DEPARTMENT OF CIVIL ENGINEERING Coplanar concurrent & Non- concurrent forces POOJA KUMARI 3RD. SE. CIVIL

Coplanar concurrent forces DEPARTMENT OF CIVIL ENGINEERING Coplanar concurrent forces

CONCURRENT FORCE SYSTEM: DEPARTMENT OF CIVIL ENGINEERING CONCURRENT FORCE SYSTEM: A concurrent force system contains forces whose lines-of action meet at some one point. Forces may be tensile (pulling)

CONCURRENT FORCE SYSTEM: DEPARTMENT OF CIVIL ENGINEERING CONCURRENT FORCE SYSTEM: A concurrent force system contains forces whose lines-of action meet at some one point. Forces may be compressive (pushing)

Force exerted on a body has two effects: DEPARTMENT OF CIVIL ENGINEERING Force exerted on a body has two effects: The external effect, which is tendency to change the motion of the body or to develop resisting forces in the body The internal effect, which is the tendency to deform the body.

DEPARTMENT OF CIVIL ENGINEERING If the force system acting on a body produces no external effect, the forces are said to be in balance and the body experience no change in motion is said to be in equilibrium. The process of reducing a force system to a simpler equivalent stem is called a reduction. The process of expanding a force or a force system into a less simple equivalent system is called a resolution.

DEPARTMENT OF CIVIL ENGINEERING A force is a vector quantity that, when applied to some rigid body, has a tendency to produce translation (movement in a straight line) or translation and rotation of body. When problems are given, a force may also be referred to as a load or weight. Characteristics of force are the magnitude, direction (orientation) and point of application.

DEPARTMENT OF CIVIL ENGINEERING Collinear : If several forces lie along the same line-of –action, they are said to be collinear. Coplanar: When all forces acting on a body are in the same plane, the forces are coplanar.

Principle of Transmissibility DEPARTMENT OF CIVIL ENGINEERING Principle of Transmissibility The principle of transmissibility states that the condition of equilibrium or of motion of a rigid body will remain unchanged if a force F action at a given point of the rigid body is replace by a force F’ of the same magnitude and the same direction, but acting at a different point, provided that the two forces have the same line of action.

DEPARTMENT OF CIVIL ENGINEERING Line of action

DEPARTMENT OF CIVIL ENGINEERING Resultant Forces If two forces P and Q acting on a particle A may be replaced by a single force R, which has the same effect on the particle.

DEPARTMENT OF CIVIL ENGINEERING This force is called the resultant of the forces P and Q and may be obtained by constructing a parallelogram, using P and Q as two sides of the parallelogram. The diagonal that pass through A represents the resultant.

DEPARTMENT OF CIVIL ENGINEERING For multiple forces action on a point, the forces can be broken into the components of x and y.

Coplanar Non-concurrent Forces. DEPARTMENT OF CIVIL ENGINEERING Coplanar Non-concurrent Forces.

DEPARTMENT OF CIVIL ENGINEERING It means that the forces which acts in a single plane but at a different point.

DEPARTMENT OF CIVIL ENGINEERING Moment Of A Force :- The moment of a force is equal to the product of the force and the perpendicular distance of line of action of force from the point about which the moment is required. M = P x X Here, M = moment P = Force X = Perpendicular distance between the line of action of force and the point about which moment is required.

Unit of moment is N.m. Or kN. m. DEPARTMENT OF CIVIL ENGINEERING Unit of moment is N.m. Or kN. m.

Examples of moment :- Sign for moment :- To tight the nut by spanner DEPARTMENT OF CIVIL ENGINEERING Examples of moment :- To tight the nut by spanner To open or close the door Sign for moment :- Generally, clockwise moment is taken as positive and anticlockwise moment is taken as negative.

DEPARTMENT OF CIVIL ENGINEERING Couple:- To equal and opposite forces whose lines of action are different form a couple. Resultant or net force of couple is zero. Hence, couple acting on a body do not create any translatory motion of the body. Couple produces only rotational motion of the body.

Types of couple :- There are two types of couple. Clockwise couple DEPARTMENT OF CIVIL ENGINEERING Types of couple :- There are two types of couple. Clockwise couple Anticlockwise couple

Anticlockwise couple Clockwise couple DEPARTMENT OF CIVIL ENGINEERING Clockwise couple It rotates the body in clockwise direction. It is taken as positive. Anticlockwise couple It rotates the body in anticlockwise direction. It is taken as negative. Arm of couple :- The perpendicular distance between the lines of action of two forces forming couple is know as the arm of couple.

Moment of couple = Forces x arm of couple M = P x a DEPARTMENT OF CIVIL ENGINEERING Moment of couple :- Moment of couple = Forces x arm of couple M = P x a unit of couple is N.M. Or KN.M

Example of couple are :- DEPARTMENT OF CIVIL ENGINEERING Example of couple are :- Forces applied to the key of a lock, while locking or unlocking it. Forces applied on the steering wheel of a car by two hands to steer the car towards left or right. To open or close wheel valve of a water supply pipe line.

CHARACTERISTICS OF A COUPLE :- DEPARTMENT OF CIVIL ENGINEERING CHARACTERISTICS OF A COUPLE :- The algebraic sum of the forces, forming the couple is zero. II. The algebric sum of the moment of the forces, forming the couple, about any point is the same and equal to the moment of the couple itself. Moment of couple M = P.a Now, taking moment @ 0, III. A couple cannot be balanced by a single force, but can be balanced only by a couple, but of opposite nature.

I. Moment = Force x Perpendicular distance M = P.x DEPARTMENT OF CIVIL ENGINEERING DIFFRENCE:- MOMENT I. Moment = Force x Perpendicular distance M = P.x It is produced by a single force not passing through C.G. of the body. The force move the body in the direction of force and rotate the body. To balance the force causing moment, equal and opposite forces is required. For example. - To tight the nut by spanner. - TO open or close the door.

- To rotate key in the lock. DEPARTMENT OF CIVIL ENGINEERING COUPLE I. Two equal and opposite forces whose lines of action are different form a couple. II. It is produced by two equal and opposite parallel, non-collinear forces. III. Resultant force of couple is zero. Hence, body does not move, but rotate only. IV. Couple can not be balance by a single force. It can be balance by a couple only. V. For example, - To rotate key in the lock. - To open or close the wheel valve of line. - To rotate the steering while of car.

CONDITION OF EQUILIBRIUM FOR COPLANER NON – CONCURRENT FORCES:- DEPARTMENT OF CIVIL ENGINEERING CONDITION OF EQUILIBRIUM FOR COPLANER NON – CONCURRENT FORCES:- If the body is acted upon by a number of co-planar non-concurrent forces. It may have one of the following stats: The body may move in any one direction. The body may rotate about itself without moving. The body may move in any one direction, and at the same time it may also rotate about itself. The body may be completely at rest.

DEPARTMENT OF CIVIL ENGINEERING END