A Small Step to Reduce the Giant Cost of Columns

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1 A Small Step to Reduce the Giant Cost of Columns Raja Rizwan Hussain Abdullah Al Mamun 001

2 A Small Step to Reduce the Giant Cost of Columns Authors: Raja Rizwan Hussain and Abdullah Al Mamun Published by 731 Gull Ave, Foster City. CA 94404, USA Copyright 2014 OMICS Group This ebook is an Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. However, users who aim to disseminate and distribute copies of this book as a whole must not seek monetary compensation for such service (excluded OMICS Group representatives and agreed collaborations). After this work has been published by OMICS Group, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Notice: Statements and opinions expressed in the book are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Cover OMICS Group Design team First published February, 2014 A free online edition of this book is available at Additional hard copies can be obtained from

3 Preface The purpose of this book is to give a direction to choose an economical section of column considering the available market price of reinforcement and concrete. Here we will also have a direction to choice the strength of concrete for an economical section. Finally we will give a direction to choice an economical section between a circular and rectangular section. Design of a column for a particular biaxial moment and axial load may vary from engineer to engineer due to neglecting optimizing criteria. While we design a section of a column the common practice to design a column is to choose an arbitrary section and check that for bending and axial load with a reinforcement about 1 to 8 % but whether is it economical or not we don t know. However for a particular moment and load only for a certain percentage of reinforcement the section is optimized. But this is not for a fixed percentage of reinforcement. As the of concrete and reinforcement may increase or decrease independently. So economic section is not fixed for 1-8% reinforcement only. This is dependent on a factor and here we termed it as price ratio. X=price of 1 cft reinforcement (490lb)/ price of 1 cft concrete. X= [price of rod (ton)/price of concrete (cft)] x223x10-3 Here we can find an optimized column section using this price ratio considering the available price of reinforcement and concrete. In designing a column its common practice to design a column with a concrete having a strength of 3000 psi-4000 psi. But now a days concrete with higher strength is very available throughout the world. Using 5000 psi concrete instead of 3000 psi concrete reduces percent of the total of a column section. Here it is also seen that using 5000 psi concrete instead of 4000 psi concrete reduces percent of the total of a column section. So if proper high strength of concrete can be attained in field condition it can be used to minimize the total of column. Considering the availability of higher strength concrete in Bangladesh, we used concrete up to 5500 psi only.

4 Again in designing a building we often provide circular column. Generally we provide a circular section as per architectural design, we don t think of the. We must have knowledge between the of a circular column and rectangular column. Here we analyzed the of various circular column and square column having same axial load and moment resisting capacity. The required for a circular column is percent more than a square column having same axial load and moment resisting capacity. Finally I hope this book will help the structural engineer to design a column section considering various economical factors. We should remember that these directions in this book are not design parameter. It is just a direction and that is not to choose a column section blindly. Again this direction can be omitted for some practical purpose like reduction in column section for parking, free space or some other practical purposes. But we should remember that the increase in the of the column section is proportional to the deviation from the above direction. Thank you, Abdullah al Mamun

5 About Authors Dr. Raja Rizwan Hussain is an assosiate Professor, CoE-CRT, Civil Engineering Department, College of Engineering, King Saud University, Riyadh, Saudi Arabia. He received his Ph.D. and M.Sc. in Civil Engineering from the University of Tokyo, Japan, for which he was ranked as outstanding and was awarded the best research thesis, prize and medal from the University of Tokyo. He has authored more than 150 publications and has received several awards, prizes and distinctions throughout his research and academic career. His research interest is in the steel reinforced concrete technology, materials & structures.

6 Abdullah al Mamun was graduated from Bangladesh University of Engineering and Technology (BUET) in civil engineering in the year 2012 and pursuing his masters from the same BUET. He is working as Lecturer in Department of Civil Engineering, Uttara University, Bangladesh. His area of research is in concrete structures.

7 Acknowledgement I am thankful to Dr. Raja Rizwan Hussain for his wise supervision in this research and publishing this book. Abdullah al Mamun

8 Introduction Concrete is the mostly used construction material of our modern society. It has a long history and development of concrete is a step by step process. It was first used by Romans. It was also used during Egyptian times. Then it was suddenly lost for 13 centuries. Then in 1756, the British engineer John Seaton invented concrete again. We cannot think our infrastructure development without concrete. It is widely used and popular due to its durability, strength, flexibility and other many advantages. Now a day s concrete is the widely used building material all over the world. However a concrete structure is composed of beam, footing slab and column. This book is just a small step to find the most economical column section. Though these directions are very simple and do not give any direction to choice the length and width of column section, but deviation from the suggestion of this book may cause a significant increase in total of construction. So the findings of this book are just One small step to reduce the giant of column. As price of concrete and reinforcement is not fixed so design of section of column should not be fixed for a certain percentage of reinforcement. So we should find an optimized percentage of reinforcement considering existing price of concrete and reinforcement. At the same time we will compare the of column for various strength of concrete (f c ). As we know with the increasing of concrete strength the required percentage of reinforcement decreases. Here we will try to find the decrease in amount reinforcement or the of reinforcement due to increase in the strength of concrete or in concrete. Then we will analyze the increase or decrease in total. Finally we will compare the required of circular column with rectangular column for similar loading condition to select an economical section.

