The characteristic equations of the stressstrain curve for fly ash concrete (ordinary grade – M30Grade) are used to study the MØ characteristics of beam sections. The theoretical procedure has been validated by conducting an experimental investigation on under reinforced fly ash concrete beams. The correlation between experimental and analytical values of moments and curvatures arrived at based on the above procedure is found to be good. The cement was replaced by10, 20, 30 and 40% fly ash obtained from near by thermal power station.
The concrete industry is responsible for the economic and safe disposal of millions of tons of industrial byproducts such as fly ash and slag. Due to their highly pozzolanic and cementitious properties, fly ash and slag can be used in large amounts as cement replacement materials in concrete. It is obvious that large scale cement replacement in concrete with these industrial byproducts will be highly advantageous from the stand point of cost economy, energy efficiency, durability and overall ecological profile of concrete.
The small size and the essentially spherical form of low calcium fly ashes particles influences the rheological properties of cement pastes, causing a reduction in the water required or an increase in workability compared with that of an equivalent paste without fly ash. Fly ash differs from other pozzolona which usually increase the water requirement of concrete mixtures. A complete stressstrain curve is needed for the analysis and rational design of concrete structures. The structures built in severe environment need durable concrete because of huge amount of construction expenses and difficulty in concrete repairs.
A stress strain curve is a graph derived from measuring load vs strain for a sample of a material. In concrete the rate of increase of stress is less than that of increase in strain because of the formation of micro cracks, between the interfaces of the aggregate and the cement paste. The stress strain behavior of concrete is a prime parameter in designing, prediction of flexural behavior and estimating the toughness of concrete.
The present work was taken up to study the rotational capacity of reinforced concrete sections and fly ash concrete sections. Due to large construction activity all over the world, the scarcity of the construction materials is becoming an obstruction for the expansion. With a
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view to utilize the mineral by products like flyash, to study its (behavioral) capacity in redistributing the moments and minimize cement content, An experimental investigation was carried on beams of under reinforced sections.
2. Models for StressStrain Curves
Many researchers developed various models for the prediction of stressstrain behavior of concrete. Some of the models are given below.
2.1 Desayi and Krishnan’s model
For Normal strength concrete, the stressstrain relationship is given by
2 Bx 1 Ax f
+ =
Where f = The Normalized stress (Stress/ultimate stress) X = Normalized strain(strain/Strain at ultimate stress)
A, B are the constants and they can be find out by using boundary conditions. This model is valid only up to ascending branch of stressstrain curve.
2.2 Saenz Model
With reference to Desayi’s model, Saenz proposed a model by taking into account both the ascending and descending portions of the stressstrain curve. This model is in the form of
Where fo) / (f y = and
=
0 x ε
ε
fo = Ultimate stress and Єo = strain at ultimate stress.
2.3 Hognested’s Model
For Normal strength concrete up to ascending portion, the stressstrain model is
However instead of using one set of the coefficients A, B, C, and D to generate the complete curve, Wang et.al, used two sets of coefficients – one for the ascending branch and the other to the descending branch, the respective coefficients being obtained from the relevant boundary conditions assigned to each part of the curve.
3. Experimental Investigation
In this phase of investigation the cylindrical specimen moulds of size 150mm dia x 300mm length were selected (M30 Grade of concrete). The proportions for the mix are 1:1.42:3.9 with a W/C ratio of 0.46. The Cement content for one cubic meter of concrete was 380 kgs. First the moulds were cleaned with kerosene, the inner surface of the moulds were lubricated with grease. The concrete was filled in the moulds in layers. To achieve full compaction 25 mm needle vibrator was used. The moulds were demoulded after 24 hours of casting. A two lettered designation is given to the specimens. PL, Letters represent the ordinary grades of concrete. The third letter indicates % of fly ash added. For ex: PH0 indicates ordinary grade concrete with 0% fly ash. The designation of the specimen was done with indelible water proof ink. The de mould specimens were kept under water for curing purpose. After curing for a period of 28 days the specimens are removed from the water and kept under shade. The cured specimens were capped with plaster of paris to provide smooth loading surface, as the casting and testing has to be done on the same face. The capping was done with the help of glass a plate and spirit level. The excess paste on the sides was removed using a cutting edge.
4. Testing Procedure
The capped specimen was attached with fabricated compressometer with three dial gauges and was placed on the movable cross head of the Tinus Olsen Testing machine and centered correctly. Strain rate control was adopted to get the complete stressstrain diagram including the post ultimate descending portion. The dial gauges having a least count of 0.002mm were used. The average of the three dial reading was taken.
