CE 203 – UQU – Weekly Sessions
June 3, 2021 20210830 18:08CE 203 – UQU – Weekly Sessions
CE 203 – UQU – Weekly Sessions
Mechanics of Materials is the branch of mechanics that studies the internal effects of stress and strain of a solid material that is subjected to external forces and moments.
In section 1, you will learn about the different types of stresses that the material can be subjected to. Normal stresses, shear stresses, and bearing stresses are covered. Also, you will learn how to design the material not to fail against externally applied loads based on the allowable stress design.
In section 2, you will learn about deformations and strain as well as their types. You will learn how to calculate axial deformation, normal strain, shear deformation and shear strain. The objective of this chapter is to quantify the changes in shape and size of material subjected to external applied forces.
In section 3, you will learn about the mechanical properties of the material. Concepts such as strength, ductility, yielding, toughness, and rigidity are explained. Also, you will learn about the stressstrain diagrams and their importance in designing for a safe and sound structure. Parameters such as the modulus of elasticity and Poisson’s ratio are defined, and Hooke’s law is explained in depth. Moreover, you will learn about the behavior of the material upon load application followed by load removal. Permanent strain, recovered strain, elastic and inelastic phase are also explained in depth. You will also learn about how the material behaves when it is subjected to stresses in more than one direction, or what is known as the general state of stress.
In section 4, you will derive a formula for axial deformation as a function of the modulus of elasticity, the length of the material, the external applied load, and the area of normal stress. Moreover, you will learn about the response of axial deformations under temperature effects. You will also learn how to solve indeterminate structures using compatibility equations.
In section 5, you will learn about torsion in circular shafts and the shear stresses they create in the beam. Also, you will learn how to calculate the angle of twist that develops from torsional moments. You will also learn how to solve indeterminate structures using compatibility equations containing the angle of twist.
In section 6, you learn about torsion in solid noncircular shafts and thin walled closed sections.
In section 7, you recall important concepts from Statics that we will be using in this course. Special attention is given to Axial, Shear, and Bending Diagrams.
In section 8, you will get to know that normal stresses are not only due to forces. Normal stresses are also caused by internal bending moments. You will learn how to calculate bending normal stresses that result from internal bending moments about single axis. Double bending (bending about both axes) is also covered in depth. You will learn the meaning of the Neutral Axis and how to locate it. Also, you will get to know what eccentric loads are and how they affect the calculations of normal stresses at any point on the cross section. Finally, chapter 6 ends with the definition of composite beams, and the method used to calculate normal stresses in composite beams.
In section 9, you will get to know the formula that reflects the variation of shear stresses in a beam’s cross section. In this chapter, you will discover that average shear stresses (force over area) are not used in shear stress calculations in the beam’s cross section. A new formula is introduced for shear stresses that are developed in cross sections subjected to shear forces. New parameters such as Q and t are introduced. Also, you will learn how to locate and calculate the maximum shear stress in a beam subjected to a given loading. Also, you will learn that shear forces can develop in two directions in a beam, and you will be able to calculate shear stresses at any point on the cross section whether it is subjected to horizontal shear, vertical shear, or both.
In section 10, we study the effect of combined loadings and moments applied to cross sections. There is no new concept here, just an application of all what we learned in sections 5, 6 and 7. We will take real life examples of cross sections subjected to a combination of shear force, normal force, and bending moments. A step by step procedure on how to solve problems regarding combined loadings is provided.
In section 11, we discuss stress transformations that result from rotating an infinitesimal element with an initial state of stress. We will learn that normal stresses and shear stresses vary upon rotation. As a result, maximum normal stresses occur on a plane different from maximuminplane shear stresses. This explains the phenomenon of cracking and how it occurs. You will be able to apply the concepts of this chapter to predict the direction of cracking of a structure subjected to combined loadings, given that you have all the sufficient information.
In section 12, you learn about beam deflections and slopes that result from applied loadings. You learn about the method of integration that we use to solve for deflections and slopes at any point of the beam.

