Elastic Constants of Polymer Modified Fiber

The Asian Review of Civil Engineering Volume 3 Number 2

July - December 2014

Contents Sl. No.

Title

Page No.

1

Stress-Strain Behaviour of Fine Grained Soils with Varying Sand Content Nagaraj Koppa

1

2

Social and Economical Benefits of Remanufacturing of Bearings B.J.Nagaraju and K.J.Rathanraj

10

3

Design of Base Isolated School Building with Elastomeric Bearing E.Niranjani and K.Aravinthan

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4

Elastic Constants of Polymer Modified Fiber Reinforced Concrete Uttam B. Kalwane, Yuwaraj M. Ghugal, and Ajay G. Dahake

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The Asian Review of Civil Engineering ISSN: 2249 - 6203 Vol. 3 No. 2, 2014, pp.1-9 © The Research Publication, www.trp.org.in

Stress-Strain Behaviour of Fine Grained Soils with Varying Sand Content Nagaraj Koppa Department of Civil Engineering, Gharda Institute of Technology, A/P Lavel, Dist: Ratnagiri, India E-mail: [email protected]

thus failure is related to the shear strength which is one of the most important engineering properties of a soil.

Abstract - The behaviour of clay is affected by the content of sand particles. How and to what degree the sand content affects on shrinkag e limit, co mpaction characteristics, stress-strain behaviour, shear parameters (angle of internal friction and cohesion) and coefficient of consolidation studied in detail. In this paper, fine grained soil like BC soil and shedi soil with different percentage of sand (10% to 60%) was prepared and compacted with water content at optimum and a systematic series of UU-Triaxial test is conducted. Results of the laboratory tests shows that at optimum content 10% to 60% of sand, the results reveal that undrained shear strength, as the sand content increases in fine soil mixture the cohesion of soil decreases with increases in frictional angle at optimum content. The percentage increased in friction angle increased at steady state from 130 to 280 and the cohesion decreased from 0.71 to 0.39 kg/cm2 with increasing sand content. Keywords: Black cotton soil, Consolidation of soil, Index properties, Shedi soil, Triaxial shear test

II. MATERIALS AND METHODOLOGY 1.Sand Locally available river sand was used in the present study. Sieve analysis was done on the sand used in the experiment, and found that sand is well graded and is clean with little or no fines. For the experimental work, sand is considered which is passing through 1 mm sieve and retained on 425 micron sieve. 2. Black Cotton Soil Expansive soils are those which show volumetric changes in response to changes in their moisture content. Such soils swell when the moisture content is increased and shrink when the moisture content is decreased. Consequently, expansive soils cause distress and damage to structures founded on them. Black cotton soil is collected from the Navanagar area of Bagalkot district; Karnataka (is located at Latitude of 18° 10' 32.55N and Longitude 71° 39' 29.88E).

I. INTRODUCTION Fine-grained soils comprising silt and clay are the most complicated engineering material in soil. it is of great importance in geotechnical engineering to make realistic predictions of the behaviour of soil under various conditions. Most geotechnical engineers consider the behaviour of fine soil as being somewhere between the behaviour of sand at one extreme, sands have modes of behaviour that are distinctly different in a number of respects, and the widely used concept of interpolating between them does not provide a realistic approach to deal with the behaviour of silts. Soils have characteristics in common with both sands and clays. They are subjected to more compression by static pressures than sands, and are subjected to more densification by vibrations than clays. Similarly understanding the behaviour of clay is not easy, as slight variations in the existing conditions will result in enormous changes in the stress, strain and strength response.

3. Shedi Soil Shedi soils are commonly found in south-west coastal belt in India. These soils typically exhibit moderate to high plasticity, low to moderate strength. Shedi soil is collected from Haliyal road of Dharwad city. At the time of collection of sample care has been taken to avoid the mixing of unwanted materials like wastes, roots and minerals. The soil is collected at a depth of 2 m from ground level at the site. Shedi soil so obtained is air dried and tested in laboratory to find its index and engineering properties according to IS codes.

Reduction in water content during sample disturbance would result in gain in strength. Also increase in disturbance would result in decrease in strength. The quantity of plastic and non plastic fines in sand influences the stress strain behaviour. Soils behaviour is complex because it is heavily dependent on numerous factors. Strength of soil is the result of the resistance to the movement (failure) of molecules connected with each other,

III. EXPERIMENTAL PROGRAM 1. Shrinkage limit Test was performed in general accordance with the procedure described in IS 2720 part 5, 1985. For determination of shrinkage limit in the present studies,

1

TARCE Vol. 3 No. 2 July - December 2014

Nagaraj Koppa

about 50 gm of soil passing at 425 microns sieve was taken and mixed with water to make creamy paste, in investigating soil the sand content was adding with different percentage. As 10%, 20%, 30%, 40%, 50%, and 60%.

3. Triaxial shear test 1

2. Compaction test Test was performed in general accordance with the procedure described in IS 2720 part 7, 1980. The laboratory compaction test was conducted on investigating fine grained soils at different sand content like 10%, 20%, 30%, 40%, 50% and 60%.

2

Test was performed in general accordance with the procedure described in IS 2720 part 12, 1981. The sample was prepared with their optimum moisture content, by adding different content of sand like 10%, 20%, 30%, 40%, 50%, and 60%, the soil sample extruded from the sampling tube, in which it has been stored, and trimmed to suit a split mould of the required sample size. Stress-strain curves from UU tests on BC soil and sand specimens at confining pressures up to 0.5 kg/cm2, 1 kg/cm2, 1.5 kg/cm2 at strain rate of 0.625mm/min.

TABLE 1 SPECIFICATIONS OF SPECIMEN

Sl. 1 2

Specifications Diameter of the Sample Height of the sample

Dimensions (cm) 3.4 7.0

for fully saturation of the specimen. Other procedures were made according to the standard test method. Then load increment 0.05, 0.1, 0.2, 0.4 and 0.8 Kg/cm2 were applied. The corresponding deformations in the dial gauge were noted in the time intervals as required for square root time fitting method. Then a graph of time v/s dial gauge for a particular loading was plot and C v was determined adopting square root time fitting method. Same procedure was fallowed for all specimens.

4. Consolidation test For a soil sample, substantial or inherent characteristics could be presented quantitatively by plasticity indices and specific gravity and other properties. Therefore in order to taking into account of these two main factors, conventional one dimension consolidation tests were conducted on each soil samples. To do this about two type of soil sample were prepared and tested with containing different percentage of sand such as 10, 20, 30, 40, 50 and 60% with their soil density. The specimens with initial water content 2 times OMC had slurry state and were filled in the fixed ring, taking care to prevent over topping. Filter papers were placed between specimen and saturated porous stones to prevent from movement of particles into the porous stone. After trimming top of the specimens and displacement of the upper porous stone and filter paper, the setting load (about 5 Kpa) was applied and the set was left for 24 hours

IV. RESULTS AND DISCUSSION 1. Shrinkage Limit (SL) The effect of sand content at different percentage on shrinkage limit of investigating soils have been presented in Table I it is observe that shrinkage limit decreases with increases sand content in investigating soil.

