Statics of Rigid Bodies in Two Dimensions

Statics of Rigid Bodies in Two Dimensions:
Rigid Body: defined as one which does not deform (bodies are not absolutely rigid).

Principle of Transmissibility:
( The external effect of a force is independent of where it is applied along its line of action ).
= =
= =
The forces are equivalent if they have the same magnitude , direction & line of action.
Moment of a Force about an Axis:
The tendency of a force to make a rigid body rotate about an axis is measured by the moment of the force about that axis.
d: perpendicular distance from “A” to the line of action of “F”

(N.m)
Or (lb.ft)
Or (lb.ft)
The moment has magnitude and sense (Clockwise ,and Counterclockwise )

Varignon’s Theorem:
The moment of a force about any axis is equal to the sum of the moment of its components about that axis.





3.1 A 120-lb force is applied to the brake pedal at A. Knowing that the distance AB is 8 in. , determine the moment of the force about B when ? is 30?.



3.2 Knowing that the distance AB is 8 in., determine the maximum moment about B which can be caused by the 120-lb force. In what direction should the force act.





3.5 Compute the moment of the 100-lb force about A (a) by using the definition of the moment of a force, (b) by resolving the force into components along BD and CD, (c) by resolving the force into components along AD and in the direction perpendicular to AD.




3.6 Determine the moment of the 300-lb force about A.




3.7 Determine the moment of the 300-lb force about B.


3.10 A force F acts at a point of coordinates r and ? as shown. The force forms an angle ?1 with a line parallel to the horizontal reference axis. Show that the moment of the force about the origin of coordinates O is F r sin(?1-?).








or




or




3.12 Two forces P and Q have parallel lines of action and act at A and B, respectively. The distance between A and B is a. Fined the distance x from A to point C about which both forces have the same moment. Check the formula obtained by assuming a = 10 in. and (a) P = 20 lb up, Q = 10 lb up; (b) P = 10 lb up, Q = 20 lb up; (c) P = 20 lb up, Q = 10 lb down; (d) P = 10 lb up, Q = 20 lb down.