FLAT PLATES 



141 



Consequently, the maximum stress in the cross strips, and therefore 

 in the original strip, is 4 



(198) 



In the preceding article it was shown that the maximum stress in 

 an elliptical plate occurs in the direction of the minor axis. There- 

 fore equation (198) gives the limiting value which the stress in an 

 elliptical plate approaches as the ellipse becomes more and more 

 elongated. 



For a circular plate of radius b and thickness h the maximum 

 stress was found to be 



(199) 



P = 



Comparing equations (198) and (199), it is evident that the maxi- 

 mum stress in an elliptical plate is given, in general, by the formula 



where k is a constant which lies between 1 and 3. Thus, for - = 1 



b a 



(that is, for a circle) k = 1 ; whereas, if - = (that is, for an infinitely 



Cv 



long ellipse), k = 3. The constant k may therefore be assumed to 

 have the value i 



which reduces to the values 1 and 3 for the limiting cases, and in 

 other cases has an intermediate value depending on the form of the 

 plate. Consequently, 



b\b z w (3a-2b)b*w 



7J~tf 



(200) 



P = (3-2-)^ = 



which is the required formula for the maximum stress p in a homo- 

 geneous elliptical plate of thickness h and semi-axes a and b. 



88. Maximum stress in homogeneous square plate under uniform 

 load. In investigating the strength of square plates the method of 

 taking a section through the center of the plate and regarding the 