Section 1: Stress
In chapter 1, you learn about stresses and their three types: Average Normal Stress, Average Shear Stress, and Bearing Stress.
 Lesson 1: Definition and Types of Stresses
 Lesson 2: Units of Stresses
 Lesson 3: Average Normal Stresses

Lesson 4: Types and Mode of Failure – Average Normal Stresses

Problem 1: Average Normal Stresses

Problem 2: Average Normal Stresses

Problem 3: Average Normal Stresses

Problem 4: Average Normal Stresses

Problem 5: Average Normal Stresses

Problem 6: Average Normal Stresses

Quiz 1 – Average Normal Stresses

Quiz 1 Solutions

Lesson 5: Average Shear Stresses

Lesson 6: Examples of Average Shear Stresses

Problem 7: Average Shear Stresses

Lesson 7: Types and Mode of Failure – Average Shear Stresses

Problem 8: Average Shear Stresses

Problem 9: Average Shear Stresses

Problem 10: Average Shear Stresses

Problem 11: Average Shear Stresses

Quiz 2 – Average Shear Stresses

Quiz 2 Solutions

Lesson 8: Bearing Stresses – Definition and Types

Lesson 9: Mode of Failure Under Bearing Stresses

Problem 12: Bearing Stresses

Problem 13: Bearing Stresses

Problem 14: Bearing Stresses

Problem 15: Extra Exercises

Problem 16: Extra Exercises

Problem 17: Extra Exercises

Quiz 3 – Bearing Stresses

Quiz 3 Solutions

Lesson 10: Allowable Stress Design

Problem 18: Allowable Stress Design

Problem 19: Allowable Stress Design

Problem 20: Allowable Stress Design

Quiz 4 – Allowable Stress Design

Quiz 4 Solutions

Section 2: Strain
In chapter 2, you learn about deformations and strain; both normal and shear.

Lesson 1: Axial Deformation

Lesson 2: Shear Deformation

Lesson 3: Shear and Normal Strain

Problem 1: Normal Strain

Problem 2: Normal Strain

Problem 3: Normal Strain

Problem 4: Normal Strain

Problem 5: Normal Strain

Problem 6: Shear Strain

Lesson 4: Law of sine and law of cosine

Problem 7: Shear Strain

Problem 7 – Continued

Quiz – Chapter 2

Quiz – solutions


Section 3: Mechanical Properties of Materials
In chapter 3, you learn about the mechanical properties of material: Strength, Ductility, Toughness, Stiffness, and Rigidity. Also, you learn about the stress strain diagram, both normal and shear.

Lesson 1: Strength and Ductility

Lesson 2: Toughness and Stiffness

Lesson 3: Tension Test

Lesson 4: Hooke’s Law and the Modulus of Elasticity

Lesson 5: Inelastic Phase

Lesson 6: Inelastic Phase – part 2

Lesson 7: Load Removal – Elastic Phase

Lesson 8: Load Removal – Inelastic Phase

Problem 1: Normal Stress Strain Diagram

Problem 1 – Continued

Lesson 9: Shear Stress Strain Diagram

Problem 2: Shear Stress Strain

Problem 3: Shear Stress Strain

Quiz 1 – Hooke’s Law and StressStrain Diagram

Quiz 1 Solutions

Lesson 10: Poisson’s Ratio

Problem 4: Poisson’s Ratio

Lesson 11: General State of Stress

Example on General State of Stress

Lesson 12: Dilation and Bulk Modulus

Problem 5: General State of Stress

Problem 6: General State of Stress

Problem 7: General State of Stress

Problem 7 – Continued

Problem 8: General State of Stress

Problem 8 – Continued

Problem 9: General State of Stress

Quiz 2 – Poisson’s Ratio and General State of Stress

Quiz 2 – Solutions


Section 4: Axial Deformations and Compatibility Equations
In this chapter, we develop an explicit formula of axial deformations due to axial forces and temperature. Also, we learn how to use axial deformations to solve indeterminate stuctures.

