Computer Program to Design Concrete Columns - Literature review Example

Computer program to design concrete columns. Literature survey. This section seeks to present information from an overview of other works on related and similar topics that give the required background for the purpose of this study. The literature survey concentrates on several sources of data explaining the reasons for the modern scientific thought that has led to the current assumptions on reinforced concrete column design according to the Eurocode 2 (Beeby and Narayanan, 1995),. For the understanding of the reinforced concrete column design topics such as shear, creep, biaxial bending, axial and moment capacity, assumptions on slenderness and optimization, a review of literature is vital in coming up with a competent and efficient program to design reinforced concrete columns that will operate in the Matlab environment. At the moment, there is scarce information on the performance of reinforced concrete columns and how they operate in a Matlab environment however, there are similar studies and articles written on this topic and the available literature is reviewed in this section. The introduction of reinforced concrete revolutionized the field of structures in the end of the previous century. Reinforced concrete refers to concrete with rebars, reinforcement plates, fibers or grids that have been integrated to strengthen the concrete when there is tension. Concrete that has been reinforced with steel or iron is called Ferro Concrete however there are other materials used to reinforce concrete that can either be organic or inorganic fibres or composites in different types. Concrete columns have used new materials that have combined the effectiveness of steel in tension, together with the resistance of concrete in compression have evolve rapidly as the prevalent structural material. Its qualities are based on the very good mechanical co-operation of the steel reinforcement with the concrete, the relatively low cost, its strength in compression, its ability to be shaped in various ways and the high endurance to microorganisms and fire and it has the following properties: High tensile strain High strength Good bond to concrete Thermal compatibility Durable in a concrete environment. Reinforced concrete usually uses steel reinforced bars that are usually placed in to add strength. Reinforced concrete columns are used to enhance tensile strength which would otherwise cause many concrete buildings to be weak. These columns can also be used to encompass many kinds of components and structures including walls, beams, slabs, frames, foundations, columns and many more. Most of the focus of reinforcing concrete columns is usually placed on the wall and vertical systems. Designing and implementing the well-organized vertical systems in a building structure is important to creating optimal strong and safe structures. Few changes in the structural design of a vertical system can have important effects on material costs, ultimate strength, construction schedule, occupancy levels, operating costs and the ultimate use of the structure being built. On the subject of the reinforced concrete columns, the fundamental principle that governs the design of concrete columns is a structural engineering problem that is based on the comparison of a design moment and axial load that derive from a conservative standardized procedure with the axial and moment capacity of the selected cross-section. Even until nowadays, there is no straightforward procedure to assess a cross-section that will satisfy immediately all the design criteria and a successful estimation will also depend on empirical data. Bresler, B (1960) states that the design of concrete columns depends on its axial load capacity which in turn depends on the axial load capacity of its longitudinal reinforcement. Its design also depends on the axial capacity by the concrete column. Following studies by MacGregor (1998) and the Eurocode 2 standards (Beeby and Narayanan, 1995),, the maximum axial load capacity PN, of a reinforced concrete column is given by the following formulae: PN = 0.85fC’ (AG-ASL) + fYLASL Where 0.85fC’ (AG-ASL) stands for the axial capacity supported by the concrete column while the term, fYLASL symbolizes the axial capacity supported by the longitudinal reinforced concrete column. fC is the specific compressive strength of the concrete column by 28th day (ksi), fYL is the strength of the longitudinal reinforcement the concrete column will succumb to (ksi), AG is the total area of the cross-section of the column and ASL is the longitudinal reinforcement area. Under the standards given by the Eurocode 2 (Beeby and Narayanan, 1995), the concrete columns should be designed with a specific moment capacity whose equation is derived from the formulae given above: MN = TS3[(h/2)-dS3] – Cc [(h/2)] + TsI[dS1- (h/2)] Where Tsi refers to the internal tensile force offered by the lateral reinforcement i, h is the depth of the cross-section, Cc stands for the internal compressive force of the concrete column and dSi is the distance between extreme compression fibers. This equation proves that the moment