mechanical engineering stress and strain

Courses: mechanic of material MECH ENG 2002
Topic : Engineering stress and strain
School: chong hwa independent high school malaysia


SHEAR AND STRAIN




OBJECTIVES:
The concepts of normal and shear stress and strain will be
introduced and specific application of the analysis will be
explained. The mechanical properties of selected materials will be
discussed with simple stress-strain diagram for a specific material.
The behaviour described by this diagram will then be discussed.




1.1 Types and system of forces
1.1.1 Types of forces

a) Normal force, N
 Force acts perpendicular to the area.
 Developed whenever the external loads to push or pull on the
two segments of the body-can be tensile and compression
forces.

b) Shear force, V
 Shear force lies in the plane of the area.
 Developed when the external loads tend to cause the two
segments of the body to slide over one another.

c) Torque or torsional moment, T
 Developed when the external loads tend to twist one segment of
the body with respect to the other.

d) Bending moment, M
 Cause by the external loads that tend to bend the body about an
axis lying within the plane of the area.
1

, 1.1.2 System of forces
 Based on equation of equilibrium.
 This chapter is the continuation from the subject of Statics and
Dynamics that you had learned before.


1.2 Types of stresses
 Stress is the internal force exerted by one part of an elastic body upon the
adjoining part.

 Stress has a dimension of Newton/m2 (or dyne/cm2; or Pascal with 1 Pa =
1 kg/m-sec2 =N/m2).

 Generally, there are 6 independent components of stress at each point in
the body namely are normal shear, σx, σy, σz and shear stress, τxy, τyz, τxz.

 The magnitude of these components depends upon the type of loading
acting on the body and the orientation of the element at the point.
.




Figure 1.1
Six independent components of stresses




Mechanics of Materials 2

, 1.2.1 Normal stress, σ (SIGMA)

 NORMAL STRESS is the intensity of the net forces acting normal
(perpendicular) to an infinitely small area dA within an object per unit
area.

 If the normal stress acting on dA pulls on it, then it is referred to as tensile
stress, whereas if it pushes on the area, it is called compressive stress. An
average normal stress at any point on the cross sectional area can be
calculated as follows:


 Normal stress includes tensile and compressive stress, the conventional
sign for normal stresses are: tensile stresses are positive (+), compressive
stresses are negative (-). The unit of stress is pascals (Pa) (1Pa=1N/m2).




where;
σ = normal stress at any point on
the cross sectional area.
P = internal resultant force applied
through the centroid of the cross
sectional area.
A = area of the bar.




Mechanics of Materials 3

, 1.2.2 Shear stress, τ (TAU)
 Shear, or shearing stress, results when a force tends to make part of the
body or one side of a plane slide past the other.
 The formula for calculation and units remain the same as tensile stress
(Figure 1.3)
where;
τ=P
τ = shear stress at the section.
A
P =internal resultant shear force at the section.
A =area at the section




Figure 1.3

1.2.3 Bearing stress
 Torsion, or torsional stress, occurs when external forces tend to twist a
body around an axis.

1.3 Strain, ε (EPSILON)

 Strain is defined as the ratio of change in length due to deformation to the
original length of the specimen (figure 1.4).




Figure 1.4

 Formula:
 

L

 It is a dimensionless quantity.
 Numerical values of strain are usually very small, especially for structural
materials, which ordinarily undergo only small changes in dimensions.
 There are two types of strains; normal strain, ε and shear strain, γ
(GAMMA).


Mechanics of Materials 4