If the depth of actual neutral axis of a doubly reinforced beam

Solution (By Examveda Team)

Understanding Doubly Reinforced Beams and Neutral Axis
Let's break down this question step-by-step to understand what it's asking.

Key Concepts:
* Doubly Reinforced Beam: This is a beam that has steel reinforcement in both the tension zone (bottom) and compression zone (top).
* Neutral Axis (NA): This is the line within the beam where there is neither tensile nor compressive stress. It's the point where the stress changes from compression to tension.
* Actual Neutral Axis: The actual position of the neutral axis in a real beam under load. It's determined by the equilibrium of forces.
* Critical Neutral Axis: This is a theoretical position of the neutral axis. It's the depth where the concrete and steel reach their maximum allowable stresses simultaneously.
Maximum Stress:
Think of 'maximum stress' as the point where the material (concrete or steel) starts to yield or fail.
Explanation of Options:
* Option A: "Is greater than the depth of critical neutral axis, the concrete attains its maximum stress earlier"
* If the actual neutral axis is *deeper* than the critical neutral axis, it means the compression zone is larger.
* A larger compression zone implies the concrete is experiencing higher compressive stresses.
* Therefore, the concrete reaches its maximum stress (and potentially fails) before the steel reaches its maximum tensile stress.

* Option B: "Is less than the depth of critical neutral axis, the steel in the tensile zone attains its maximum stress earlier"
* If the actual neutral axis is *shallower* than the critical neutral axis, it means the tension zone is larger.
* A larger tension zone means the steel is experiencing higher tensile stresses.
* Therefore, the steel reaches its maximum stress (and potentially yields) before the concrete reaches its maximum compressive stress.

* Option C: "Is equal to the depth of critical neutral axis; the concrete and steel attain their maximum stresses simultaneously"
* This is the definition of the *critical* neutral axis.
* When the actual neutral axis matches the critical neutral axis, both the concrete and steel reach their maximum allowable stresses at the *same time*. This is the ideal balanced design.

* Option D: All the above
* Since options A, B, and C are all correct under their respective conditions, this is the correct answer.

Therefore, the correct answer is D: All the above.