350 
Theodore Sedgwick Johnson 
held apart at the top by a horizontal strut. The ends will be 
considered fixed and the same bending moment will be assumed 
at all corners. For a pressure P and width h and length I of the 
tank this negative bending moment will be found (by equating 
the moments from each side) to be (b^ — U = P). 
If the corners were hinges, the maximum bending moment 
would be in the center, but it is reduced by the negative 
bending moments produced by fixed ends. The value then be- 
comes — 2 hi — 2 52 ) as the maximum on the side where 
I and h are the lengths of the sides. The pressure of the earth 
will be calculated from Rankine's formula 
p = wh 
Z + sin 0 
I — sin (j) 
where w = 100 pounds cubic feet and = 30°. 
The pressure of the water will be determined by the usual hy- 
drostatic law, p = wh. This would mean an earth pressure of 
533 pounds per square foot and 998.4 pounds per square foot 
for water or total pressures on a vertical strip 1 foot wide of 
3600 pounds and 6739.2 pounds. 
If the long walls of the tank should be supported in the middle, 
the design would change to the condition of a continuous beam 
of two equal spans with fixed ends and consequent negative bend- 
ing moments at each end and over the center support. 
In this case, the maximum positive moment would be 
and the maximum negative moment tk the lower por- 
tion of the wall a great deal of the stresses will be taken to the 
sloping bottom, but it will be on the safe side to assume the wall 
as continuous over three supports. ¥/hen the slab is reinforced 
in both directions, the analysis becomes more complex. For 
square slabs such as this would be, if not supported in the middle, 
the reinforcement would be equal in all directions. For rec- 
tangular slabs the relative amount of stress on the system par- 
allel to the long side of the slab becomes less. 
In the case of the side walls in the tank under consideration, if 
a beam is used to strengthen the slab in the center, they become 
oblong panels, while they remain approximately square if not 
so supported. This theoretical consideration cannot be of any 
effect in this case, because one side of the slab, i.e., the top, is 
unsupported. 
