dynamics of rigid bodies subjected to a force under various conditions) and its importance in engineering field.
- Demonstrate knowledge and understanding of Strength of Materials (stress-strain relationship, behaviour of materials (both rigid and deformable) subjected to various exposure conditions and selection of materials (both rigid and deformable) for a particular service based on its characteristics) and its importance in engineering field.
- Apply data to the solution of Mechanics of Materials problems, undertake self-learning in Mechanics of Materials and be able to produce simple written reports of some tasks.
Instructor: Ir. Philbert HABIMANA
Room: 1R11 in Einstein Block (Former KIST 2 Building)
Email: phabimana@ur.ac.rw/titiriva10@gmail.com
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I. STATICS:
Force Systems
- Introduction to Engineering Mechanics
- Principles of Mechanics
- Characteristics of a force
- Types of forces
- Moment of a force
Equilibrium of a particle
- Equilibrium of a particle
- Equilibrium of a particle in two and three dimensions
- Equilibrium of a rigid body
- Equations of equilibrium or conditions of equilibrium
- Lami’s theorem
Plane truss analysis
- Type of supports and reaction
- Static determinacy
- Plane trusses
- Solution of plane trusses with method of joints and method of sections
- Frames and machines
Properties of areas
- Centroid or centre of gravity
- First moment of area or statical moment of area
- Second moment of area or moment of inertia
- Polar moment of inertia (perpendicular axis theorem)
- Parallel axis theorem
- Section modulus
- Radius of gyration
Friction
- Theory of friction.
- Types of friction
- Applications of friction
II. DYNAMICS:
- Kinematics: Rectilinear and curvilinear motion of particle.
- Kinetics: Equation of motion, angular momentum, work and energy, and impulse and momentum.
III. STRENGTH OF MATERIALS:
- Mechanical properties of materials: introduction, various definition, properties of materials, behaviour of ductile and brittle materials.
- Simple stresses and strains: introduction, simple stresses, types of stresses, simple strains, types of strains, stress-strain diagram, thermal stresses, thermal stresses in bars of varying section, and thermal stresses in composite bars. Numerical problems.
- Elastic constant: types, modulus of elasticity, Hooke’s law, modulus of rigidity (shear modulus), bulk modulus, Poisson’s ratio, relationship between three moduli, derivation of various formulae, typical elastic constant for different engineering materials, load and stress limit, allowable load/allowable stress, and selection of factor of safety. Numerical problems.
- Strain energy: introduction, strain energy due to gradually applied load, strain energy due to suddenly applied load, and strain energy due to shear stress. Numerical problems.
- Compound stresses and strains: state of stress at a point (general 2D system), principal planes and principal stresses, biaxial direct stress, uniaxial direct stress, case of pure shear stress, Mohr’s cycle for stresses, construction of Mohr’s cycle, and principal strains and strain energy due to principal stresses. Numerical problems.
- Equilibrium of beams-Shear force (SF) and bending moment (BM): introduction, types of loading, types of beams, shear force and bending moment diagrams, sign convention for shear force and bending moment, important points for drawing shear force (SF) and bending moment (BM) diagrams, methods for constructing shear force and bending moment diagrams, shear force (SF) and bending moment (BM) diagrams for various types of beams with different loading conditions, numerical examples, relationships between load, shear force and bending moment.
- Bending and shear stresses in beams: introduction, theory of simple bending with assumptions made, theory of simple bending, expression for bending stress, moment of resistance, bending stresses in symmetrical sections, section modulus, bending stresses in unsymmetrical sections, shear stresses, shear stress formula. Numerical problems.
- Combined direct and bending stresses: introduction, resultant stress when a column of rectangular section is subjected to an eccentric load, stress distribution due to the position of the applied load, and resultant stress when a column of rectangular section is subjected to a load which is eccentric on both axes. Numerical problems.
- Deflection of beams: introduction, relationships between loading, shear force (SF), bending moment (BM), slope and deflection of beam, methods for deflection of beams, and formulae for slope and deflection of beams. Numerical problems.
- Torsion: introduction, pure torsion, polar moment of inertia, torsion rigidity, power transmitted by a shaft, and composite shafts. Numerical problems.
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Unit I: Statics _ Force systems, equilibrium of a particle and plane truss analysis, properties of areas, and friction.
