In contrast to the forces on a particle, the
forces on a rigid-body are not usually
concurrent and may cause rotation of the
body (due to the moments created by the
forces).
Equilibrium of a Rigid bodies
2
Couple moment
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Equilibrium of a Rigid bodies Part 1-Basic Mecanical Engineering-Lecture Slides, Slides of Mechanical Engineering
Prof. Dasmaya Sidhu delivered this lecture at National Institute of Industrial Engineering for Basic Mechanical Engineering course. It includes: Equilibrium, Rigid, Bodies, Forces, Particle, Moments, Rotation, Concurrent, Condition, Vector, Sum
Typology: Slides
2011/2012
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In contrast to the forces on a particle, theforces
on
a^
rigid-body
are
not
usually
concurrent and may cause rotation of thebody (due to the moments created by theforces).
Equilibrium of a Rigid bodies
2
Couple moment
An obvious condition for equilibrium is that the net force acting must be zero.Although this is the only requirement necessary for a point mass to be in equilibrium it is notsufficient to guarantee the equilibrium of a rigid body
Equilibrium of a Rigid body
3
In all three cases the net force on the stick is zero.
For above fig in the last case the stick does not remain at rest. It rotates clockwise. We aretherefore forced to conclude that while a necessary condition for equilibrium is that the net forceis zero, this is not a sufficient condition for a rigid body. A second condition is required to insure rotational equilibrium.^ There must be no net turning effect of forces rotating an object about a pivot point if the rigid object is to be in equilibrium.
To analyze such situations we follow the simple procedureoutlined below:
Isolate the body for discussion.
Draw all the forces acting on the body.
Procedure For Drawing A Free Body Diagram
5
Choose a point about which the moments will bedetermined
Find out the moments
Procedure For Drawing A Free Body Diagram
6
Idealized model
Free body diagram
- Draw an outlined shape. Imagine the body to be isolated or cut “free” from its
constraints and draw its outlined shape.
- Show all the external forces and couple moments. These typically
include:
a)^ Applied loads b) Support reactionsc) Weight of the body
The three common types of connections which join a built structure to itsfoundation are;
Roller Support 2.
Pinned Support 3.
Fixed Support
These supports can be located anywhere along a structural element.
Commonly used Supports
8
They are found at the ends or at the midpoints, or at any otherintermediate points.
Pin Support
Roller Support
Fixed Support
FIXED SUPPORTS Fixed supports can resist vertical and horizontal forces as well as
moment.
These supports restrain both rotation and translation, they are also known as rigidsupports. This means that a structure only needs one fixed support in order to be stable. A flagpole set into a concrete base is a good example of this kind of support
Commonly used Supports-Fixed Support
9
A flagpole set into a concrete base is a good example of this kind of support Such supports can be welded or screwed
A pinned support can
resist both vertical and horizontal forces
but not a
moment.They will allow the structural member to rotate, but not to translate inany direction
Commonly used Supports-Pinned Support
11
Pin Support
Reactions of the Supports
Reactions of the Supports
14
As a general rule, if a support prevents translation of a body in a givendirection,A force is developed on the body in the opposite direction. Similarly, ifrotation is prevented, a couple moment is exerted on the body.
Reactions of the Supports
Reactions of the Supports
x
y
F^1
F^3
F^4
O
A body is subjected to a system of forcesthat
lie
in
the
x-y
plane.
When
in
equilibrium, the net force and net momentacting on the body are zero (as discussedearlier).
This
2-D
condition
can
be
represented
by
the
three
scalar
equations
20
F^2 O
represented
by
the
three
scalar
equations
F
x^
F
y^
M
O^
Where point O is any arbitrary point.
Example
21
A fixed crane has a mass of 1000 kg and is used to lift a 2400 kg crate.^ It is held in place by a pin at
A^
and a rocker at
B. The center of gravity of the
crane is located at
G
.
Determine the components of the reactions at
A^
and
B.