I HAVE A FORMULA FOR DIRECTLY GETTING THE AREA OF STEEL 2

[nedians]

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

 

[Taro]

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.

 

[Qshake]

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)))

 

[JBALUCI]

can you explain the derivation of As = Mu/4d?
thanks

 

[Taro]

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.

 

[sadman]

Taro ,
how u got the value of (d-a/2) how u supposed the value of a.

 

[Ingenuity]

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!

 

[pravi]

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))