Software-interface for Design of Hybrid Fibre Reinforced Concrete Slabs-on-grade

DEVELOPING SOFTWARE-INTERFACE FOR DESIGN OF HYBRID FIBRE REINFORCED CONCRETE SLABS-ON-GRADE

 

 

ACKNOWLEDGEMENT

We are very pleased to present this project work. This period of our student life has been truly rewarding a number of people were of immense help to us during the course of my project work and preparation of this book.

 First, we wish to thank God Almighty who created the heaven and the Earth, who helped us in completing this project.

 We would like to thank Ms. P.Karthika, Assistant professor, Department of Civil Engineering, Nandha Engineering College (Autonomous), Erode internal guide of this project, for her guidance and his help. Her insight during the course of our research and regular guidance were invaluable to us.

 And also I thank Ms. R.Pradeepa, Assistant professor, Department of Civil Engineering, Nandha Engineering College (Autonomous), for her encouragement and cooperation throughout the project.

 And also I thank Dr. E.K. Mohanraj, Dean, Department of Civil Engineering, Nandha Engineering College (Autonomous), Erode, for his encouragement and support.

 And also I thank my parents, who encouraged and supported me in all possible ways and to my friends who has given good support along the way.

 I would also thank the entire management of our college, for extending their help.

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Hybrid fibre system has best performance characteristics of each constituent fibre system to the composite material. Though lead fibres offer better radiation shielding properties, the strength and toughness of lead fibre concrete is very low. The addition of steel fibres improves the ductility and energy absorption capacity of structural elements. Therefore, in order to use the shielding properties of lead fibres and improved energy absorption of steel fibres, a combination of these two fibres into a hybrid concrete is made and investigated.

 

MATLAB is a software package of high-performance numerical computation and visualization. It provides an interactive environment with hundreds of built-in functions for technical computations. It also provides easy extensibility with its own high-level programming language. The aim of this work is to develop a software-interface for the developed design methodology of hybrid fibre reinforced concrete.

 

Keywords: Hybrid fibre, radiation shielding, ductility, energy absorption capacity, MATLAB.

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TABLE OF CONTENTS

 

ACKNOWLEDGEMENT…………………………………………………………………..iv

ABSTRACT……………………………………………………………………………………….v

LIST OF TABLES……………………………………………………………………………..vi

LIST OF FIGURES……………………………………………………………………………vii

CHAPTER 1 INTRODUCTION

CHAPTER 2 OBJECTIVES

CHAPTER 3 PROBLEM STATEMENT

CHAPTER 4 EXPERIMENTAL INVESTIGATION

CHAPTER 5 SYSTEM METHODOLOGY

5.1  Design Inputs

5.2 Calculation of a/l

5.2.1 Radius of Relative stiffness (l)

5.2.2 Contact radius (a)

5.3 Determination of stresses due to temperature

5.4 Determination of equivalent flexural strength

5.5 Design Check

5.6 Design Framework

CHAPTER 6 RESULTS AND DISCUSSIONS

CHAPTER 7 CONCLUSIONS

CHAPTER 8 REFERENCES    

 

 

 

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LIST OF TABLES

 

Table 4.1 Mix proportions of the concrete mix adopted……………..2

Table 5.1 Assumptions of curling stresses………………………………5

Table 5.2 Bradbury’s co-efficient, C……………………………………..5

Table 6.1 Results of HFRC……………………………………….13

Table 6.1 Design Example 1 – Input data………………………………14

Table 6.2 Design Example 2 – Input data………………………………15

LIST OF FIGURES

Fig 5.1 Code for calculation of relative stiffness……………………..4

Fig 5.2 Code for calculation of contact radius………………………..6

Fig 5.3 Code for calculation of equivalent flexural strength ……..7

Fig 5.4 Code for Design check……………………………………………7

Fig 6.1 Output for design example 1…………………………………..14

Fig 6.2 Output for design example 2…………………………………..15

Fig 6.3 Specimens casting and testing…………………………..16

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The Hybrid fibre reinforced concrete is a significant advancement in the building technology. Common practice of design of HFRC is a time consuming process, MATLAB is a software package which provides an interactive environment with hundreds of built-in numerical functions for technical computations, graphics and animations. The aim of this work is to study the method of analysis and design of HFRC slabs-on-grade with MATLAB programming for easy application and to check whether the results obtained from the various tests remains the same when we analyze them with the help of MATLAB.

