FLAT PLATES ]39 



If the plate remains intact, the two strips AB and CD must deflect 

 the same amount at the center. Therefore D l = D z , and hence 



;- 



For the beam AB of length 2 a the maximum external moment is 



R^. Also, since AB is assumed to be of unit width, / = and e = - - 

 Hence the maximum stress p r in AB is 



Similarly, the maximum stress p" in CD is 



"- fi b 

 Consequently, , p n 



7? 7> 8 



or, since from equation (86) - = > 



RI a 



JLJL. 



p" a 3 



r.v liypothesis, a > b. Therefore p" > p'', that is to say, the maxi- 

 mum stress occurs in the strip CD, or in the direction of the shorter 

 axis of the ellipse. In an elliptical plate, therefore, rupture may be 

 expected to occur along a line parallel to the major axis, a result 

 which has been confirmed by experiment. 



119. Maximum stress in homogeneous elliptical plate under 

 uniform load. The method of finding the maximum stress in an 

 elliptical plate is to consider the two limiting forms of an ellipse, 

 namely, a circle and a strip of infinite length, and express a continu- 

 ous relation between the stresses for these two limiting forms. The 

 method is therefore similar to that used in Article 85 in obtaining 

 the modified form of Euler's column formula. 



Consider first an indefinitely long strip with parallel sides, sup- 

 ported at the edges and bearing a uniform load of amount w per unit 

 of area Let the width of the strip be denoted by 2 b, and its thickness 