Fig.1 Shrinkage samples (BC and shedi soil)


2

Stress-Strain Behaviour of Fine Grained Soils with Varying Sand Content TABLE II EFFECT OF SHRINKAGE LIMIT IN BC SOIL WITH VARYING SAND CONTENT

Sl.No.

Sand content (%)

1 2 3 4 5 6 7

0 10 20 30 40 50 60

BC Soil Shrinkage limit (%) 14.60 13.5 12.08 10.86 9.87 9.46 8.98

Shedi Soil Shrinkage limit (%) 21.38 21.20 20.85 20.44 20.38 20.25 20.05 SL for BC soil SL for Shedi soil

24 22 20

Shrinkage Limit(%)

18 16 14 12 10 8 6 4 2 0 0

10

20

30

40

50

60

Sand content(%)

Fig. 2 Variation in shrinkage limit with different content of sand

From the Fig. 2 it is observe that in BC soil shrinkage limit decreases significantly as sand content increases. In case of

shedi soil there is marginal change in shrinkage limit as the sand content increases. SL of BC soil SL of shedi soil

22 20

Shrinkage limit (%)

18 16 14 12 10 8 6 4 2 0 0

10

20

30

40

50

60

Sand content (%)

Fig.3 Percentage decreased in shrinkage limit with different content of sand

From fig. 3 at 10% sand content in BC soil the percentage decrease in shrinkage limit was 7.5%. In case of shedi soil at 10% sand content the percentage decrease in shrinkage limit was 0.08%. It indicates that as sand content increases in BC soil shrinks more than shedi soil. Based on experimental study of shrinkage limit, as the sand content increases in soil there is decrease in shrinkage limit and by comparing black cotton and shedi soil as the sand content increases, black cotton soil shrinks significantly about 32% and shedi soil shrinks marginally about 5%.

2. Effect of Sand Content on Compaction Characteristics The effect of sand content at different percentage on compaction properties of investigating soils have been presented in Table III and IV; it is observe that as the sand content increases in investigating soils there increases in maximum dry density and decreases in optimum moisture content.

3


Nagaraj Koppa TABLE III VARIATION IN OPTIMUM MOISTURE CONTENT AND MAXIMUM DRY DENSITY OF BC SOIL

% of sand

OMC (%)

1

0

15.70

MDD (gm/cc) 1.80

2

10

14.80

1.95

3 4

20 30

14.20 13.60

2.10 2.20

5

40

13.00

2.30

6

50

12.40

2.30

7

60

12.10

2.40

SI

TABLE IV VARIATION IN OPTIMUM MOISTURE CONTENT AND MAXIMUM DRY DENSITY OF SHEDI SOIL

SI

% of sand

OMC (%)

1 2 3 4 5 6 7

0 10 20 30 40 50 60

17.70 17.40 16.90 16.10 15.40 14.10 12.70

MDD (gm/cc) 1.74 1.80 1.89 1.92 1.97 2.20 2.40

3. Effect of sand content on optimum moisture content of black cotton and shedi soil
1.5 sec., usually 2.0-3.0 sec.). Because the period is increased beyond that of the earthquake, resonance is avoided and the seismic acceleration response is reduced. The benefits of adding a horizontally compliant system at the foundation level of a building can be seen in Figure 1. In Figure 1, note the rapid decrease in the acceleration transmitted to the isolated structure as the isolated period increases. This effect is equivalent to a rigid body motion of the building above the isolation level.

I. INTRODUCTION During earthquake attacks, the traditional building structures in which the base is fixed to the ground, respond with a gradual increase from ground level to the top of the building. This may result in heavy damage or total collapse of structures. To avoid these results, while at the same time satisfying in-service functional requirements, flexibility is introduced at the base of the structure, usually by placing elastomeric isolators between the structure and its foundation. The mechanism of the base isolator increases the natural period of the overall structure, and decreases its acceleration response to earthquake / seismic motion.

It is seen that most base isolated buildings around the world are important buildings such as hospitals, universities, schools, firehouses, nuclear power plants, municipal and governmental buildings, and some high technology buildings that house sensitive internal equipment or machinery. The aim of this study is to obtain dynamic characteristics which are natural frequencies and mode shape of the structure using modal analysis and to carry out analytical modal analysis of the structure. Response spectrum analysis is carried out. Design procedures used for base isolated systems are discussed and form the basis for preliminary design procedures.

19


E.Niranjani and K.Aravinthan

Fig. 1 Acceleration response spectrum

II.DESCRIPTION OF THE STRUCTURES The structures, used for the analyses, are assumed to be serving as school building. The school building is designed as per IS 8827-1978 ‘Recommendations for Basic Requirements of School Buildings’ .The detailed descriptions of the building is as follows:

as concrete frames with columns size of (360X360) mm in size, and beams of dimension (250X400)mm in longitudinal direction and (250X300)mm in transverse direction . Each floor slab has100mm thickness and the story height is 4 meters. Imposed load considered is 3KN/m^2.

The three-storey building has a regular plan (54m x 16m) as shown in Figure 3.1. The structural system is selected

Fig. 2 Column Location of School Building

III. ANALYSIS METHODS In this section, response spectrum analysis is discussed. It is a Linear dynamic method. This method of analysis is based on dynamic response of the building idealised as having lumped mass and stiffness. Modal analysis gives us idea to avoid resonant vibrations. It locates critical points and we can safe guard our structure before damage. Modal analysis gives us idea about the response of

structure to dynamic loading. First mode shape is most critical because its time period is largest among all time periods of vibrations. The response of a N-DOF can be computed in which the system can be considered as if made of N single DOF whose response is superimposed.

Preliminary Data for Analysis Type of structure - multi-storey RCC framed structure Seismic zone - III(coimbatore) Number of stories-four(G+3) Floor height-4m Imposed load-3.5 kN/m2 Size of columns-360mm x 360mm TARCE Vol. 3 No. 2 July - December 2014

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Design of Base Isolated School Building with Elastomeric Bearing

Depth of slab – 100mm thick Size of beams-250mm x 450mm in longitudinal Size of beams -250mm x 400mm in transverse direction Response spectra- as per IS 1893 (Part I):2002

Fig.3 Elevation and lumped mass model

Calculation of lumped mass M 1 = M 2 = M 3 = 547.2T M 4 =288T K=12EI/L3 =5868.15KN/m = 28*5868.15=164.3X10^3 KN/m

M=

Φ= T=2 Modal participation factor P k =

(1)

Modal mass M=(

(2) TABLE I FREQUENCY AND TIME PERIOD

Frequency, rad/sec 6.7

Mode no 1

Time period, T secs 0.93

2

19.36

0.32

3

29

0.21

4

34.6

0.18

TABLE II PK, M AND MODAL MASS CONTRIBUTION

Mode no

Pk

M

1 2 3 4

44 12.79 -11.09 -0.76

1754 148.79 116.9 0.55 21

Modal mass contribution 86.82% 7.30% 5.78% 0.027% TARCE Vol. 3 No. 2 July - December 2014


Lateral force at each floor in each mode Q=A h A h1 =Z/2*I/R*Sa/g

(3)