9 Main objectives of our research are: To find an optimized percentage of reinforcement considering existing price of concrete and reinforcement. To compare the of column for various strength of concrete ( f c ). To compare the required of circular column with rectangular column for similar loading condition. I hope this book will help the structural engineer to design a column section considering various economical factors. We should remember that these directions in this book are not design parameter i.e. it does not give any direction to choice length and width of column section. It is just a direction and that is not to choose a column section blindly.

10 Table of Contents Contents Page # Abstract 12 Chapter 1: Introduction 1.1 General Background and Objective Scope and Methodology To Find a Optimized Percentage of Reinforcement Considering Existing Price of 14 Concrete and Reinforcement To Compare the Cost of Column for Various Strength of Concrete ( Fc') To Compare the Required Cost of Circular Column with Rectangular Column for 14 Similar Loading Condition Chapter 2: Literature Review 2.1 Introduction Component of Column Reinforcement Concrete A Ready Mix Concrete (Rmc) General Design Methods of Reinforced Concrete Structure a Change of Design Methods According to Aci 318 Code (Pca, 1999) b The Working Stress Design (Wsd) c Ultimate Strength Design (Usd) d Condition Factored Load or Load Effect Column Design Behavior Under Combined Bending and Axial Loads Interaction Diagram between Axial Load and Moment Axial Load and Moment Interaction Diagram General Non-Dimensional Interaction Diagrams Design Using Non-Dimensional Interaction Diagrams Design of a Column Using Software Design of a Column Using Pca Col Design of a Column Using Etabs Selection of Percentage of Reinforcement Considering Existing Price Comparison of the Cost of Column for Various Strength of Concrete (Fc') Comparison of the Cost of Circular Column with Rectangular Column for Similar 20 Loading Condition 2.10 Summary 20 Chapter 3: An Optimized Percentage of Reinforcement Considering Existing Cost 3.1 General Analysis of Cost Selection of a Structure a Selection of a 6 Story Structure b Selection of a 20 Story Structure Result and Discussion Summary 24 Chapter 4: Comparison of the Cost of Column for Various Strengths of Concrete (Fc') 4.1 General Analysis of Cost Selection of a Structure a Selection of a 10 Story Structure b Selection of a 6 Story Structure 28

11 4.3c Selection of a 10 Story Structure Result and Discussion Summary 32 Chapter 5: Comparison of the Cost of Circular Column with Rectangular Column for Similar Loading Condition 5.1 General Design Method Selection of Column Analysis of Cost Analyzing the Cost Changing the Concrete Area Analyzing the Cost Changing the Reinforcement Result and Discussion Summary 35 Chapter 6: Conclusions 6.1 General Findings from the Analysis One Percent is Optimized Percentage of Reinforcement Using 5000 psi or More Compressive Strength (Fc') of Concrete Reduces the 35 Cost of Column Square Column is More Economical than Circular Column Scope of Future Study 36 References 36

