Elastic Modulus of Concrete – Empirical Coefficient in Ec Relation If fck is the characteristic cube strength of concrete in N/mm^2, the short-term modulus of elasticity is expressed as Ec = a * sqrt(fck). What is the empirical constant a used in common Indian practice?

Introduction / Context:
The static modulus of elasticity Ec of concrete correlates with compressive strength. Empirical formulas of the form Ec = a * sqrt(fck) are widely used for initial sizing and serviceability checks such as deflection.

Given Data / Assumptions:

• Strength term: fck in N/mm^2 (MPa).
• Empirical model: Ec = a * sqrt(fck).
• Objective: identify coefficient a used in common Indian practice for short-term Ec.

Concept / Approach:

Different standards suggest slightly different a values to reflect aggregate type and testing method. The value 5700 is frequently adopted in competitive exams and many Indian references for short-term Ec estimation with normal-weight concrete.

Step-by-Step Solution:

Verification / Alternative check:

Comparisons with measured Ec values for common fck (for example fck = 25 to 40) show that 5700 * sqrt(fck) predicts within practical bounds for preliminary design when proper curing and quality are assumed.

Why Other Options Are Wrong:

• 5900, 5800: Slightly higher than typical; may overestimate stiffness and underpredict deflection.
• 5600, 5500: Slightly lower; conservative but not the commonly cited coefficient for short-term Ec in normal-weight concrete.

Common Pitfalls:

Using Ec directly from cube strength without considering long-term effects. For serviceability, creep and cracking reduce effective stiffness, so designers often adopt reduced Ec or moment of inertia in checks.

Final Answer:

5700