Solved Numericals for Singly reinforced Sections | Design Method 2

Design of Singly reinforced Sections | Method 2

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

Find the position of the neutral axis of a reinforced concrete beam 150mm wide and 400mm deep (effective). Area of tensile steel is 804mm2. (modular ratio = m = 18.66)

Step One:

Given that:

b = breadth of a rectangular beam = 150mm

d = effective depth of a beam = 400mm

Ast = cross-sectional area of steel in tension = 804mm2

x = depth of neutral axis below the compression edge

m = modular ratio = 18.66

Taking moments of area of compression and tension sides about neutral axis,

bx.x/2 = mAst (d – x)

150×2/2 = 18.66 x 804 (400 – x)

75×2 = 15002.64(400-x)

75 x2 = 6001056 – 15002.64x

x2 + 200x – 80014 = 0

After solving the quadratic equation, we will get two values (a negative value and a positive value)

x = 200mm