MECHANICS OF SOLIDS SUBJECT CODE: 2130003

2. Fundamentals of Statics

Prof. Jigar Suthar

SYSTEM OF FORCES

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

COMPOSITION OF CONCURRENT COPLANAR 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

COMPOSITION OF CONCURRENT COPLANAR FORCES

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

Solution

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 wrenchAdjustable 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.

The principle of moments

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.

Crane_falls_off_Bridge_medium.mp4

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 ofthe 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

Continue………

Examples

solution

Fy Fx

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=0ΣM@any point =0

COMPOSITION OF COPLANAR NON-CONCURRENT FORCE SYSTEM

Where ΣM= sum of the moment of no. of forces From given point(in above figure point A)R= resultant of no. of forcesd= is perpendicular distance of resultant force from given pointα= inclination of the resultant R to x direction

d1d2

d3

d

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

αRX

d

Note: if forces on this figure are given at some angle then follow the below procedure1.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 forces4. For finding out the moment again we will use the above figure, not transfer angles .

Here consider θ=α

= some value

= some value

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.

Equation is same as sine rule but lami’s theorem is differentIt dose not required triangle it required three mutually perpendicular forces.

Sine Rule

3090

p

1500

R

90

2

3