A uniform movement was achieved by adjusting the inlet valve of the testing machine, throughout the period of testing with the help of control dial gauge attached to the cross head of the testing machine and the stopwatch. For the satisfactory recording of strains the cross head movement of 1mm per minute was suggested by the previous investigators. The stress strain curves for conventional fly ash concretes were developed by the author in the form
2 Bx 1 Ax f
+ =
Where f = The Normalized stress (Stress/ultimate stress)
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X = Normalized strain(strain/Strain at ultimate stress) The stress –strain curves are shown in figures 1. to 5. for various fly ash percentage replacements. The values of the constants were derived using boundary conditions. A, B and A′, B′ values for various % of fly ash are Tabulated in Table 1.The area under the stress – strain curves were calculated and are tabulated in Table 1.
5. Development of MØ Diagrams for Beam Sections
In order to generate the MΦ diagram for any cross section , it can be seen that for any concrete strain ( Єu), in the extreme fibre :
Cc = fa.b(n.d)
Where ∫
=
ε
ε ε 0
1 d f f a
∫
=
ε
ε ε ε 0
2
d f nd b M c
c
The corresponding curvature can be obtained by Ø = ( Єc / nd )
The evaluation of integrals
∫ c
d f ε
ε 0
leads to the expressions :
Cc = fa.b(n.d )
∫
=
ε
ε ε 0
1 d f f c
a
( ) ∫ +
=
c
u
ck
c a B
d f f
ε
ε ε
ε ε ε
ε 0 2 2
u
/ 1
A 1
( ) ( ) 2 2 2 / log 2 / 1 u u u ck a B B A f f ε ε ε ε
ε +
=
( )( ) ( ) ( ) ( ) { } u u u u ck u B Tan B B B A f d Bn M ε ε ε ε ε ε ε / / / / / 1 2 3 2 2 2 2 − − =
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For obtaining the complete moment curvature relationship for any cross section, discrete values of extreme fibre concrete strains(Єu) were selected such that the even distribution of the points on the plot, both before and after the maximum moments were obtained.
The procedure used in the computation is as follows.
For a selected values of Єc , the extreme fibre concrete strain, a neutral axis depth ‘nd’ is assumed initially.
• For the assumed value of ‘nd’ the compressive force ‘Cc’ and the value of moment ‘Mc’ of this resultant compressive force about neutral axis is calculated.
• The strain in tension steel Єs is calculated on the basis of strain compatibility. • The tensile force Ts, in the tension steel is arrived at by taking the corresponding stress
from stressstrain diagram of steel and multiplying with the area of steel. The corresponding moments Ms about the neutral axis is Ms= Ts (dnd).
• The values of Cc and Ts are compared. If Cc and Ts are same, then the assumed position of neutral axis is correct. Then moment Mc and curvature Øc are calculated for a particular fibre strain.
• If Cc is not equal to ‘Ts’ a new value of neutral axis depth is assumed based on judgment whether Cc is greater or smaller than Ts .The above procedure is repeated until the equilibrium condition Cc = Ts is satisfied.
The above analytical procedure enables the assessment of flexural strength of fly ash Concrete sections. The assumption made is a) Variation of strain across the section is linear up to failure. In addition to above assumption, the following three basic relationships
• Equilibrium of forces, Cc = Ts
• Compatibility of strains(Єc /nd= Єs /dnd ) and • Stress strain relationship of the material.
TS
Cc
b
D d
nd
fa
Ast
εc
εs
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Results derived from the above proposed – analytical procedure are compared with the experimental data. The beams have shown very good results in comparison. All the beams were tested under symmetrical two point loading on a simply supported span of 1700 mm. Figure11 shows simply supported beam testing arrangements. Specially fabricated extensometer and compressometers were used in addition to deflectometers. The deflections were taken at 5 different points over the entire span of the beam. Displacement control was used to obtain the complete profile of momentcurvature behavior, especially in the post ultimate moment region. Momentcurvature diagram were generated for all the beams based on the characteristic stress – strain diagram. The experimental values of moments and curvatures are plotted as discrete points on the momentcurvature diagrams. The experimental ultimate moments and theoretical moments computed based on the characteristic stress – strain curve of reinforced concrete are represented on correlation diagrams.
