General concepts of stress and strain

• The end of the chapter, the students should be able to:

– Find internal forces of a body

– Calculate the average normal stress and average shear stress of a body subject to axial forces and shear forces respectively

– Calculate the normal strain from a body`s deformation

– Understand and be able to apply the relationship between stress and strain.

– Locate and identify material characteristics associated with a tensile test stress-strain diagram

– Solve the problems of modulus of elasticity, modulus of rigidity and poisson`s ratio

– Calculate a factor of safety, axial strain and lateral strain

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Chapter 1

General concepts of stress and strain

1.0 Introduction

• Strength of materials is a branch of applied mechanics that deals with the behavior of solid bodies subjected to various types of loading. Other names for this field of study are mechanics of materials, mechanics of solids and mechanics of deformable bodies.

• The main objective of the study of mechanics of materials is to provide the future engineer with the means of analyzing and designing various machines and load bearing structures

• Both the analysis and design of a given structure involve the determination of stresses and deformations.

1.1 Normal stress and strain

• Axial load/force is an external load/force directed along the axis (centroid axis) of the member, resulting in either tension or compression in the prismatic bar (straight member with constant cross section)

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Chapter 1

General concepts of stress and strain

X Y

P

P

P

X

Y

Axial force

a) Tension force

Axis

b) Compression force

• Internal force can be seen from the cutting plane x-x and y-y as below.

• Internal forces are the forces which hold together the particles forming the rigid body

– R – resultant internal force

– Rn – component force (perpendicular to plane y-y)

– Rt – component force (tangent to plane y-y)

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Chapter 1

General concepts of