As the hook’s law said, ” Stress is directly proportional to strain up to proportional limit’; to make stress and strain equal there should a constant term is to be multiplied. Which is denoted by ‘E’, is called Young’s Modulus of Elasticity. This term is generally gives the strength of material. Stress and strain, already discussed are axially.
E= Stress/Strain
Incase of concrete, under uniaxial compression, it is valid for only initial region of stress and strain curve.
Modulus of Elasticity is further classified into
a. Tangent Modulus of Elasticity
b. Secant Modulus of Elasticity
Tangent Modulus of Elasticity
Tangent Modulus of Elasticity at any point on Stress-Strain curve of concrete is slope is slope of tangent at that point.
This is also term as instantaneous Modulus of Elasticity. It indicates the value of strain that will be observed with increase in stress.
Et = Increase in stress/Increase in Strain
Initial Tangent Modulus of Elasticity
Modulus of Elasticity of concrete at origin is termed as initial tangent modulus of Elasticity. It is also termed as dynamic Modulus of Elasticity. It is measured by methods are :
- Resonant frequency test
- UPV test
E1t = (Increase in stress/Increase in Strain)at origin
Secant Modulus of Elasticity
Total value of strain already observed due to continuous stress applied on a material called secant modulus of Elasticity. It is also termed as Static modulus of Elasticity. It is equal to slope of line joining origin to any point stress-strain curve. Generally taken as fck/3 ie, FOS = 3 is considered.
Es = Total Increase in stress/ Total Increase in Strain
- Within Elastic limit Et =E1t=Es are same
- Modulus of Elasticity of concrete as per IS456:2000
E=5000√(f_ck )
