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ABSTRACT

A comprehensive study of the existing analysis and design techniques for the design of short columns o

arbitrary shape, subject to biaxial eccentric compression, was carried out during the initial phase of the projec

The study revealed that present design methods are largely confined to rectangular and circular columns, and t

some extent, other rectangular shapes such as the L, T, channel and plus sections. There is an evident need t

develop design aids for column sections of any arbitrary shape, subjected biaxial compression. In today

computer age, it is appropriate that the design aids should be in the form of software that is user friendly an

offers wide flexibility. This formed the objective and motivation for the project.

The analysis of arbitrary shaped columns formed the next phase of the project and programs we

developed to achieve this. The software provides for flexibility in the output format to suit the users preference

The entire interaction surface or the relevant load contour or the relevant theta plane containing th

coordinates of Pu, Mux, Muy can be generated. Various applications of the software have been demonstrated an

the programs validated.

Based on the methods studied, the exact version of the load contour method was found most suitable to b

extended to accommodate the design of column sections of any arbitrary shape. This formed the final phase of th

project and it involved the development of design programs. The main feature of the programs developed is that

allows the user to use his engineering judgment in deciding the pattern of reinforcement and hence the user nee

not comply with set patterns of reinforcement. This software developed could be used for any column section an

it makes no approximation.

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TABLE OF CONTENTS

CERTIFICATE

ACKNOWLEDGEMENT

ABSTRACT

LIST OF FIGURES

CHAPTER 1: INTRODUCTION

1.1 R .C. Columns: Loading and Geometry.01

1.2 Problem Definition03

1.3 Methodology..04

1.4 Organization of the Thesis .05

CHAPTER 2: LITERATURE SURVEY

2.1 Two Methods for Analysis and Design of Short columns.06

2.2 Failure Interaction Surfaces...06

2.2.1 Load Contour..08

2.2.2 Theta Plane..08

2.3 The Load Contour Method.09

2.3.1 Breslers Method: Using Uniaxial Interaction Curves09

2.3.2 Exact Formulation...10

2.4 The Theta Plane Method11

2.5 Principal Axes1 2

2.6 Choice of Method for Computer Aided Programing.13

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CHAPTER 3: DEVELOPMENT OF ANALYSIS SOFTWARE

3.1 Basic Features of the Analysis Software...14

3.2 Program to Obtain the Centroid and the Principal axes.14

3.2.1 Inputs to the Problem..14

3.2.1.1 Sample Input15

3.2.1.2 Functions that take care of the inputs..16

3.2.2 Functions and Procedure involved in Computing the Centroid..16

3.2.3 Outputs17

3.2.4 Flowchart for the above Program...18

3.3 Program to Evaluate the Load Contour.19

3.3.1 Inputs to the Problem..19

3.3.2 Functions and the Procedure involved in Computing the

Load contour...20

3.3.2.1 Procedure to evaluate a point on the 3D interaction

Surface22

3.3.3 Basic Flowchart for the above Problem..25

3.4 Variation of the Above Program27

3.5 Outputs...27

CHAPTER 4: APPLICATIONS OF ANALYSIS SOFTWARE

4.1 Sample Sections for Analysis28

4.2 Case 1: Rectangular Column Section29

4.3 Case 2: Lshaped section.31

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4.4 Case 3: Tshaped section.33

4.5 Case 4: Channel section.35

4.6 Case 5: Plus section...37

4.7 Case 6: Circular section.39

4.8 Discussion and Validation of Results41

4.9 Implementation of the Analysis Software..42

CHAPTER 5: DESIGN SOFTWARE AND ITS APPLICATIONS

5.1 Design Program.43

5.1.1 Inputs to the Problem..43

5.1.2 Method employed in the Design Procedure43

5.1.3 Capacity factor45

5.1.4 Basic Flowchart of the design method46

5.2 Design Examples...48

5.2.1 Square section.48

5.2.1.1 Design by IS code method...48

5.2.1.2 Design using the software developed..50

5.2.2 Rectangular Section51

5.2.3 Lshaped section...52

5.2.4 Tshaped section...53

5.2.5 Channel section...54

5.2.6 Plus section.56

5.2.7 Circular section...57

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CHAPTER 6: CLOSURE

6.1 Summary and Conclusions59

6.1.1 Review of Prevailing design methods..59

6.1.2 Development of Analysis Software..59

6.1.3 Development of Design Software.....60

6.2 Scope for Further work.60

APPENDIX A: THE DESIGN PROGRAM

REFERENCES.

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LIST OF FIGURES

FIGURE NUMBER AND TITLE PAGE NO.

1.1 Columns subject to biaxial eccentricities .011.2 Regular shapes of columns usually found in practice..021.3 Example of irregularshaped column encountered in practice...021.4 Analysis of design strength for a given location of the neutral axis.032.1 Typical interaction surface ...072.2 Approximation of load contour ...103.1 Sample crosssection .153.2 Basic Flowchart of program to obtain the centroid of any shape.193.3 Strain profiles for a given neutral axis.21 3.4 Significance of the angle of the neutral axis.21 3.5 Characteristic and design stressstrain curves for concrete in flexural compression.233.6 Characteristic and design stressstrain curves for Fe 250 grade mild steel233.7 Characteristic and design stressstrain curves for Fe 415 grade coldworked steel243.8 Flowchart for obtaining the load contour .264.1 Rectangular crosssection chosen for analysis.. .294.2 Load contours for the Rectangular column ..294.3 Zerodegree theta plane (Rectangular section) ..304.4 Ninetydegree theta plane (Rectangular section)...304.5 Lshaped crosssection chosen for analysis .314.6 Load contours for Lshaped crosssection ...31

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4.7 Zerodegree theta plane (Lshaped section)32 4.8 Ninetydegree theta plane (Lshaped section).32 4.9 Tshaped crosssection chosen for analysis.334.10 Load contours for Tshaped crosssection..334.11 Zerodegree theta plane (Tshaped section)34 4.12 Ninetydegree theta plane (Tshaped section)34 4.13 Channel section chosen for analysis .354.14 Load contours for the Channel section.354.15 Zerodegree theta plane (Channel section)....364.16 Ninetydegree theta plane (Channel section) .364.17 Plus section chosen for analysis..374.18 Load contours for the Plus section...374.19 Zerodegree theta plane (Plus section)..384.20 Ninetydegree theta plane (Plus section)...384.21 Circular section chosen for analysis .394.22 Load contours for Circular section ...394.23 Zerodegree theta plane (Circular section)....404.24 Ninetydegree theta plane (Circular section) ...40

5.1 Capacity factor..455.2 Flowchart for the design problem.475.3 Design adopted using IS Code method (for square section).505.4 Design adopted using software (for square section).515.5 Rectangular section assumed51 5.6 Lsection assumed.52

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5.7 Tsection initially assumed53 5.8 Tsection finally adopted..545.9 Channel section initially assumed545.10 Channel section finally adopted...555.11 Plus section initially assumed...565.12 Plus section finally adopted..575.13 Trial section for circular column..575.14 Final circular section adopted...58