Q1=

Q2=

Q3=

Q4=

Storey shear force in each mode

V ik =

(4)

V1=

V2=

V3=

V4=

Mode No

V (KN)

F (KN)

1

525.9

58.9KN

2

467

148KN

3

319

186.6KN

4

132.2

132.2KN

V=Storey shear force due to all mode F =lateral shear force at each storey


22


IV. ISOLATOR PROPERTIES AND MODELLING The design process starts with preliminary design of a fixed base structure. Following is the preliminary design of the base isolators. A design methodology for bilinear elastomeric isolation systems, those with lead rubber in particular, is presented here. First basic characteristics (like time period, mode shape, base shear) of non-base isolated building are obtained. Then, for the base isolated building a target value of time period or maximum lateral displacement is set. Using these target values, isolator details are worked out and its stiffness and damping are decided. Using this base isolator, building is analyzed and

seismic force and lateral displacement are obtained. If the result is within target values, then design of base isolation is right, else another set of properties are considered and analysis is done again. The detailed procedure is explained below: First, select the material properties for the bearing: Effective yield stress of lead (fyl), shear modulus of rubber (Gr), material constant for rubber (k). Determine the maximum loads on isolator (PD+L).

TABLE III NATURAL RUBBER PROPERTIES

Hardness IRHD±2

Young’s Modulus E (MPa)

Shear Modulus G (MPa)

Material Constant k

Elongation at Break Min, %

50

2.2

0.64

0.73

500

The steps followed are explained below: Assumed values for trial B b = 330mm B pl = 140mm t i = 8mm T r = 100mm Step 1: Vertical Stiffness and Load Capacity

Fig. 4 Shape Factor

Shape Factor, S = (A b -A pl ) / ( B b t i ) =8.45 Vertical stiffness, K vi = (E c A r )/ t i = 2470245.6 N/mm Step 2 Compressive Rated Load Capacity The vertical load capacity is calculated by summing the total shear strain in the elastomer from all sources. The total strain is then limited to the ultimate elongation at

break of the elastomer divided by the factor of safety appropriate to the load condition.

The shear strain from vertical loads, sc =6S c = 1.46 t sh The shear strain due to lateral loads is, sh = / T r

23



=1/100 = 0.01 For service loads such as dead and live load the limiting strain criteria are based on AASHTO f u > sc where f=1/3 (factor of safety 3) 1/3 x (500/100) > 1.46 1.67 > 1.46 Therefore strains are within the limit And for ultimate loads which include earthquake displacements f u > sc + sh where f = 0.75 (factor of safety 1.33) 0.75 x (500/100) > 1.46 + 0.01 3.75 > 1.47 Therefore the strains are within the limit Combining these equations, the maximum vertical load, P at displacement can be calculated from P = { K vi t i (f u =19.45 x 10^2 KN

sh )}/6

S

Step 3 Buckling Load Capacity For bearings with a high rubber thickness relative to the plan dimension the elastic buckling load may become critical. The buckling load is calculated using the Haringx formula as follows: The moment of inertia, we calculated as I = B b 4/64 for circular bearings =5.81 x 10^8 mm^4 The height of the bearing free to buckle, that is the distance between mounting plates is H r = (n t i ) + (n-1)t sh An effective buckling modulus of elasticity E b = E (1+0.742S2) =118.75 N/mm The buckling load at zero displacement is ] P cr 0 = R/2 [ = 1894.95 KN For an applied shear displacement the critical buckling load at zero displacement P cr

P cr 0 x (A r /A g ) = 1505.23 KN =

Step 4 Lateral Stiffness And Lead Rubber Bearing Hysteresis

Fig. 5 Bilinear Force deformation behavior


24


The lead rubber isolation bearing is modeled by a bilinear model based on the three parameters: Ku, Kd, and Qd as shown in Fig. 3. Isolation bearings will have high initial stiffness, Ku, and after yielding they will have lower stiffness, Kd. The initial stiffness Ku is estimated as a multiple of post yield stiffness Kd for lead–plug bearings. The hysteretic damping of this bearing is due to the plastic deformation of the lead. The force intercept at zero displacement is termed Qd, the characteristic strength, where: Q d = y A pl = 161.55 KN The post-elastic stiffness, Kd, is equal to the shear stiffness of the elastomeric bearing alone: Kr = G Ar/ T r = 546.33 N/mm The shear force in the bearing at a specified displacement is: Fm = Qd + Kr = 162.09 KN

From which an average, or effective, stiffness can be calculated as K eff = F m / = 162.09 KN/mm The sum of the effective stiffness of all bearings allows the period of response to be calculated as: Te = 2 = 4 secs Seismic response is a function of period and damping. For lead rubber bearings the hysteresis area is calculated at displacement level ∆m as A h = 4 Q d (∆ m -∆ y ) = 323106 mm2 From which the equivalent viscous damping is calculated as )) β = 1/2 (A h /( = 31 % For β = 31% B = 1.7 The isolator displacement can be calculated from the effective period, equivalent viscous damping and spectral acceleration as: 2 ) m = (S a T e )/(4 = 70mm

Fig. 6 Connection of Bearing to the Structure

V. SUMMARY OF RESULTS TALE IV MAXIMUM RESPONSE FOR THE BUILDING

Mode no

Frequen cy rad /sec

Time period sec

Base shear (KN)

1 2 3 4

6.7 19.36 29 34.6

0.93 0.32 0.21 0.18

525.9 467 319 132.2

25

Force at all floors (KN) 58.9 148 186.8 132.2

Displace ment (mm) 0.3 0.6 0.74 0.8


E.Niranjani and K.Aravinthan TABLE V ISOLATOR PROPERTIES

DIMENSIONS Overall diameter

330mm

Lead core diameter

140mm

Total height

118mm

Total rubber thickness

100mm

Thickness of individual layer

8mm

No of layers

23

The number of rubber layers and lead core sizes are set by a trial-and-error procedure to achieve the required seismic performance. So the solution for seismic performance requires an iterative procedure. On further iteration, the design can be made economical.

REFERENCES [1]

[2]

VI. CONCLUSION [3]

In order clarify the use of base isolation, a step-by-step procedure is given in this study. Like any structural design, the base isolation design is also iterative in nature. The expected lateral displacement or time period of base isolation system is assumed and the base isolation properties are obtained. At the end it is checked if required time period or displacement is actually obtained. Using the stiffness and damping of base isolation, building is analyzed using response spectrum analysis and seismic response is obtained. Although, this study involves elastomer based lead rubber bearing which have bilinear behaviour, other isolation elastomer based isolation systems will have similar behavior.

[4]

[5]

[6]

[7]

Base isolation is known to be quite effective vibration control device However, in this studies, it is shown that base isolation is effective in reducing the response as compared to fixed base system. In the present work, building structure with elastomeric lead rubber bearing having bilinear force deformation behavior is used.

[8] [9]

Base isolation helps in reducing the design parameters i.e. base shear and bending moment in the structural members above the isolation interface. The absolute displacements increases but relative displacements are reduced thus reducing the damage to the structure when subjected to an earthquake. The shear and bending moments are reduced due to the higher time period of the base isolated structure which results in lower acceleration acting on the structure and also, due to the increased damping in the structure due to the base isolation devices.

