Fundamentals of statics

MECHANICS OF SOLIDS
SUBJECT CODE: 2130003
2. Fundamentals of Statics
Prof. Jigar Suthar

Coplanar concurrent force
• For solving the problem of coplanar concurrent
force system we learnt following laws:
• Law of parallelogram of forces
• Law of triangle of forces
• Law of polygon of forces
• Lami’s theorem

COMPOSITION OF CONCURRENT COPLANAR FORCES
Analytical method consists in finding the components of given
forces in two mutually perpendicular directions and then
combining them to get the resultant. Finding the component
of a force is called resolution of forces and is exactly the
opposite to the process of composition of forces

Note: here for horizontal
forces sign will be (_) for
left hand force and (+) for
right hand force
Note: here for vertical
force sign will be - for
Downward force and +
For upward force.
Note: Instead
of applying
above rules
we can use
moment sing
convention
also for
second stape

Another Method which reduce work of sign convention
Note: In this method you need not to worry about sign and direction of force

Note : you can use any of the method to solve the problem

Coplanar non concurrent force
• In coplanar non concurrent force system we will
learn following points:
• Moments & couples,
• Characteristics of moment and couple,
• Equivalent couples,
• Force couple system,

Continue………..
• Varignon’s theorem,
• Resultant of non-concurrent forces by analytical
method and graphical method,
• Equilibrium conditions of coplanar non-concurrent
force system,
• Application of these principles

Moment(Torque)
• Moment is defined as the product of the magnitude
of the force and the perpendicular distance of the
point from the line of action of the force.
Pipe wrenches
box wrench
Adjustable wrench
Hammer
N-m

Sign Convention of Moment
• Moment directions may be accounted for by using a
stated sign convention, such as a plus sign (+) for
counterclockwise moments and a minus sign (-) for
clockwise moments, or vice versa.
• During this course of MOS we will consider + sign
for clockwise moment and – sign for counter
clockwise moment.

couple
• A special case of moments is a couple.
• A couple consists of two parallel forces that are
equal in magnitude, opposite in sense.
• It does not produce any translation, only rotation.
• The resultant force of a couple is zero. BUT, the
resultant of a couple is not zero; it is a pure
moment
Example of car steering

Here is the example of street lamp
Here lamp is creating moment which is resisted by
the couple generated by the tubes of supporting
arms.

Problem if principal of moment will not satisfy
• Video is about crane disaster during lifting of bus
from river.
• This could be avoided if they understand the
principal of moment , and also understand that for
resisting any moment opposite moment or couple
is required.

Varignon’s Theorem
• states that the moment of a force about any point is
equal to the sum of the moments of the
components of the force about the same point.

Lets Prove it
To prove this theorem, consider the force R acting in the plane of
the body shown in figure (a)
The forces P and Q represent any two
nonrectangular components of R.
The moment of R about point O is

EQUILIBRIANT OF A FORCE SYSTEM
• If we apply a force equal and opposite to the
resultant, the body should come to the equilibrium
state.
• Such a force is called equilibrant.
• Thus an equilibrant of a system of forces may be
defined as the force which brings the body to the
state of equilibrium and obviously, this forces is
equal in magnitude, but opposite in the direction to
the resultant.

Equilibrium conditions of coplanar non-concurrent force
system
• The resultant of coplanar system of forces acting on
a body is zero when
1. The algebraic sum of moment of all the forces
about any point in the plane is zero (rotational
moment is zero).
2. The algebraic sum of the component of forces
along each of the two mutually perpendicular
directions is zero (translatory motion is zero).
ΣPx=0 and Σpy=0
ΣM@any point =0

COMPOSITION OF COPLANAR NON-CONCURRENT FORCE
SYSTEM
d1
d2
d3
d
Where ΣM= sum of the moment of no. of forces
From given point(in above figure point A)
R= resultant of no. of forces
d= is perpendicular distance of resultant force
from given point
α= inclination of the resultant R to x direction

Find out the x AND y INTERCEPTS OF RESULTANT
In this kind of problems
where R Is at some angle α,
perpendicular Distance d is
not at 90 degree with
Respect to the original axis
in this case we need to
determine X intercept of R
α
α
X R
d

Here consider θ=α
Note: if forces on this figure are given at some angle then follow the below procedure
1.Here first we transfer all the Forces at single point as we did in coplanar concurrent forces .
2.Then we will change the angle of all the forces with respect to +X axis
3. Then and for finding out the resultant of given forces
4. For finding out the moment again we will use the above figure, not transfer angles .

FREE BODY DIAGRAM
• A diagram of the body in which the body under consideration is freed
from all the contact surfaces and shows all the forces acting on it
(including reactions at contact surfaces), is called a Free Body
Diagram (FBD).

Lami’s theorem
• Lami’s theorem states : If a body is in equilibrium
under the action of three forces, each force is
proportional to the sine of the angle between the
other two forces.
Sine Rule
Equation is same as sine rule but lami’s theorem is different
It dose not required triangle it required three mutually perpendicular
forces.

Fundamentals of statics

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Fundamentals of statics