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:

• 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

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 σ_cbc = 5 N/mm², σ_st = 140 N/mm², m = 18.66

To find Neutral Axis (NA)

σ_cbc /(σ_st/m) = x_c/(d – x_c)

5/(140/18.66) = x_c/(d – x_c)

Therefore, x_c  = 0.399d mm= 0.4dmm

To find lever arm

z = d – x_c/3

= d – 0.4d/3

= 0.867dmm

= 0.87d mm

To find Moment of resistance

M_r = C x z

= bx_c (σ_cbc/2)z

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

= 0.87 bd² N-mm

To find the percentage of steel

Equating, C = T

bx_c.σ_cbc/2 = A_st. σ_st

Therefore, Ast = bx_c.σ_cbc/2 σ_st

 = [b (0.4d)(5/2)]/140

= bd/140 mm²

P_t = Ast. 100/bd

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

= 0.71