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- Concrete Technology - CT
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**Visvesvaraya Technological University Regional Center - VTU**- Civil Engineering
- B.Tech
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• 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, and 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), 4

Where θ is creep coefficient and Creep coefficient is the ratio of creep strain to elastic strain ELong < Eshort Dynamic modulus of elasticity (Ed) for concrete Modulus of elasticity determined through the longitudinal vibration test by velocity of sound or frequency of sound is termed as dynamic modulus of elasticity (Ed) Dynamic modulus of elasticity of concrete (Ed) is approximately taken as equal to the initial tangent modulus of elasticity of concrete. Ed is more as creep effect is not considered. Dynamic modulus of elasticity for normal and light weight concrete in GN/m2 (GPa) is given by Ec = 1.25 Ed – 19 - for Normal weight concrete and Ec = 1.04 Ed – 4.1 - for light weight concrete, GN/m2 If M20 NWC is used, Ec = 22.4 GPa, Ed = 33.12 GPa, 48% more Conduct NDT on concrete prism Subject beam to longitudinal vibration at its natural frequency and measure the resonant frequency (n, Hz) or the UPV (km/s) through it. Ed = Kn2L2ρ ; If L in mm, ρ in kg/m3, then Ed = 4x10-15n2L2ρ, in GPa Appx. Ranges of Resonant Frequencies of Concrete beam 100 x 100 x 500 mm Transverse 900–1600 Hz, Longitudinal 2500–4500 Hz. If n= 4000 Hz, Ed = 38.4 GPa Conduct NDT on concrete prism and measure the UPV (km/s) through it. UPV = Path length/Transit time 5

µ = Poisson’s ratio, 0.2 - 0.24 If V in km/s, ρ in kg/m3 Ed in MPa Let V= 4km/s, µ = 0.2, ρ =2400 kg/m3 Ed = 34560 MPa = 34.6 GPa Here Ed is more as there is no creep Determination of modulus of elasticity of concrete Testing of cube or cylinder in uni-axial compression test. Measure load and the corresponding deformation as the load is increased. Draw the stress strain curve. Strain =Dial gauge reading/gauge length = dl/L Stress = Load/Cross sectional area= P/A Use Compressometer and Extensometer to measure deformations. Draw stress strain diagram and determine the required modulus. Deflection: E can be determined from testing of beam also. For central point load Max. deflection, δ = WL3/48EIxx Poisson’s ratio In analysis and design of some type of structure the knowledge of poisson’s ratio is required. When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression. This phenomenon is called the Poisson effect. Poisson's ratio µ is a measure of the Poisson effect. The Poisson ratio is the ratio of the fraction (or percent) of expansion divided by the fraction (or percent) of compression, for small values of these changes. µ = 0.15 - 0.20 – Actual value to be found from strain measurements on concrete cylinder using extensometer. 6

An alternate method for finding Poisson’s ratio is from UPV test and by finding the fundamental natural frequency of longitudinal vibration of concrete beam. The Poisson’s ratio can be found from the following equation. The Poisson’s ratio is slightly higher and it ranges from 0.2 to 0.24. Where V = Pulse velocity mm/s n = Resonant frequency in Hz and L= Length of the beam in mm. ρ = The density of concrete Ed = Dynamic modulus of elasticity of concrete , Factors affecting modulus of elasticity 1. Cement and aggregate factors Since concrete is a composite material, consisting of cement paste and aggregate, its modulus of elasticity depends on the moduli of elasticity and the volume fractions of cement paste and aggregate, as follows: Ec = [ {(1-Va)Ep + (1+Va) Ea} / {(1+Va)Ep + (1-Va) Ea}]Ep Where, Ec = modulus of elasticity of concrete Ep = modulus of elasticity of cement paste Ea = modulus of elasticity of aggregate Va = volume fraction of aggregate = 1-Vp Vp = volume fraction of cement paste = 1-Va • Ep depends on the porosity of cement paste and the porosity of cement paste depends on the gel/space ratio (Ep is approximately proportional to the cube of the gel/space ratio) and gel/space ratio finally depends on the w/c ratio (gel/space ratio is inversely proportional to w/c ratio) Note: The reason behind relating Ep with compressive strength of concrete lies in the fact that the compressive strength is also affected in the same way as, Ep • Ea for lightweight aggregates is found to be much lower than that for the normal weight aggregate. This is why the elastic modulus of lightweight concrete is less than that of the normal-weight aggregate (Ec, light weight concrete = 0.4 to 0.8 Ec, normal weight concrete) 2. Moisture condition factor The moisture condition of the specimen is a factor: a wet specimen has a modulus of elasticity higher than by 3 to 4 GPa than a dry one. 7

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