UNION COLLEGE

Civil & Environmental Engineering Department

Spring 2025

Mechanics of Materials

CEE-244

Lectures: T&Th 10:55 - 12:40 PM, Olin-306. Labs: T 1:55 - 4:45 PM, Olin-307.

COURSE DESCRIPTION

Mechanics of Materials is a basic engineering course and is a branch of applied mechanics that deals with the behavior of solid bodies subjected to various types of loading. The solid bodies considered in this course include axially loaded members, shafts in torsion, thin shells, beams, and columns, as well as structures that are assemblies of these components. The objectives of mechanics of materials analysis are the determination of the stresses, strains, and displacements, produced by the loads. Knowing these quantities for all values of load up to the failure load gives a complete picture of the mechanical behavior of the body. Classroom lectures are supplemented with physical demonstrations. The course includes a laboratory where students have an opportunity to build an appreciation for the phenomenon being discussed in lecture.

COURSE GRADE

• Assignments & Quizzes = 25%
• Laboratory Reports = 25%
• Term Test (Th, 6th week) = 25%
• Final Examination = 25%

NOTES

• Attendance of exams is mandatory.
• If you must miss the midterm test due to extraordinary circumstances beyond your control (a letter from the Dean of Students will be required in this case), your 25 points of the midterm test will be automatically transferred to the final exam, i.e., your final will be graded out of 50 points. No makeup for the midterm test will be allowed for any reason. If you miss the midterm without a supporting letter from the Dean of Students, there will be 5 points penalty, i.e, the maximum score you can earn in your final exam is 45/50.
• If you must miss the final exam due to extraordinary circumstances beyond your control (a letter from the Dean of Students will be required in this case), your grade in the course will be prorated based on the components of your term work. No makeup for the final exam will be allowed for any reason.
• Due date for assigned course work will be announced in class. Late submission is assessed at -1 point per day or part thereof.
• The academic performance of the students in this course will be held to the standards of Union College's Honor Code.
• Students with disabilities will be accommodated as per Union College's Policy.

TEXTBOOKS

• Beer, F.P., Johnston, E.R. DeWolf, J., Mazurek, D. (2020). "Mechanics of Materials," 8th Edition, McGraw Hill Publishing Co., New York, NY. ISBN-10: 1260403866, ISBN-13: 978-1260403862. (Required)

• Gere, J.M., and Timoshinko, S.P. (1997). "Mechanics of Materials," Fourth Edition, PWS Publishing Co., Boston, MA. (Not Required)

1.      INTRODUCTION–CONCEPT OF STRESS
1.1 Introduction
1.2 Forces and Stresses
1.3 Axial Loading; Normal Stress
1.4 Shearing Stress
1.5 Bearing Stress in Connections
1.6 Application to the Analysis of Simple Structures
1.7 Stress on an Oblique Plane under Axial Loading
1.8 Stress under General Loading Conditions; Components of Stress
1.9 Ultimate and Allowable Stress: Factor of Safety
Review and Summary

2.      STRESS AND STRAIN – AXIAL LOADING
2.1 Introduction
2.2 Normal Strain under Axial Loading
2.3 Stress-Strain Diagram
2.5 Hooke’s Law; Modulus of Elasticity
2.6 Elastic versus Plastic Behavior of a Material
2.7 Repeated Loadings; Fatigue
2.8 Deformations of Members under Axial Loading
2.9 Statically Indeterminate Problems
2.10 Problems Involving Temperature Changes
2.11 Poisson’s Ratio
2.12 Multiaxial Loading; Generalized Hooke’s Law
2.14 Shearing Strain
2.15 Discussion of the Deformations under Axial Loading
2.16 Stress and Strain Distribution under Axial Loading; Saint-Venant’s Principle
2.17 Stress Concentrations
2.18 Plastic Deformations
Review and Summary

3.      TORSION
3.1 Introduction
3.2 Preliminary Discussion of the Stresses in a Shaft
3.3 Deformations in a Circular Shaft
3.4 Stresses in the Elastic Range
3.5 Angle of Twist in the Elastic Range
3.6 Statically Indeterminate Shafts
3.7 Design of Transmission Shafts
3.8 Stress Concentrations in Circular Shafts
Review and Summary

4.      PURE BENDING
4.1 Introduction
4.2 Prismatic Members in Pure Bending
4.3 Preliminary Discussion of the Stresses in Pure Bending
4.4 Deformations in a Symmetric Member in Pure Bending
4.5 Stresses and Deformations in the Elastic Range
4.6 Deformations in a Transverse Cross Section
4.7 Bending of Members Made of Several Materials
4.8 Stress Concentrations
4.13 Eccentric Axial Loading in a Plane of Symmetry
4.14 Unsymmetric Bending
4.15 General Case of Eccentric Axial Loading
Review and Summary

