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1.1 Historical Background
According to the historical record, the first aluminum alloy has been used as structural elements in Europe in the early fifties. In more recent times, the 20 century, the commercial applications of aluminum become more popular. From the Figure 1, the world-wide trends in production of aluminium may recognize that aluminum and its alloys can be considered as a competitive material in different applications.
Figure 1. 1 History of primary aluminium production
An English chemist, Sir Humphry Davy predicted the possibility of isolating the aluminium element from alumina salts in 1807, and revealed at the end of the eighteenth century by Guyton De Morveau during his studies on the ancient 'allume'.
Bauxite is the major raw material to form the aluminum which is to be found in the tropics and in the Caribbean area, South Africa, West Indies, South America and Australia. First, the bauxite is mined then refined into aluminum oxide trihydrate (alumina) by means of the Bayer Process. Then the smelting process will be carried out to produce aluminium with high purity which is suitable for most applications.
Interest in Civil and Structural Engineering
The mechanical and physical properties of aluminium and its alloy are the basic reasons of favour as constructional material and it is able to compete with steel in the structural field. Nowadays, aluminium is the metal of choice for leading designers, architects and engineers, who expect a material that involves functionality and cost effectiveness with innovative form and design potential. The following major benefits of this unique metal as:
Aluminium mixed with some different metal to form alloys, whose mechanical properties cover the range offered by the common mild steels
Natural coating of aluminium oxide provide a good barriers to the air, water and chemical attack
The lightweight aluminium benefit in weight reduction hence in reducing energy consumption and greenhouse gas emissions
The tailored shape of structural member can be easily shaped by any of the main industrial metalworking processes such as rolling and extrusion.
1.2 The main construction applications
The advantages above stated clearly that the reason of architects and design choose the aluminium material to achieve creative and innovations in design. Aluminium's flexibility, high strength to weight ratio, corrosion resistance, and ease of recycling make it ideal for:
Figure 1. 2 Scottish Exhibition & Conference Centre, ScotlandFacades and cladding
The widest applications in the field of façade engineering using aluminium material as curtain wall system. Attractive surface appearance and corrosion resistance can greatly reduce the additional cost for external finishing. The conference centre (Figure 1.1) covered in eight aluminium-skinned arches that cross the building,
The shapes created in the roof & walls are filled alternately with glass & white aluminium panels. (Figure 1.3)
Figure 1. 3 Serpentine Gallery, England
The HSBC Headquarter (Figure 1.3), main structure elements are covered with aluminum cladding.
Figure 1. 4 HSBC, Hong Kong
Aluminum cladding is mounted on Singapore Pavilion (Figure 1.4) to demonstrates
the benefits of building sustainable cities . Recyclable building materials such as aluminium is featured extensively.
Figure 1. 5 Singapore Pavilion, Shanghai World Expo 2010, China
Structural & Roofs
Aluminium buildings and roofs is providing a good thermal insulation and reflect the heat energy from the sun light.
Aluminium inserts for glazing bar repairs - invisible in the final work but giving the required 'bite' to the glass in every instance. (Figure 1.5)
Figure 1. 6 Enid A Haupt Conservatory, New York
Figure 1. 7 NatWest Media Centre, London
The NatWest Media Centre is the world's first aluminium semi-monocoque building.
The doubly-curved aluminium outer plate provided a seamless, watertight, corrosion-resistant finish.
Figure 1. 8 Interior of NatWest Media Centre
The advantages of light weight and strong all contribute a growing use of aluminium. However, the low Young's modulus of aluminium, which is around one third of steel, may cause aluminium member failed in buckling mode. The American Aluminium Design Manual (AA 2000), Australian/New Zealand Standard (AS/NZS 1997), and European Code (EC9 2000) provide design rules for aluminium structural members.
Referring Australian/New Zealand Standard, two basic design methods for cold-formed aluminium members are formally available in design specifications which are the traditional "Effective Width Method" and the new "Direct Strength Method". The effective width method is a worldwide for formal use in design,
while the direct strength method has only been adopted in North America, and
1.3 Objectives and scope of works
The objective of this report is to study analytically the actual buckling load of different shapes of aluminium columns under uniform distributed load in compression using a program called 'THIN-WALL'. It is also aimed at find out the maximum axial load capacity to its own weight of the member.
This report is divided into six chapters. Chapter 2 was given a brief description of physical and mechanical properties of aluminium, production of aluminium, and behavior of different buckling mode
In Chapter 3 was discussed on the theoretical background and the formula used in the prediction of buckling stress and actual buckling load.
