Modulus of Elasticity of Concrete

The modulus of elasticity of concrete is given by means of 3 varieties of specifically Preliminary Tangential Modulus, Tangent Modulus and Secant Modulus. Not like metal, we can’t resolve the modulus of elasticity by means of the components E = Tension/Pressure. It’s because concrete is an inelastic subject matter and subsequently the stress-strain curve may be very asymmetric in nature. So at other issues of the curve, other slope (elastic modulus) is decided. So now we have 3 elastic modulus of concrete. 

Let’s be informed intimately the 3 varieties of modulus of elasticity of concrete the usage of a normal stress-strain curve illustration of a concrete. 

Sorts of Modulus of Elasticity of Concrete

The 3 varieties of elastic modulus of concrete are:

1. Preliminary Tangential Modulus (Eit) or Dynamic Modulus
2. Tangent Modulus (Et) 
3. Secant Modulus (Es)

Let’s imagine the stress-strain curve of a hardened concrete as proven in figure-1.   

Tension-Pressure Curve of Standard Concrete Representing Choice of Modulus of Elasticity

1. Preliminary Tangent Modulus (Eit) or Dynamic Modulus

The preliminary tangent modulus of concrete may also be decided by means of taking the slope of the tangent drawn on the foundation of the stress-stress curve of the concrete. Within the determine, the tangent drawn on the foundation O is OA. The slope is Eit. 

Preliminary Tangent modulus is utilized in:

🔴Theoretical Analyis

🔴Subject material Modeling

🔴Early-stage elastic reaction research

📊 Helpful for figuring out, no longer for regimen design.

2. Tangent Modulus (Es)

Tangent modulus is the slope of tangent drawn at any level at the stress-strain curve of the concrete. Believe some extent B at the curve and draw a tangent. The slope of this tangent is the tangent modulus at B.

The place it’s used
🔴Complicated structural research
🔴Nonlinear finite part research (FEA)
🔴Analysis and educational research

🔬 This modulus lives extra in instrument and labs than on website online.

3. Secant Modulus (Es)

Secant modulus (Es) is the slope of line becoming a member of the foundation and any level at the stress-strain curve of the concrete. 

The place it’s used
🔴Design calculations in follow
🔴Serviceability prohibit state research
🔴IS 456 explicitly makes use of this idea

📐 It provides a practical stiffness for operating a lot.

Quick-Time period (Ec) and Lengthy-Time period Elastic Modulus (Ecl)

Quick time period and longer term elastic modulus is laid out in IS:456-2000, 

Quick-Time period Elastic Modulus (Ec)

Quick time period modulus of elasticity (Eci) is the price of the secant modulus on the level positioned at 1/third of the utmost compressive power. 

As in line with IS:456-2000,

  Ec = 5000 √fck  (fck in N/mm2)

📌 That is the modulus in most cases discussed in design codes.

Secant Modulus of Concrete

Lengthy Time period Elastic Modulus (Ecl)

This elastic modulus considers creep and shrinkage of the concrete in longer term. An adjusted modulus that considers creep and sustained loading through the years

Ecl = Ec / (1+θ)

Ec =  Quick Time period Elastic Modulus

θ = Creep Coefficient

⏳ Concrete slowly relaxes beneath long-term a lot, and this modulus captures that fact.

Each quick and longer term elastic modulus are modulus values taken on the preliminary degree of concrete and longer term age of concrete respectively. 

In on a regular basis design, static (secant) modulus is king. However whilst you transfer into trying out, diagnostics, earthquakes, or complex research, different moduli quietly step onto the degree.