Strength of Materials, Lecture - 1. Introduction + Recommended Books Mehran University of Engineering and Technology. Department of Mechanical Engineering.

1. 1
Recommended Books:
1.Mechanics of Materials by F. P. Beer
2.Strength of materials By R.K .Rajput
3.Mechanics of Materials by Ansel C.
Ugural
4.Strength of Materials by F.L. Singer

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6. Introduction
Three fundamental areas of
Engineering Mechanics are Statics,
Dynamics and Strength of
materials.
Statics and dynamics are concerned
to the study of the external effects of
forces on rigid bodies, that is bodies for
which the change in shape
(deformation) can be neglected.
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•In contrast Strength of materials deals with the
relations between externally applied loads and their
internal effects on bodies.
•Moreover, the bodies are no longer assumed to be
rigid; the deformations, however small are of
major interest.
•In Mechanical design, the Engineer must consider
both dimensions and material properties to
satisfy requirements of strength and rigidity.
•When loaded a machine part or structure should
neither break nor deform excessively.
[F. L Singer P-1]

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•The main objective of the study of
Mechanics / Strength 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. [F.P Beer P-2]

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•In material science, the strength of a
material is its ability to withstand an applied
stress without failure.
•The applied stress may be tensiletensile,,
compressivecompressive oror shearshear..
[http://en.wikipedia.org/wiki/Strength_of_materials]

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The study of Strength of Materials is concerned
specifically with the following issues:
1. The internal forces of a member caused by the
external forces acting on that member or system.
2. The changes in dimension of a member caused
by these forces.
3. The mechanical properties of the material in the
member (hardness, toughness, ductility,
brittleness, elasticity, plasticity, stiffness).

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• The term strength of materials most
often refers to various methods of
calculating stresses in structural or
machine members, such as beams,
columns and shafts, pressure vessels,
pipes and joints, springs, connecting
rod, flywheel, piston, bearing and
gears.

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• The strength of any material relies on three
different type of analytical method:
• Strength: means load carrying capacity
• Stiffness: means deformation or elongation
• Stability: means ability to maintain its initial
configuration.

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• A variable that can be used as a measure of
strength of a structural member.
• The force per unit area or the intensity of the
internal resisting force is called stress.
• A positive sign(+ve) will be used to indicate a
tensile stress ( member in tension) and a negative
sign (-ve) indicate a compressive stress ( member
in compression).
• σ = P/ A = N/mm2 or N/m2 or Pa, KPa,
MPa, GPa, lb/in2 or PSi, KSi
[Beer see exp. Page -5]

14. Stress
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• Another important aspect of the analysis and
design of structure relates to the deformation
caused by the loads applied to a structure.
• The deformation of a member per unit length.
Є = δl / L= no unit.
Where δl = change in length
L= Original length
[see Beer P- 48]
strainnormal==
L
δ
ε

16. Types of loadings
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• Axial loading : The applied forces are collinear (same line) with
the longitudinal axes of the members. The forces causes the member
to either stretch or shortens as shown fig.
• To determine the internal force in the rod and the corresponding
stress was perpendicular to the axis of the rod; the internal force
was therefore normal to the plane of the section and the
corresponding stress is described as a normal stress. The normal
stress in a member under axial loading: σ = P/ A

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18. Types of loadings
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• Transverse loading: Forces applied
perpendicularly to the longitudinal axis of a
member.
• Transverse loading causes the member to
bend and deflect from its original position,
with internal tensile and compressive strains
accompanying change in curvature.

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Types of loadings
• Transverse loading
Deflection,
L

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Deflection
• The deflection (Δ) is the vertical displacement
of the of the beam as a result of the load P.
Deflection, Δ
L

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• Torsional loading: torsion, or torsional
stress, occurs when external forces tend to
twist a body around an axis. [See Beer p-7]

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• The internal forces are uniformly
distributed across the section, it follows
from the elementary statics that the
resultant P of the internal forces must be
applied at the centroid C of the section.
• This means that a uniform distribution of stress is possible
only if the line of action of the concentrated loads P and P’
passes through the centroid of the section. This is
referred to as centric loading.

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.
• This mean that the internal forces in given section and a
couple M of the moment M=Pd. The distribution of
forces can’t uniform.
• If a two-force member is loaded
axially but eccentrically as
shown in fig: 9 p-9 beer

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• Tensile Stress: the state of stress caused by an applied load that
tends to elongate the material in the axis of the applied load. The
stress induced is called tensile stress and corresponding strain is
called tensile strain.
• Materials loaded in tension are capable to stress concentrations
such as material defects or sudden changes in geometry.
• Compressive stress : the state of stress caused by an applied
load that tends to reduce the length of the material in the axis of
the applied load. The stress induced is called compressive stress
and corresponding strain is called compressive strain.
• Compressive strength of materials is generally higher than
that of tensile stress. However, structures loaded in compression
are subjected to additional failure modes of materials, such as
buckling (Column).

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Types of Stress and strain

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Types of Stress and strain

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• Shear Stress: is defined as the stress which is applied parallel
or tangential to a face of a material, as opposed to a normal
stress which is applied perpendicularly.
• In other words the stress caused by sliding faces of the material
relative to one another. The stress induced is called shear stress
and corresponding strain is called shear strain.
• [See Beer p-9].
Example: bolts, pins, rivets, which are used to connect various
machine members.
The formula to calculate average shear stress is: τ = P / A
τ = the shear stress;
P = the force applied;
A = the cross sectional area.

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A
F
A
P
==aveτ
Single Shear
A
F
A
P
2
ave ==τ
Double Shear

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• Bolts, pins, rivets create stresses in the member they
connect along the bearing surface or surface in contact.
• The compressive stress at area of contact between two
machine member is called bearing or crushing stress.
• Bearing stress is the contact pressure between the separate
bodies. It differs from compressive stress, as it is an internal
stress caused by compressive forces.
• σ = P / A = P / td
Where t = plate thickness; d = diameter of the bolts.
[ see Beer P -11]
Sample Prob: 1.1 See beer p-16] and
Sample prob p-17 (H.W)

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• Bolts, rivets, and pins create
stresses on the points of
contact or bearing surfaces of
the members they connect.
dt
P
A
P
==bσ
• Corresponding average force
intensity is called the bearing
stress,
• The resultant of the force
distribution on the surface is
equal and opposite to the force
exerted on the pin.

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Analysis of Internal forces

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To my understanding from Literature and
product terminology in plants, rod means wire
rods which is differentiated from bars on
following technical reasons
THE DIFFERENCE BETWEEN ROD AND BAR.