The main objective of using lead in concrete is due to its better nuclear shielding characteristics. However, the properties of concrete with hybrid (lead and steel) are comparable to steel fibres.

To understand the method of analysis and design of hybrid fibre reinforced concrete and to develop a MATLAB based interface for the easy application of the design of Hybrid fibre reinforced concrete.

3.  PROBLEM STATEMENT:

Lead tends to accumulate in the body, similar to other heavy-metal poisons, and continues producing toxic effects for many years after exposure. Hence it is desirable to eliminate lead from many of its present users, including radiation shielding. Concrete shielding systems now completely dominate the market for shielding of radioactive materials due to its ease of casting the material into the desired form in order to assure structural stability.

To overcome the above problem it is necessary to study the behaviour of lead in the form fibre added to concrete. The addition of lead to composite action, which may also permit reduced thickness for concrete element.

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4. EXPERIMENTAL INVESTIGATION:

4.1 MATERIALS USED

 In the present investigation, Ordinary Portland Cement of 53 grade was used. The river sand available was used having a fineness modulus 2.73. locally available blue granite crushed stone aggregate of size 20mm were used having a dry rodded weight of 1550kg/m3 and fineness modulus of 7.15. in concrete, the water-binder ratio is generally kept as low as possible. Hence, to obtain the given degree of workability, chemical admixtures, sulphonated naphthalene formaldehyde (CONPLAST SP 430) was used.

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 Two types of lead fibres, one pure lead and the other lead with 4% antimony in coil form having a diameter of 1mm were procured from market. These were cut into fibres of length 50mm. A lead fibre content 0f 2% and 3% by volume of concrete was chosen for fibre reinforced concrete. Since it was not possible to increase the fibre volume fraction beyond 3% due to constraints in the workability, a different technique of production called Slurry Infiltrated Fibrous Concrete (SIFCON) was adopted. A fibre volume fraction of 10% for lead fibre was chosen for SIFCON investigation.

4.2   HFRC MIX PROPORTION:

 ACI method of mixture proportioning was adopted for the design of the concrete mix.

However, the final proportions were arrived at after several trial mixes. The final corrected mixture proportion adopted in the current investigation for a target strength of 40MPa is given in the table1.

Table 4.1. Mix proportions of the concrete mix adopted.

Sl.No

Description of Materials

Quantity in kg/m3

1

Cement

400

2

Sand

800

3

Coarse aggregate

1000

4

Water

188

5

w/b ratio

0.47

6

Super plasticiser

0.3% to 1%

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5.0 SYSTEM METHODOLOGY:

5.1 DESIGN INPUTS

Fibre Reinforced Concrete slabs-on-grade may be analyzed by any method as long as they satisfy the strength and load requirements. The design of the HFRC slabs-on-grade uses the values of thickness of the slab(h), width of the slab(b), joint spacing(w), grade of concrete and fibre type and dosage are assumed. The following details are received as an input from the user,

Subgrade details – subgrade modulus

The value of subgrade modulus varies from 0.7 to 1.0 or even 1.2

Load characteristics

a)     Type of load – point load, axle load and uniformly distributed load

b)    Magnitude of load

c)     Base plate dimensions

Concrete characteristics

a)     Minimum grade of concrete

b)    Compressive strength of concrete- from actual test results or codal recommendations

Fibre characteristics

a)     Type of fibre

b)    Minimum / maximum dosage

Slab dimensions

a)     Thickness of slab

b)    Width of slab

c)     Joint spacing

5.2 CALCULATION OF a/I

5.2.1 RADIUS OF RELATIVE STIFFNESS (I)

  The value of radius of relative stiffness can be calculated from the formula,                                    

 

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fig 5.1 Code for calculation of relative stiffness

5.2.2 CONTACT RADIUS (a)

  The value of contact radius can be calculated depending upon the type of load as follows,

fig 5.2 Code for calculation of contact radius

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5.3 DETERMINATION OF STRESSES DUE TO TEMPERATURE

 For the calculation of curling stresses due to temperature differential, the following data is assumed,

Table 5.1Assumptions for curling stresses

Co-efficient of thermal expansion,σ

0.00001

Temperature differential

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The value of bradbury’s co-efficient, C is calculated from interpolation of following data:

 