12 A Small Step to Reduce the Giant Cost of Columns Abstract According to the ACI code , the past research claims that the ratio of longitudinal steel area (A st ) to gross concrete cross section (A g ) is in the range from 0.01 to The lower limit is necessary to reduce the effects of creep and shrinkage of concrete under sustained compression. Ratios higher than 0.08 not only are uneconomical but also would cause difficulty owing to congestion of the reinforcement while we design a section of a column the common practice to design a column is to choose an arbitrary section and check that for bending and axial load with a reinforcement about 2 to 5 % but whether is it economical or not we don t know. Design of a column for a particular biaxial moment and axial load may vary from engineer to engineer due to neglecting optimizing criteria. However, for a particular moment and load there is only one section which is economical, it means only for a certain percentage of reinforcement the section is optimized. But this is not for a fixed percentage of reinforcement. Because the section has its component i.e. concrete and reinforcement and the of these material are different which may increase or decrease independently. For example, let at 2012 the of one cft reinforcement (490 lb) is 50 times of one cft concrete (ready mix). For this criteria, a particular section of column is optimized at 1% reinforcement. Let at 1980 the of one cft reinforcement was 20 times of one cft concrete. For that criteria, is the particular section of column was optimized at 1% reinforcement.? Of course not. Using % or more reinforcement was economical on that time. In the similar way it may be more than 50 times like 100 or more at As the value changes independently so economic section is not fixed for a certain percentage of reinforcement only. However for a particular moment and load only, for a certain percentage of reinforcement, the section is optimized. But this is not for a fixed percentage of reinforcement. As the of concrete and reinforcement may increase or decrease independently so economic section is not fixed for 2-5% reinforcement only. This is dependent on a factor called price ratio X. X=price of 1 cft reinforcement (490lb)/price of 1 cft concrete. Raja Rizwan Hussain 1 * and Abdullah Al Mamun 2 1 Department of Civil Engineering, College of Engineering, King Saud University, Riyadh, Saudi Arabia 2 Department of Civil Engineering, Bangladesh University of Engineering and Technology, Bangladesh *Corresponding author: Raja Rizwan Hussain, Department of Civil Engineering, College of Engineering, King Saud University, Riyadh, Saudi Arabia, Tel: ; Fax: ; raja386@hotmail.com X= [price of rod (ton)/price of concrete (cft)] x223x10-3 Analyzing the present of reinforcement and concrete, it is seen that a column section is optimized at 1-1.2% of reinforcement. This is true for every column that after a certain price ratio (generally 25) the column section is optimized at 1% of reinforcement on that loading and moment condition. For present price ratio it is seen that with same axial load capacity a column of larger section with a reinforcement around 1-1.2% is more economical than a column of smaller section with a reinforcement of 2-5. To optimize the section we should select a column with 1-1.2% reinforcement, when the price ratio is greater than 25. In many cases it is seen that using 2-3% reinforcement s about 1.5 to 2 times of 1% reinforcement. In designing a column its common practice to design a column with a concrete having a strength of 3000 psi psi. But now a day s concrete with higher strength is very available throughout the world. Using 5000 psi concrete instead of 3000 psi concrete reduces percent of the total of a column section. Here it is also seen that using 5000 psi concrete instead of 4000 psi concrete reduces percent of the total of a column sections if proper high strength of concrete can be attained in field condition, it can be used to minimize the total of column. Considering the availability of higher strength concrete in Bangladesh, we used concrete up to 5500 psi only. Again in designing a building we often provide circular column. Generally we provide a circular section as per architectural design. We don t think of the. We must have knowledge between the of a circular column and rectangular column. Here we analyzed the of various circular column and square column having same axial load and moment resisting capacity. The required for a circular column is percent more than a square column having same axial load and moment resisting capacity. Introduction General Concrete is the mostly used construction material of our modern society. We cannot think our infrastructure development without concrete. It is widely used and popular due to its durability, strength, flexibility and other many advantages. It has a long history and development of concrete is a step by step process. It was first used by Romans. It was also used during Egyptian times. Then it was suddenly lost for 13 centuries. Then in 1756, the British engineer John Smeaton invented concrete again. Now a day s concrete is the widely used building material all over the world. It can be truly said that many of the achievements of our modern civilization have depended on concrete, just as many of the enduring achievements of the earlier civilization of Rome were made possible by the use of the forerunner of modern concrete. However a concrete structure is composed of beam, footing slab and column. Column or compression member is for brevity and in conformity with general usage. 0012

13 Three types of reinforced concrete compression members are in use: 1. Members reinforced with longitudinal bars and lateral ties. 2. Members reinforced with longitudinal bars and continuous spirals. 3. Composite compression members reinforced longitudinally with structural Steel shapes, pipe, or tubing, with or without additional longitudinal bars, and various types of lateral reinforcement. The main reinforcement in columns is longitudinal, parallel to the direction of the load and consists of bars arranged in a square, rectangular, or circular pattern. The ratio of longitudinal steel area Ast to gross concrete cross section Ag is in the range from 0.01 to 0.08 according to ACI Code The lower limit is necessary to ensure resistance to bending moments not accounted for in the analysis and to reduce the effects of creep and shrinkage of the concrete under sustained compression. Ratios higher than 0.08 not only are uneconomical but also would cause difficulty owing to congestion of the reinforcement particularly where steel must be spliced. Generally, the larger diameter bars are used to reduce placement s and to avoid unnecessary congestion According to ACI Code , a minimum of four longitudinal bars is required when the bars are enclosed by spaced rectangular or circular ties and a minimum of six bars must be used when the longitudinal bars are enclosed by a continuous spiral. Columns may be divided into two broad categories: short columns, for which the strength is governed by the strength of the materials and the geometry of the cross section and slender columns, for which the strength may be significantly reduced by lateral deflections. A number of years ago, an ACI -ASCE survey indicated that 90 percent of columns braced against side sway and 40 percent of unbraced columns could be designed as short columns. The behavior of short, axially loaded compression members, for lower loads for which both materials remain in their elastic range of response, the steel carries a relatively small portion of the total load. The nominal ultimate strength of an axially loaded column can be found recognizing the nonlinear response of both materials by summing the strength contributions of the two components of the column. P n =0.85 f c A c +A st f y Or P n =0.85 f c (A g A st )+A st f y At this stage, the steel carries a significantly larger fraction of the load than was the case at lower total load. According to ACI Code , the useful design strength of an axially loaded column is to be found based on above equation with the introduction of certain strength reduction factors. The ACI factors reflect differences in the behavior of tied columns and spirally reinforced columns that will be discussed in Sec 2. A basic φ factor of 0.75 is used for spirally reinforced columns and 0.70 for tied columns according to ACI Code for spirally reinforced columns. φp n (max)=0.85 φ [0.85 f c (A g A st ) f y A st ] with φ=0.75. For tied columns φp n (max)=0.85 φ [0.85 f c (A g A st ) f y A st ] with φ=0.70 The nominal ultimate strength of an axially loaded column can be found, when the column is in by-axial bending we use Load Contour Method or Reciprocal Load Method to design a section of a column. Background and objective The ratio of longitudinal steel area (A st ) to gross concrete cross section (A g ) is in the range from 0.01 to 0.08, according to ACI Code The lower limit is necessary to reduce the effects of creep and shrinkage of the concrete under sustained compression. Ratios higher than 0.08 are not only uneconomical but also would cause difficulty owing to congestion of the reinforcement. While we design a section of a column, the common practice to design a column is to choose an arbitrary section and check that for bending and axial load with reinforcement about 2-.5 % but whether it is economical or not we don t know. Design of a column for a particular biaxial moment and axial load may vary from engineer to engineer due to neglecting optimizing criteria. However for a particular moment and load, there is only one section which is economical; it means only for a certain percentage of reinforcement the section is optimized. But this is not for a fixed percentage of reinforcement because the section has its component i.e. concrete and reinforcement and the of these materials are different which may increase or decrease independently. For example let now at 2012 the of one cft reinforcement (490 lb) is 50 times of one cft concrete (Ready Mix). For this criterion a particular section of column is optimized at 1% reinforcement. Let at 1980 the of one cft reinforcement was 20 times of one cft concrete. For that criterion, is the particular section of column was optimized at 1% reinforcement? Ofcourse not. Using % or more reinforcement was economical on that time. In the similar way it may be more than 50 times like 100 or more at As the value changes independently, economic section is not fixed for a certain percentage of reinforcement only. However for a particular moment and load only for a certain percentage of reinforcement the section is optimized. But this is not for a fixed percentage of reinforcement. As the of concrete and reinforcement may increase or decrease independently, the economic section is not fixed for 2-5% reinforcement only. This is dependent on a factor called price ratio X. X=Price of 1 cft reinforcement (490lb)/ Price of 1 cft concrete. Or, X= [price of rod (ton)/price of concrete (cft)] x223x10-3 At the same time we will design a section of column for various strength of concrete and we will compare the section for strength of concrete (f c ). We will compare the required of circular column with rectangular column for same loading condition. Main objectives of our research are: 1. To find an optimized percentage of reinforcement considering existing price of concrete and reinforcement. 0013

