Q1: The modular ratio m of a concrete whose permissible compressive stress is C, may be obtained from the equation.

ANS:C -

The modular ratio (m) of a concrete material can be obtained from the equation: m=Ec/​Es​​ Where:

• Es​ = Modulus of elasticity of steel reinforcement
• Ec​ = Modulus of elasticity of concrete

However, this equation only gives the ratio of the moduli of elasticity of steel and concrete, not the permissible compressive stress (C). The permissible compressive stress (C) for concrete is typically determined by the concrete's strength and the safety factors applied according to design codes and standards. It's often calculated using the formula: C=​fc′/γc​​ Where:

• ′fc′​ = Characteristic compressive strength of concrete
• γc​ = Safety factor for concrete

The value of γc​ depends on various factors such as the type of structure, material properties, and design codes used. So, to determine the modular ratio (m), you need to know the moduli of elasticity of steel and concrete, as well as the characteristic compressive strength of concrete and the applicable safety factors. Once these values are known, you can use the first equation mentioned to calculate the modular ratio.