Table 5.2Bardbury’s co-efficient, C

 

 

L/l or W/l

1

0

2

0.04

3

0.175

4

0.44

5

0.72

6

0.92

C=0.972426

7

1.03

8

1.075

9

1.08

10

1.075

11

1.05

12

1

 

 

 

 

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fig 5.3 Code for calculation of curling stresses

 

5.4 DETERMINATION OF REQUIRED EQUIVALENT FLEXURAL STRENGTH

 Depending upon the value of a/I the value of equivalent flexural strength can be determined as follows:

 For a/I >0.2,

 

For a/I=0,

 

For a/I<0.2,

 

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fig 5.4 code for calculation of equivalent flexural strength

5.5 DESIGN CHECK

 

 Finally design check is made between the allowable load and design load, if the design is not safe, it should be redesigned with higher thickness

Pallowable>Papplied

fig 5.5 Design check

5.6 DESIGN FRAMEWORK :

For the purpose of designing a fibre reinforced concrete, a design framework is followed by a comparison of the suggested method with existing design guidelines and methods. According to the framework, the input data, assumptions and results are determined and a design program was developed.

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6.0 RESULTS AND DISCUSSIONS

 From the various inputs and assumptions the following output will be obtained

a)     Characteristic flexural strength

b)    The value of a/I

c)     Curling stresses due to differential

d)    The equivalent flexural strength for each loading case

Table 6.1  Results of HFRC mixes

Mix ID

Density Kg/m3

Compressive strength MPa

Split tensile strength MPa

Flexural strength MPa

Cracking

Peak

CON

2450

40.81

2.88

3.60

3.77

L11

2611

41.72

3.65

3.74

3.99

L12

2715

40.01

3.52

4.06

4.24

S11

2432

43.39

3.01

4.05

4.39

S12

2469

45.56

5.10

4.77

4.84

L11S1

2613

43.43

3.71

4.55

5.01

L12S1

2709

45.33

3.97

4.55

5.27

L21S1

2632

47.20

3.83

4.81

5.02

L22S1

2777

47.28

3.49

4.63

4.82

L11S2

2640

45.24

4.93

4.69

5.22

L21S2

2609

43.49

4.07

4.29

4.88

 

 

 

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Design Example 1:

The various input data provided are as follows:

Table 6.1 Input data for design example 1

 

DESIGN INPUT

DATA

Subgrade modulus

0.04 N/mm3

Minimum thickness of slab

200 mm

Applied load

80000 N

Slab dimension

150 mm × 150 mm

Assumed maximum temperature differential in slab

10°C

Grade of concrete

M35

Elastic modulus

21000

Poisson’s ratio

0.15

Coefficient of thermal expansion

0.00001 /°C

The outputs obtained from these input are as follows:

fig 6.1. Output for design example 1

 

 

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Design Example 2:

The various input data provided are as follows:

Table 6.3 Input for design example 2

DESIGN INPUT

DATA

Subgrade modulus

0.15 N/mm3

Minimum thickness of slab

300 mm

Applied load

80000 N

Slab dimension

150 mm × 150 mm

Assumed maximum temperature differential in slab

10°C

Grade of concrete

M35

Elastic modulus

32000

Poisson’s ratio

0.15

Coefficient of thermal expansion

0.00001 /°C

The outputs obtained from these input are as follows:

fig 6.2 Output for design example 2

 

 

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Fig 6.3 Specimens casting and testing

7.0 CONCLUSIONS

It is observed that, the time required for manual design is much greater than in case of MATLAB which gives results in micro seconds. Basically the calculations routines have been programmed into a M-file (“frp.m”). For simple calculations, the command can be typed directly into the MATLAB command window. However, for more complex programs that require a great number of operations, the commands can be grouped into a single file, known in MATLAB as ‘M-file’. The numerical results obtained by using MATLAB software were compared with those results obtained by various tests.

Dimosthenisfloros ., Olafuragustingason. “Modelling and simulation of reinforced concrete”. Chalmers University of Technology, Goteborg, 2013.

RafealAlves de Souza., Viadimir Jose Ferrari. “Automatic design of the flexural strengthening of reinforced concrete beams”. UniversidadeEstadual de Maringa, Colombo.

Muhammad Ishaq., “MATLAB toolbox for the design of Reinforced Concrete structural members”. ACI 318-02.

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