Solved numerical examples | Design of Singly reinforced sections

Guide to design of Singly reinforced Sections | Building Construction

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


Now we will move on with our next solved numerical example in which we will make use of the formulas that we have derived in our earlier articles.

Numerical Problem

Determine the following:

a)      The position of the neutral axis

b)      Lever arm

c)       Moment of resistance

d)      Percentage of steel

(For a rectangular beam section of width b mm and effective depth d mm. Take σcbc = 5 N/mm2, σst = 140 N/mm2, m = 18.66

To find Neutral Axis (NA)

σcbc /(σst/m) = xc/(d – xc)

5/(140/18.66) = xc/(d – xc)

Therefore, xc  = 0.399d mm= 0.4dmm

To find lever arm

z = d – xc/3

= d – 0.4d/3

= 0.867dmm

= 0.87d mm

To find Moment of resistance

Mr = C x z

= bxccbc/2)z

= b (0.4d)(5/2)(0.87d)

= 0.87 bd2 N-mm

To find the percentage of steel

Equating, C = T

bxccbc/2 = Ast. σst

Therefore, Ast = bxccbc/2 σst

 = [b (0.4d)(5/2)]/140

= bd/140 mm2

Pt = Ast. 100/bd

= (bd/140) x (100/bd)

= 0.71

4 thoughts on “Solved numerical examples | Design of Singly reinforced sections”

  1. A single support R.C C beam 250mm wide and 450mm deep is reinforced with 4_18mm diameter and shear reinforced of span 5m if m20 grade of concrete and Fe 415 steel is used and beam is subjected to a shear force of 150kn at sevice state…plzz ans yhis

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