[10]

[11]

[12]

[13] [14] [15]


26

Anil K. Chopra, Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4th Edition, Prentice Hall, Englewood Cliffs, New Jersey, 2012. Byung-Young Moon, Gyung-Ju Kang, Beom-Soo Kang and Dae-Seung Cho (2004) ‘Design Of Elastomeric Bearing System And Analysis Of It Mechanical Properties’ KSME International Journal, Vol. 18 No. 1, pp. 20~ 29. Fabio Mazza, Alfonso Vulcano and Mirko Mazza(2012) ‘Nonlinear Dynamic Response of RC Buildings with Different Base Isolation Systems Subjected to Horizontal and Vertical Components of Near-Fault Ground Motions’ The Open Construction and Building Technology Journal. Gomase O.P and Bakre S.V(2011) ‘Performance of NonLinear Elastomeric Base-Isolated building structure’ International Journal Of Civil And Structural Engineering Volume 2, No 1. Himat T Solanki, Vishwas R Siddhaye and Gajanan M Sabnis(2008) ‘Seismic Isolation For Medium Rise Reinforced Concrete Frame Buildings’ 33 rd Conference on Our World In Concrete & Structures pp 25 – 27. Hossein Shakeri Soleimanloo and Mehdi Shekarisoleimanloo (2012) ‘A Survey study on design procedure of Seismic Base Isolation Systems’ J. Appl. Sci. Environ. Manage. Vol. 16 (4), pp.299 -307. Mehmet Komur, Turan Karabork and Ibrahim Deneme (2011) ‘Nonlinear Dynamic Analysis Of Isolated And FixedBase Reinforced Concrete Structures’ Gazi University Journal of Science . Pankaj Agarwal,Earthquake Resistant Design Of Structures,PHI learning Pvt.Ltd. R.W.G. Blakeiey , A. W. Charleson , H.C. Hitchcock , L . M . Megget , M.J.N. Priestley bf R.D. Sharpe and R.I. Skinner ‘Recommendations For The Design and Construction of Base Isolated Structures’. S.M. Kalantari, H. Naderpour and S.R. Hoseini Vaez ‘Investigation Of Base-Isolator Type Selection On Seismic Behavior Of Structures Including Story Drifts And Plastic Hinge Formation’, The 14 the World Conference on Earthquake Engineering, October 12-17, 2008, Beijing, China. Satish Nagarajaiah, Andrei M. Reinhorn, Member, ASCE, and Michalakis C. Constantinou, Associate Member, ASCE ‘Nonlinear Dynamic Analysis Of 3-D- Base-Isolated Structures’. IS 1893 (Part 1):2002 ‘Criteria for Earthquake Resistant Design of Structures’ Part 1- General Provisions and Buildings. IS 8827-1978 ‘Recommendations for Basic Requirements of School Buildings’ National Building Code of India. M. C. Constantinou, I. Kalpakidis, A. Filiatrault and R.A. Ecker Lay, ‘LRFD-Based Analysis And Design Procedures For Bridge Bearings And Seismic Isolators’.

The Asian Review of Civil Engineering ISSN: 2249 - 6203 Vol. 3 No. 2, 2014, pp.27-40 © The Research Publication, www.trp.org.in

Elastic Constants of Polymer Modified Fiber Reinforced Concrete Uttam B. Kalwane1, Yuwaraj M. Ghugal2, and Ajay G. Dahake3 1

Principal, Dr. D Y Patil School of Engineering and Technology, Pune (MS), India 2 Professor, Government College of Engineering, Karad (MS), India 3 Associate Professor, Marathwada Institute of Technology, Aurangabad (MS), India E-mail: [email protected], [email protected] Abstract - The results of an experimental investigation to study the effects of hooked steel fibers with varying dosage and polymer latex with fixed dosage in concrete are studied. In this experimental study, varying volume fraction of hooked steel fibers from 0% to 7% by weight of cement at the interval of 1% of fiber and SBR latex polymer of fixed volume of 15% by weight of cement were used. All specimens of only fiber content were water cured and specimens of polymer with fiber content were air cured. At the end of 28 days of curing period, destructive tests were carried out on concrete specimens to determine the elastic constants of fiber reinforced concrete and polymer modified steel fiber reinforced concrete. For the analysis of structures, the elastic constants are very important. The elastic constants are static modulus of elasticity (E s ), dynamic modulus of elasticity (E d ), Poisson’s ratio (µ) and modulus of rigidity (G), etc. Keywords: Polymer modified fiber reinforced concrete, modulus of elasticity, modulus of rigidity, Poisson’s ratio

methods of fabrication, fiber reinforced concrete can be an economic and useful construction material [4]. In slabs on grade, mining, tunneling, an excavation support applications, steel and synthetic fiber reinforced concrete and shotcrete have been used in lieu of welded wire fabric reinforcement [5]. Polymers being organic in nature have coefficients of thermal expansion several times higher than those of inorganic materials such as concrete or steel. Therefore, when a polymer concrete overlay is subjected to temperature changes, it undergoes greater volumetric changes than the substrate, creating stresses at the bond line. The cumulative effect of these stresses, particularly at very low temperatures, may cause deboning due to adhesive failure at the interface or shear failure in either the polymer concrete or the substrate [6]. It is also known as polymer Portland cement concrete. Polymer modified concrete mixtures are normal Portland cement concrete mixtures to which a water soluble or emulsified polymer has been added during the mixing process. As the concrete cures, hardening of the polymer also occurs, forming a continuous matrix of polymer throughout the concrete. A wide variety of polymers have been investigated for the use in polymer modified concrete [7]. Of these, the latex polymers have been most widely used and accepted. Styrene butadiene is excellent for exterior exposure or environments where moisture is present.

I. INTRODUCTION Concrete is one of the most widely used construction material all over the world in view of its strength, high mould ability, structural stability and relative low cost. Rapid advances in Construction materials technology have enabled civil and structural engineers to achieve impressive gains in the safety, economy, and functionality of structure built to serve the common needs of society. There are clear indications that the use of fibers in concrete will increasingly continue to be the preferred choice for many repair and rehabilitation projects involving construction of bridges, Industrial floors, airport pavements, overlays, high rise buildings, TV towers, parking garages, offshore structures, historic monuments etc.

