Mechanics of
Materials
Chapter 1
Stress
Introduction
Mechanics of materials is a branch of
mechanics that studies the internal effects of
stress and strain in a solid body that is
subjected to an external loading
Stress is associated with the strength of the
material from which the body is made, while
strain is a measure of the deformation of the
body.
Today, you will...
Specific
Review some of the applications of the
important principles Concepts of analysis and design
of statics and show normal and shear of members
how they are used to stress will be subjected to an
determine the introduced. axial load and direct
internal resultant shear will discussed.
loadings in a body.
Historical Development
17th Century when Galileo performed experiments to
study the effects of loads on rods and beams made of
various materials.
18th Century experimental methods for testing materials
were vastly improved. Theoretical studies undertaken
primarily in France, by such notables as Saint-Venant,
Poisson, Lamé, and Navier.
But did you know that a force can also
change the SHAPE or SIZE of an object?
Equilibrium of a
Deformable Body
External Loads. A body is subjected
to only two types of external loads;
namely surface forces of body
forces.
Surface Forces
Surface forces are caused by the
direct contact of one body with
the surface of another. In all
cases these forces are
distributed over the area of
contact between the bodies. If
this area is small in comparison
with the total surface area of the
body, then the surface force can
be idealized as a single
concentrated force, which is
applied to a point on the body.
Body Forces
Body Forces is
developed when one
body exerts a force on
another body without
direct physical
contact between the
bodies.
Gravitation- Weight of the body and
acts through the body’s center of
gravity
Support Reactions
The surface forces that develop
at the supports or points of
contact between bodies are
called reactions.
Equations of Equilibrium
Equilibrium of a body requires
both a balance of forces, to prevent the
body from translating or having
accelerated motion along a straight or
curved path and a balance of moments
to prevent the body from rotating
Internal Resultant Loadings
In mechanics of materials, statics is
primarily used to determine the resultant
loadings, that acts within a body.
Four types of resultant
loadings:
1.Normal Force, N
2.Shear Force, V
3.Torsional moment or Torque, T
4.Bending Moment, M
Normal Force, N
This force acts
perpendicular to the area.
It is developed whenever
the external loads tend to
push or pull on the two
segments of the body.
Shear Force, V
The shear force lies in the
plane of the area and it is
developed when the external
loads tend to cause the two
segments of the body to slide
over one another.
Torsional moment or Torque, T
This effect is developed when
the external loads tend to twist
one segment of the body with
respect to the other about an
axis perpendicular to the area.
Bending Moment, M
The bending moment is
caused by the external
loads that tend to bend the
body about an axis lying
within the plane of the area.
PROCEDURE FOR ANALYSIS
Decide
segment of If it has a support or
the body to connection.
Determine the
Apply necessary
be reaction by drawing equations of
considered free-body diagram equilibrium
Example No.1
Determine the resultant internal loadings acting on the cross section at C of
the cantilevered beam shown below
Example No.2
Determine the resultant internal loadings acting on the cross section at point
B.
Example No.3
Determine the resultant internal loadings acting on the cross section at C of
the machine shaft shown. The shaft is supported by journal bearings at A and
B, which only exert vertical forces on the shaft.
Example No.4
The 500-kg engine is suspended from the crane boom. Determine the
resultant internal loadings acting on the cross section of the boom at point E.
