130 STATICS. [216. 



Let r be the radius of the shaft, R that of the wheel, i.e. the lever- 

 arm of the force F, and let F be inclined to the vertical at an angle 6 ? , 

 then, with the co-ordinates and notations of the figure, the conditions 

 2X=o, 2Y=o, 2Z=o, give 



A,+B t = o, A,+B V - W-Fcos B = o, A z + 2 +Fs'm (9 = o, 



where A x , A y , A, are the components of the unknown reaction at A ; 

 B xy B y , B s , those at B. 



Taking moments about each of the co-ordinate axes, we find 



FR = Wr, (a + 6)Fsm + IB Z = o, a W+ (a+Z>)Fcos 6-lB y = o, 



where /= a -f- b + c is the length of the shaft. 



A x and B x must evidently be separately zero. Solving the equations,. 

 we find 



216. As another example, consider a rigid body of weight W, sup- 

 ported at three points Aj, A 2 , A 3 ; and let it be required to determine the- 

 distribution of the pressure between the three supports. 



Let the vertical through the centroid of the body meet the plane 

 of the triangle A^A^A^ in a point G, whose distances from the sides 

 A 2 A 3 , A 3 A l} A^A Z we may denote by / lf / 2 , A- Then, if A lf A 2 , A z be 

 the unknown reactions, and h ly h 2 , h z the altitudes of the triangle, we 

 have 



and, taking moments about A 2 A 3 , A 3 A lr 



Hence, A, = W y A,= W, A> = w. 



M! "2 "3 



Substituting these values into the first equation, we find the condition, 



