If grades of steel and concrete are respectively Fe 415 and M 20 in a beam reinforced in tension side with 4-20 T and of width 30 cm and having effective depth 55 cm, then the depth of neutral axis of the section is

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BPSC AE Paper 5 (Civil) 14 Oct 2022 Official Paper
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  1. 109.9 mm
  2. 209.9 mm
  3. 309.9 mm
  4. None of the above

Answer (Detailed Solution Below)

Option 2 : 209.9 mm
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Detailed Solution

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Concept: 

Moment of resistance for balanced section,

\({M_{u,lim}} = Q{f_{ck}}b{d^2}\)

Fy

250

415

500

Q

0.148

0.138

0.134

Force from the compression side,

C = 0.36 × fck × b × xu

Force from the tension side,

T = 0.87 × f× Ast

To determine the Ast, we have to equate the compressive and tensile forces 

 0.36 × fck × b × Xu = 0.87 × f× Ast

0.36 × 20 × 300 × Xu = 0.87 × 415 × 4 × π × 202/4

XU = 209.9 ≈ 210 mm

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