Anupam Singh et al [8] has carried out the study of polymer modified concrete and reported that concrete polymer materials with their increased strength, stiffness and durability properties appear to provide the answer to age-old problem of cracking and deterioration of concrete under adverse environmental conditions. James S. Davidson et al [9] have demonstrated an innovative use of thin-membrane elastomeric polymers to prevent breaching and collapse of unreinforced masonry walls subjected to blast. ACI committee 548 [10] has given standard specifications for latex modified concrete overlays. Semisi Yazici et. al [11] have investigated the effects of aspect ratio and volume fraction of steel fiber on the compressive strength, split tensile strength, flexural strength and ultrasonic pulse velocity of steel fiber reinforced concrete. Christopher K. Y. Leung et al [12] have reported that the flexural strength of fiber reinforced shotcrete is slightly higher than that for fiber reinforced concrete in most cases, but the residual load carrying capacity in post cracking regime can be significantly lower. Due to addition of fibers in concrete, the increase in compressive strength is up to 23% and tensile strength

The greatest benefit of using fiber reinforcement is improved long-term serviceability of the structure. By the use of fibers in concrete, substantial time and cost savings can be attained by reducing the cost intensive labors to prepare, place and control ordinary reinforcement. Hence fiber reinforced concrete has been modern and cost efficient construction material [1]. Fiber reinforcement has been shown to improve the ductility, toughness, flexural strength and shear strength of cementitious materials, to reduce shrinkage cracking and permeability and to enhance fatigue and impact resistance. Fiber reinforcement is used to improve the brittle nature of cementitious composites [2]. Fibers are discontinuous and are generally distributed randomly throughout concrete matrix. Fibers are being used in structural applications with conventional reinforcement [3]. Because of the flexibility in 27


Uttam B. Kalwane, Yuwaraj M. Ghugal, and Ajay G. Dahake

increases up to 60% [13]. Moncef Nehdi et al [14] have used fiber- reinforced self consolidating concrete (FRSCC) for the research work and concluded that some steel fiber combinations seemed to increase the compressive strength of FRSCC beyond what could be achieved by single type steel fibers. Synthetic macro fibers tended to decrease compressive strength but this effect could be reduced when such fibers were used in hybrid blends along with steel fibers, likely due to a better control of micro-macro cracking and the higher stiffness of steel fibers. Charles Nutter et al [15] have performed the experimental investigation to determine the performance characteristics of concretes reinforced with a polypropylene structural fiber. They reported that, in all fiber reinforced concretes the mode of failure was changed from a brittle to a ductile failure when subjected to compression or bending. The average residual strength increased with increase in the fiber content. The modulus of elasticity of fiber reinforced concrete increased up to 30% to 80% higher than that of plain concrete [16]. The modulus of elasticity of concrete is largely controlled by the volume and modulus of the aggregate. Small addition of steel fibers would not be expected to greatly alert the modulus of the composites.

compressive strength, modulus of elasticity and Poisson’s ratio due to the addition of steel fibers was found to be quite small (less than 10%) in various grades of concrete (M35, M65 and M85). The maximum increase in the tensile strength, namely, split tensile strength and modulus of rupture due to the addition of steel fibers, was found to be about 40% in various grades of concrete and is the primary justification for using fibers in concrete. The post- cracking response is significantly enhanced with fiber dosages across the different concrete grades. The modulus of elasticity of fiber reinforced concrete increased up to 30% to 80% higher than that of plain concrete [4]. The modulus of elasticity of concrete is largely controlled by the volume and modulus of the aggregate. Small addition of steel fibers would not be expected to greatly alert the modulus of the composites. In this paper, effect of polymer modified fiber reinforced concrete on modulus of elasticity, modulus of rigidity and Poisson’s ratio over plain concrete is studied. II.EXPERIMENTAL PROGRAMME Experimental work was aimed to study the effect of polymer modification along with hooked steel fibers on various properties of concrete and its feasibility in the actual field of construction, especially flexural strength, compressive strength, modulus of elasticity, etc of modified high strength concrete after some preliminary trials.

Sedat Kurugol et.al [17] have studied the effect of steel fiber reinforcement and polymer modification on the young’s modulus of lightweight concrete aggregates. They concluded that, the young’s modulus of elasticity of the concrete decreases with the change of coarse aggregate fraction with lightweight aggregate and by increasing its volume fraction. The same trend can be observed in steel fiber reinforced lightweight concrete mixtures. The rate of decrease depends strongly on the aggregate volume fraction. The effect of the polymer on modulus of elasticity is that for lower polymer volume ratio it has a positive effect. Modulus of elasticity of the polymer concrete, increases by approximately 13%. V. Bhikshma and L. Jail Singh [18] have reported that, the increase in modulus of elasticity for M30 grade concrete with addition of 0.25%, 0.5% and 1.0% of steel fibers was observed to be 16%, 41% and 50% respectively when compared with plain concrete. Similarly for M35 grade concrete the increase in strength with addition of steel fibers was observed to be 25%, 43% and 55% respectively when compared to plain concrete. The modulus of elasticity of recycled aggregate concrete with addition of 1.0% of steel fibers to be 50% more compared to plain concrete.

For preparation of steel fiber reinforced concrete (SFRC) and polymer modified steel fiber reinforced concrete (PMSFRC), materials used were cement, fine aggregate, coarse aggregate (20mm), coarse aggregate (10mm), hooked end steel fibers, polymer latex, super plasticizer and water. The cement used in this experimental work was 53 grade Ordinary Portland Cement (OPC) conforming to IS: 12269-1987, the fineness moduli of fine and coarse agreegates were 2.872 and 6.97 respectively. Bekaert–Dramix® high tensile steel fibers with hooked ends are made from prime quality high carbon steel wire were used. They had hooked ends and were collated into clips of about10 individual fibers using water soluble adhesive as shown in Figure 1. The collation reduces the tendency for balling of fibers during the mixing process. The adhesive dissolved in the mixing water in about one minute, facilitating the distribution of individual fibers. A hooked end which slowly deforms during pull-out is generally considered as the best form of anchorage. These fibers are manufactured by the BEKAERT, a Belgium based company with the trade name of Dramix® and type RC80/60 BN. These fibers are supplied by M/s Shakti Commodities Pvt. Ltd., New Delhi.

Job Thomas and Ananth Ramaswamy [19] have carried out the experimental study and an analytical assessment of the influence of addition of fibers on mechanical properties of concrete. They reported that the maximum increase in the


28

Elastic Constants of Polymer Modified Fiber Reinforced Concrete

Fig. 1 Hooked End Steel Fibers

Physical properties of fibers used for the experimental work are shown in Table I. TABLE I PHYSICAL PROPERTIES OF FIBER

Description Type of fiber Length of fiber (l) Thickness (diameter) of fiber (d) Aspect ratio (l/d) Tensile Strength Specific gravity Modulus of Elasticity

Value Hooked end steel fiber 60 mm 0.75 mm 80 2000 N/mm2 7.8 200 Gpa

Polymer latex additive ‘Monobond’ is used as a polymer. This polymer is available in liquid form containing 40% solids and 60 % water. The water contained in the polymer has included in the total water content of the mix i.e. reduce the amount of water contained in polymer from the quantity of w/c ratio while adding the water to the concrete mix. This

is a non-epoxy thermosetting polymer. It is a latex emulsion manufactured and marketed by a Mumbai based company M/s Krishna Conchem products Pvt. Ltd. under the trade name ‘Monobond®’. Properties of this polymer are shown in Table II.

TABLE II PROPERTIES OF POLYMER

Property Polymer system Type Base Appearance Setting characteristics Viscosity at 270c (± 2) Specific Gravity at 270c (± 2) pH

Description Polymer Latex additive (Monobond) Latex Polymer Latex Milky White Slow 15 sec 1.08 10.40

Roff Super plast 320 have been used as super plasticizer to improve the workability of concrete. Dosage used in this experimental work was 1.75% by weight of cement. This Super plasticizer is added to mixing water first and then this mixture is added to the dry mix concrete.

