FLAT PLATES 143 



ABC is 2 abw, and it is applied at the center of gravity of the triangle, 



which is at a distance of - from A C. Consequently, the total moment 



o 



of the load about A C is Therefore the total external moment 



J7 at the section AC is 



2 abwc abwc 



M = abwc = > 



o o 



and the maximum stress in the plate is 



abwc h 



Me ~3~ 2 2 wabc 

 P= -J = -dh^ = -dh^' 



12 

 or, since cd = 4 ab, 



(91) p = w h*' 



which gives the required maximum stress. 



For a square plate a = b and c = a \/2, ,and formula (91) reduces 

 to formula (90) for square plates, obtained in the preceding article. 



Problem 145. A wnuight-iron trapdoor is 6 ft. long, 3 ft. wide, and f in. thick. 

 How great a uniform load will it bear ? 



122. Non-homogeneous plates ; concrete-steel floor panels. The 

 formulas derived in the preceding articles apply only to flat plates of 

 homogeneous material. If a plate is composed of non-homogeneous 

 material, such as reenforced concrete, the maximum stress is given by 

 the formula 



win -re 1' is the moment of inertia of the equivalent homogeneous 

 section obtained from the non-homogeneous section as explained in 

 Article 48, and e' is the distance of the extreme fiber of this equivalent 

 homogeneous section from its neutral axis. 



Thus, from Article 116, the external moment M on half of a uni- 



*/* 1JJ 



formly loaded circular plate is M = > and, consequently, the maxi- 



o 



iniiin stress in a uniformly loaded, non-homogeneous, circular plate is 



given by the formula 



r*we f 



02) P^r, 