14 2. To compare the of column for various strength of concrete (f c ). 3. To compare the required of circular column with rectangular column for similar loading condition. Scope and methodology To find an optimized percentage of reinforcement considering existing price of concrete and reinforcement: We know that the coming axial load and moment to the column is resisted by concrete and reinforcement simultaneously. For a specific loading condition if we increase the gross section of column, then the required percentage of reinforcement will decrease. This will decrease until a certain section and after it the required amount of reinforcement will increase. Here we design a column for various sections and percentage of reinforcement for a specific loading condition. We analyze the column for various price ratios and found the optimized percentage of reinforcement for different price ratio. To design the column here we use ETABS 9.7 and PCA COL and to select an optimized section we use Programming Language c ++ a) A building was chosen where the arrangement of column was not symmetrical. b) For a specific column, a section was chosen for which the required reinforcement was 8 % of gross area. c) The section was increased with the decreasing of reinforcement gradually form 7.5.7, 6.5 to 1.0 percent. Here we increased the section until required amount of reinforcement decreased. d) Then analysis of different section with 1-8% of reinforcement for a specific price ratio was done and most economical section i.e., most economic percentage of reinforcement was found for that price ratio. e) Again the analysis for different price ratio (1 to 100) of that specific column was done and most economic percentage of reinforcement was found for the price ratio (1 to 100). This is done for various columns of a specific building where the axial load and bi-axial moment are different. g) The whole process is repeated for different types of building models. Here the data we obtained was observed graphically and a direction was found in selecting the designed percentage of reinforcement. To compare the of column for various strength of concrete (f C ): In designing a column it is common practice to design a column with a concrete having a strength of 3000 psi psi. But now-a-days, concrete with higher strength is very available throughout the world. South Wacker Drive, Chicago one of the tallest Building of the world is the example where high strength concrete (12000 psi) was used (courtesy of Portland cement association). Considering the availability of higher strength concrete in Bangladesh, we used concrete up to 5500 psi only. a) A building was chosen where the arrangement of column was not symmetrical. b) For a specific column a section was chosen for which the required strength of concrete is 2000 psi. c) The section was designed for different strengths of concrete (2000, 2500, 3000, 3500, 4000, 4500, 5000, and 5500) psi for a fixed gross area of concrete using ETABS. d) The required percentage of reinforcement decreases as the strength of concrete increases. e) Then analysis of the same section with different percentages of reinforcement for a specific price ratio was done and most economical section was found. To compare the required of circular column with rectangular column for similar loading condition: In designing a building we often provide circular column. We provide a circular section as per architectural design, we don t think of the. We must have knowledge between the of a circular column and rectangular column. However first of all we need to develop a relation between a circular column and a rectangular one. To develop a relation between a circular column and a rectangular column here we follow two approaches: 1. Comparing the axial load capacity and moment resisting capacity between a circular column and a rectangular column having an equal gross concrete area and reinforcement. 2. Design a circular column and rectangular column for a specific load and moment and compare the required. Literature Review Introduction Short columns, for which the strength is governed by the strength of the materials and the geometry of the cross section, and slender columns, for which the strength may be significantly reduced by lateral deflections. A number of years ago, an ACI -ASCE survey indicated that 90 percent of columns braced against side sway and 40 percent of unbraced columns could be designed as short columns. The behavior of short, axially loaded compression members, for lower loads for which both materials remain in their elastic range of response, the steel carries a relatively small portion of the total load. The nominal ultimate strength of an axially loaded column can be found. When the column is in by-axial bending, we use Load Contour Method or Reciprocal Load Method to design a section of a column. Component of column Reinforcement: Reinforcing is an essential component in reinforced concrete. Concrete has a high compression but very low tensile stress. Due to this fact reinforcing or rebar is necessary to provide added tensile strength. To achieve adequate tying yet hold the number of ties to a minimum, ACI Code gives the following rules for tie arrangement: All bars of tied columns shall be enclosed by lateral ties, at least No.3 in size for longitudinal bars up to No.10, and at least No. 4 in size for Nos.11, 14, and 18 and bundled longitudinal bars. The spacing of the ties shall not exceed 16 diameters of longitudinal bars, 48 diameters of tie bars, or the least dimension of the column. The ties shall be so arranged that every corner and alternate longitudinal bar shall have lateral support provided by the corner of a tie 0014