In Chapter 4 ,a comparison of results of all section will be given. The effect of irregular shape of closed section on the actual buckling load will be discussed.
The final chapter presents the conclusion and recommendation for further research works
2.1 Production processes: from alumina to structural elements
High purity alumina (Al2O3) is used for aluminium production. It is relies on Bayer process to produce alumina from bauxite. The refining process by the Hall-Heroult Process, invented in 1886. The process uses as electrolyte molten salts called Cryolite (Na3AlF6) capable of dissolve the alumina. Carbon anodes are immersed into the electrolyte (usually referred as the "bath") carrying electrical current which then flows into the molten cryolite containing dissolved alumina. As a result, the chemical bond between aluminum and oxygen in the alumina is broken, the aluminum is deposited in the bottom of the cell, where a molten aluminum deposit is found, while the oxygen reacts with the carbon of the anodes producing carbon dioxide (CO2) bubbles. The alumina reduction process is described by the following reaction:
Once passed through the bath, the electrical current flows into the molten aluminum deposit and is then collected by the bottom of the pot, usually called "cathode".
The metal is now ready to be forged, processing into the shapes and forms depending on the application required. Aluminium can be alloyed with other materials to make an array of metals with different properties. The different shapes and forms can be commonly formed by Rolled, Extruded and Forged. The application for structural member is mainly produced by Rolled and Extruded methods.
The molten metal is cast after refining and alloying processes into slabs with around 500 to 600mm thick, then preheating up to 500 C prior to successive passes through a hot rolling mill where the aluminium is reduced in thickness to about 4-6mm (see Figure 2.3)
After the hot rolling process, aluminium plate passes through the roller several times again , which the temperature will be keep thermal temperature around 100 C by coolant., and then rolled to sheet thickness of around 0.05mm.
Aluminium extrusion is a plastic deformation process of a pre-heated aluminium billet which is forced to flow by compression through a steel or ceramic die with an aperture of a smaller cross-sectional area than the original billet. This process is normally done at room temperature for aluminium. The advantages of this over hot extrusion are the lack of oxidation, higher strength due to cold working and fast production time.
Aluminium extrusion can be produced in an infinite number of shapes, at a relative low cost, and with the ability to incorporate design features that reduce fabrication costs. In addition aluminium extrusion has a high strength to weight ratio and has equivalent mechanical properties of steel if the correct design and alloy is chosen
2.2 Aluminium properties
The aluminium and its alloy become the world's second most used metal after steel which is due to its competitive and attractive properties such as appearance, light weight, fabricability, physical properties, mechanical properties and corrosion resistance. In the following, the physical properties and mechanical properties will be illustrated.
The main physical properties of aluminium at room temperature, compared with aluminium alloy and steel, are represented in table 2.1. With regard to the most important parameters for structural behaviour, it can be observed that
The principal mechanical properties can be derived from a tensile test. First of all, it can be observed that the elastic modulus of aluminium is with 70000 N/mm² only a third of the steel modulus. This has essential consequences for the geometry of the design, since deflections of beams, bearing capacity of columns, i.e. lateral buckling and local buckling directly depend on the elastic modulus.
From the Figure 2.1, it can be observed that metals including steel and aluminium have a linear stress-strain relationship up to the yield point as shown. The stress falls after the yield point. This is due to the interaction of carbon atoms and dislocations in the stressed steel. However, aluminium which is made of cold formed work does not show this effect. The yield strength value does not have a well defined. The yield strength is typically defined by the "0.2% offset strain". The yield strength at 0.2% offset is determined by finding the intersection of the stress-strain curve with a line parallel to the initial slope of the curve and which intercepts the abscissa at 0.2%. A stress-strain curve typical of aluminum along with the 0.2% offset line is shown in the figure.
Cold Working Properties
Rolling and extruding to alter the shape or size of a metal will produce the dislocation of its grains at room temperature by plastic deformation. As the working continues, however the movement of the dislocations becomes more difficult. This increases both of the tensile strength and yield strength, while ductility is decreased. Depending on the grain structure mainly influenced by the alloy composition, one or two annealing sessions for recrystallisation have to be integrated into the production programme to permit a continuation of the rolling passes and to fulfil the final requirements of the product specification.
2.3 Member buckling mode
When the thin wall aluminium is subjected to compressive stress, which may be caused by a bending moment or axial load, the element will tend to respond in plane to the compressive stress, but also out of plane due to the low bending rigidity of the element. The out-of-plane movement is strongly associated with the elastic buckling stress of the element. Elastic buckling is occurs when the change in energy associated with out-of plane deformation response to an in plane load is equal to the change in energy for in plane response to the same in-plane load. The figures below are three modes for elastic buckling response of thin wall aluminium members: local, distortional, and lateral-torsional buckling.
