#### Design of Singly reinforced Sections | Method 1

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

- Basic definitions and formulas
- Understanding stresses and modular ratios
- Assumptions for singly reinforced sections
- Design procedure for Singly reinforced section – I
- Solved Numericals for Singly reinforced beam | Method I
- Design of Singly reinforced sections | Design Method 2
- Solved Numericals for Singly reinforced beam | Method 2
- Moment of Resistance for Singly reinforced sections
- Solved numerical example | Moment of resistance
- Solved numerical example 2 | Guide to singly reinforced sections

#### 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

You can leave a response, or trackback from your own site.

#1 by

owolabion May 26, 2013 - 2:30 pmI was going through ur calculation and I got confuse, how do u determine ur modular ratio

#2 by

BenzuJKon June 9, 2013 - 5:46 amHi,

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

#3 by

Najeebon July 23, 2014 - 2:43 pmThanx… easy method..

#4 by

thinleyon September 20, 2014 - 6:32 ammodular ratio is calculated by 280/(3*Sigma cbc)

#5 by

¥unu$on September 26, 2015 - 7:17 amBut in this problem modular ratio is given

#6 by

BenzuJKon September 29, 2015 - 7:56 pmModular 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.

#7 by

rabinon April 14, 2017 - 3:55 pmplzz upload problems on doubly reinforced beams

#8 by

BenzuJKon June 7, 2017 - 5:56 pmSure. Will do.