Equilibrium of Rigid Body

Equilibrium of Rigid Body:
Conditions : ? Fx = 0 ; ? Fy = 0 ; ? M = 0
Sketch the F.B.D
1- Known external forces generally include the weight of the free body and forces applied for a given purpose.
2- Unknown external forces usually consist of the reactions through which the ground & other bodies oppose a possible motion of the free body.
Reaction may be divided in to:
Support or Connection Reaction Number of Unknowns
1-Reaction equivalent to a force with known line of action.

Roller Rocker Frictionless Surface
Force with known line of action 1

Short cable Short link

Force with known line of action 1

Collar on frictionless rod Frictionless pin in slot
Force with known line of action 1
2-Reaction equivalent to a force of unknown direction.

Frictionless pin or hinge Rough surface
Force of unknown direction 2
3-Reactions equivalent to a force of unknown direction and a couple.

Fixed support
Force and couple 3
3.44 A 13-in lever is hinged at B and attached to a control cable at A . Knowing that the magnitude of the force P is 400 lb , find the tension in the cable and the reaction at B.



















3.50 Find the maximum force which may be safely exerted by link AB on the bell crank if the maximum allowable value for the reaction at O is 500 lb .

























3.55 A movable bracket is held at rest by a cable attached at C and by frictionless rollers at A and B . For the loading shown , determine the tension in the cable and the reaction at A and B .



3.56 A light bar AD is suspended from a cable BE and supports an 800-lb load at point C . The extremities A and D of the bar are in contact with smooth , vertical walls . (a) If d=8 in., determine the tension in cable BE and the reaction at A and D. (b) Find the maximum distance d which may be safely used if the maximum allowable value for the reaction at A is 500 lb .








3.64 Assuming that the maximum allowable value of the reaction at B is 2000 lb and that the reaction




































3.75 The control rod AB is acted upon by the vertical force P and by the two forces T exerted by the cable which passes over frictionless pulleys of negligible diameter. Assuming that the free ends of the cable remain horizontal, determine the value of ? corresponding to equilibrium .



3.76 For the control rod of Prob. 3.75 the following values are given: L = 20 in., a = 8 in., b = 5 in., T = 150 lb, and P = 100 lb. If possible, determine the value of ? corresponding to equilibrium (a) neglecting the diameter of pulleys, (b) assuming that the diameter of each pulley is 1 in. (c) neglecting the diameter of pulleys and assuming that the force P is directed horizontally to the right.