III.SYSTEM DEVELOPMENT A. Compression test The compression test was performed to find out compressive strength of steel fiber reinforced concrete and polymer modified steel fiber reinforced concrete on test specimens cubical in shape of size 150mm, confirming to IS: 100861982. Compression testing machine of capacity 3000 kN was used.

29



Fig. 2 Compression test setup

The compressive strength of the specimen is calculated by using the formula,

f cu =

Pc A

(1)

f cu = Compressive strength of concrete in MPa P c = Maximum applied load in N A = Cross sectional area in mm2

where,

uppermost surface as cast in the mould, along two lines spaced 200mm apart i.e. two point load. The axis of the specimen shall be carefully aligned with the axis of the loading device. The load was applied without shock and increasing continuously at a rate of 400 kg/min. The appearance of the fractured faces of concrete and any unusual features in the type of failure was noted.

B. Flexure test To find out flexural strength of concrete, prism specimens of size 150mm × 150mm × 700mm were used. The arrangement for loading of flexure test specimen is shown in Figure 3. The prism specimen shall be placed in the machine in such a manner that the load shall be applied to the

Figure 3: Loading Arrangement for Flexu

Fig. 3 Loading Arrangement for Flexure Test

The flexural strength of the specimen shall be expressed as the modulus of rupture (fb) and calculated by using following expression fb =

Pl bd 2

(2)

when ‘a’ is greater than 200 mm, or fb =

3Pa bd 2

(3) when ‘a’ is less than 200 mm but greater than 170 mm. where, P = Maximum applied load to the specimen in kN a = the distance from the line of fracture to the nearer support, measured on the center line of the tensile side of the specimen in mm (Note: if ‘a’ is less than 170mm then the results of the test shall be discarded TARCE Vol. 3 No. 2 July - December 2014

30


b = measured width of the specimen in mm. d = measured depth of the specimen at the point of failure in mm. l = length of the span on which the specimen is supported in mm. The results of compressive strength (f cu ) and flexural tensile strength (f b ) of concrete are shown in Table 3. C. Modulus of elasticity The modulus of elasticity (E) is primarily influenced by the elastic properties of the aggregate, age of the concrete, conditions of curing, the type of cement and mix proportions. Small additions of steel fibers would not be expected to greatly alter the modulus of composite. The modulus of elasticity is normally related to the compressive strength of E s = 5.0 f cu Using IS 456:2000,

E = 9.1 ( f )

concrete. The static modulus of elasticity of steel fiber reinforced concrete and polymer modified steel fiber reinforced concrete can be determined by using formulae given by Indian code IS 456: 2000 and British code BS: 8110 depending upon compressive strength of concrete. It is given by the following expressions (4)

0.33

s cu (5) Using BS 8110 :( Part2)-1985, where, E s = Static modulus of elasticity in GPa f cu = Cube compressive strength of concrete in N/mm2 Dynamic modulus of elasticity is obtained according to BS 8110: (Part2)-1985 by the following expression Ed = 7.6 ( f cu ) 0.33 + 14 (6) where, E d = Dynamic modulus of elasticity of the PMSFRC in GPa f cu = Cube compressive strength of PMSFRC in N/mm2

The relation between static modulus of Elasticity (Es) and dynamic modulus of Elasticity (E d ) (from Eqn. 5) of concrete as per BS: 8110 (Part-2)–1985 is given below

Es = 1.25Ed − 19

(7)

D. Poisson’s ratio At the point of initial cracking the strain on the tension face of a beam in flexure and the lateral tensile strain in compression specimen in uniaxial compression are of the f Poisson’s ratio, µ= b

same magnitude. Based on this research finding and using stress strain relation of solid mechanics Neville has derived the formula for Poisson’s ratio as follows (8)

f cu

where, µ = Static Poisson’s ratio f b = Tensile stress at cracking in flexure in MPa f cu = Compressive stress at cracking in a compression specimen in MPa E. Modulus of rigidity The modulus of rigidity (G) of steel fiber reinforcement concrete and polymer modified steel fiber reinforced concrete is obtained from following equation E (9) G= 2(1 + µ )

where,

E = Modulus of elasticity µ = Poisson’s ratio

Results of the static modulus of elasticity, dynamic modulus of elasticity, Poisson’s ratio of the composite and modulus of rigidity from the above expressions are presented in tables and graphically also. IV. RESULTS AND DISCUSSION A. Compression strength and flexural / tensile strength Results of compressive strength and flexural / tensile strength are shown in Table III.

31


Uttam B. Kalwane, Yuwaraj M. Ghugal, and Ajay G. Dahake TABLE III COMPRESSIVE STRENGTH AND FLEXURAL / TENSILE STRENGTH

Sr. No.

Mix Designation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

M0 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15

Fiber Content (Vf) % 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

Polymer Content %

0

15

Compressive Strength (f cu ) MPa 44.59 46.67 47.02 49.51 54.22 54.13 51.56 48.09 47.88 49.88 50.52 52.89 56.36 55.73 52.53 49.35

Flexural/Tensile Strength (f b ) MPa 3.17 4.17 5.37 5.46 5.08 4.71 4.63 4.48 3.87 4.60 5.44 5.56 5.17 4.76 4.65 4.62

Variations of modulus of elasticity (E s ) from IS: 456-2000, BS: 8110, variation of dynamic modulus of elasticity (E d ) with respect to fiber content (Vf) are plotted as shown in Figure 4, Figure 5 and Figure 6 respectively. Also variation of modulus of elasticity (E s ) from IS: 456-2000 and BS: 8110 with respect to compressive strength (f cu ) are plotted as shown in Figure 6 and Figure 7.

B. Modulus of elasticity The results of static modulus of elasticity (Es) obtained from Eqn. (4) and Eqn. (5) and dynamic modulus of Elasticity (E d ) obtained from Eqn. (6) for steel fiber reinforced concrete (SFRC) and polymer modified steel fiber reinforced concrete (PMSFRC) are shown in Table 4.

TABLE IV EXPERIMENTAL RESULTS AND RESULTS OF REGRESSION ANALYSIS OF MODULUS OF ELASTICITY (E) OF SFRC AND PMSFRC

Sr. No.

