Tension Stiffening in Composite Concrete Reinforced with BFUP and Inox 

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Application of Inoxydable Steel in Construction

The physical characteristics of inoxydable steel makes it well suited to use in construction; it possesses high strength and stiffness (comparable with carbon steel), very high ductility (approximately two times that of carbon steel), and excellent corrosion resistance, which means, suitably specified that it requires no protective coatings [18]. Inoxydable steel also offers better retention of strength and stiffness than carbon steel at elevated temperatures [19]. The principal disincentive for the application of stainless steel in construction is the initial material cost, though considered on a whole life basis, cost comparisons with carbon steel become more favorable.

Investigation of Tension Stiffening

This tension stiffening phenomenon has been observed experimentally by numbers of researchers through a uniaxial tension test [9], [10], [11], and [12]. Most of these researches involved the study of concrete reinforced with construction steel and fiber-reinforced polymer (FRP) material. For these studies, the reinforced concrete specimen and the reinforcement bars are equipped with strain gauges and LVDT to record changes in stress before the specimen starts to crack until failure. Specific arrangements are also required to support the reinforced concrete sample while applying direct tension.
Sooriyaarachchi, 2005 [9] uses a specially manufactured FRP bar built with a series of strain gauges closely distances along the bar. The bar is cut longitudinally in half and strain gauges were placed at the centre of the bar to avoid interference between the bar surface and concrete since a number of strain gauges are used. Using test specimens ranges from 1.3 to 1.5 meter, the samples is subjected to uniaxial tension and tension stiffening parameter is verified on the area where crack is initially introduced. LVDT is fixed on the beam member to determined strain of the overall member. This type of setting has successfully observed and studied the tension stiffening in FRP bar when subjected to direct tension. Changes and increases in stress are observed along the reinforcement bar before and after the formation of cracks.
However, due to the difficulties of conducting the direct tension test, only limited and often conflicting results are available. Nayal and Rasheed, 2006 [30] has applied bending test results to study tension stiffening parameter in concrete beam reinforced with carbon steel. Through the combination of nonlinear numerical analysis, tension stiffening model are inversely estimated from the nonlinear analysis of beam section and the experimental results. The study however did not observe the tension stiffening phenomenon for concrete structure under bending; the changes in stress when load is applied as per observe in the direct tension test.

Inoxydable Steel in Structural Elements

The behavior and effects of inoxydable steel in structural elements are analyzed and compared with construction steel bars based on three types of analysis;
i) Free vibration analysis.
ii) Push-over analysis.
iii) Time history analysis.
Push-over is a static nonlinear analysis, and time history analysis is dynamic nonlinear.

Free Vibration Analysis

Free vibration can be expressed by means of the motion of a structure without any dynamic excitation-external force or support motion. A structure is undergoing free vibration when it is disturbed from its static equilibrium position and then allowed to vibrate without any external dynamic excitation. An example of a pagola and water tank is depicted in Figure 2.9. Free vibration analysis is used to obtain natural frequencies, analytically, and damping ratio, experimentally.

Push-Over Analysis

The term “push-over analysis” describes a modern variation of the classical „collapse analysis‟ method. It refers to an analysis procedure whereby an incremental-iterative solution of the static equilibrium equations carried out to obtain the response of a structure subjected to monotonically increasing lateral load patterns. This method has been extensively verified in many years for building assessment. But the application of push-over analysis for building assessment study has been a limited subject up till nowadays, Pinho et al, 2007 [32].
Push-over analysis which is also known as Nonlinear Static Procedure (NSP) is a performance-based analysis that refers to a methodology in which structural criteria are expressed in terms of achieving a performance objective for different damage states. A performance level described a limiting damage condition which may be considered satisfactory for a given structure and earthquake ground motion. The objective of the Push-over analysis is to calculate the building‟s performance point which represents the building‟s ultimate deformation under the design earthquake. The performance point can also be described as the intersection of building‟s seismic capacity curve and seismic demand curve. The seismic capacity curve is derived from the base shear versus pier‟s top displacement curve. This curve is generated by increasing forces imposed on the building‟s nonlinear structural model, and updating element stiffness and redistributing seismic forces whenever yield or collapse of any structural elements are detected. The seismic demand curve is represented by plot of building‟s spectral acceleration versus its spectral displacement, which could be derived from the design Response Spectrum. There are four standard performance levels expressed under push-over analysis; operational, immediate occupancy, life safety and collapse prevention (Figure 2.10).

Mechanical Properties of Inoxydable Steel

Inoxydable steel are often selected for their corrosion resistance, but they are at the same time constructional materials. For structural application, mechanical properties such as strength, ductility and deformation are thus important. The difference in the mechanical properties between inoxydable steels and carbon steel can be seen most clearly in the stress-strain curves. Therefore in this study, tensile test is conducted on inoxydable steel sample and the ordinary carbon steel to investigate these differences closely between the selected steels.

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Laboratory Test Preparation

Tensile test is conducted on the austenitic stainless steel and carbon steel to study the stress-strain performance. Test procedure and sample preparation is based on BS EN 10002-1 [48]. Two types of austenitic stainless steel are tested (Fig. 3.1); austenitic-hot and austenitic-cold together with the carbon steel. Sample of each type of steel bar is prepared as shown in Fig. 3.2. Detailing of dimension for the samples is shown in Fig. 3.3. The inoxydable steel type used is summarized in Table 3.1.

