In working-stress/limit-state theory for reinforced cement concrete (R.C.C.) beams, which basic assumptions are adopted for analysis and design of a singly reinforced, balanced section?

Introduction:
Design of R.C.C. beams rests on standard assumptions that enable a simple yet reliable stress–strain model for composite action. Recognizing these assumptions is essential for computing neutral axis depth, internal forces, and moment of resistance.

Given Data / Assumptions:

• Plane sections remain plane after bending.
• Perfect bond between steel and concrete.
• Concrete resists compression; steel resists tension.
• Working-stress or compatible limit-state approach within design limits.

Concept / Approach:
In singly reinforced beams under sagging, concrete's tensile capacity is neglected; tension is carried by steel. Adequate bond ensures strain compatibility, allowing steel and adjacent concrete to have the same strain at a level. Within the design range, stresses are kept within permissible/limit values to ensure serviceability and safety.

Step-by-Step Solution:
1) Assume zero tensile strength of concrete in bending → tension carried by steel.2) Assume perfect bond → linear strain distribution; use modular ratio or code-defined stress blocks.3) Compute internal compression in concrete and tension in steel, enforce C = T.4) Determine lever arm and moment capacity accordingly.

Verification / Alternative check:
Design results align with code provisions (e.g., stress blocks, strain limits) that inherently rely on these assumptions.

Why Other Options Are Wrong:
Any single statement alone is incomplete; R.C.C. analysis needs all three simultaneously.

None of the above contradicts established R.C.C. theory.

Common Pitfalls:
Counting on concrete tension in service; ignoring bond quality and strain compatibility; exceeding strain limits.

Final Answer:
all of the above