CHAPTER 1 Basic concepts of prestressed concrete

Contents
1.1 Basic concepts
1.2 The functions of prestress or prestressing force
1.3 Prestress level
1.4 Classification of prestressed concrete
   1.4.1 Classification by stressing methods
   1.4.2 Classification by prestress level
   1.4.3 Classification by the level of crack control
   1.4.4 Classification by bonding condition between the prestressing tendons and the concrete
1.5 Prestressed versus reinforced concrete
   1.5.1 High crack resistance
   1.5.2 High shear resistance
   1.5.3 High durability
   1.5.4 High fatigue resistance
   1.5.5 Ability to control the deflection actively
   1.5.6 Ability to build long-span structures with lighter self-weight
   1.5.7 Efficient utilization of high-strength materials
   1.5.8 Good economy
1.6 Concise history of prestressed concrete
Suggested readings

2 Prestressing materials

Contents

2.1 Concrete
   2.1.1 Basic requirements for concrete
   2.1.2 Concrete strength
   2.1.3 Modulus of elasticity
   2.1.4 Fatigue strength and fatigue modulus of concrete
   2.1.5 Creep
   2.1.6 Shrinkage
   2.1.7 Temperature effects
2.2 Prestressing tendons
   2.2.1 Basic requirements for prestressing tendons
   2.2.2 Classification of prestressing tendons
   2.2.3 Bonded prestressing steels
      2.2.3.1 High-strength steel wires
      2.2.3.2 Steel strands
      2.2.3.3 High-strength threaded steel bars
   2.2.4 Unbonded prestressing steels
      2.2.4.1 Unbonded prestressing steels arranged inside the concrete
      2.2.4.2 External prestressing steels arranged outside the concrete
   2.2.5 Mechanical properties of prestressing steels
      2.2.5.1 Stressestrain curve
      2.2.5.2 Mechanical properties
      2.2.5.3 Modulus and strength of prestressing steels
   2.2.6 Prestressing FRPs and their mechanical properties
   2.2.7 Relaxation
   2.2.8 Fatigue strength of prestressing tendons
Suggested readings

CHAPTER 3 Prestressing methods and anchorage systems

Contents

3.1 Prestressing methods
3.2 Pretensioning method
3.3 Post-tensioning method
3.4 Anchorage system
   3.4.1 Performance of anchorage system
      3.4.1.1 Efficiency coefficient and elongation of the prestressing tendoneanchorage assembly
      3.4.1.2 Efficiency coefficient and elongation of the prestressing FRPeanchorage assembly
   3.4.2 Anchorage system for prestressing steels
      3.4.2.1 Wedge-type anchorage
      3.4.2.2 End bearing anchorage
      3.4.2.3 Extruding anchorage
      3.4.2.4 Wrapping anchorage
      3.4.2.5 Coupler
   3.4.3 Anchorage systems for prestressing FRP
3.5 Jacks for stretching tendons
3.6 Duct grouting and anchorage sealing in post-tensioned concrete
References

CHAPTER 4 The strategy of analysis and design

Contents

4.1 Knowledge system of prestressed concrete
4.2 Analysis of prestressed concrete structures
   4.2.1 Contents of analysis
   4.2.2 Stress analysis based on the knowledge system
   4.2.3 General strategy for analysis
      4.2.3.1 The functions of the prestressing tendons
      4.2.3.2 Characteristics in stress analysis in prestressed concrete structures
      4.2.3.3 Characteristics in the calculations of deflection of prestressed concrete members
      4.2.3.4 Some professional terms
      4.2.3.5 Sign conventions
      4.2.3.6 Units
4.3 General issues for the design of prestressed concrete structures
   4.3.1 Design objectives
   4.3.2 Actions and combinations
   4.3.3 Major steps of design
Suggested readings