Method of Ramberg-Osgood

A constitutive law for full range stress-strain curve of austenitic is developed based on the experimental work described above. Method applied by Rasmussen, 2001 [40] is being referred to in developing the stress-strain expression. This approach is based on the Ramberg-Osgood base formulation. Stress-strain relationship in steel has been developed by Ramberg and Osgood, 1943 [41] and cited by many researchers. This relationship however is not suitable for the design and numerical modeling of stainless steel members and elements which reach stresses beyond the 0.2% proof stress in their ultimate limit state. In this stress range, current stress-strain curve based on the Ramberg-Osgood expression become seriously inaccurate principally because they are extrapolation of curve fits to stresses lower than the 0.2% proof stress. In other words, the extrapolation becomes particularly inaccurate for alloys with pronounced strain hardening. A study conducted by Rasmussen [40] has developed expressions for determining the ultimate tensile strength ( ) and strain ( ) for given values of the Ramberg-Osgood parameters ( ). Based on expressions for ( ) and ( ), the entire stress-strain curve is then constructed from the Ramberg-Osgood parameters ( ). This approach is applied as a base to develop the stress-strain relationship of austenitic steel using data obtained from experimental work. Comparison is made to verify the suitability of this relationship and amendments are suggested to achieve accurate constitutive law for austenitic steel as part of the inoxydable steel group.

Application of Inoxydable Steel

For developing expressions for Inoxydable steel, the stress-strain curve is plotted in two phases: for stress less than 0.2% proof stress (Fig. 3.6), and stress between the 0.2% proof stress and the ultimate tensile strength, (Fig. 3.7). For austenitic steel, Eq. (3.14) that has been proposed to determine gives higher values of strain as compared to the laboratory results. This can be observed in Fig. 3.8(i), where the stress-strain values obtained from Eq. (3.14) are compared with the tensile test results. While the ultimate tensile stress predicted by the equation resembles the experimental results, the strain predicted is very high. The ultimate strain for austenitic-hot is 3 times higher than the experimental values, and it is 12 times higher for the austenitic-cold. This is shown in Fig. 3.8(a) and 6(b) respectively. A new expression is suggested to have the best fit curve for this type of steel;
It can be observed that the parameter 0.2 from Eq. (3.14) is replaced by 0.12. Referring to Eq. (3.14) and (3.16), for a given value of the non-dimensional proof stress; , the new parameter indicates inoxydable steel has lower ratio of Parameter (sharpness of the stress-strain curve) is lower. This shows that the studied steel have lower proportional limit, and extended strain hardening capability.

Table of contents :

1. Introduction
1. 1 Objectives
1. 2 Significant of Study
1. 3 Methodologies
1. 4 Arrangement of Thesis
2. Bibliography
2. 1 Types of Inoxydable Steel
2. 2 Application of Inoxydable Steel in Construction
2. 3 Composition of Inoxydable Steel
2. 4 Inoxydable Steel in Composite Concrete
2.4. 1 Tension Stiffening Model
2.4. 2 Investigation of Tension Stiffening
2. 5 Inoxydable Steel in Structural Elements
2.5. 1 Free Vibration Analysis
2.5. 2 Push-Over Analysis
2.5. 3 Time History Analysis
3. Material Models
3. 1 Mechanical Properties of Inoxydable Steel
3.1. 1 Laboratory Test on Inoxydable Steel
3.1. 2 Tensile Test Results
3. 2 Constitutive Laws of Inoxydable Steel
3.2. 1 Method of Ramberg-Osgood
3.2. 2 Application to Inoxydable Steel
3.2. 3 The Developed Equations
3. 3 Mechanical Properties of Concrete
3.3. 1 Standard Plain Concrete
3.3. 2 Ultra-high Performance Fiber-reinforced Concrete (BFUP)
3. 4 Interaction Model in Composite Concrete
3. 5 Laboratory Investigation
3.5. 1 Samples and Settings
3.5. 2 Tension Stiffening Phenomenon
3. 6 Nonlinear Numerical Analysis
3.6. 1 Method and Approach
3.6. 2 Material Models
3.6. 3 Section Analysis
3.6. 4 Beam Analysis
3.6. 5 Tension Stiffening Model for Inoxydable Steel
3.6. 6 Comparison with Carbon Steel
3. 7 Finite Element Analysis
3.7. 1 Modeling Strategies
3.7. 2 Inelastic constitutive model for concrete
3.7. 4 Comparison of experimental and numerical results
3. 8 Tension Stiffening in Composite Concrete Reinforced with BFUP and Inox
3. 9 Remarks and Conclusions
4. Inoxydable Steel in Structural Elements
4. 1 Reinforced Concrete Beam
4. 2 Reinforced Concrete Frame
4.2. 1 Free Vibration Analysis
4.2. 2 Nonlinear Push-Over Analysis
4.2. 3 Time History Analysis
4. 3 Remarks and Conclusion
5. Conclusions and Recommendations
6. References
7. List of Abbreviations and Symbols
8. Annex
8.1 Analytical Procedures in NNA
8.2 Code developed using MATLAB


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