Civil Engineering - RCC Structures Design - Discussion

Discussion Forum : RCC Structures Design - Section 2 (Q.No. 6)
6.
If the permissible compressive and tensile stresses in a singly reinforced beam are 50 kg/cm2 and 1400 kg/cm2 respectively and the modular ratio is 18, the percentage area At of the steel required for an economic section, is
0.496%
0.596%
0.696%
0.796%
none of these.
Answer: Option
Explanation:

Taking Moment of area of tension and compression zone for a singly reinforced beam:

Discussion:
19 comments Page 1 of 2.

Rashik Koundal said:   5 years ago
If the area of steel given than % of steel

p=100.ast/b.d

ast =area of steel
b.d= eff. Breadth and depth of the beam

But in this case, ast(area of steel) not given.
Then,
p= 50 * k^2 / m(1-k).

{k = N.A factor}
k= mc/mc+t.
m= modular ratio.
{ symbol/ mens divde by}.
{ k^2 means to raise to power 2}.


So now put values in formula find( k) 1st.
k= 18 * 50 / 18 * 50 + 1400 = 900/900+1400.
=900/2300,
k=0.39.
Now p= 50 * 0.39^2/18 (1-0.39) = 0.696 answer.
(2)

Er. Taba Tallum said:   3 years ago
Alternate solution:
c=50kg/cm2 , t=1400kg/cm2 and m=18
Critical N.A depth, n=(m*c)xd/(t+m*c)=0.39*d.

Equating total compression force to the total tension force.
=> bxnxc/2 = Ast*t.
=>b*0.39d*50/2 = Ast*1400
=>Ast/(bd) = (0.39*25)÷1400 = 0.00696.
Percentage steel, Pt = Ast*100/(bd) = 0.00696*100 = 0.696%.
(2)

Aswathy said:   6 years ago
BXX/2 = mAst (d-X) ..... (1)
X= critical depth of neutral axis

X = kd
X= (mc/mc+t)d...... (2)

We have,
m = 18
C = 50kg/cm2
t = 1400kg/cm2

From this by substituting in formula (2) we get X = 0.39d

And then by substituting X in (1) we get
Ast/bd =pt= 0.696%

Shilendra singh said:   8 years ago
P=50k^2/m (1-k).

Because
K = mc/(mc+t).
= 18 *50/(18 *50+1400).
= 0.391.

The value of k put in above eq.
= (50 *0.391^2)/18 (1-0.391),
= 0.697.

So option C is correct.

Rohit said:   10 years ago
First find value of n in form of d i.e. effective depth.

Then from relation moment of area of compression zone = moment of area of equivalent tensile zone we can find value of AST.

Arnab said:   9 years ago
Here, p = (k * c * 100)/(2 * t).
Then k = (18*50)/((18*50) + 1400) = 9/23.

Putting value of k in p we get p.
So, p = 0.698%.

Malla said:   7 years ago
%At=m/(2r*(m+r))*100 where r=t/c.

r=1400/50 = 28
%At = 18/(2 * 28 * (18+28)) * 100 = 0.698%.

Aniket gawnde said:   5 years ago
P=50 * n1^2/m(1-n1) %.
n1 = m/(m+r).
r = tensile stress/compressive stress.

Harry bhai said:   8 years ago
And is 0.704166666%
Using Xc= 0.40d

Then,
PS= 50*x^2÷(md(d-x)).
(1)

Vasantha devi said:   8 years ago
@Shilendra Singh.

Where is this formula given? Explain the formula.
(1)


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