15 having an included angle of not more than 135, and no bar shall be farther than 6 inch clear on either side from such a laterally supported bar. Deformed wire or welded wire fabric of equivalent area may be used instead of ties. Where the bars are located around the periphery of a circle, complete circular ties may be used. For spirally reinforced columns ACI Code requirements for lateral reinforcement may be summarized follows: Spirals shall consist of a continuous bar or wire not less than 83 inch in diameter and the clear spacing between turns of the spiral must not exceed 3 inch nor be less than 1 inch. Concrete: There are two types of concrete: Concrete made at the site Ready Mix concrete For different company price of one cft concrete is almost same for ready mix where price of concrete made at site may vary largely from site to site. Here we will analyze only on ready mix for simplification. Ready Mix Concrete (RMC): A modern version of conventional concrete is getting a huge response from builders mainly due to its scientific maintenance of standard and quick delivery. It also does not need an extra space to be made on a construction site as it can be got readymade from an RMC manufacturing company. RMC is the construction paste blended in a factory or batching plant in a controlled environment where proportionate use of RMC raw materials such as sand, cement and crushed stone is ensured through a computerized system. The process allows producing quality RMC quickly and according to a set recipe. The company now supplies RMC to at least 50 real estate companies through its 24 dedicated vehicles. After preparing RMC the company s special vehicles can preserve the mixture from 2-6 hours and carry it to distant places. Each such vehicle generally carries 221 cft of paste and is allowed to run in daytime on city thoroughfares. Sector people said the demand for RMC is more in the large and high-rise building projects where producing concrete manually or through mixture machines take a huge time. People who want to finish their projects quickly also use the product. By using RMC it is possible to increase work speed manifold as an RMC plant can produce around 30,000 cft of concrete a day, while a traditional mixture machine can hardly produce 1,000 cft of paste. Describing another positive side of the paste, Islam said it took around 9 days for RMC-made floor to get its full strength if a certain chemical is used in preparing RMC, while it requires around 28 days for a newly constructed building made with conventional concrete mixture. General Design methods of reinforced concrete structure: Two major calculating methods of reinforced concrete have been used formerly 1900 s to current. The first method is called Working Stress Design (WSD) and the second is called Ultimate Strength Design (USD). Working Stress Design was used as the principal method from early 1900 s until the early 1960 s. Since Ultimate Strength Design method was officially recognized and permitted from ACI318-56, the main design method of ACI 318 Code has gradually changed from WSD to USD method. The program of this book is based on ACI Code USD Method, published in Design Methods of Reinforced Concrete Structure: Change of Design Methods according to ACI 318 Code (PCA, 1999). The Working Stress Design (WSD) The Ultimate Strength Design (USD) Condition Factored load or load effect U The strength reduction factors Change of design methods according to ACI 318 code (PCA, 1999) ACI : USD was first introduced (1956) ACI : WSD and USD were treated on equal basis ACI : Based entirely on strength Method (USD) WSD was called Alternate Design Method (ADM) ACI : ADM relegated to Appendix B ACI : ADM back to Appendix A ACI : ADM still in Appendix A Unified Design Provision was introduced in Appendix B was deleted from Appendix A (ACI,2002) ACI : ADM The Working Stress Design (WSD): Traditionally, elastic behavior was used as a basis for the design method of reinforced concrete structures. This method is known as Working Stress Design (WSD) and also called the Alternate Design Method or the Elastic Design Method. This design concept is based on the elastic theory that assumes a straight-line stress distribution along the depth of the concrete section. To analyze and design reinforced concrete members, the actual load under working conditions, also called service load condition, is used and allowable stresses are decided depending on the safety factor. For example allowable compressive bending stress is calculated as if the actual stresses do not exceed the 0.45f allowable stresses, the structures are considered to be adequate for strength. The WSD method is easier to explain and use than other method but this method is being replaced by the Ultimate Strength Design method. ACI 318 Code treats the WSD method just in a small part. Ultimate Strength Design (USD): The Ultimate Strength Design method, also called Strength Design Method (SDM), is based on the ultimate strength when the design member would fail. The USD method provides safety not by allowable stresses as for the ASD method but by factored loads, nominal strength and strength reduction factors, both defined by the ACI code. The load factors are 1.7 for live load and 1.4 for dead load. Other factors are given below Condition factored load or load effect U 0015