Lesson 1: Axial Deformation – Formula

Lesson 2: Sudden Change in Load

Lesson 3: Sudden Change in Area

Lesson 4: Sudden Change in Modulus of Elasticity

Lesson 5: Continuous Change in Load

Lesson 6: Continuous Change in Area

Lesson 7: Temperature Effects

Lesson 8: Example on Temperature Effects

Quiz 1 – Axial Deformations

Quiz 1 – solutions

Lesson 9: Indeterminate Structures

Lesson 10: Compatibility Equation – Form 1

Problem 1: Compatibility Equation – part 1

Problem 1 continued: Compatibility Equation

Problem 2: Compatibility Equation

Lesson 11: Compatibility Equation – Form 2

Problem 3: Compatibility Equation

Lesson 12: Compatibility Equation – Form 3

Problem 4: Compatibility Equation

Problem 4 continued: Compatibility Equation

Lesson 13: Compatibility Equation – Form 4

Problem 5: Compatibility Equation

Lesson 14: Compatibility Equation – Form 5

Quiz 2 – Indeterminate Structures

Quiz 2 solutions

Quiz 3 – Indeterminate Structures

Quiz 3 solutions

Recommended Exercises – UQU – Axial Deformations

Recommended Exercises – UQU – Solutions


Mock Exams (Sections 1 to 4)

Mock Exam 1

Mock Exam 1 Solution

Mock Exam 2

Mock Exam 2 Solution


Section 5: Torsion of Circular Shafts
In this section, we learn about torsion and the stresses it creates on the cross section.

Lesson 1: Torsion

Problem 1: Torsion

Problem 2: Torsion

Problem 3: Torsion

Lesson 2: Angle of Twist

Problem 4: Angle of Twist

Lesson 3: Gears in Mesh

Lesson 4: Power Transmission

Lesson 5: Statically Indeterminate Structures

Problem 5: Statically Indeterminate Structures

Quiz: Torsion

Quiz Solution


Section 6: Torsion of Solid NonCircular and ThinWalled Sections
In this section you learn about torsion in solid noncircular sections and thinwalled closed sections.

Lesson 1: Torsion of Solid NonCircular Sections

Lesson 2: Torsion of ThinWalled Sections


Section 7: Statics Review Shear and Bending Diagrams
In this section, we review how to find internal reactions of a beam and draw the axial, shear, and bending moment diagrams using the equation method and the area method.

Lesson 1: Statics Review Part 1

Lesson 2: Statics Review Part 2

Lesson 3: Statics Review Part 3

Lesson 4: Statics Review Part 4

Problem 1: Statics Review

Problem 1 – Continued

Problem 2: Statics Review

Problem 3: Statics Review

Lesson 5: Method of Equations

Problem 4: Method of Equations

Lesson 6: Method of Integration

Lesson 7: Method of Integration

Problem 5: Method of Integration

Problem 6: Method of Integration

Problem 7: Method of Integration


Section 8: Bending Stresses
In this chapter, you discover that normal stresses are not only the result of axial forces. They are also caused by internal bending moment. Long story short: Internal bending Moments create normal stresses.

