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 stress-strain 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 non-circular 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 maximum-in-plane 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.