STRESSES IN PANELS.
331
wh2 .
As the pressure increases with the depth, the total pressure, —2_> 18
distributed unequally between these two members, in the proportion of
1 to 2, the amount being — g- at the top and —g— at the sili.
The verticals may accordingly be treated as independent beams, sus-
taining a uniformly increasing load. Under these conditions it is evident
that the maximum bending moment cannot be at the centre. The bending
moment at any point X may be found thus :—The pressure on the surface
AX (fig. 265) of the gate is —acting at a point g above X. Conse-
quently the bending moment at X is
Fig. 264. Fig. 265.
To obtain the maximum value of this expression it is only necessary to
differentiate with respect to x and equate to zéro.
d^ = dx (h2 - x2) = _ 3a;2 = 0
dx dx
whence
J3x = h.
(65)
In other words, the maximum bending moment is situated, not at the
centre of pressure but at a point
0
—— below the surface of the water.
The maximum bending moment at this point is
wh^ whs wh3
“6^3 18 73 9 73’
• (66)
and the dimensions of the girder can easily be calculated by any of the
methods applied to instances of beams under similar conditions of loading.
Subsidiary horizontal members are introduced between the verticals to
transmit the pressure from the plating, which is made as thin as is con-
sistent with durability and strength.
Stresses in Panels.—For all practical purposes the pressure on each
unsupported area of plating or planking between tlie gate framing may be
taken as uniform, an assumption which is, of course, to a certain extent.