i have a formula for directly getting the area of steel

huangyhg

i have a formula for directly getting the area of steel
hello,
  i want to know if there are no aci charts avaiable for getting the values of "row" or as ( area of steel ) then is there any direct formula for finding this if we have the moment mu or ku avaiable in case of footing design. i have a formula but i want to confirm it with you guys please help me out :-
   row = 1/m ( 1- under-root 1-ku/f)  , here m = fy/0.85f'c and f= 0.3825f'c. is it correct to use this or is there any other formula for finding the area of steel and then spacing of the bars in case of foundation design
a convenient rule of thumb is:
as = mu/4d
where mu is in k-ft units, d is in inches
this will usually get you within a few percent of the exact answer.
the formula that i've gotten accustom to using is below.  see wang and salmon for further clarification...
m = (fy/(0.85*f'c)) and
ru = mu/(phi*b*d^2) and
rho = (1/m)*(1-sqrt(1-((2*m*ru)/fy)))
can you explain the derivation of as = mu/4d?
thanks
the rule of thumb is easy to derive.  the equation for flexural strength of a singly-reinforced rectangular concrete beam is:
mu = phi*mn = phi*as*fy*(d-a/2)/12
now substitute these values:
phi = 0.9
fy = 60 ksi
(d-a/2) = 0.9d
therefore, as = mu/(4d).  like i said, it's just a rule-of-thumb.  but it almost always is within a few percent of the exact answer if you just need a quick & dirty calculation for a reality check.
taro ,
  how u got the value of (d-a/2) how u supposed the value of a.
sadman,
taro's value of 0.9d is an approximate value of (d-a/2) and is not exact - as he clearly stated. re-arranging it is based upon "a" not exceeding 0.2d - ie ku=0.2
this is a very common approximation, and is okay for sections that are not "over-reinforced" and hence they are ductile and the neutral axis depth (or parameter, ku) is small.
it also works fine for t-sections provided the na is in the compression flange!
i have come across a formula in one of the indian technical publications wherein you can find ast directly if you know
mu= moment of resistance in n-mm
fck= characteristic strength of concrete in n/mm2
fy= yield strength of steel in n/mm2
b= width of section in mms
d= eff. depth in mms
than,
ast=(0.5*fck*b*d/fy)*(1-sqrt(1-(4.6*mu/(fck*b*d*d))