In a reinforced cement concrete (R.C.C.) beam subjected to positive bending (sagging), where are the main longitudinal steel bars embedded within the beam depth for efficient resistance to tension?

Introduction:
R.C.C. beams rely on composite action between concrete (strong in compression) and steel (strong in tension). For sagging bending, tension occurs at the beam's soffit, dictating the placement of main reinforcement.

Given Data / Assumptions:

• Simply supported or continuous beam segments in positive bending.
• Plane sections remain plane; perfect bond between steel and concrete.
• Service loading within elastic behavior for basic placement rationale.

Concept / Approach:
Under sagging, the bottom fibers are in tension and the top fibers in compression. Concrete is weak in tension and is therefore relieved by embedding tensile steel near the tension zone (bottom). Compression is resisted primarily by concrete at the top, sometimes aided by compression steel in special cases.

Step-by-Step Solution:
1) Determine bending sign: sagging ⇒ tension at bottom.2) Provide main longitudinal steel near the bottom cover region.3) Use stirrups for shear and to hold longitudinal bars; compression zone near the top resists compressive stresses.4) Ensure adequate cover for durability and fire resistance per code.

Verification / Alternative check:
Negative bending (over supports) reverses stress zones; then top steel becomes main tension reinforcement. This confirms placement follows the tension zone.

Why Other Options Are Wrong:
Near the top: correct only for negative bending zones.

Centre / any position / random: ineffective in tension control and violates code-based detailing practices.

Common Pitfalls:
Placing bars symmetrically without considering bending sign; ignoring cover and anchorage requirements.

Final Answer:
near the bottom