Introduction to strength of Material

1. Department of Mechanical Engineering
Approved by AICTE, Government of India & affiliated to Dr. A.P.J. Abdul Kalam Technical
University, Lucknow
Subject : Strength of Material
Subject Code : KME 502
Lecture 1: Introduction of subject and definition of stress
Prepared by Dr. Nagendra Kumar Maurya

2. Strength of materials
 It 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 and
mechanics of deformable bodies.
 The solid bodies considered in this subject includes bars with axial loads,
shafts in torsion, beams in bending, helical spring and columns in
compression.
Unit –I Introduction to strength of materials

3. Objective of the Subject:
 The principal objective of this subject is to determine the stresses,
strains, and displacements in structures and their components due to the
loads acting on them.
 An understanding of mechanical behavior for the safe design of all
types of structures, such as airplanes, buildings, bridges, machines,
motors, or ships and spacecraft.
 To determine the stresses and strains, we use the physical properties of
the materials as well as numerous theoretical laws and concepts.

4.  Analysis of experimental results have equally important roles in
strength of material. We use theories to derive formulas and equations for
predicting mechanical behavior, but these expressions cannot be used in
practical design unless the physical properties of the materials are known.
 Such properties are available only after careful experiments have been
carried out in the laboratory.
Classification of Problems:
 Understanding the logical development of the concepts: It is
accomplished by studying the derivations, discussions, and examples that
appear in each chapter
 Applying those concepts to practical situations: It is accomplished
by solving the problems at the ends of the chapters.

5. Stress:
 Stress is the internal resisting force per unit cross-sectional
area. It is denoted by symbol σ (sigma).
 Stress is always defined at point and mathematically it can be
expressed as
(a) (c)(b)
Figure1 Stress at a point

6. Stress on Material
Amount of resistive force per unit area
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7. X
Y
z
P
Direction of
Force
YZ
Plane
Direction of Force
XZ
Plane
Note: Stress is a second order tenser quantities. It has two directions. the first
component represent outward normal direction to the plane and second
component represent direction of force
σxx
Outward normal direction to the plane
Direction of force
Figure 2 direction of force

8.  Stress Components
σxx = σx (normal stress perpendicular to the yz plane)
σyy = σy (normal stress perpendicular to the xz plane)
σzz = σz (normal stress perpendicular to the xy plane)
σxy = τxy (shear stress in xy plane)
σyz = τyz (shear stress in yz plane)
σzx = τzy (shear stress in zx plane)

9. Classification of stress
Direct Stress
Indirect Stress
Tensile Stress Compressive
Stress
Shear stress
Torsional shear
stress
Bending stress
Prismatic bar:
A prismatic bar is a straight structural member having the same cross section
throughout its length, and an axial force is a load directed along the axis of the
member, resulting in either tension or compression in the bar.
Figure 3 Classification of stress

10. Direct Stress
Tensile stress
Prismatic bar in tension:
(a) free-body diagram of a segment of the bar
(b) segment of the bar before loading
(c) segment of the bar after loading, and
(d) normal stresses in the
When two equal or opposite pull is applied on a
body resulting tensile stress will developed in the
body. However, load must be passing from the
centroid of the body

11. Limitations
The equation σ = P/A is valid only if the stress is uniformly distributed over
the cross section of the bar. This condition is realized if the axial force P acts
through the centroid of the cross-sectional area. When the load P does not
act at the centroid, bending of the bar will result, and a more complicated
analysis is necessary.
Figure 4 Steel eyebar subjected to tensile loads P

12. Compressive stress
When two equal or opposite puss is applied on a body than compressive stress
will developed in the body. However, the line of action of force must be passing
from the centroid of the body.
P
P
Compressive stress (σc =P/A)
Figure 5 Steel pipe in

13. SHEAR STRESS
When two equal and opposite force is acting on a body and their line of action
of force is not same , producing shear stress in the body. Shear stress acts in the
tangential direction to the surface of the material. Shear stress is denoted by a
symbol τ . Mathematically it can be expressed as :
τ = P/As
Where P is the applied load and As is the shear area

14. Figure 6:Bolted connection in which the bolt is loaded in double shear

15. Figure: 7 Bolted connection in which the bolt is loaded in single shear

16. Figure 8 : Failure of a bolt in single shear
Figure 9: Element of material subjected to shear stresses and
 Shear stresses on opposite (and parallel) faces of
an element are equal in magnitude and opposite in
direction.
 Shear stresses on adjacent (and perpendicular)
faces of an element are equal in magnitude and have
directions such that both stresses point toward, or both
point away from, the line of intersection of the faces.

17. References
Mechanics of materials by James M Gere
MECHANICS OF MATERIALS I by E. J. HEARN