Graph showing Nor. Stress Vs Nor. Strain For 0% Fly Ash in Ordinary
Grade Concrete
0
0.5
1
1.5
0 0.5 1 1.5
Normalised Strain
Normalised
Stress
Theor
Exp
A=1.93332 5
Graph showing Nor. Stress Vs Nor. Strain For 10% Fly ash in Ordinary
Grade Concrete
0 0.2 0.4 0.6 0.8 1
1.2
0 0.5 1 1.5
Normalised Strain
Normalised
Stress
Theo Exp
A=2.10465 B=1.10465
Graph Showing Nor. Stress Vs Nor. Strain For 20% Fly ash in Ordinary
Grade Concrete
0 0.2 0.4 0.6 0.8 1
1.2
0 0.5 1 1.5
Normalised Strain
Normalised
Stress
Theo Exp
A=2.07504 9
Graph Show ing Nor.Stress Vs Nor. Strian For 30% Fly ash in Ordinary
Grade Concrete
0 0.2 0.4 0.6 0.8 1
1.2
0 0.5 1 1.5
Normalised Strain
Normalised
Stress
Theo Exp
A=2.01188 9
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Figure 3: Theoretical – Experimental Moment – Curvature Graphs
5.2 Correlation
It can be seen that the procedures developed for obtaining the complete profile of moment – curvature diagram of Fly Ash Concretes sections based on the characteristic stress – strain curves for Fly Ash Concrete predict the experimental behavior satisfactorily (Figs2 to 6). There is a good agreement between the analytical and experimental ultimate moments, as can
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be seen from the correlation diagram (Figs7 to 11). The lack of very good correlation in curvatures may be attributed to the fact that, the analytical curvature at a section computed to satisfy the equilibrium and compatibility conditions, where as the experimental curvature is the curvature measured over a gauge length of 200 mm and hence represents the average curvature over gauge length including localized high curvatures at the cracks.
Figure 12: Failed beam specimen after testing
Figure 13: Test arrangement for the beam
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Notations: D,b = Lateral dimensions of beams. d = Effective depth. f, Є=Stress and corresponding strain. Cc =Compressive force in fly ash concrete beams. fck = Concrete cube strength at 28 days Mue=Experimental ultimate moment Mut=Theoretical ultimate moment Øue= Experimental curvature at ultimate load Øut= Theoretical curvature at ultimate load Ts=Tensile Force Cc=Force in compression zone
6. Conclusions
1. An analytical model was developed for obtaining the complete moment curvature diagram for Fly Ash ordinary grade Concrete.
2. The ultimate moments obtained from the proposed analytical procedure are found to be in good agreement with the experimental values.
3. Fly ash replacement (up to 30%) in concrete has shown good improvement in flexural strength.
7. References
1. Chava Srinivas., Gopala Krishnayya. and Raju.P.S.N. 2004 “Effect of FA addition on Compressive Strength, stressstrain behaviour and durability of concrete exposed to
INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 1, No 3, 2010
sulphuric acid”. ICACC2004. Proceedings of International Conference on Advances In Concrete and Construction. 1618 December, Vasavi College of Engineering, Hyderabad. India. pp 647656.
2. Hsu, L. S. M. and Hsu, T.T. (1994), “StressStrain Behavior of SteelFiber High Strength Concrete under compression,” ACI Structural Journal, V. 91, No. 4, July August, pp 448457.
3. Papworth, F. and Ratcliffe, R. (1994), “HighPerformance ConcreteThe concrete Future,” Concrete International, V. 16, No. 10, pp 3944.
4. Pendyala .R.S., (1997).”The behavior of High strength concrete flexural members” Ph.D Thesis, The university of Melbourne.
5. Reddi. S.R. (1974) “Behavior of concrete in rectangular binders, and its application in flexure of reinforced concrete structures“Ph.D Thesis J.N T.University, Hyderabad.
6. Seshu. D.R., et.al.(2004) “Compressive strength of high volume fly concretes of different grades”, Proceeding of National work shop on “Advances in materials and mechanics of concrete structures”, pp 1115 July 2 nd & 3 rd , IIT Chennai
8. Bouzoubaa.N and Fournier.B.(2003). “Optimization of FA content in concrete. Part – I. Nonairentrained concrete made without Superplastizer”. Cement and Concrete Research., Vol.33, pp 10291037.
9. Hongsted,F.et.al.(1955), “Concrete stress distribution in ultimate strength design”,Journal of ACI Proc.vol.52 ,No.4, Dec, pp.455480.
