Q1: If the permissible compressive stress for a concrete in bending is C kg/m², the modular ratio is

ANS:C - 2800/3C

The modular ratio (m) in reinforced concrete design is the ratio of the modulus of elasticity of steel (Es​) to the modulus of elasticity of concrete (Ec​). It is denoted by m and can be expressed as: m=Ec/​Es​​ Where:

• Es​ is the modulus of elasticity of steel.
• Ec​ is the modulus of elasticity of concrete.

In this case, if the permissible compressive stress for concrete in bending is C kg/m², we'll use it as the compressive strength of concrete, fc​. The modulus of elasticity of concrete (Ec​) is related to its compressive strength (fc​) by empirical formulas. One common formula used is: Ec​=5000fc​​ Now, substituting C for fc​, we have: Ec​=5000C​ So, the modular ratio (m) can be expressed as: m=Ec​Es​​=5000C​Es​​ Given that Es​ is typically taken as 2.8 × 10^6 kg/m², we can substitute this value into the equation: m=5000C​2.8×106​=C​2800​ So, the modular ratio is: ​2800​/3