PRESTRESSED CONCRETE DESIGN This page is intentionally left blank. PRESTRESSED CONCRETE DESIGN Praveen Nagarajan Department of Civil Engineering NIT Calicut, Kerala Copyright © 2013 Dorling Kindersley (India) Pvt. Ltd. Licensees of Pearson Education in South Asia No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s prior written consent. This eBook may or may not include all assets that were part of the print version. The publisher reserves the right to remove any material in this eBook at any time. ISBN 9789332513754 eISBN 9789332517615 Head Office: A-8(A), Sector 62, Knowledge Boulevard, 7th Floor, NOIDA 201 309, India Registered Office: 11 Local Shopping Centre, Panchsheel Park, New Delhi 110 017, India To my parents, Mrs. Rani Nagarajan and Dr N. M. Nagarajan, and my Teachers at NIT Calicut and IIT Madras This page is intentionally left blank. Contents Preface xv About the Author xvii Chapter 1 Basic Principles 1 1.1 Introduction—1 1.2 Need for Prestressed Concrete—1 1.3 Brief History of Prestressed Concrete—2 1.4 Structural Behaviour of Prestressed Concrete Member—3 1.5 Methods of Prestressing—6 1.5.1 Pre-tensioning 6 1.5.2 Post-tensioning 7 1.6 Types of Prestressed Concrete—11 1.6.1 Classifi cation as per IS:1343–1980 11 1.6.2 Other Classifi cations 11 1.7 Comparison with Reinforced Concrete—12 1.8 Applications of Prestressed Concrete—13 1.9 Design Code—13 Chapter 2 Materials 15 2.1 Introduction—15 2.2 Prestressing Steel—15 2.2.1 High Tensile Steel 15 2.2.2 Need for High Tensile Steel 16 2.2.3 Types of Prestressing Steel 19 2.2.4 Modulus of Elasticity of Prestressing Steel 23 2.2.5 Maximum Initial Prestress in Tendon 23 viii Contents 2.3 Concrete—24 2.3.1 Need for High Strength Concrete 24 2.3.2 Compressive Strength of Concrete 24 2.3.3 Tensile Strength of Concrete 25 2.3.4 Modulus of Elasticity of Concrete 27 2.3.5 Time-dependent Deformation of Concrete 28 Chapter 3 Limit State Design 31 3.1 Introduction—31 3.2 Limit States—33 3.3 Characteristic and Design Load—33 3.4 Characteristic and Design Strength of Material—35 3.5 Characteristic and Design Stress–Strain Curves—36 3.5.1 Stress–Strain Curves for Concrete 36 3.5.2 Stress–Strain Curves for Prestressing Steel 37 3.6 Design Requirements as per LSM—38 3.7 Limit State Design of Prestressed Concrete Members—39 Chapter 4 Losses in Prestress 43 4.1 Introduction—43 4.2 Immediate Losses—44 4.2.1 Loss Due to Elastic Shortening of Concrete 44 4.2.2 Loss Due to Friction 52 4.2.3 Loss Due to Slip in Anchorage 57 4.3 Time Dependent Losses—61 4.3.1 Loss Due to Shrinkage of Concrete 61 4.3.2 Loss Due to Creep of Concrete 62 4.3.3 Loss Due to Relaxation of Steel 63 4.4 Total Loss in Prestress—65 Problems 66 Chapter 5 Analysis of Sections 67 5.1 Introduction—67 5.2 Analysis at Serviceability Limit State—68 Contents ix 5.2.1 Combined Load Approach 70 5.2.2 Internal Couple Approach 81 5.2.3 Concept of Equivalent Loads 88 5.3 Load Balancing—103 5.4 Decompression Moment (M )—105 dec 5.5 Cracking Moment M —106 cr 5.6 Additional Stress in Tendon Due to Bending—108 5.7 Flexural Behaviour of Prestressed Concrete Member—109 5.7.1 Load Defl ection Behaviour 109 5.7.2 Stress in Tendon 110 5.7.3 Modes of Failure in Flexure 111 5.7.4 Types of Section 111 5.8 Analysis at Ultimate Limit State—112 5.8.1 Analysis of Rectangular Sections with Bonded Tendons 113 5.8.2 Analysis of Post-tensioned Rectangular Beams Having Unbonded Tendons 119 5.8.3 Analysis of Flanged Sections 120 Problems 127 Chapter 6 Shear and Torsion 129 6.1 Introduction—129 6.2 Design for Shear—130 6.2.1 Effect of Prestress in Shear Strength 130 6.2.2 Identifi cation of Zones for Shear Design 130 6.2.3 Ultimate Shear Resistance 133 6.2.4 Ultimate Shear Resistance of Concrete V 133 uc 6.2.5 Design of Shear Reinforcement 137 6.2.6 Minimum Shear Reinforcement 138 6.2.7 Maximum Ultimate Shear Force (V ) 139 u, max 6.2.8 Steps for Shear Design 139 6.3 Design for Torsion—145 6.3.1 Equilibrium Torsion and Compatibility Torsion 145 6.3.2 Failure of Concrete Member Due to Torsion 146