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

• Jun 4, 2001

2
• #2

Taro

Structural

Nov 29, 2000

713

US

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.

 

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• Jun 6, 2001

• #3

Qshake

Structural

Jul 12, 2000

2,672

US

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)))

 

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• Aug 2, 2001

• #4

JBALUCI

Structural

Jul 17, 2001

3

US

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

 

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• Aug 3, 2001

• #5

Taro

Structural

Nov 29, 2000

713

US

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.

 

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• Feb 13, 2002

• #6

sadman

Structural

Feb 13, 2002

1

PK

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

 

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• Feb 13, 2002

• #7

Ingenuity

Structural

May 17, 2001

2,374

US

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!

 

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• Feb 14, 2002

• #8

pravi

Structural

Jan 3, 2002

7

IN

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))

 

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