capacity of the concrete column depends entirely on the cross-section of the concrete column. The moment capacity of the concrete column is reached if and only if there are no axial loads supported by the column (Tomaszewicz, 1995). Another factor that affects the design of concrete columns is the shear capacity of the columns that depends on the shear capacity of the concrete VC being used. The shear capacity supported by the reinforcement VST, in the concrete column also determines the design of the concrete columns. The Eurocode 2 follows the work by MacGregor (1998) giving the equation used to determine the maximum shear capacity, VN of a concrete column with regard to combined shear, axial compression and moment loading: VN = VC + VST = 2[1 + (P/[2000AG])]√fC’bWd + (ASTfYTd)/s Where P represents the axial load, bW stands for the width of the cross-section of the column, s is the transversal reinforcement spacing, and d is the distance between the extreme compression fibers to the maximum tensile reinforcement. AST is the transversal reinforcement area, FYT is the yield strength of the reinforcement. For a concrete column that is fixed at both ends has a design susceptible to shear deformation when the lateral load leads to shear stress at the end of the column resulting in displacement (Elwood. & Moehle, 2003). The design of concrete columns is also depended on the different assumptions available on the slenderness of the column. Some of these assumptions are: The slenderness of concrete columns will affect their lateral stability especially when there is no lateral bracing. Slender beams are made stable by laterally bracing them from adjacent members like the roof or floor elements. Slenderness also affects the balance supports of the concrete beams and this is corrected in the design by introducing a lateral deflection of 1/300 as an imperfection to be adopted in the computer software. The criteria for neglecting the second order effects of the slenderness of the columns s different in different conditions and is corrected as per the particular condition. Buckling is usually a major concern for the stability of concrete columns because it is a failure mode that is usually characterized by sudden failures of building structures when they are under elevated compressive stress. According to the Erocode 2 standards (Beeby and Narayanan, 1995), the word buckling is only reserved for the ‘“pure”, hypothetical buckling of an initially straight member or structure, without load eccentricities or transverse loading’ (Jean-Pierre Jacobs, ed, 2008). It is meaningful to note that pure buckling does not relevantly limit the state of real structures but this is due to the presence of eccentricities, transverse loads and eccentricities. Due to this reason, the word buckling has been left out in the title of 5.8 of the Eurocode 2 (Beeby and Narayanan, 1995). However, Euler’s contribution to the interpretation of the occurrence of buckling instability entails inevitably a concern of major importance in the structural design of reinforced concrete columns. The effective length of a concrete column depends on its end conditions would be a criterion for its classification as slender and non-slender (or short). This length is given as a function of the radius of the gyration of the cross-section of the column referred to as the slenderness ration of that particular column. This ratio helps to classify columns and a short concrete column is the one with a ratio of length with the least cross-sectional dimensions of more than 10. A short concrete column under the stress of an axial load will therefore fail by buckling. Leonhard Euler derived formulae in 1757 giving the maximum axial load that an ideal column that is long and slender can support without buckling. An ideal concrete column is perfectly homogeneous, straight and without any initial stress. The critical load is the maximum load that makes the column to be in a form of unstable equilibrium, therefore, any addition to the load will cause the column to fail by buckling. The formula that Euler derived is as follows: Where F stands for the vertical load exerted on the column, E represents the modulus of elasticity, I is the area moment of inertia of the concrete column, L symbolizes the unsupported column length and K represents the length factor of the column whose value is a function of the end support of the column in the following conditions: For both ends hinged, free to rotate, K = 1.0. For one end pined and the other fixed, K= 0.699….. For one free to laterally move and the other fixed, K = 2.0 For both ends fixed, K = 0.50 It is important to note that if lateral forces are considered, the value of the critical load of the column remains barely unchanged (Lindberg, and Florence, 1987). There is scarce information on structures bending around the axis, the very informative work by Bresler assists greatly in the interpretation of biaxial bending phenomenon. Biaxial bending in concrete column should be separated into different unaxial bending components following the conditions laid down in the Eurocode 2 5.8.9 (Beeby, and Narayanan, 1995). Pure biaxial, with the bending