140 STEENGTH OF MATERIALS 



by h. Then, if this strip is cut into cross strips of unit width, each 

 of these cross strips can be regarded as an independent beam, tin-, 

 load on one of these unit cross strips being 2bw, and the maximum 



moment at the center being - - Consequently, tin- maximum 



8 



stress in the cross strips, and therefore in the original strip, is 



(87) 



In the preceding article it was shown that the maximum 

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

 fore equation (87) 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 radiu< / and thickness // the maximum 

 stress was found to be 



<> ,-5?. 



Comparing equations (87) and (88), it is evident that the maximum 

 stress in an elliptical plate is given, in general, 1>\ tin- formula 



p = * . 



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



I a 



that is, for a circle, k = 1; whereas, if - = that is, for an in tin 



a 



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

 have the value 



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, 



(89) p , 



