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If the depth of neutral axis for singly reinforced rectangular section is represented by " Kd " in working stress design, then the value of " K " for balance section where ' D " is the effective depth, \(\sigma_{\text{st}}\) permissible stress in steel in tension and \(\sigma_{\text{cbc}}\) is permissible stress in steel in bending compression.

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  1. Depends on \(\sigma_{\text{st}}\) only
  2. Depends on \(\sigma_{\text{cbc}}\) only
  3. Depends on Both \(\sigma_{\text{st}}\) and \(\sigma_{\text{cbc}}\)
  4. Is independent of Both \(\sigma_{\text{st}}\) and \(\sigma_{\text{cbc}}\)

Answer (Detailed Solution Below)

Option 1 : Depends on \(\sigma_{\text{st}}\) only
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Detailed Solution

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Explanation:

  • The depth of neutral axis (K D) in a balanced section depends on the limiting tensile stress in steel (σst).

  • The permissible stress in concrete (σcbc) affects overall capacity but not the position of neutral axis in balanced section.

  • The strain compatibility forces the neutral axis to be positioned based on how much the steel can be stressed.

  • Therefore, K depends only on σst

F10 Chandramouli 19-1-2021 Swati D4

\(k=\frac{280}{3\sigma_{st}+280}\)

Additional InformationA balanced section is a condition where steel reaches its permissible tensile stress and concrete reaches its permissible compressive stress simultaneously when subjected to bending.

In a bending section, the neutral axis is the horizontal axis where no tensile or compressive stress occurs.

  • Above this axis → compression zone

  • Below this axis → tension zone

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More Working Stress Method Questions

Q1.If the depth of neutral axis for singly reinforced rectangular section is represented by " Kd " in working stress design, then the value of " K " for balance section where ' D " is the effective depth, \(\sigma_{\text{st}}\) permissible stress in steel in tension and \(\sigma_{\text{cbc}}\) is permissible stress in steel in bending compression.
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Q4.If the depth of neutral axis for singly reinforced rectangular section is represented by " Kd " in working stress design, then the value of " K " for balance section where ' D " is the effective depth, \(\sigma_{\text{st}}\) permissible stress in steel in tension and \(\sigma_{\text{cbc}}\) is permissible stress in steel in bending compression.
Q5.In which situation is a doubly reinforced beam preferred over a singly reinforced beam?
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