248 OF THE PARTS OF [SECT. vit. 



T ,1 . 4 x 50 x 9 9 



In this case, 6000~~ = ' an ^ 9 _ 3.3 x '3 = '4 ; 



to which adding '5 for wear, it is 0'9 inches. 



521. Of the strength of flat plates to bear the pressure of steam, or other elastic 



fluids. The strength of a plate is limited by the curvature it takes by the strain ; 



and when the length and breadth are equal, the resistance is the same in both 



directions ; but in any other case the two flexures do not correspond, and the 



resistance depends chiefly on the curvature in the shortest direction of support. 



From the laws of deflexion it will be Z 2 : J* :: 1 : -^, the resistance in the Ion- 



7 2 



gitudinal direction ; and 1 + ^ , multiplied by the resistance in the shorter 



direction, gives the whole resistance. 



When a plate is fixed at the edges, the flexure lessens the quantity of strain on 

 the resisting part, but only in a small degree ; and in bending to the new position, 

 the inner part of the matter must be partially compressed, and the resistance to 

 tension will extend only to a little more than half the thickness, and varies as the 

 distance from the neutral line : hence it is only one-fourth oftf, when one-fourth of 

 the thickness is an inch, t being the whole thickness, and / the cohesive force of a 

 square inch ; and allowing for riveted plates, 



t f 3 t f 

 ~4~ x "3" = ~g~ = the resistance in one direction ; 



and 1 1 + ^ J j = t h e wno i e resistance. 



The stress is as the force on a given portion of the curve, resolved into its 

 tendency to split the material. If z be a part of the curve, and r the radius of 

 curvature, 1 we have z : r : : 1-27 p z : 1-27 p r, the stress, p being the pressure 



1 But the curvature is limited by the stretching and bending in the shorter direction ; sup- 

 pose it to be wholly by bending, and we have, 



e : 1 :: "a : r = ^ ; 



therefore in this case, 



/ 



T" f 



MO*}/ 



Hence we find, that the resistance of a plate is quite independent of its thickness when it bends 