This unit I focuses on the introduction to Mechanics, force systems, equilibrium of particles and bodies, truss analysis, friction and its application in engineering, properties of areas and the importance of geometry and positioning in Civil Engineering including Transportation Engineering.
ILOs:
At the end of this unit, you will be able to:
1. Describe a force, a particle and a structure such as plane truss. In addition,
you will be able to describe the effects of a force on particles, rigid bodies
and different force systems
2. Understand the basic principles of Mechanics and the basics of equilibrium
in Mechanics
3. Apply data to the solution of Mechanics of Materials problems
4. Understand the importance of positioning and referencing in Mechanics,
apply various theorems and principles involved in solving problems related
to plane surfaces, understand the concept of friction, analyse a given
scenario and produce a free body diagram (FBD), and understand
different methods used for solving problems related to plane truss analysis
Learning resources
1. Read carefully the attached lecture notes
2. Read the relevant parts of various reference books attached on this course
3. Re-do yourself various solved examples available in the attached lecture notes
4. Solve different relevant tutorials attached on this course
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Students mustMark as done
Instructions:
1. You should work in small groups of students, and please do not exceed
the maximum number of 7 students for each group.
2. The report should be simple, concise and clean.
3. Present your work in a legible writing and organized format.
4. Submit the soft copies on phabimana@ur.ac.rw by 10:59 AM on
03/03/2025.
5. Under no circumstances a late submission can be accepted.
6. Submit the hard copies by 10:59 AM in class (Muhazi – 0R05).
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This unit emphases on the dynamics of rigid bodies as it is offered in Mechanics. Both kinematics (rectilinear and curvilinear motion of particle) and kinetics (equation of motion, angular momentum, work and energy, and impulse and momentum) are dealt in details here.
ILOs:
At the end of this unit, you will be able to:
1. Describe a particle subjected to a dynamic system
2. Identify the basic relations between displacement, velocity and acceleration
3. Understand the principles of kinematics and kinetics
4. Apply data to the solution of Mechanics of Materials problems
Learning resources
1. Read carefully the attached lecture notes
2. Read the relevant parts of various reference books attached on this course
3. Re-do yourself various solved examples available in the attached lecture notes
4. Solve different relevant tutorials attached on this course
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This unit focuses on properties of materials, application of forces on deformable bodies and their effects (stresses and strains).
It introduces to you stress and strain characteristics and their application in engineering field. In Laboratory, tests, particularly, of tension, compression, shear, etc. are performed to strengthen the theory on mechanical properties of some materials and its behaviour.
It also provide knowledge and skills necessary for understanding various activities leading to the generation of strain energy in Mechanics.
The selection of adequate materials which fulfill both durability and economic requirements may also be made based on the knowledge gained through this unit.
The elastic constants, factor of safety, allowable load, and other typical characteristics of materials are also undertaken here.
ILOs:
At the end of this unit, you will be able to:
1. Get insights into various terminology and definitions
2. Understand the main properties of materials and be able to select a
materials based on its characteristics and the service to be accomplished
in a define life span
3. Describe a scenario and evaluate the associated strain energy
4. Apply data to the solution of Mechanics of Materials problems
Learning resources
1. Read carefully the attached lecture notes
2. Read the relevant parts of various reference books attached on this course
3. Re-do yourself various solved examples available in the attached lecture notes
4. Solve different relevant tutorials attached on this course
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This unit emphases on state of stress at a point (general 2d system), principal stresses, biaxial direct stress, uniaxial direct stress, case of pure shear stress, Mohr’s cycle for stresses, construction of Mohr’s cycle and principal strains and strain energy due to principal stresses.
It is essential to the understanding on what happen inside a particular body subjected to some loading conditions.
The knowledge gain through this unit may serves a base to understand other future courses such as Soil Mechanics, Soil Dynamics, Foundation engineering, etc.
ILOs:
At the end of this unit, you will be able to:
1. Understand compound stresses and strains
2. Establish differences between simple and compound stresses, and simple
and compound strains
3. Describe Mohr’s cycle
4. Apply data to the solution of Mechanics of Materials problems
Learning resources
1. Read carefully the attached lecture notes
2. Read the relevant parts of various reference books attached on this course
3. Re-do yourself various solved examples available in the attached lecture notes
4. Solve different relevant tutorials attached on this course
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Unit V: Equilibrium of beams-Shear force (SF), bending moment (BM), bending and shear stresses, deflection, and torsion in members.