5 Calculation of effective stress in prestressing tendons

Contents

5.1 Concept of effective stress in prestressing tendons
   5.1.1 Control stress in tendons at stretching
   5.1.2 Types of prestress loss
5.2 Effective stress in prestressing tendons immediately after transfer
   5.2.1 Prestress loss due to friction between the tendons and the anchorage
   5.2.2 Prestress loss due to friction between the tendons and the duct wall
      5.2.2.1 Friction caused by the curvature
      5.2.2.2 Friction caused by unintentional displacement
      5.2.2.3 Total prestress loss due to friction
   5.2.3 Prestress loss due to anchorage set
      5.2.3.1 sl2ðxÞ in the pretensioned members
      5.2.3.2 sl2ðxÞ in the post-tensioned members
   5.2.4 Prestress loss due to heat treatment curing
   5.2.5 Prestress loss due to elastic shortening
      5.2.5.1 sl4ðxÞ in the pretensioned members
      5.2.5.2 sl4ðxÞ in the post-tensioned members
   5.2.6 Effective stress in prestressing tendons immediately after transfer
5.3 Long-term effective stress in prestressing tendons
   5.3.1 Unified approach to calculate long-term prestress loss
   5.3.2 Calculation of long-term prestress loss specified in the codes
      5.3.2.1 Prestress loss due to relaxation specified in the codes
      5.3.2.2 Prestress loss due to shrinkage and creep specified in the codes
5.4 Estimation of effective stress in simplified analysis and preliminary design
5.5 Example 5.1
5.6 Solution
   5.6.1 Parameters
   5.6.2 Strand N4
   5.6.3 Strand N6
5.7 Example 5.2
5.8 Solution
   5.8.1 Material properties
   5.8.2 Geometric parameters of the strands
   5.8.3 Prestress loss due to friction
   5.8.4 Prestress loss due to the anchorage set
   5.8.5 Prestress loss due to elastic shortening
   5.8.6 Prestress loss due to relaxation of strands
   5.8.7 Prestress loss due to shrinkage and creep of concrete
   5.8.8 Total prestress loss at midspan section
5.9 Example 5.3
5.10 Solution
   5.10.1 Material properties
   5.10.2 Convert a hollow section into an I-section
   5.10.3 Geometrical properties of the section
   5.10.4 Prestress losses at the first stage
   5.10.5 Prestress loss at the second stage
   5.10.6 Total prestress losses in the service period
References

CHAPTER 6 Effects of the prestressing force on structures

Contents

6.1 Equivalent loads of the prestressing force
6.1.1 Equivalent loads of the straight prestressing tendon
6.1.2 Equivalent loads of the broken-line prestressing tendon
6.1.3 Equivalent loads of the parabolic prestressing tendon
6.2 Primary internal forces produced by the prestressing force
6.3 Secondary internal forces produced by the prestressing force
6.4 Linear transformation and concordant tendon
6.4.1 C-line
6.4.2 Concordant tendon and linear transformation principle
6.5 Redistribution of the prestress-caused moment due to creep
References

CHAPTER 7 Stress analysis of prestressed concrete flexural members

Contents

7.1 Flexural behavior of a prestressed concrete flexural member
   7.1.1 Stage of transfer of the prestressing to the concrete
   7.1.2 Stages of transportation and erection
   7.1.3 Stage of service before cracking
   7.1.4 Stage of service after cracking
7.2 Stress analysis before cracking
   7.2.1 Analysis of normal stress in the uncracked section
      7.2.1.1 Normal stress at transfer
      7.2.1.2 Normal stress during transportation and erection
      7.2.1.3 Normal stress in the service period
   7.2.2 Shear stress and principal stresses before cracking
      7.2.2.1 Calculation of shear stress
      7.2.2.2 Calculation of principal stresses
7.3 Stress analysis after cracking
   7.3.1 Cracking moment
   7.3.2 Stress analysis in the cracked section
      7.3.2.1 General procedures for stress analysis of the cracked section
      7.3.2.2 Stresses in the cracked T-section
      7.3.2.3 Stress calculation in the cracked section of a railway structure (Q/CR 9300-2018)
      7.3.2.4 Stress calculation in the cracked section of a highway structure (JTG 3362-2018 code)
7.4 Verification of crack resistance
   7.4.1 Verification of crack resistance in the normal section
   7.4.2 Verification of crack resistance in the oblique section
7.5 Example 7.1
7.6 Solution
   7.6.1 Parameters
   7.6.2 Geometrical properties
   7.6.3 Stresses of concrete and prestressing strands at transfer
   7.6.4 Stresses of concrete and prestressing strands in the service period
   7.6.5 Verification of crack resistance of the normal section in the service period
7.7 Calculation and verification of fatigue stress
7.8 Stress analysis in the anchorage zone of pretensioned members
7.9 Stress analysis in the anchorage zone of post-tensioned structures
Suggested readings

