64 



THE HUMAN MOTOR 





Example : Take a hollow rod, .of which the external radius is 

 R, the internal radius is R' ; the 

 full section is : :rR 2 :rR' 2 = TC 

 (R 2 R' 2 ) ; a solid rod of equal 

 cross section must have a radius 

 r so that : 



*r 2 = (R2 R'2) (fig. 78). 



Apply the formula (2a) and F - 



4FL 3 



4FL 3 . 

 v' = ?r~ , in the other. 



Suppose that R = 2 R' ; then 



- 2 ) or r 2 = f R*. 



Consequently 

 4FL 3 



3E. 



. , 



16 ) 



64FL 3 4FL 3 



-= 45E.R 3 ' : ~ 9 



^* 



The two deflections are therefore to each other as 27 and 45. 

 V __1 1 27 _ 3 

 y' : ~45'27 = ~ 45 ~ 5 



In other terms, the resistance of the solid rod is f of that of a 

 hollow rod of the same sectional area of which the external radius 

 is double the internal radius. 



The ratio will be slightly less than 1 to 4 if R' = | R. In the 

 long bones of man ( 66), R' generally falls between \ R and f R : 

 Usually R' = J R for the thigh bone or femur. 



According as a beam is simply supported (fig. 79), or is fixed 

 (fig. 80) at its two extremities, the deflections are, respectively : 



FL FL 8 



= 



that is to say, 16 and 64 times less. 



\F 



Fio 79 FIG. 30- 



Calculation also shows that the cross section of a rod fixed at 

 one end can be progressively reduced towards the outer, and 