5.      TRANSVERSE LOADING
5.1 Introduction
5.2 Transverse Loading of Prismatic Members
5.3 Basic Assumption Regarding the Distribution of the Normal Stresses
5.4 Determination of the Shear on a Horizontal Plane
5.5 Determination of the Shearing Stresses in a Beam
5.6 Shearing Stresses in Common Types of Beams
5.8 Shear on an Arbitrary Longitudinal Cut
5.9 Shearing Stresses in Thin-Walled Members
5.11 Stresses under Combined Loadings
Review and Summary

6.      TRANSFORMATIONS OF STRESS AND STRAIN
6.1 Introduction
6.2 Transformation of Plane Stress
6.3 Principal Stresses; Maximum Shearing Stress
6.4 Mohr’s Circle for Plane Stress
6.5 General State of Stress
6.6 Application of Mohr’s Circle to the Three-Dimensional Analysis of Stress
6.9 Stresses in Thin-Walled Pressure Vessels
Review and Summary

7.      DESIGN OF BEAMS AND SHAFTS FOR STRENGTH
7.1 Introduction
7.2 Basic Considerations for the Design of Prismatic Beams
7.3 Shear and Bending-Moment Diagrams
7.4 Relations among Load, Shear, and Bending Moment
7.6 Principal Stresses in a Beam
7.7 Design of Prismatic Beams
Review and Summary

8.      DEFLECTION OF BEAMS BY INTEGRATION
8.1 Introduction
8.2 Deformation of a Beam under Transverse Loading
8.3 Equation of the Elastic Curve
8.5 Statically Indeterminate Beams
8.7 Method of Superposition
Review and Summary

9.      DEFLECTION OF BEAMS BY MOMENT-AREA METHOD
9.1 Introduction
9.2 Moment-Area Theorems
9.3 Application to Cantilever Beams and Beams with Symmetric Loadings
Review and Summary

10.    COLUMNS
10.1 Introduction
10.2 Stability of Structures
10.3 Euler’s Formula for Pin-Ended Columns
10.4 Extension of Euler’s Formula to Columns with Other End Conditions
10.6 Design of Columns under a Centric Load
10.7 Design of Columns under an Eccentric Load
Review and Summary

11.    ENERGY METHODS
10.1 Introduction
11.2 Strain Energy
11.3 Strain-Energy Density
11.4 Elastic Strain Energy for Normal Stresses
11.5 Elastic Strain Energy for Shearing Stresses
11.7 Impact Loading
11.8 Design for Impact Loads
11.9 Work and Energy under a Single Load
11.10 Deflection under a Single Load by the Work-Energy Method
Review and Summary

LABORATORY SCHEDULE
The following are the tests planned for this course:

Lab (1):  Tensile Strength of Metals – Axially loaded members (steel, aluminum, brass).
Lab (2):  Non-Destructive Testing – Metals subjected to tensile forces - Stress and strain of loaded members (steel, aluminum, brass).
Lab (3):  Non-Destructive Testing – Metals subjected to torsion - Stress and strain of loaded steel.
Lab (4):  Non-Destructive Testing – Metals subjected to bending - Stress and strain of loaded steel.
Lab (5):  Destructive Testing – Metals subjected to torsion - Stress and deformation in circular bars (steel, aluminum, brass).
Lab (6):  Pure Bending of Beams – Stress and deformation in aluminum I-beams.
Lab (7):  Columns – Centric loading of structural members (steel, aluminum, other materials).

SPECIFICATIONS OF LAB REPORT

Students will work in randomly selected groups. A group may submit a collective report. Students who wish to be evaluated on their individual effort may submit their own reports. If the partners of a given group feel that a member of the group is not doing his/her fair share of the work they should inform the instructor who will require this person to write an individual lab report. The lab report shall include a cover page with the names of all partners in the group, course and test titles, and date. The report itself shall contain the objective of the test, procedure, detailed figures of equipment used, tables of data recorded, presentation of results in charts and graphs, and conclusions. The report should emphasize the technical aspect of the test. Emphasis in grading will be placed on the technical content of the report as well as clarity, creativity, and correctness of writing.

STUDENTS TAKE AWAY

• Students will be able to identify and formulate elementary level engineering problems related to mechanics and strength of materials in the conceptual form as well as in terms of mathematical and physical models.
• Students will learn how to apply the basic principles of mechanics and strength of materials to the analysis of solid bodies subjected to various types of loading.
• Students will receive training that enable them to conduct tests related to studying materials behavior under conventional loading conditions. Students will be able to make measurements, record data, interpret results, and draw conclusions regarding the selection and use of materials in engineering applications.
• Students will be able to generalize the basic principles of strength of materials analysis, and to extrapolate those concepts to engineering structures not necessarily covered in this course.

RELATIONSHIP OF COURSE TO ABET PROGRAM OUTCOMES

• an ability to apply knowledge of mathematics, science and engineering.
• ability to design and conduct experiments, as well as to analyze and interpret data.
• ability to design a system, component or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability and sustainability.
• an ability to identify, formulate and solve engineering problems.
  
• an ability to communicate effectively.
• a recognition of the need for and ability to engage in life-long learning knowledge of contemporary issues.
• an ability to use techniques, skills and modern engineering tools necessary for engineering practice.

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