Mix Designation

Fiber Content (Vf) %

1 2 3 4 5 6

M0 M1 M2 M3 M4 M5

0 1 2 3 4 5

7 8

M6 M7

6 7

9 10 11 12 13 14 15 16

M8 M9 M10 M11 M12 M13 M14 M15

0 1 2 3 4 5 6 7

Polymer Content %

0

15


Modulus of Elasticity (E) MPa Es (GPa) using IS: 456 Eqn. (4) 33.39 34.16 34.29 35.18 36.82 36.79

From Eqn. (10) and (11)

Es (GPa) using BS: 8110 Eqn. (5)


33.500 33.769 34.564 35.555 36.412 36.805

31.86 32.35 32.43 32.98 33.99 33.97

31.930 32.102 32.592 33.196 33.710 33.930

Ed (GPa) using Eqn.(6) 40.61 41.01 41.08 41.55 42.39 42.37

35.90 34.67

36.404 34.879

33.43 32.67

33.652 32.672

41.92 41.28

42.194 41.426

34.60 35.31 35.54 36.36 37.54 37.33 36.24 35.12

34.650 35.072 35.804 36.594 37.190 37.340 36.792 35.294

32.62 33.06 33.20 33.71 34.42 34.30 33.63 32.95

32.650 32.911 33.356 33.829 34.174 34.235 33.856 32.881

41.24 41.61 41.73 42.15 42.75 42.64 42.09 41.52

41.270 41.489 41.866 42.275 42.590 42.685 42.434 41.711

32

From Eqn. (14) and (15) 40.670 40.814 41.226 41.738 42.182 42.390

Elastic Constants of Polymer Modified Fiber Reinforced Concrete 38

Es = -0.043Vf3 + 0.283Vf2 + 0.178Vf + 34.65 R² = 0.936

Modulus of Elasticity (GPa)

37 36 35 34

Es = -0.056Vf3 + 0.428Vf2- 0.104Vf + 33.50 R² = 0.937 SFRC

33

PMSFRC

32 31 30 0

1

2

3 4 Fiber Content (Vf %)

5

6

7

Fig.4 Variation of modulus of elasticity (Es) (IS: 456-2000) with respect to fiber content.

35.0 Es = -0.026Vf3 + 0.171Vf2 + 0.116Vf + 32.65 R² = 0.937

34.5


34.0 33.5 33.0 32.5

Es = -0.034Vf3 + 0.260Vf2 - 0.051Vf + 31.93 R² = 0.938

32.0

SFRC

31.5

PMSFRC

31.0 30.5 30.0 0

1

2

3 4 Fiber Content (Vf %)

5

6

7

Fig.5 Variation of modulus of elasticity (Es) (BS:8110) with respect to fiber content (Vf).

33



44 Ed = -0.021Vf3 + 0.141Vf2 + 0.101Vf+ 41.26 R² = 0.937

Dynamic Modulus of Elasticity (GPa)

43 42

Ed = -0.028Vf3 + 0.219Vf - 0.047Vf+ 40.66 R² = 0.939

41 40

SFRC PMSFRC

39 38 37 0

1

2

3

4

5

6

Fiber Content (Vf %) Fig.6 Variation of dynamic modulus of elasticity (Ed) with respect to fiber content (Vf).

38


37 Es = 0.345fcu + 18.05 R² = 0.999

36 35

Es = 0.354fcu + 17.60 R² = 0.999

SFRC PMSFRC

34 33 32 31 42

45

48

51

54

57

60

Compressive Strength (MPa) Fig.7 Variation of modulus of elasticity (Es) (IS: 456-2000) with respect to compressive strength (fcu).


34

7



35

34

Es = 0.212fcu + 22.48 R² = 0.999 Es = 0.219fcu + 22.11 R² = 0.999

33

SFRC PMSFRC

32

31 42

45

48

51

54

57

60

Compressive Strength (MPa) Fig. 8 Variation of modulus of elasticity (Es) (BS: 8110) with respect to compressive strength (fcu).

35 34

Es = -0.027Vf3 + 0.176Vf2 + 0.126Vf + 32.58 R² = 0.937


33 Es= -0.036Vf3 + 0.274Vf2 - 0.059Vf + 31.83 R² = 0.939

32

SFRC

31

PMSFRC

30 29 28 27 26 0

1

2

3

4

5

6

7

Fiber Content (Vf %) Fig. 9 Variation of modulus of elasticity (Es) from dynamic modulus of elasticity (Ed) with respect to fiber content.

Mathematical analysis of the test results is done by using regression analysis. Regression analysis is the dependence of a variable on one or more variables. Results obtained in this experimental research work are compared by regression analysis and are presented in the tables. Expressions for static modulus of Elasticity (Es) (using IS 456:2000) in 3rd degree polynomial in terms of fiber content (Vf) are obtained from the Figure 2 and are given below (10) For SFRC, Es = – 0.055 Vf 3 + 0.428 Vf 2 – 0.104 Vf + 33.50 (11) For PMSFRC, Es = – 0.042 Vf 3 + 0.281 Vf 2 + 0.183 Vf + 34.65 Expressions for static modulus of Elasticity (Es) (using BS 8110: (Part 2)-1985) in 3rd degree polynomial in terms of fiber content (Vf) are obtained from the Figure 2 and are given below 35



For SFRC, For PMSFRC,

Es = – 0.034 Vf 3 + 0.261 Vf 2 – 0.055 Vf + 31.93 Es = – 0.026 Vf 3 + 0.170 Vf 2 + 0.117 Vf + 32.65

(12) (13)

Expressions for dynamic modulus of Elasticity (Ed) (using BS: 8110 Part2-1985) in 3rd degree polynomial in terms of fiber content (Vf) are obtained from the Figure 4 as below (14) For SFRC, Ed = – 0.028 Vf 3 + 0.218 Vf 2 – 0.046 Vf + 40.67 (15) For PMSFRC, Ed = – 0.021 Vf 3 + 0.142 Vf 2 + 0.098 Vf + 41.27 Graphs have plotted for static modulus of Elasticity (Es) (using IS; 456-2000) versus compressive strength (fcu) and static modulus of Elasticity (Es) (using BS: 8110 Part 2-1985) versus compressive strength (fcu) are as shown in Figure 5 and Figure 6. (16) For SFRC, Es = – 0.036 Vf 3 + 0.274 Vf 2 – 0.059 Vf + 31.83 (17) For PMSFRC, Es = – 0.027 Vf 3 + 0.176 Vf 2 + 0.126 Vf + 32.58 It is observed from the results shown in Table V, Figure 3, Figure 4 and Figure 5 that, the modulus of elasticity of the specimens containing fibers only (SFRC) have increased up to 4% of fiber content as compared to the normal mix and then it is reduced with the increase in fiber content. Also the modulus of elasticity of the specimens containing fibers with polymer (PMSFRC) have increased up to 4% of fibers with polymer content and then it is reduces with the increase in fiber content. It is also observed that the values of dynamic modulus of elasticity are slightly more as compared to the values of static modulus of elasticity.

C. Poisson’s ratio The results of Poisson’s ratio (µ) obtained from Eqn. (8) and results of regression analysis obtained via Eqn. (18,19) for steel fiber reinforced concrete (SFRC) and polymer modified steel fiber reinforced concrete (PMSFRC) are shown in Table 5 and variations of Poisson’s ratio (µ) with respect to fiber content (Vf) are plotted as shown in Figure 10.

TABLE V EXPERIMENTAL RESULTS AND RESULTS OF REGRESSION ANALYSIS FOR POISSON’S RATIO (µ) OF SFRC AND PMSFRC.

Sr. No.