16 Basic U=1.4D+1.7L U=0.75(1.4D+1.7L+1.7W) Winds U=0.9D+1.3W U=1.4D+1.7L U=0.75(1.4D+1.7L+1.87E) Earthquake U=0.9D+1.43E U=1.4D+1.7L U=1.4D+1.7L+1.7H Earth pressure U=0.9D+1.7H U=1.4D+1.7L Settlement, creep, shrinkage, or U=0.75(1.4D+1.4T+1.7L) Temperature change effects U=1.4(D+T) Factored load combinations for determining required strength U However, deflections are based on service load rather than factored load. The strength reduction factors are given below: Different factors are used for beams, tied column, or spiral column. Flexure, without axial load 0.90 Axial tension Axial compression with flexure 0.90 Axial compression Axial compression with flexure member 0.70 Axial compression Axial compression with flexure member with spiral reinforcement 0.75 Shear and torsion 0.85 Bearing on concrete 0.70 Strength reduction factors in the ACI Code (Nilson, 1997) Column design Behavior under combined bending and axial loads: In designing a column, we select a section with reinforcement 1-8 percent to resist the axial load and biaxial-moment. Usually moment is represented by axial load time s eccentricity in (Figure 2.4.1), i.e. Figure 2.4.1: Eccentric loading on column. Interaction diagram between axial load and moment in (Figure 2.4.2). 0016

17 Figure 2.4.2: Behavior under combined bending and axial loads. Axial load and moment interaction diagram-general in [Figure (a), (b)]: (a) (b) Figure 2.4.3: Any combination of P and M outside the envelope will cause failure. Figure 2.4.3: Any combination of P and M outside the envelope will cause failure. Resultant Forces action at Centroid P = C + C T n s1 c s2 compression is positive 0017

18 Moment about geometric center h h h a M = Cs1 * d1 + Cc * + Ts2 * d 2 n Non-dimensional interaction diagrams (Figure 2.4.4): Figure 2.4.4: Non-dimensional interaction diagrams. Design using non-dimensional interaction diagrams a. Calculate factored loads (Pu, Mu) and e for relevant load combinations b. Select potentially governing case(s) c. Use estimate h to calculate gh, e/h for governing case(s) d.use appropriate chart (App. A) target rg ϕ Pn Ag Ag = Pu ϕ Pn Ag Select b & h Ag = b*h e. If dimensions are significantly different from estimated (step 3), recalculate (e / h) and redo steps 4 & 5. Revise Ag if necessary f. Select steel, Ast=ρ Ag g. Using actual dimensions & bar sizes to check all load combinations (use charts or exact: interaction diagram) h. Design lateral reinforcement Design of a column using software Design of a column using PCA COL: There are various codes to design a column by PCA COL softwares like ACI ; CAN 3-A23; CAN3-M84; ACI Design of a column using ETABS: There are various codes to design a column by ETABS softwares like ACI /IBC2003; ACI ; CAN 3-A23; CAN3-M84; UBC-97:ACI ; Indian IS etc. In designing column section by above method the ratio of longitudinal steel area Ast to gross concrete cross section Ag is in the range from 0.01 to 0.08, if we follow ACI Code We will discuss only on design of column by ACI Code as it is similar to BNBC Here it is seen that the design of column section is confined with reinforcement about 1-.8 % but whether is it economical or not we don t know. Design of a column for a particular biaxial moment and axial load may vary from engineer to engineer. For example a column may be designed with a reinforcement of 5 percent with a section X. It may also be designed with reinforcement 2% with a section Y. Here Y is larger than X. But we don t know which one is economical. Section X may be economical for a price of steel and concrete where section Y may be economical for a different price of steel and concrete. Because the section has its component i.e., concrete and reinforcement and the of these material are different which may increase or decrease independently. However for a particular Selection of percentage of reinforcement considering existing price 0018

