According to Whitney's theory, depth of stress block for a balanced section of a concrete beam is limited to

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BPSC AE Paper V Civil 19 Dec 2024 Official Paper
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  1. 0.537 d
  2. 0.637 d
  3. 0.8 d
  4. 0.75 d

Answer (Detailed Solution Below)

Option 1 : 0.537 d
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Explanation:

  • According to Whitney’s stress block theory and IS 456, the depth of the neutral axis xu,maxx_{u, \text{max}} for a balanced section (where steel yields just as concrete reaches its ultimate strain) is limited to about 0.53 to 0.537 times the effective depth dd.

  • This ensures the maximum permissible depth of the stress block for safe design before concrete crushing dominates.

Additional Information

  • Whitney simplified the actual nonlinear stress distribution in concrete to an equivalent rectangular block.

  • The factor 0.53d is key in limiting the depth of compression zone in design calculations.

  • It helps distinguish between under-reinforced, balanced, and over-reinforced sections in concrete beam design.

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