132 STATICS. [218. 



From this table the six conditions of equilibrium are at once obtained : 



= o, (i) 



= o, (2) 



= o, (3) 



=o, (4) 



Wb sin cos < + ( A z + B z )a = o, (5) 



= o. (6) 



If the reactions were not required, equation (4) alone would be suffi- 

 cient, as it furnishes the value of F, viz., 



F=-cos0sm<f>.W r . 

 P 



This relation can of course be found directly by taking moments about 

 the axis of the hinges. It shows that, for a given inclination of the hinges, 

 F is greatest when < = ?r/2. 



The remaining five equations are sufficient to determine A x + B x , 

 A y , A z , B y , B z . 



To find the reactions for a door with vertical axis, we have to put 

 6 = 7T/2, which gives, of course, F=o, and 



A y -B y = -- Wsm 4>, A Z -B Z = -- 

 a a 



as </> may be assumed = o in this case, we find 



The signs indicate that the upper hinge A is pulled out while the 

 lower one B is pressed in. 



2. CONSTRAINTS. 



218. It has been shown in Art. 213 that the number of the 

 conditions of equilibrium is six, for a rigid body that is perfectly 

 free. This number will be diminished whenever the body is 

 subject to conditions restricting its possible motions. Such 



