1) The document discusses engineering mechanics concepts related to moments including how to calculate the moment of a force using the cross product of the force and perpendicular distance from the axis. 2) It also covers parallel force systems and how to calculate the resultant force of coplanar forces that are parallel, unlike, equal or unequal. 3) The key properties of moments and couples are defined including how couples can only be balanced by another couple of the opposite sense.

1. ENGINEERING MECHANICS
GROUP DISCUSSION
 To finding moment of force with cross product.
 Parallel force system and their resultant numerical.
G.D TOPIC :
Submitted to:Professor
ATUL SURI
Submitted by :
ANAMI PRASAD (164006)
ANKIT KUMAR SHARMA(164007)
B.TECH 2ND YEAR
CIVIL , BATCH C1

2. Find momet of force with cross product
Introduction to Moments
The tendency of a force to rotate a rigid body about any
defined axis is called the Moment of the force about the
axis .

3. Moment caused by a Force
The Moment of Force (F) about an axis through Point
(A) or for short, the Moment of F about A, is the
product of the magnitude of the force and the
perpendicular distance between Point (A) and the line
of action of Force (F)
MA = Fd
Units of a moment
The units of a Moment are:
• N·m in the SI system
•ft·lbs or in·lbs in the US Customary system

4. Properties of a Moment
Moments not only have a
magnitude, they also have a
sense to them.
The sense of a moment is
clockwise or counter-
clockwise depending on
which way it will tend to
make the object rotate .

5. Properties of a Moment
The sense of a Moment is defined by the direction it is
acting on the Axis and can be found using Right Hand Rule.

6. Varignon’s Theorem
 The moment of a Force about any axis is equal to the sum of
the moments of its components about that axis.
 This means that resolving or replacing forces with their
resultant force will not affect the moment on the object
being analyzed.
Principle of Moments
The moment of a force about a point is equal to the sum of
moments of the components of the force about the point:

7. Notation for Moments
•In simpler terms the Moment of a Force about the y-axis (My)
can be found by using the projection of the Force on the x-z
Plane.
•The Notation used to denote Moments about the Cartesian
Axes are (Mx, My, and Mz)

8. APPLICATION
Beams are often used to bridge gaps in walls. We have
to know what the effect of the force on the beam will
have on the beam supports.

9. Carpenters often use a hammer in this way to pull a stubborn
nail. Through what sort of action does the force FH at the
handle pull the nail? How can you mathematically model the
effect of force FH at point O?

10. Question: Moment about O is equal to
the product of the force and the
perpendicular distance between the line
of action of the force and O. Since the
force tends to rotate the lever clockwise,
the moment vector is into the plane of
the paper.
Example problem
 
  in.12lb100
in.1260cosin.24



O
O
M
d
FdM
inlb1200 OM

11. Parallel force system and their resultant numerical
Coplanar force
•Parallel force
•Like
•Equal
•Unequal
Non parallel
•Unlike
•Equal
•Unequal
Non parallel forces

12. Coplanar Parallel Forces

13. Resultant of Two Unlike and Unequal Parallel
Forces
Like parallel forces
• The forces, whose lines of action are parallel to each
other and all of them act in the same
• Direction

14. Unlike parallel forces
The forces, whose lines of action are parallel
to each other and all of them do not act in
the
same direction
Couple

15. A pair of two equal and unlike parallel forces (i.e. forces equal
in magnitude, with lines of action parallel to each other and
acting in opposite directions) is known as a couple.
Arm of Couple
• The perpendicular distance (a), between the lines of action of
the two equal and opposite parallel forces, is known as arm of
the couple.

16. MOMENT OF A COUPLE
1 Clockwise couple
2 Anticlockwise couple.

17. CHARACTERISTICS OF A COUPLE
• A couple (whether clockwise or anticlockwise) has the
following characteristics :
• The algebraic sum of the forces, constituting the couple, is
zero.
• The algebraic sum of the moments of the forces, constituting
the couple, about any point
• is the same, and equal to the moment of the couple itself.
• A couple cannot be balanced by a single force. But it can be
balanced only by a couple of
• opposite sense.

18. • Any no. of coplaner couples can be reduced to a single
couple, whose magnitude will be
• equal to the algebraic sum of the moments of all the
couples.

19. BIBLIOGRAPHY
 R.C hibbler
(Chapter-force system and resultant)
Nptel –moment
Google-moment and cross product
Resultant force system

20. THANK YOU