Working-stress design relation: If C is the permissible compressive stress in concrete (kg/cm²), the modular ratio m used in working-stress R.C.C. design is commonly taken as which of the following?

Introduction / Context:In classic working-stress design (WSD), a modular ratio m converts concrete area to an equivalent steel area. Many objective questions test the empirical relation connecting m with the permissible compressive stress in concrete.

Given Data / Assumptions:

• Permissible compressive stress in concrete = C (kg/cm²).
• WSD philosophy with long-term effects implicitly included in m.

Concept / Approach:A standard empirical expression frequently adopted is m = 280 / (3 C). This accounts in a simplified manner for creep and long-term effects by reducing the effective stiffness contribution of concrete when transformed to steel.

Step-by-Step Solution:Recall WSD relation: m = 280 / (3 C).Check units and that C is the permissible compressive stress (not characteristic strength).Select option matching the standard formula.

Verification / Alternative check:Several traditional design manuals use 280/(3C); some variations exist historically, but this expression remains a common exam value.

Why Other Options Are Wrong:

• 280/C: ignores the one-third factor used in the conventional empirical relation.
• 350/(3C) or 230/(3C): nonstandard constants for this context.

Common Pitfalls:Confusing permissible stress C with characteristic strength; applying this WSD relation in limit-state design without proper conversion.

Final Answer:m = 280 / (3 C)