Q1: If the maximum bending moment of a simply supported slab is M Kg.cm, the effective depth of the slab is (where Q is M.R. factor)

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To find the effective depth (d) of the simply supported slab given the maximum bending moment (M) and the modular ratio factor (Q), we can use the formula derived from the modular ratio method: d=M/Q⋅σc​ Where:

• M is the maximum bending moment (in kg⋅cm),
• Q is the modular ratio factor,
• σc​ is the permissible compressive stress of concrete.

This formula represents the balance of moments between the compressive force in the concrete and the tensile force in the steel reinforcement. Given that Q is the modular ratio factor and not explicitly defined in terms of compressive and tensile strengths, it's essential to recognize that Q is related to the ratio of the modulus of elasticity of steel to that of concrete. The permissible compressive stress of concrete (σc​) typically ranges from 60 to 80 kg/cm² in reinforced concrete design, depending on the concrete grade and design codes. Therefore, the effective depth (d) of the slab can be calculated using the given maximum bending moment (M), modular ratio factor (Q), and permissible compressive stress of concrete (σc​). If more specific values for Q and σc​ are provided, we can calculate the effective depth accordingly.