It involves primarily plate bending of the elements, and with respect to the cross section deformations, the junction of the elements remain at same position, but merely rotate as each compression element buckles out of plane.Figure 2. 6 Local buckling
It involves part of the flange elements twisting about the element junction and part of web elements undergoes plate bending.
Figure 2. 7 Distortional buckling
It involves buckling where the whole cross section, without distortion, bend and rotate simultaneously
Figure 2. 8 Lateral-torisonal buckling
The Direct Strength Method
The Direct Strength Method (DSM) is developed by Schafer and Pekoz (1998) and provide a new approach in determining member flexural and compression strength and it is now gain acceptance in North America and Australia/New Zealand. The advantages of this method may be summarized as follow
1) The engineer may consider the distortional buckling by DSM, which is important for that members have their strength controlled by distortional buckling.
2) The engineer is convenient to predict the strength of thin-wall members with optimized cross sections. In this dissertation, computer program, THIN-WALL, will be used for performing an elastic buckling analysis, it is possible to obtain the buckling loads for members with any type of cross section.
The DSM has been used extensive amount of testing result for calibration which is included 267 pre-qualified columns and 569pre-qualified beams. (Schafer 2006). Therefore, the user to be aware of the types of cross-sections which are
included in the derivation of a particular DSM. If the sections within the range of sections used in the development of the DSM, the prescribed safety factors will be used for the design. Otherwise, conservative safety factors should be adhered to.
3.1 The DSM for columns
The nominal strength due to local, distortional and overall buckling can be determined from the elastic instabilities of the section in combination with the yield stress fy. A slenderness parameter Î» is defined as follows:
where Noc =A is the least of elastic buckling stress for local, distortional or overall buckling, which can be determined from an analytical or a numerical method such as the finite strip method. The local, distortional or overall buckling resistance is then determined from a direct equation. For the design of compression members, the nominal member capacity in compression (Nc) in accordance with AS4600-2005 section 220.127.116.11 to 18.104.22.168 will be the least of minimum member capacity compression (Ncc) for lateral-torsional buckling, capacity of member in compression for local buckling and capacity of member in compression for distortional buckling. The corresponding member capacity of a member in compression (Ncc) are calculated as follows:
where Ny = Afy
Local buckling strength in accordance with AS4600-2005 section 22.214.171.124:
Distortional buckling strength in accordance with AS4600-2005 section 126.96.36.199:
3.2 Finite strip buckling analysis
The Direct Strength Method predicts the member strength based on the member's elastic buckling loads. Finite strip analysis is one of the most efficient and popular method to determine the elastic buckling loads. It is developed by Cheung and explains the basic theory of finite strip method in structural analysis. The application of finite strip method to buckling was illustrated by Plank and Wittrick. Hancock and Schafer provide specific details for stability analysis with this method.
The Finite strip analysis is a specialized variant of the finite element method. The member section is subdivided into longitudinal strips. The displacement functions used to describe the variation in the longitudinal direction while polynomial functions are used to describe the variation in the transverse direction.Figure 3. 1 Strip Analysis of I-Beam
The finite strip buckling analysis can be showed in matrix format by
where K and G are the stiffness and stability matrices of the folded plate system and is the load factor against buckling under the initially assumed applied stress used to assemble the matrix G
3.3 The limitations of the DSM
If the section contains a slender elements, the local buckling load would be tends to become zero. The member strength calculated based on DSM would be overly conservative in this case. Since the DSM based on finite strip analysis for determining elastic buckling but finite strip method does have limitations, the model assumes the ends of the member are simply supported, and the cross-section may not vary along its length.
Strength-based minimum weight has always been an important factor in the
design and processing of aluminim structures. Because a high cost of aluminium sections is raw material, the amount of aluminium in the section must be minimized for it to become a viable alternative to steel. As a result, the most successful companies in the industry are those who have developed their section to have high design capacity whilst keeping the same aluminium content. This study will explore numerical ways in which section design might be optimized to achieve enhanced axial design capacity of aluminium closed formed section without increasing the material content.
To investigate the buckling strength of different aluminium sections under compression load, a program THIN-WALL with capability to perform a buckling analysis of member under longitudinal stress using the finite strip method is implemented. The buckling modes calculated include local, distortional and flexural-torsional buckling and the program can display a graph which shows the maximum stress in the section at buckling versus buckle half-wavelength. Based on the result of buckling load, the axial capacity of the member can be obtained by the direct strength method.
