Numerical example 2 | Singly reinforced Sections

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Guide to design of Singly reinforced Sections | Civil Engineering

For “Singly reinforced sections” article series, we have covered the following:

 

Now we will move on with our next solved example in which we will make use of formulas derived earlier. That is why it is necessary that you go through the entire step by step guide in order to gain complete understanding.

Numerical Problem

Calculate the moment of resistance of an RC beam 250mm wide, the depth of the centre of reinforcement being 500mm. Assume σcbc = 5N/mm2, σst = 140 N/mm2, modular ratio = 18.66

Given that,

b = width of the beam = 250mm

d = depth of the beam = 500mm

σcbc = permissible compressive stress in concrete in bending = 5N/mm2

σst = permissible stress in steel = 140 N/mm2

m =  modular ratio = 18.66

To find Neutral Axis (NA)

σcbc /(σst/m) = xc/(d – xc)

5/(140/18.66) = xc/(500 – xc)

Xc = 199.95mm = 200mm

To find lever arm

z = d – xc/3

= 500 – 200/3

= 433.33mm

To find Moment of resistance

Mr = C x z

= bxc (σcbc/2)z

= 250 x 200 x 5/2 x 433.33

= 54166250 N-mm

= 54.166 kN-m

OR

Mr = T x z

= Ast. σst.z —————————equation 1

To find Ast

Equating, C = T

bxc.σcbc/2 = Ast. σst

Therefore, Ast = bxc.σcbc/2 σst

Ast = (250 x 200 x 5/2)/140

Ast = 892.85 mm2

Substituting the value of Ast in equation 1;

Mr = T x z

= Ast. σst.z

= 892.85 x 140 x 433.33

= 54165817 N-mm

= 54.1658 kN-m

From the above example, it is clear that in case of a balanced section, the Mr can be calculated either as Mr = C x z or as Mr = T x z. The values obtained for moment of resistance are the same for both the formulas.   

3 thoughts on “Numerical example 2 | Singly reinforced Sections”

  1. FROM THIS PROBLEM I HAVE GAIN A CLEAR CONCEPTION ABOUT RCC SINGLY REINFORCED BEAM DESIGN AND IT IS HELP FULL FOR DIPLOMA CIVIL ENGINEERING STUDENTS AND RCC DESIGNERS ALSO.

    THANK YOU VERY MUCH

  2. kindly advise a structural design of 65 feet x 80 feet godown with RCC column and 4.5 in thick roof for black cotton soil. it case a no columns in the hall
    case b with one row of column in the hall.

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