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Research Article: Tawashi & AlAmoudi 70
parts were different. As close as possible to the The proposed mathematical model describes
POPOVICS curve in the ascending part and the the behavior of concrete up to 90% approximate,
EURO-CEB in the descending one through whatever the quantity of cement.
comparing the proposed formula that describes
the behavior of SCC as mentioned in formula ϭ
1.0
.17. with that of POPOVICS, which takes the
form 20. below:
0.8
= [ ] (20) 0.6
)
′ ( −1)+(
Through the observation of the two formulas, 0.4
there is an incomplete similarity in general.
0.2 SCC-3500-550
However. this similarity can be complete when SCC-3500-500
the value of the constants as below: C550 Propoed Curve Model
0.0 ξ=∆L/L
0 0.2 0.4 0.6 0.8 1 1.2 1.4
= = 2
Fig. 10. Stress-Strain Curves for The SCC Proposed
The proposed and POPOVICS formulas takes the Mathematical Formula
following form 21:
References
2 1. American Society for Testing and Materials, ASTM.
= (21) Standard Specification for Chemical Admixtures for
)
′ 1+( 2
Concrete. C 494 – 03. Annual Book of ASTM
Standard. United States; 2003. Vol: 04.02.
It can also verify the conformity of the 2. Mohammed H M. Stress-strain behavior of normal
behaviour proposed in Eq.21 with the actual and high strength self-compacting concrete.
samples graphically. Below are the stress-strain Materials Science and Engineering. 2020; 737:1-9.
3. Jianjie Yu. Research on the Mechanical Properties of
curves of the proposed formula and the
Self-compacting Waste Rubberised Aggregate
experimental sample. It has been found that the
Concrete. International Conference on Civil:
mathematical equation 21 in which the Transportation and Environment ICCTE; 2016. p. 88-
POPOVICS formula and the proposed formula 92.
are similar, gives graphic curves describing the 4. Salvi K, Mahendran T, Atthikumaran N. Experimental
Investigation on Modulus of Elasticity of Self-
behavior of local SCC with a convergence of up
Compacting Concrete. Journal of Applied Physics and
to 90%. Engineering (JAPE). 2016; 1(2): 5-8.
5. BIBM, CEMBUREAU, EFCA, EFNARC, ERMCO. The
Conclusion European Guidelines for Self-Compacting Concrete
This paper aimed to understanding the Specification, Production and Use. SCC European
mechanical behavior of SCC samples. Through Project Group SCC 028 European Federations; 2005.
laboratory verification and mathematical p.1-63.
6. Wang P T, Shah S P, Naaman A E. Stress-Strain Curve
analysis. The key findings of this study are
of Normal and Lightweight Concrete in Compression.
presented below: ACI Journal. 1978; 75(11): 603-611.
The possibility to produce an acceptable Self- 7. Hognestad E. A study on combined bending and axial
Compacting Concrete SCC from Syrian raw load in reinforced concrete members. United State:
materials. University of Illinois Engineering Experiment Station
Bulletin Series; 1951.
Outputting a mathematical model that enables 8. Kent DC, Park R. Flexural members with confined
us to directly calculate the behavior of all types concrete. Journal of the Structural Division. 1971;
of SCC samples, and to represent it graphically. 97(ST7): 1969-1990.
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