4.2 Section Design and Geometry
A THIN-WALL program was conducted on high strength aluminum closed formed sections subjected to concentrated bearing load. Seventy different sections were created and it is assumed that using high strength aluminium alloy T6-6061, and the initial material properties were used in the analysis are shown in Table 4.1
Cross Area =1000mm2
The both side end condition of the element is pin-ended. The specimens having the nominal thickness 1mm and sectional area is 1000mm2.
In the design of innovative shape of columns are mainly bring out the idea from 10 numbers of common shape such as square, rectangle, trapezoid, triangle and parallelogram. For example, profile C13 is combining with the shape of C1 and C3 (see Figure 4.2)
4.3 Thin wall analysis on local, distortional and lateral-torsional model.
Prediction of local buckling modes in compression for members using finite strip analysis program THIN WALL are demonstrated in Figure 4.3
Figure 4. 3 Thin Wall Analysis of C14 in Compression.
The curve displays two distinct minima. The first minimum, corresponding to the shorter wavelength, is associated with the local buckling mode, while the second minimum, corresponding to intermediate wavelengths, is linked to distortional buckling. The asymptotic curve for the higher wavelengths corresponds to overall buckling.
Once the maximum buckling stress of local, distortional and overall mode was found, the design capacity of the member can be determined by Direct Strength Method which is included in the THIN WALL program. In the figure below, the axial force capacity at different mode is given, and the normal axial force capacity will be the least of 3 axial force capacities.
Figure 4. 4 Design capacity results of C14 Column
4.4 Analysis Result
In view of the thin wall analysis results of the buckling stress for section C1 to C103 in the table 4.2 to 4.4. It was revealed that the higher buckling stress on local, distortional and lateral distortional mode for the section C5. Since C5 section is circle shaped as a result of hoop stress are produced in the wall due to external pressure. So it will be have high compression resistance. Therefore, this analysis will be neglected the result of C5 and compare the analysis results with others.
In the thin wall analysis, the material properties and testing specimen areas are assumed to be the same. The buckling stress of different shape of sections so can be compared with each other. In the Figure 4.5 to 4.6, the row number is representing the maximum stress at different buckling mode and the colour label is the half wavelength. From the result, the testing shape of C100, C102 and C103 (Fig. 4.5) are the highest three of local buckling stress. The average buckling stress is about 65 MPa at 60 mm half wavelength.
Max. Stress at local buckling mode
Figure 4.6 Maximum local buckling stress C1~C103 (except C5)
All modes are not guaranteed to occur in all members ,so the distortional buckling mode at a half-wavelenght intermediate to local and overall buckling mode may not shown on the graph of maxminium stress versus buckle half-wavelength such as column C1. The graph in Fig. 4.7 shows only one distinct minimum points. The first minium occurs at a half-wavelenght of 230mm and represents local buckling of the section.
At lengths greater than 6000mm, the column buckles in a flexural-torsional mode as shown in Figure 4.8
In the distortional buckling mode, the sections C61, C79 and C103 with high maximum stress. Their buckling occur at half-wavelenght about 3000 for C61 & C79 and 1200 for C103. (see Fig. 4.9)s
The lateral distortional buckling mode occurs mostly at half-wavelength 6000mm and average buckling stress range in 75 to 125 MPa. The distributions of max stress in distortional and overall buckling mode are on average. From the Fig. 4.10, it shows C1, C10 & C93 have the higher buckling stress on this mode.
Based on the buckling analysis, the direct strength method used to determine the design capacity of the section. In the figure 4, the maximum design capacity of section is C100, it can take load of 76.5kN and minimum design capacity of section is C63, it can take load of 11.6kN.
Conclusions and Recommendations
An innovation aluminium closed form sections are presented, with assisted with AutoCad program to create 70 different profiles section It was carried out the numerical test by using "Thin Wall" finite strip analysis program. The overall tested sections are to maintain the same cross section area and material properties.
In accordance with elastic buckling analysis result, it can observe that the rectangle and square section are in favour of maximum stress on both local and overall buckling mode. The section C100 & C102 are original from the square shape section added with different intermediate stiffer. In refer to the analysis results of the innovative section in design capacity under compression, the average compression capacity is 29.5kN, the highest section capacity is C100 with 76.5kN which is 1.5 times above the average values. In order to achieve the Strength-based minimum weight aluminium secetion, the section optimized should be based on the square/rectangle profiles and additional intermediate stiffener will be strength the section to resist the local buckling and overall buckling.
Further study of the location and intermediate stiffener affecting the design capacity of member can be. Compare the open section against closed section with the same design properties. In this report, the thickness of aluminium section are the same, it is suggest to test the thinner thickness.