STRENGTH OF BEAMS 



55 



Therefore, substituting in the formula p = , we have 



Pb = 



te 2 



12 



6P 



Consequently, 



whence 



and 



Pm&x = Pb Pa = 

 min 



(-1) 



P 



bx 



Pmax = 2+- 



Pmin = 



As a numerical example, let I = 5 ft., P = 200 lb., 6 = 4 in., and p = 600 lb./in. 2 

 (for ordinary brickwork). Then, solving the above equation by the formula for 

 quadratics, 



2 P 



whence, by substituting the above 

 numerical values, 



z = 5.6in. 



104. Find the required dimen- 

 sions for the arms of a cast-iron 

 pulley of external diameter Z) for 

 a tension in the belt of T^ on the 

 tight side and T 2 on the slack side. 

 Arms assumed to be elliptical in cross sectipn, of dimensions h = 2b (Fig. 51). 



Solution. According to Bach the load may be assumed to be carried by one 

 third of the spokes, and the working stress taken as 4500 lb./in. 2 Let n denote 

 the number of spokes. Then the maximum moment on one spoke is approximately 



FIG. 51 





The moment of inertia of an ellipse about its minor axis is , and its section 



T 2 





modulus is Z = Therefore, substituting these values in the formula p = 

 we have 



4600 = 



whence 



h = 



