8 BULLETIN 789, U. S. DEPARTMENT OF AGRICULTURE. 
For any effective depth to steel the maximum resisting moment, 
which is developed when the steel and concrete are simultaneously 
stressed to the assumed allowable values for f; and f,, is given by 
the equation: ’ 
M =f.jpbd? 
For selected values of f;, f., and n and for b=12, the product 4; 
f-jp is a constant and | 
M=C# 
The area of steel required is given by the equation 
a= pbd 
The area of steel may also be-figured from the equation 
q= are or 
oes <a 
pe ea? 
TD pak) a 
For selected values of f,, f., and m and for different values of m 
and d the product m xf; X7 Xd 1s a constant which may be designated 
12 
by &. Then 
The thickness of the wall is determined by the bending moment at’ 
the bottom, and, as this thickness is maintained for the full height, 
it will be greater in the upper portion of the wall than required to 
develop the assumed stresses. The stress in the concrete will de- 
crease from bottom to top and, as the thickness of the wall is usually 
selected in even inches, the stress at the bottom will generally be less 
than the assumed allowable value. In some cases, however, a wall 
thickness may be chosen slightly less than actually required for the 
moment at the bottom, in which case the stress in the concrete at that 
level will exceed the assumed value. 
With each change from the bottom to the top in the spacing or 
size of the reinforcing bars, there is a decrease in the value for the 
percentage of steel, and, assuming n to be constant, a corresponding 
increase in the value for 7. Therefore, the results obtained by use 
of the formula L LS forwhich # has been computed foraconstant 
value of 7, are not absolutely correct. Im any case, however, the 
error is small and, moreover, is on the safe side, because, if the 
increased value for 7 was used, slightly larger values for L, the allow- 
able pressure for a given steel area, would be obtained. 
