Notes on the Final Sections of Chapter 1 and Beginning of Chapter 2

Last week I finished taking notes on Chapter 1 with a re-introduction to linear elasticity and Hooke's law and an introduction to Poisson's ration. This blog post will contain my general notes on the topics above as well as the contents of Chapter 2.

Linear Elasticity:
Many structural materials such as wood, plastics, and most metals behave both elastically and linearly when an initially loaded. The stress-strain curves of these materials, consequently, begin with a straight line that passes through the origin.
A material is therefore said to be linearly elastic when it exhibits elastic behavior and possesses a linear relationship between stress and strain.
Linearly elastic materials are very important in engineering because structures and machines which are designed in this linearly elastic region do not permanently deform when yielding occurs.

Hooke's Law:
English scientist Robert Hooke was the first person to scientifically investigate the elastic properties of materials. He measured the stretching of long wires supporting weights and was able to establish the linear relationship between applied loads and the resulting elongation.

Hooke's Law describes the linear relationship between stress and strain for a bar in simple tension or compression through the equation:

\(\sigma  = E\varepsilon \)

Where \(\sigma\) is the axial stress, \(\varepsilon\) is axial strain and \(E\) is the modulus of elasticity for the given material.

Poisson's Ratio:
The ratio between the lateral strain \(\varepsilon '\) and the axial strain \(\varepsilon\) acting on an object is known as Poisson's ratio.

This ration can be denoted as:

\(v =  - \frac{{Lateral strain}}{{Axial strain}} =  - \frac{{\varepsilon '}}{\varepsilon }\)

The minus sign is inserted into the equation to counteract the opposite signs of the lateral and axial strains when acting on a material. 

Starting Chapter 2:

Chapter 2 of the Mechanics of Materials textbook pertains to axially loaded members. an axially loaded member is any structural component subjected only to tensile or compressive forces. After an intro in section 2.1, section 2.2 deals with the changing lengths of axially loaded members. This sections gives information on springs, prismatic bars, and cables. 

My next blog post will deal with my notes last week of sections 2.3 through 2.5

Thanks for reading,

-Nick