components lying on the centroids axis of inertia, the there will be computational difficulties. To ensure that the construction of reinforced concrete columns is up to the Eurocode standards then a Computer Aided Design (CAD) has to be used. CAD has really changed the way designs are done in engineering. More than ¼ a century ago, almost all designs produces in the world were done in ink or with pencil on a paper (Digital Equipment Corporation, 1992). Changes and corrections were done by erasing and redrawing the entire design from scratch. If a change in one design affected other designs then it was dependent on another person to manually identify the need and it meant making changes in other designs as well. However, CAD has greatly changed since then with the introductions of computer programmers to ease the work in the design of various building structures such as concrete columns (Steven, 2003). Early programming languages used in CAD were designed to carry out specific tasks with more precise purposes. Each language has its won characteristics, syntax and vocabulary. CAD for engineering after 1990 included Dassault Systems by IBM who developed CADAM and CATIA that developed the best features in CAD. They allowed the engineer to make operations concurrently like 3D designing, creation of engineering drawings and analysis of products. They helped speed up the construction process. Several other CAD engineering programs were developed like CAD designs for DOS in 1994 and the end of the 1990s saw the integration of different designs like Mechanical Desktop V.2 integrated with the AutoCAD V.14 that helped the integration of several structures in a building (Null & Lobur, 2006). The modern engineering programming languages used in CAD like MatLAb perform the analysis of several finite elements like the ones involved in the designing of concrete columns. The small elements like axial load, biaxial bending, and the maximum axial load allowed, the length, width of the concrete columns among other things (Hanselman, & Littlefield, 1997). MatLab is a very important programming language used in engineering and when it was discovered it brought tremendous developments in the designing of building structures like the concrete columns. It has assisted scientists and engineers to produce more productive and powerful building designs in the CAD environment beyond those achieved when such programs as C and FORTRAN are used. Matlab combines comprehensive graphic and mathematical functions with a high-level powerful language and can be used to develop a good design to be used come up with good concrete columns for modern buildings ((Hanselman, & Littlefield, 1997)). MatLab as a computer language written in a mathematical scripting code is very much similar to C++ and has the following advantages over other programs: It uses efficient vector and matrix computations Allows for string processing Allows for easy creation of engineering graphics It is object-oriented It has tool boxes that can be used for extensibility. Due to the many vector and matrix computations and manipulations of algorithms (Bunch, et al, 1979) applied in MatLab, the program can be successfully used to model, design and simulate complex systems of equations that will lead to the designing of reinforced concrete columns in the modern world. Reference: Beeby, A W and Narayanan, R S: Designers’ Handbook to Eurocode 2, Part 1.1. Thomas Telford, London, 1995. Bresler, B: Design Criteria for Reinforced Columns under Axial Load and Biaxial Bending. Bunch J. R., Dongarra, J. J., Moler, C. B., & Stewart G. W.  (1979).   LINPACK User's Guide.  Society for Industrial and Applied Mathematics. Digital Equipment Corporation. "Information Technology - Database Language SQL (Proposed revised text of DIS 9075)". ISO/IEC 9075:1992, Database Language SQL. http://www.contrib.andrew.cmu.edu/~shadow/sql/sql1992.txt. Retrieved June 29, 2006. Elwood, K.J. and Moehle, J.P. “Shake Table Tests and Analytical Studies on the Gravity Load Collapse of Reinforced Concrete Frames”, PEER Report Series, November 2003/01. ACI Journal, November 1960. Hanselman, Duane & Littlefield, Bruce. The student edition of MATLAB:  version 5, user's guide.  New Jersey:   Prentice-Hall, Inc. 1997 Jean-Pierre Jacobs, ed, June 2008, Commentary Eurocode 2, European Concrete Platform ASBL. Lindberg, H. E., and Florence, A. L., Dynamic Pulse Buckling, Martinus Nijhoff Publishers, 1987, pp. 11-56, 297-298. MacGregor, J. G. G. Reinforced Concrete: Mechanics and Design. Prentice Hall Null, L. and J. Lobur, 2006, The essentials of computer programme integration and architecture, Edition 2, Jones & Bartlett Publishers, , ISBN 0763737690, p. 435 Professional Technical Reference, 1996. Robert A. Edmunds, 1985, The Prentice-Hall standard glossary of early computer languages, Prentice-Hall, p. 91 Steven R. Fischer, 2003, A history of Computer Aided Design, Reaktion Books, ISBN 186189080X, p. 205 Tomaszewicz, A., (1995) High –Strength Concrete. SP2 – Plates and Shells. Report 2.3 “Punching Shear Capacity of Reinforced Concrete columns”, Report No. STF70 A93082, SINTEF Structures and Concrete, Trondheim, 36 pp. Read More