Solved numericals for Singly reinforced Sections | Design Method 1





Design of Singly reinforced Sections | Method 1

In our article series for Singly reinforced sections, we have covered the following:

 

Numerical Problem

An RC beam 200mm wide has an effective depth of 350mm. The permissible stresses in concrete and steel are 5N/mm2 and 140 N/mm2 respectively. Find the depth of neutral axis, area of steel and percentage of steel. (modular ratio (m) = 18.66)

Step One:

Given that:

b = breadth of a rectangular beam = 200mm

d = effective depth of a beam = 350mm

x = depth of neutral axis below the compression edge = ?

Ast = cross-sectional area of steel in tension = ?

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

σst = permissible stress in steel = 140 N/mm2

m = modular ratio = 18.66

From the concrete stress diagram, the formula is given as,

σcbc/(σst/m) = x/(d – x)

5/(140/18.66) = x/(350-x)

Therefore, x = 139.97mm

Step two:

To find area of steel

Equating total compressive force (C) to total tensile force (T)

C = T

C = area x average compressive stress

= (b.x) X (σcbc + 0)/2

= bx (σcbc/2)

T = area x tensile stress

= Ast x σst

Therefore, bx (σcbc/2) = Ast x σst

200 x 139.97 x 5/2 = Ast x 140

Therefore, Ast = 499.89 mm2

Calculating area of Steel (pt)

Area of steel is expressed as a percentage. The formula for percentage of steel is as follows;

pt = Ast x 100/ bd

= 499.89 x 100/(200×350)

= 0.714

 



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  1. #1 by owolabi on May 26, 2013 - 2:30 pm

    I was going through ur calculation and I got confuse, how do u determine ur modular ratio

    • #2 by BenzuJK on June 9, 2013 - 5:46 am

      Hi,
      You don’t have to determine the modular ratio. Modular ratio is generally given in the problem.

  2. #3 by Najeeb on July 23, 2014 - 2:43 pm

    Thanx… easy method..

  3. #4 by thinley on September 20, 2014 - 6:32 am

    modular ratio is calculated by 280/(3*Sigma cbc)

  4. #5 by ¥unu$ on September 26, 2015 - 7:17 am

    But in this problem modular ratio is given

    • #6 by BenzuJK on September 29, 2015 - 7:56 pm

      Modular ratio is the ratio of modulus of elasticity of steel and concrete. Thus, m = Es/Ec. where Es is the modulus of elasticity of steel which is 200000 N/mm2, which is a constant. so, the value of m depends on the modulus of elasticity of concrete, which can change. In the above example, we know the strength of concrete used. So, we know the value of modular ratio.

  5. #7 by rabin on April 14, 2017 - 3:55 pm

    plzz upload problems on doubly reinforced beams

    • #8 by BenzuJK on June 7, 2017 - 5:56 pm

      Sure. Will do.

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