19 moment and load, there is only one section which is economical. It means only for a certain percentage of reinforcement, the section is optimized. We may see the research paper where they obtained graph is as below in (Figure 2.7.1). Figure 2.7.1: Optimization process of RC beam [9]. This is also true for a column section of a building that for a particular moment and load there is only one section which is economical, it means only for a certain percentage of reinforcement the section is optimized. Here we can see the change in price of steel for last 20 years in (Figure and 2.7.3): Figure 2.7.2: Decrease in steel price. Source: The U.S. Steel Industry Where We Have Been and Where We Are Going - Keith Busse (President and CEO, Steel Dynamics, Inc. National Association of Pipe Distributors) Las Vegas, February 26, Figure 2.7.3: Increase in steel price. Source: The U.S. Steel Industry Where We Have Been and Where We Are Going -Keith Busse (President and CEO, Steel Dynamics, Inc. National Association of Pipe Distributors) Las Vegas, February 26, From above figure, it is very clear that the price of steel fluctuate vary randomly. In 2012 the price of 60 grade steel is BDT per ton. Again the price of concrete changes but not like steel. Price of concrete for different strengths is below (Table 2.7): Terms and Conditions: The rate below are excluding VAT & IT 0019

20 Strength (Psi) at 28 days Performance Materials Combination Price (BDT) per cft of RMC Including pump 2000 PSI Normal Strength 100% crushed stone PSI Normal Strength 100% crushed stone PSI Normal Strength 100% crushed stone PSI Normal Strength 100% crushed stone PSI Normal Strength 100% crushed stone PSI Normal Strength 100% crushed stone PSI Normal Strength 100% crushed stone PSI Normal Strength 100% crushed stone Table 2.7: Price of concrete for different strengths. Source: Various Construction Firm, Bangladesh, August Average Price (BDT) per cft of RMC Including pump From the above analysis it is clear that the price of concrete and steel changes. So the selection of percentage of reinforcement in designing a column should not be done abruptly neglecting the price of steel and concrete. As the of concrete and reinforcement may increase or decrease independently, the economic section is not fixed for 2-5% reinforcement only. This is dependent on a factor called price ratio X. X=Price of 1 cft reinforcement (490lb)/Price of 1 cft concrete. Or X=[price of rod (ton)/price of concrete (cft)]x223x10-3 Comparison of the of column for various strengths of concrete (f c ) In designing a column, it is common practice to design a column with a concrete having a strength of 3000 psi psi and But now a day s concrete with higher strength is very available throughout the world. South Wacker Drive, Chicago one of the tallest Building of the world is the example where high strength concrete (12000psi) was used (courtesy of Portland cement association). Considering the availability of higher strength concrete in Bangladesh, we used concrete up to 5500 psi only. Comparison of the of circular column with rectangular column for similar loading condition In designing a building, we often provide circular column. We provide a circular section as per architectural design, we don t think of the. We must have knowledge between the of a circular column and rectangular column. However first of all we need to develop a relation between a circular column and a rectangular one to compare them. Summary As price of concrete and reinforcement is not fixed, so design of section of column should not be fixed for a certain percentage of reinforcement. So we should find an optimized percentage of reinforcement considering existing price of concrete and reinforcement. At the same time we will compare the of column for various strengths of concrete (f c ). As we know with the increasing concrete strength the required percentage of reinforcement decreases. Here we will try to find the decrease in amount reinforcement or the of reinforcement due to increase in the strength of concrete or in concrete. Then we will analyze the increase or decrease in total. Finally we will compare the required of circular column with rectangular column for similar loading condition to select an economical section. An Optimized Percentage of Reinforcement Considering Existing Cost General We know that the coming axial load and moment to the column is resisted by concrete and reinforcement simultaneously. For a specific loading condition, if we increase the gross section of column then the required percentage of reinforcement will decrease. This will decrease until a certain section and after it the required amount of reinforcement will increase. Here we design a column for various sections and percentage of reinforcement for a specific loading condition. We analyze the column for various price ratios and found the optimized percentage of reinforcement for different price ratio. To design the column, here we use ETABS 9.7 and PCA COL and to select an optimized section, we use Programming Language c ++. Analysis of Here we analyzed the required for a 10 ft column (Ground floor) for different price ratio. Here for simplification we only use 60 grade reinforcement and 4000 psi concrete. Cost of 60 grade reinforcement= BDT /ton; Cost of 4000 psi concrete (RMC)=210 BDT/cft Selection of a structure Different building was chosen where the arrangement of column was not symmetrical. As the arrangement was not symmetrical so the coming moment and axial load on column was different.here selections of column was done for reinforcement 1 to 8 percent of gross area. Here wind load, dead load, live load and earthquake load was chosen as per BNBC Selection of a 6 story structure: A 6 story building like below was chosen, it is shown in [Figures (a) and (b) and Tables (a) and (b)]. 0020

21 Figure (a): 3-D view of structure. Figure (b): Plan view of structure. L (in) B (in) Acon (in2) Ast(in2) Percentage of steel x=1 x=5 x=10 x=15 x=20 x=25 x=30 x= (BDT) for x= Table (a): For column F-2, F-3, A-2, A