Mix Designation


1

M0

2

Poisson’s Ratio (µ) Polymer Content %

Experimental Value from Eqn. (8)


0

0.071

0.068

M1

1

0.089

0.097

3

M2

2

0.114

0.108

4

M3

3

0.110

0.107

5

M4

4

0.094

0.100

6

M5

5

0.087

0.093

7

M6

6

0.090

0.092

8

M7

7

0.093

0.103

9

M8

0

0.081

0.078

0

10

M9

1

0.092

0.096

11

M10

2

0.108

0.096

12

M11

3

0.105

0.078

13

M12

4

0.092

0.042

14

M13

5

0.085

-0.012

15

M14

6

0.089

-0.084

16

M15

7

0.094

-0.174


15

36


μ = 0.000Vf3 - 0.009Vf2 + 0.027Vf + 0.078 R² = 0.857

0.12 Poisson's ratio (μ)

0.10 0.08 μ = 0.001Vf3 - 0.012Vf2 + 0.040Vf + 0.068 R² = 0.871

0.06 0.04

SFRC PMSFRC

0.02 0.00 0

1

2 3 4 5 Fiber Content (Vf %)

6

7

Fig.10 Variation of Poisson’s ratio (μ) with respect to fiber content (Vf).

Experimental results and results of regression analysis for Poisson’s ratio (µ) of SFRC and PMSFRC are presented in Table V. (18) For SFRC, µ = 0.001 Vf 3 – 0.012 Vf 2 +0.040 Vf + 0.068 (19) For PMSFRC, µ = 0.000 Vf 3 – 0.009 Vf 2 + 0.027Vf + 0.078 It is observed from the results shown in Table 5 and Figure 9 that, the Poisson’s ratio of the specimens containing fibers only (SFRC) have increased up to 3% of fiber content as compared to the normal mix and then it is reduced with the increase in fiber content. Also the Poisson’s ratio of the specimens containing fibers with polymer (PMSFRC) have increased up to 2% of fibers with polymer content and then it is reduces with the increase in fiber content. D. Modulus of rigidity The of modulus of rigidity (G) has been find out by using Eqn. (9) and the results obtained from regression analysis are presented in Table 6 and graphically shown in Figure 11-13. TABLE VI EXPERIMENTAL RESULTS AND RESULTS OF REGRESSION ANALYSIS FOR MODULUS OF RIGIDITY (G) OF SFRC AND PMSFRC

Modulus of Rigidity (G) MPa Sr. No.

Mix Designation


1 2

M0 M1

0 1

Polymer Content %

Experimental Result Gs (GPa) From Eqn. (9)


Experimental Result Gs (GPa)


Experimental Result Gd (GPa)


15.88 15.68

15.94 15.45

15.16 14.85

15.19 14.70

19.32 18.83

19.35 18.68

3

M2

2

15.39

15.58

14.56

14.69

18.44

18.58

4

M3

3

15.85

16.04

14.86

14.99

18.72

18.82

5

M4

4

16.83

16.58

15.53

15.38

19.37

19.18

0

6

M5

5

16.92

16.94

15.63

15.68

19.49

19.46

7

M6

6

16.47

16.85

15.33

15.67

19.23

19.43

8

M7

7

15.86

16.04

14.95

15.17

18.88

18.89

9 10

M8 M9

0 1

16.11 16.27

16.17 16.02

15.19 15.24

15.14 14.94

19.20 19.18

19.26 18.96

11

M10

2

16.04

16.23

14.98

15.03

18.83

18.98

12

M11

3

16.45

16.62

15.25

15.27

19.07

19.19

15

13

M12

4

17.19

17.01

15.76

15.52

19.57

19.43

14

M13

5

17.20

17.20

15.81

15.66

19.65

19.57

15

M14

6

16.64

17.01

15.44

15.52

19.33

19.45

16

M15

7

16.05

16.254

15.06

14.99

18.98

18.95

37


Uttam B. Kalwane, Yuwaraj M. Ghugal, and Ajay G. Dahake 17.5 Gs = -0.031Vf3 + 0.275Vf2 - 0.394Vf + 16.17 R² = 0.854

Modulus of Rigidity (GPa)

17.0 16.5 16.0

Gs = -0.044Vf3 + 0.435Vf2 - 0.874Vf + 15.94 R² = 0.879 SFRC

15.5 15.0 14.5 14.0

0

1

2

3

4

5

6

7

Fiber Content (Vf %) Fig. 11 Variation of modulus of rigidity (Gs) (IS: 456-2000) with respect to fiber content.

16.0 15.8

Gs = -0.023Vf3 + 0.214Vf2 - 0.392Vf + 15.24 R² = 0.811

Modulus of Rigidity (GPa)

15.6 15.4 15.2 15.0 14.8

Gs = -0.033Vf3 + 0.346Vf2 - 0.808Vf + 15.19 R² = 0.866

14.6 14.4

SFRC PMSFRC

14.2 14.0

0

1

2

3

4

5

6

Fiber Content (Vf %) Fig. 12 Variation of modulus of rigidity (Gs) (BS: 8110) with respect to fiber content (Vf).


38

7


Dynamic Modulus of Rigidity (GPa)

20.0 Gd = -0.024Vf3 + 0.235Vf2 - 0.514Vf+ 19.26 R² = 0.763 19.5

19.0 Gd = -0.036Vf3 + 0.388Vf2 - 1.018Vf+ 19.35 R² = 0.870

18.5

SFRC PMSFRC 18.0

17.5

0

1

2

3

4

5

6

7

Fiber Content (Vf %) Fig.13 Variation of dynamic modulus of rigidity (Gd) with respect to fiber content (Vf).

(20) For SFRC, Gs = – 0.044 Vf 3 + 0.435 Vf 2 – 0.874 Vf + 15.94 (21) For PMSFRC, Gs = – 0.031 Vf 3 + 0.275 Vf 2 – 0.394 Vf + 16.17 Expressions for static modulus of rigidity (Gd) in 3rd degree polynomial using BS: 8110 in terms of fiber content (Vf) are obtained from the Figure 11 and are mentioned below (22) For SFRC, Gs = – 0.033 Vf 3 + 0.346 Vf 2 – 0.808 Vf + 15.19 (23) For PMSFRC, Gs = – 0.023 Vf 3 + 0.214 Vf 2 – 0.392 Vf + 15.24 Expressions for dynamic modulus of rigidity (Gd) in 3rd degree polynomial in terms of fiber content (Vf) are obtained from the Figure 12 and are mentioned below (24) For SFRC, Gd = – 0.036 Vf 3 + 0.388 Vf 2 – 1.018 Vf + 19.35 (25) For PMSFRC, Gd = – 0.024 Vf 3 + 0.235 Vf 2 – 0.514 Vf + 19.26 It is observed from the results shown in Table 6 and Figure 10-12 that, the modulus of rigidity of the specimens containing fibers only (SFRC) and that of with polymer (PMSFRC) have increased up to 5% of fiber content as compared to the normal mix and then it is reduced with the increase in fiber content.

REFERENCES [1]

[2]

[3]

V. CONCLUSION On the basis of results obtained from experimental work, observations made during casting and testing of specimens, and results of the behavior of fiber reinforced concrete and normal concrete. For the analysis of structures, the elastic constants are very important. The elastic constants are static modulus of elasticity (Es), dynamic modulus of elasticity (Ed), Poisson’s ratio (µ) and modulus of rigidity (G), etc. Experimental results and results obtained by regression analysis are in excellent agreement with each other.

[4]

[5] [6] [7] [8]

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