This unit focuses on types of loading, types of beams, shear force (SF) and bending moment (BM) diagrams, sign convention for shear force and bending moment, important points for drawing shear force (SF) and bending moment (BM) diagrams, methods for constructing the shear force and bending moment diagrams, shear force (SF) and bending moment (BM) diagrams for various types of beams with different loading conditions, and relationships between load, shear force, and bending moment.
It introduces you to bending stresses, theory of simple bending with assumptions made, theory of simple bending, expression of bending stress, moment of resistance, bending stress in symmetrical sections, section modulus, bending stresses in unsymmetrical sections, shear stresses and shear stress formula.
Introduction to combined stresses, resultant stress when a column of rectangular section is subjected to an eccentric load, stress distribution due to the position of the applied load, and resultant stress when a column of rectangular section is subjected to a load which is eccentric on both axes
Introduction to defection and slope, relationships between loading, shear force, bending moment, slope and deflection of beam, methods for deflection of beams and formulae for slope and deflection of beams.
Introduction to torsion, pure torsion, polar moment of inertia, torsion rigidity, power transmitted by a shaft, and composite shafts.
It is essential to the understanding on how loading and both longitudinal and lateral dimensions of any structural elements influence its behaviour.
The knowledge gain through this unit may serves a base to understand other future courses such as Theory of Structures, Introduction to Finite Elements, Bridge Engineering, etc.
ILOs:
At the end of this unit, you will be able to:
1. Describe the behaviour of structural elements such as beams considering
loads and other factors
2. Understand all steps involved in determining shear force (SF), bending
moment (BM), bending and shear stresses, deflection, and torsion and their respective
effects on structural elements/members
3. Establish differences between bending moment (BM) and deflection
4. Apply data to the solution of Mechanics of Materials problems
Learning resources
1. Read carefully the attached lecture notes
2. Read the relevant parts of various reference books attached on this course
3. Re-do yourself various solved examples available in the attached lecture notes
4. Solve different relevant tutorials attached on this course
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-
Students mustMark as done
Instructions:
1. You should work in small groups of students, and please do not exceed the maximum number of 7 students for each group.
2. The report should be simple, concise and clean.
3. Present your work in a legible writing and organized format.
4. Submit the soft copies at UR E-learning platform by 10:59 AM on 05/05/2025.
5. Under no circumstances a late submission can be accepted.
6. Submit the hard copies by 10:59 AM in class (Muhazi – 0R05).
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In this section, the tentative course schedule is proposed based on the date that course should have been delivered.
Date for important tasks such assignments and CATS were proposed including the possible rooms and time.
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This section contains a couple of references. Some focus on engineering mechanics, others on strength of materials and on mechanics of materials.
You are encouraged to read as many references as possible and solve a couple of exercises (self-learning) in order to succeed in this course.
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This section contains the following subtopics:
1. Introduction
2. Some pre-requisites and co-requisites
3. Brief description of aims
4. Intending learning outcomes
5. Course content
6. Assessment tasks
7. Allocation of study and teaching hours
8. Assessment pattern
9. Tentative lecture schedule
10. Classroom rules of conduct
11. How to study Mechanics of Materials
12. Some important point of Academic regulations amended and approved by the UR Senate of the 21st November 2018
14. Access to UR e-learning platform
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- Home Assignments: There are 3 home assignments each in small groups of students has to submit within a given time period.
- Tests: There are two tests. The first test will be done after 18 lecture-hours and the second one after 48 lecture-hours.
- Examination: Examination will be conducted at the end of the trimester. The examination is divided into two sections, Section A with a compulsory question and Section B where students choose two questions out of three. However, each Section may contain Theory questions as well as Problem solving.
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A list of reference books have been provided, however, one of them was selected and attached here for your own interest.
This book focuses on Statics and Dynamics as part of Mechanics of Materials.
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A list of reference books have been provided, however, some of them were selected and attached here for your own interest.
These books focus on Statics, Dynamics and Strength of Materials as part of Mechanics of Materials.
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A list of reference books have been provided, however, two of them was selected and attached here for your own interest.
The reference book 1 focuses on Statics and Strength of Materials as part of Mechanics of Materials.
The reference book 2 focuses on Strength of Materials also commonly know as Mechanics of Materials.
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