Lesson 1: Normal Stresses Due to Bending

Lesson 2: Linear Variation and the Neutral Axis

Lesson 3: Locating the Neutral Axis for Single Bending

Lesson 4: Locating the Centroid of the Cross Section

Problem 1: Locating the Centroid of the Cross Section

Problem 2: Locating the Centroid of the Cross Section

Problem 3: Locating the Centroid of the Cross Section

Quiz 1: Locating the Centroid

Quiz 1 solutions

Lesson 5: Moment of Inertia

Problem 4: Moment of Inertia

Problem 5: Moment of Inertia

Problem 6: Moment of Inertia

Quiz 2: Moment of Inertia

Quiz 2 solutions

Lesson 6: Pure Bending About A Horizontal Axis

Problem 7: Pure Bending About A Horizontal Axis

Problem 8: Pure Bending About A Horizontal Axis

Problem 8 – Continued

Problem 9: Pure Bending About A Horizontal Axis

Problem 9 – Continued

Problem 10: Pure Bending About A Horizontal Axis

Problem 10 – Continued

Quiz 3: Pure Bending About A Horizontal Axis

Quiz 3 solutions

Lesson 7: Pure Bending About A Vertical Axis

Problem 11: Pure Bending About A Vertical Axis

Lesson 8: Double Bending About Both Axes

Lesson 9: Locating The Neutral Axis in Double Bending

Problem 12: Locating The Neutral Axis in Double Bending

Problem 12 – Continued

Problem 13: Locating The Neutral Axis in Double Bending

Problem 13 – Continued

Quiz 4: Double Bending and the Neutral Axis

Quiz 4 Solutions

Lesson 10: Eccentric Loads – part 1

Lesson 11: Eccentric Loads – part 2

Problem 14: Eccentric Loads

Quiz 5: Eccentric Loads

Quiz 5 solutions

Lesson 12: Composite Beams

Problem 15: Composite Beams

Problem 16: Composite Beams

Lesson 13: Composite beams in Circular Cross Sections

Quiz 6: Composite Beams

Quiz 6 solutions


Section 9: Shear Stresses and Shear Flow
In this section, you learn about how the shear stress varies along the beam's depth when the beam is subjected to a shear force. Also, you will learn the concept of shear flow and where it used in design.

Lesson 1: Vertical Shear Stresses – part 1

Lesson 2: Vertical Shear Stresses – part 2

Problem 1: Vertical Shear Stresses

Problem 1 – Continued

Problem 2: Vertical Shear Stresses

Lesson 3: Horizontal Shear Stresses

Problem 3: Horizontal Shear Stresses

Lesson 4: Shear Flow

Quiz 1: Shear Stresses

Quiz 1 solutions

Problem 4: Shear Flow

Problem 4 – Continued

Problem 5: Shear Flow

Quiz 2: Shear Flow

Quiz 2 solutions


Mock Exams (Sections 5 and 6)

Mock Exam 1

Mock Exam 1 Solution

Mock Exam 2

Mock Exam 2 Solution

Mock Exam 3

Mock Exam 3 Solution


Section 10: Combined Loadings
In this section, you learn how to calculate normal shear stresses of sections subjected to a combination of shear forces, normal forces, bending moments, and torsion.

Lesson 1: Combined Loadings – Part 1

Lesson 2: Combined Loadings – Part 2

Lesson 3: Combined Loadings – Part 3

Lesson 4: Combined Loadings – Part 4

Problem 1: Combined Loadings

Problem 1: Continued

Problem 2: Combined Loadings

Problem 3: Combined Loadings

Problem 3: Continued

Problem 4: Combined Loadings

Quiz 1 – Combined Loadings

Quiz 1 – solutions


Section 11: Stress Transformation
In this section we discuss stress transformations, principal stresses and planes, inplane maximum shear stresses and planes, and Mohr's circle

Lesson 1: Introduction to Stress Transformations

Lesson 2: Introduction to Equations Method

Lesson 3: Equations Method

Lesson 4: Principal Stresses and Principal Planes

Problem 1: Principal Stresses and Principal Planes

Lesson 5: Maximum In Plane Shear Stresses

Problem 2: Maximum In Plane Shear Stresses

Lesson 6: Introduction to Mohr’s Circle

Lesson 7: Mohr’s Circle for Principal Stresses and Principal Planes

Lesson 8: Mohr’s Circle for Maximum inplane Shear Stresses

Lesson 9: Mohr’s Circle for Rotating an Element with Angle Theta

Problem 3: Mohr’s Circle with Combined Loadings

Quiz: Stress Transformation

Quiz Solution


Section 12: Beam Deflections

Final Mock Exam (All Sections)

Final Mock Exam 1

Final Mock Exam 1 Solution

Final Mock Exam 2

Final Mock Exam 2


Adbulrahman alesa
تقييم
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