Chapter 2.
UNIT II
TYPES OF FORCES ON A BODY
Before taking up equilibrium conditions of a body, it is necessary to identify the various
forces acting on it. The various forces acting on a body may be grouped into:
(a) Applied Forces
(b) Non-applied Forces
(a) Applied Forces
These are the forces applied externally to a body. Each of the forces is having contact with
the body. Depending upon type of their contact with the body, the applied forces may be
classified as:
(i) Point Force
(ii) Distributed Forces
(i) Point Force: It is the one which has got contact with the body at a point. Practically there
is no force which will have contact with the body at a single point. However, when the
contact area is small compared to the other dimensions in the problem, for simplicity of
calculation the force may be considered as a point load. If a person stands on a ladder, his
weight be taken as an applied point load.
(ii) Distributed Forces: Distributed forces may act over a line, a surface or a volume.
Correspondingly they are known as linear, surface and body forces.
Linear Force: A linear force is one that acts along a line on the body. It is usually represented
with abscissa representing the position on the body and ordinate representing the magnitude
of the load.
Surface Force: Force acting on the surface of a body is known as surface force. The
hydrostatic pressure acting on a Dam is an example of surface force.
Body Force: A body force is the force exerted from each and every particle of the mass of the
body. Example of this type of force is the weight of block acting on the body under
consideration.
(b) Non-applied Forces
There are two types of non-applied forces: (a) Self weight and (b) Reactions.
Self weight: Everybody subjected to gravitational acceleration and hence has got a self
weight. W = mg Where m is mass of the body and g is gravitational acceleration (9.81 m/sec2
near the earth surface)
Self weight always acts in vertically downward direction. When analysing equilibrium
conditions of a body, self weight is treated as acting through the centre of gravity of the body.
If self weight is very small, it may be neglected.
Reactions: These are self-adjusting forces developed by the other bodies which come in
contact with the body under consideration. According to Newton’s third law of motion, the
reactions are equal and opposite to the actions. The reactions adjust themselves to bring the
body to equilibrium.
If the surface of contact is smooth, the direction of the reaction is normal to the surface of
contact. If the surface of contact is not smooth, apart from normal reaction, there will be
frictional reaction also. Hence the resultant reaction will not be normal to the surface of
contact.
2.12 FREE BODY DIAGRAM
In many problems, it is essential to isolate the body under consideration from the other bodies
in contact and draw all the forces acting on the body. For this, first the body is drawn and
then applied forces, self weight and the reactions at the points of contact with other bodies are
drawn. Such 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 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.
Thus, for the system of forces shown in Fig. 2.32(a).
Proof: Draw the three forces F1, F2 and F3 one after the other in direction and magnitude
starting from point a. Since the body is in equilibrium (resultant is zero), the last point must
coincide with a. Thus, it results in triangle of forces abc as shown in Fig. 2.32(b). Now, the
external angles at a, b and c are equal to β, γ and α.
Note: While determining the direction of the reaction on a body note that if the body is in
equilibrium under the action of only three coplanar forces, those three forces must be
concurrent
Equilibrium of the Rigid Bodies:
Statics deals primarily with the description of the force conditions necessary and sufficient to
maintain the equilibrium of engineering structures.
When a body is in equilibrium, the resultant of all forces acting on it is zero. Thus the
resultant force R and the resultant couple M are both zero. And have the equilibrium
equations.
R =∑𝐹 = 0
M = ∑𝑀 = 0
These requirements are both necessary and sufficient conditions for equilibrium.
A mechanical system is defined as a body or group of bodies which can be conceptually
isolated from all other bodies. A system may be a single body or a combination of connected
bodies.
Once we decide which body or combination of bodies to analyze, we then treat this
body or combination as a single body isolated from all surrounding bodies. This isolation is
accomplished by means of the free body diagram, which is diagrammatic representation of
the isolated system treated as a single body. The diagram shows all forces applied to the
system by mechanical contact with other bodies, which are imagined to be removed.
The free body diagram is the most important single step in the solution of problems
in mechanics.
Equilibrium conditions:
As we defined equilibrium as the condition in which the resultant of all forces and
moments acting on a body is zero. Stated in another way, a body is in equilibrium if all forces
and moments are applied to it are in balance.
The third equation represents the zero sums of the moments of all forces about any point O
on or off the body. These equations are sufficient conditions for complete equilibrium in two
dimensions. They are necessary conditions because, if they are not satisfied, there can be no
force or moment balance. They are sufficient because once they are satisfied , there can be no
imbalance, and equilibrium is assured.
Categories of equilibrium:
Category 1, equilibrium of collinear forces, clearly requires only the one force equation in the
direction of the forces (x-direction), since all other equations are automatically satisfied.
Category 2 equations of forces which lie in a plane (x-y plane ) and are concurrent at a point
O, requires the two forces equations only, since the moment sum about O, that is about a Zaxis through O, is necessarily zero. Included in this category is the case of the equilibrium of
a particle.
Category 3 equilibrium of parallel forces in a plane requires the one force equation in the
direction of the forces (x-direction) and one moment equation about an axis (z-axis) normal
to the plane of the forces.
Category 4 equilibrium of a general system of forces in a plane (x-y), requires the two force
equation in the plane and one moment equation about an axis (z-axis) normal to the plane.
EQUILIBRIUM OF CONNECTED BODIES
When two or more bodies are in contact with one another, the system of forces appears as
though it is a non-concurrent forces system. However, when each body is considered
separately, in many situations it turns out to be a set of concurrent force system. In such
instances, first, the body subjected to only two unknown forces is to be analysed followed by
the analysis of other connected body/bodies.