248 
OF THE PARTS OF 
[sect. vii. 
t , r • 4x 50 x9 0 . 9 . 
In this case, —^— = *3 ; and g—^ ' 3 = * 4 J 
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. 
¿2 
From the laws of deflexion it will be / 2 : ¿ 2 :: 1 : jj 9 the resistance in the lon- 
¿2 
gitudinal direction; and 1 + 71, 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 of t f when one-fourth of 
the thickness is an inch, t being the whole thickness, and f the cohesive force of a 
square inch; and allowing for riveted plates, 
tf 2 tf . 
4 x "g" = ~g~ = the resistance in one direction ; 
and { 1 + (t) } 
-0— = the whole resistance. 
The stress is as the force on a given portion of the curve, resolved into its 
tendency to split the material. If 2 be a part of the curve, and r the radius of 
curvature, 1 we have z : r :: T27 p z : T27 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, 
therefore in this case, 
1-27 p t 
2 e 
ft 
6 ’ 
p - 3-8 
Hence we find, that the resistance of a plate is quite independent of its thickness when it bends