Stress-Strain Relationship Of Confined And Unconfined Concrete

Stress-Strain Relationship of Confined and Unconfined Concrete Paper by M.M. Attard and S. Setunge
Discussion by Ergin Arıoğlu

By ERGİN ARIOĞLU
Professor of Mining Engineering, Istanbul Technical University, Maslak, Istanbul, Turkey Application of high strength concrete (HSC) technology is growing in the construction sector at an increasing rate due to the advantages on mechanical propertiesand durability of concrete. This issue calls for identification of the mechanical properties of HSC and thus establishment of the design equations for HSC. The authors' contributions to this aim are outstanding and they should be acknowledged herein for their excellent article. The discusser, being stimulated from the authors' study on aggregate effect, would like to contribute on two subjects:First, an equation is presented to determine modulus of elasticity of concrete based on mechanical properties of the aggregate. Second, the strain of concrete at peak stress, as determined by Attard-Setunge's formula is compared with the discusser's earlier study. • Modulus of elasticity of high strength of concrete is directly related to mechanical properties of the aggregate. In the recentliterature, modulus of elasticity of concrete is proposed as in the following32:

′ E c = 8430 α β f c 0.333
where

′ (10 MPa ≤ f c ≤ 115 MPa)
(10 GPa ≤ Ea ≤ 115 GPa)

(A-1)

α β = 0.1485 E a

(A-2)

However, the latter expression can be easily expressed in terms of the uniaxial strength of intact rock, which is a more convenient property to measure in a common laboratory. The followingexpression by Arıoğlu 33 to determine modulus of elasticity of rock from its uniaxial strength, is based upon N=467 samples of rock including metamorphic, volcanic and sedimentary rocks and has a very high correlation coefficient.
0 E a = 0.41 f a .93 (N=467, r=0.804, 15 MPa ≤ fa ≤ 400 MPa)

(A-3)

Substituting Eqs.(A-1) and (A-2) into Eq.(A-3) one obtains:
0 ′ E c = 801.578f a .465 f c 0.333(A-4)

is In equations (A-1) to (A-4), Ea is the modulus of elasticity of intact rock (aggregate) [GPa], Ec the modulus of elasticity of concrete [MPa], fa is the uniaxial compressive strength of intact rock [MPa], f 'c is the uniaxial compressive strength of concrete [MPa] and αβ is a coefficient related to the rock (aggregate) type. For example, for basalt having fa=200 MPa, αβ may beestimated to be about 1.12. For a range of concrete strength from normal strength to very high strength, the modulus of elasticity values obtained from Eq.(A-5) are compared with Carasquillo et al.'s26 formula (Eq.5) for air dry unit weight of concrete at time of test ρ=2320 kg/m3 (Fig.A.). The following conclusions can be derived from Fig.A. :

 ρ  (A-5) ′ E c = 3320 f c + 6900    2320  Inhigh-strength concrete, modulus of elasticity of concrete is very sensitive to the uniaxial compressive strength of aggregate. Carasquillo et. al.'s equation falls within the range of aggregate strength widely used in structural applications and confirms its validity. However, their formula defines a minimum aggregate strength value of 150 MPa. This outcome points out an efficient control inselection of the aggregate for HSC.

(

)

1.5

Ec (MPa)
60000 50000 40000 30000 20000 10000 0 0 20 40 60 80 100 120 140 160

fa =150 MPa fa =200 MPa

Modified Gutierrez-Canovas Carasquillo et.al. (ρ=2320 kg/m3 )

fa =100 MPa

fc' (MPa)
Fig.A. Comparison of Carasquillo et.al.'s Formula with Eq (A-1) through (A-3)

• The equation proposed by Attard and Setunge for prediction of strainof concrete at peak compressive stress (εc, %o) is compared with Arıoğlu's equation33,34 (Eq. [A-6]) and it is found that the two are in close agreement with each other (Fig.B[a]). The equation by Arıoğlu33 can additionally take into account the volume of the specimen (Eq.[A-6]-Fig.B[b]). The error involved in prediction capacity of the equations are evaluated based on deviation (∆) of the...