22 Figure (b): Graphical analysis of for various price ratios. Selection of a 20 story structure: Shown in [Figures (a), (b), (c) and (d) and Tables (a) and (b)]. Figure (a): 3-D view of structure. L (in) B (in) Acon (in2) Ast(in2) Percentage of steel x=1 x=5 x=10 x=15 x=20 x=25 x=30 x=50 x= Table (a): For column A

23 Figure (b): Plan view of structure. Figure (b): Graphical analysis of for various price ratios. L (in) B (in) Acon (in2) Ast(in2) Percentage of steel x=1 x=5 x=10 x=15 x=20 x=25 x=30 x=50 x= Table (b): For column 1-B. Figure (c): Graphical analysis of for various price ratios. 0023

24 Result and discussion Data tables and graphs of analysis are shown below. For current price of reinforcement (60000 BDT/ton) and concrete (210 BDT/cft) price ratio is 64. It is seen at [Table 3.1 (a)] that using 1 percent of reinforcement for a price ratio 64 the for 10 feet column section (Ground floor) is 9471 BDT. Using 2.47 percent of reinforcement for same price ratio it s BDT. The difference in 2569 BDT may seems very small. But this is only for a column section of 10 feet. When we will estimate it for 20 columns and 6 stories it will be no smaller. Here increase in the is percent. It can be said that using 2.47 percent of reinforcement instead of 1 percent of reinforcement increases the column percent. Again it is seen that using a section 22x18 instead of 20x16 i.e., percent increase in gross area reduces the percent. In [Table (b)] it is seen that using 2.76 percent of reinforcement instead of 1 percent causes percent increase in column. In [Table (b)] it is seen that using 2.98 percent of reinforcement instead of 1.01 percent causes percent increase in column. If we provide, it is seen that using 6.5 percent reinforcement s almost 2 times of the of using 1percent reinforcement at a price ratio 64. Using percent reinforcement s about 1.5 times of 1 percent reinforcement at a price ratio 64. In [Figure 3.4 (a)] we can see how the reinforcement percentage changes with the changes of. When the price ratio (price of 1cft reinforcement/price of 1 cft concrete) is one, then we can use 8 percent reinforcement or even more if we can avoid the difficulty owing to congestion of the reinforcement, particularly where the steel must be spliced. To avoid difficulty 8 percent reinforcement is chosen. But when the price ratio increases, then percent of reinforcement also changes and after a certain price ratio the economical percentage of reinforcement becomes 1 percent. For example we can see the graph and table below; for a price ratio 1-100, the percentage of reinforcement changes. It can be said that generally when X (price ratio) is 1-15 it is 6.5 percent reinforcement, at X=15-18 it is 3 to 6 percent, at X=18-20 it is 2 to 3 percent, at X=20-22 it is 1 to 2 percent and after X=22 it is only percent [Table 3.4 (a)]. This is true for every column that after a certain price ratio it is optimized only at percent reinforcement on that loading and moment condition. We can t avoid percent of reinforcement to make it more economical as the lower limit is necessary to ensure resistance to bending moment not accounted for the analysis and to reduce effects of creep and shrinkage of concrete under sustained compression. Without this concrete have only 1/10 tensile strength of its compressive strength and zero tensile strength after crack. Figure 3.4 (a): Price Ratio VS Percentage of Reinforcement Graph. X=[(price of rod (ton)/price of concrete (cft)]x223x10-3 Summary Price ratio X Optimized percentage of reinforcement 1 to 15 Greater than 6 15 to 18 3 to 6 18 to 20 2 to 3 20 to 22 1 to 2 Greater than 22 1 Table 3.4 (a): Optimized percentage of reinforcement for various price ratios X. Analyzing the present of reinforcement and concrete, it is seen that a column section is optimized at percent of reinforcement. This is true for every column, that after a certain price ratio (generally 22) the column section is optimized at 1percent of reinforcement on that loading and moment condition. For present price ratio 40-70, it is seen that with same axial load capacity a column of larger section with reinforcement around percent is more economical than a column of smaller section with a reinforcement of 2-5. To optimize the section we should select a column with percent reinforcement, when the price ratio is greater than 22. When the price ratio decreases, selection of percentage of reinforcement may increases up to 7 or 8 percent gradually as seen in Table 3.4 (a). However we should remember that this Table 3.4 (a) does not give any direction to design a column or to select width and length of column. It just gives us a direction to select a percentage of reinforcement considering existing price of reinforcement and concrete. Again this direction can be omitted for some practical purpose like reduction in column section for parking, free space or some other practical purposes. But we should remember that the increase in the of the column section is proportional to the deviation from the above direction. Comparison of the Cost of Column for Various Strength of Concrete (F C ) General Generally we design our structure by 3000 to 4000 psi concrete. Now a day s high strength is very available throughout the world. Even in Bangladesh high strength concrete is very common. We will analyze the required reinforcement for a column of fixed section for different strength of concrete. Then we will analyze its for different strength. Analysis of Here we will analyze the required for a 10 ft column for different price and strength of concrete Here for simplification we only use 60 grade reinforcement only. Cost of 60 grade reinforcement= BDT /ton; 0024

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