This document provides an overview of basic concepts in strength of materials, including stress, strain, and different types of stresses. It defines stress as the internal force of resistance per unit area offered by a body against deformation. Stress is calculated as force divided by area. Normal stress acts perpendicular to the cross-sectional area and can be tensile or compressive. Shear stress refers to a cutting action and is represented by the symbol tau. The document also defines strain as the change in length divided by the original length, represented by epsilon. It provides stress elements and equations to calculate direct normal and shear stresses.

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Strength
Of
Material

2. Module 2: Basic Concepts in
Strength of
Material.
Topic: Simple stresses and strain
Recap:
• Products, machines and structures
must be designed to be safe and to
provide satisfactory performance
during the intended use.
• Loads and different Classifications
of loads
Learning outcomes..
• Concept of direct normal stress
• Represent normal stress or stress
elements
• Concept of normal strain
• Concept of direct Shear stress

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2Concept of stress:
The study of strength of material depends
on the understanding of the principle of
stress and strain produced by applied
loads on a structure or machine and the
members that make up such systems.
Stress
This is: the internal force of resistance per
unit area, offered by a body against
deformation.
The concept of stress can be expressed
mathematically as
Stress =
𝐹𝑜𝑟𝑐𝑒
𝐴𝑟𝑒𝑎
=
𝐹
𝐴
Stress in US units is typically reported in one
of the following forms Lb/in2 or psi’
in the S.I unit as N/c or Pascal(pa)
e of N/m2 to be equal to Mpa
Assume that a force of 10000N is
exerted over a square area of 50mm on
a side.
10,000 N
50mm
Stress =
𝟒.𝟎 𝑵
mm2
Stress =
𝟒.𝟎 𝑁
m2𝟏𝟎−6
stress = 4 ×𝟏𝟎−6 N/m2
Stress = Mpa
Stress =
𝟏𝟎,𝟎𝟎𝟎
𝟐𝟓𝟎𝟎

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Tensile Compressive
Normal stress
Direct Normal Stress
one of the most fundamental type of
stress that exists is the normal stress,
indicated by the lowercase Greek
letter δ(sigma); in which the stress
acts perpendicular, or normal to the
cross section of the load carrying
member.
If stress is uniform across the
resisting area is called the direct
normal stress.

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Mathematically,
Equation of direct normal stress is given
by;
Direct Normal stress(δ) =
𝐴𝑝𝑝𝑙𝑖𝑒𝑑𝐹𝑜𝑟𝑐𝑒
𝐶𝑟𝑜𝑠𝑠 −𝑆𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐴𝑟𝑒𝑎
The area of cross section is taken
perpendicular to the line of action of the
force.
Stress Elements For Direct Normal Stress;
it is more convenient to visualize the
stress condition on small (infinitesimal)
element.
This element used to analyse the stress
condition of a material is called the stress
Element

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Stress Element For Compressive Stress Stress Element For Tensile Stress

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Concept Of Strain
Strain also called ‘’ unit
Deformation’’ is found by dividing
the total deformation by the
original length of the bar. The
lower case Greek letter
epsilon (ε) is used to denote
strain. Strain ε =
𝑻𝒐𝒕𝒂𝒍 𝒅𝒆𝒇𝒐𝒓𝒎𝒂𝒕𝒊𝒐𝒏
𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍
Direct Shear Stress
Shear stress refers to a cutting
like action .
The applied Shearing Force is
resisted Uniformly by the area of
the part in shear, producing a
uniform level of shearing Force
across the entire area being
sheared.
The symbol used for shear stress
is τ, the lowercase Greek letter
tau.

8. Than
k You
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L.E Eze
ezelotachukwu91@gmail.com