The limiting depth of neutral axis for a beam having effective depth of 400 mm with Fe 250 grade steel is:

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SSC JE CE Previous Year Paper 12 (Held on 23 September 2019 Evening)
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  1. 609 mm
  2. 318 mm
  3. 425 mm
  4. 212 mm

Answer (Detailed Solution Below)

Option 4 : 212 mm
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Concept:

The ratio of limiting depth of neutral axis to the effective depth of the beam is given by

\(\frac{{{x_u}}}{d} = \frac{{{\rm{Max\;strain\;concrete}}}}{{\frac{{{\rm{Grade\;of\;steel}}}}{{{\rm{Modulus\;of\;Elasticity\;of\;steel}} \times {\rm{F}}.{\rm{O}}.{\rm{S}}}} + 0.002 + {\rm{Max\;strain\;concrete}}}}\)

Note:

Without getting into the tedious calculation,

We know the standard values of the ratio of limiting depth of neutral axis to the effective depth (k) of the beam for different steel sections as following:

Grade of Steel

Fe 500

Fe 415

Fe 250

‘k’ value

0.46

0.48

0.53

Calculation:

∴ For Fe 250, xu ≈ 0.53 × 400 = 212 mm.

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