1. Applied mechanic (Statics) Unit II Forces

2. Principle of transmissibility and its limiations The principle of transmissibility states that “ The state of rest or motion of a rigid body is unaltered if a force acting on the body is replaced by the another force of the same magnitude and direction but acting anywhere on the body along the line of action of the replaced force”. In the figure below if F=F’ then the effect of force on the body is same.

3. Limitation of transmissibility of force Let’s apply two equal and opposite force at the two end of the steel bar AB as shown in the figure. Now this metallic bar will be under tension. According to principle of transmissibility of force, we transfer the force at end A to B which is of same magnitude and direction. This is just equivalent to two equal and opposite force at a point which has no physical significance, so we can eliminate the force at end A. This results no external force on A But in real case the elongation of the bar takes place which depends on the length, cross-section area of bar, modulus of elasticity of bar and magnitude of force. This principle of transmissibility is only applicable to rigid bodies in which we can neglect the internal effect.

4. Lami’s Theorem

5. Resolution and composition of the forces The process of splitting the given force in numver od components without changing the effect on the body is known as resolution of forces.

6. Moment of a force about a point The turning effect of a force on a body about a fixed point or a line is known as moment of a force. 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.

7. Moment of a force about a point Contd. Thus we can say that the moment of force doesn’t characterize the point of application of a force in its all line of action.

8. Moment of a force about an Axis

9. Varignon’s theorem

10. Couple The moment of a couple is the product of the magnitude of one of the forces and the perpendicular distance between their lines of action. M = F x d.

11. Resolution of force into force and a couple Let a force P action on the body at A as shown in the figure. Now it can be shown that P at A can be replaced in to Force P at B and a couple moment M =P.d, d is the perpendicular distance of B from the line of action of P through A.

12. Couple moment as Free Vector

13. Proof: Couple as a free Vector

14. Proof: Couple as a free Vector contd.

15. Example-1