Modulus of elasticity for concrete determined from an experimental stress-strain
relation curve, as described above, is generally termed as static modulus of
elasticity (Ec) whereas the modulus of elasticity determined through the
longitudinal vibration test is termed as dynamic modulus of elasticity (Ed)
Static modulus of elasticity (Ec)for concrete
Static modulus of elasticity of concrete has been related to its compressive
strength by the various Standards
Relationship between modulus of elasticity of concrete and compressive strength
BS 8110:Part 2:1985 has recommended the following expression for 28-day Ec in
terms of 28-day cube compressive strength (fcu), for normal weight concrete (i.e.
concrete with density, ρ ≈ 2400 kg/m3):
Ec28 = 20 + 0.2 fcu28 (where Ec28 is in GPa and fcu28 is in MPa)
Note: For lightweight concrete the above values of Ec28 should be multiplied by
the factors (ρ/2400)2 and (ρ/150)2 respectively.
ACI Building Code 318-89 recommends the following expression for (Ec) in terms
of cylinder compressive strength (fcyl), for normal weight concrete (i.e. concrete
with density, ρ ≈ 2400 kg/m3):
Ec = 4.7 (fcyl)0.5 (where Ec is in GPa and fcyl is in MPa)
Ec, 28 = 9.1fcu0.33 - for normal weight concrete of density = 2400 kg/m3,
Ec, 28= 1.7ρ2 fcu0.33 x10-6 for lightweight concrete - (ρ) =1400–2400 kg/m3
CEB - FIP Model Code (Euro-International)
E = 2.15 X 104 (fcm/10)1/3, E in MPa and fcm in MPa.
Static modulus of elasticity (Ed) for concrete
Experimental stress-strain relation curve, as described above, is generally termed
as static modulus of elasticity (Ec) and is short term modulus.
• If creep effect is considered at a given load, the modulus determined is referred to
as long term modulus of elasticity.
ELong = EShort/(1+θ),