CHAPTER 8 Calculation and control of deformations and cracks

Contents

8.1 The significance of deformation and crack control
8.2 Calculation and control of deflection and rotation angle
   8.2.1 Flexural behavior and assumptions in deflection calculations
   8.2.2 Short-term deflection of the flexural members
      8.2.2.1 Bilinear method
      8.2.2.2 Single-line method
   8.2.3 Long-term deflection of the flexural members
      8.2.3.1 General concerns on long-term deflection calculation
      8.2.3.2 Time-dependent coefficient-modified method
      8.2.3.3 Stiffness-modified method
   8.2.4 Calculation of rotation angle at the beam end
   8.2.5 Control of deformation and set of camber during construction
      8.2.5.1 Limits for highway beam deflection
      8.2.5.2 Limits for railway beam deflection and end angle
      8.2.5.3 Limits for building beam deflection
      8.2.5.4 Set of camber for prestressed concrete beams during construction
8.3 Example 8.1
8.4 Solution
   8.4.1 Parameters
   8.4.2 Flexural rigidity of the uncracked section
   8.4.3 Flexural rigidity of the cracked section
   8.4.4 Calculation of deflection
   8.4.5 Verify the deflection caused by the static live load
8.5 Example 8.2
8.6 Solution
   8.6.1 Parameters
   8.6.2 Geometrical properties
   8.6.3 Train loads
   8.6.4 Rotation angle at the girder end
8.7 Example 8.3
8.8 Solution
8.8.1 Parameters
8.8.2 The deflection due to the frequent combination of actions
8.8.3 The camber produced by the effective prestressing force
8.8.4 Camber set during construction
8.9 Example 8.4
8.10 Solution
   8.10.1 Sectional properties
   8.10.2 Short-term flexural rigidity
   8.10.3 Long-term flexural rigidity
   8.10.4 Verification of deflection
8.11 Calculation and control of cracking
   8.11.1 General concerns on cracking in the prestressed concrete structures
   8.11.2 Cracking behavior and cracking analysis
   8.11.3 Calculation of crack width in the codes
      8.11.3.1 Calculation of crack width for railway beams
      8.11.3.2 Calculation of crack width for highway members
      8.11.3.3 Calculation of crack width for members in the buildings
   8.11.4 Crack control in the prestressed concrete members
      8.11.4.1 General expression for crack control by limiting crack width
      8.11.4.2 Allowable crack width in the railway members
      8.11.4.3 Allowable crack width in highway members
      8.11.4.4 Allowable crack width in building members
8.12 Example 8.5
8.13 Solution
    8.13.1 Parameters
    8.13.2 Calculation and verification of crack width
8.14 Example 8.6
8.15 Solution
    8.15.1 Parameters
    8.15.2 Calculation of equivalent stress in tensile reinforcement
    8.15.3 Calculation and verification of crack width
8.16 Example 8.7
8.17 Solution
    8.17.1 Parameters
    8.17.2 Calculation of equivalent stress in tensile reinforcement
8.17.3 Calculation and verification of crack width
Suggested readings

CHAPTER 9  Ultimate bearing capacity of flexural members

Contents

9.1 General concepts of ultimate bearing capacity of flexural members
9.2 Flexural bearing capacity of the normal section
   9.2.1 Failure patterns and assumptions in the calculation of flexural bearing capacity
   9.2.2 Relative boundary depth of the compression zone
      9.2.2.1 xb for the prestressing tendons with an obvious yield point
      9.2.2.2 xb for the prestressing tendons without an obvious yield point
      9.2.2.3 xb specified in the codes
   9.2.3 Flexural bearing capacity of the normal section
      9.2.3.1 Flexural bearing capacity of the rectangular section
      9.2.3.2 Flexural bearing capacity of the T-section
      9.2.3.3 Discussion on restriction conditions for formulas
9.3 Example 9.1
9.4 Solution
   9.4.1 Parameters
   9.4.2 Judge the location of the neutral axis
   9.4.3 Calculate and verify the flexural bearing capacity
9.5 Example 9.2
9.6 Solution
   9.6.1 Parameters
   9.6.2 Judge the location of the neutral axis
   9.6.3 Calculate and verify the flexural bearing capacity
9.7 Example 9.3
9.8 Solution
   9.8.1 Parameters
   9.8.2 Judge the location of the neutral axis
   9.8.3 Calculate and verify the flexural bearing capacity
9.9 Shear bearing capacity of the oblique section
   9.9.1 Failure patterns due to shear force and the influencing factors
      9.9.1.1 Failure patterns due to shear force
      9.9.1.2 The influencing factors on shear resistance
   9.9.2 Shear bearing capacity of the oblique section
      9.9.2.1 General model for shear resistance of the oblique section
      9.9.2.2 Shear bearing capacity of the railway beams
      9.9.2.3 Shear bearing capacity of the highway beams
      9.9.2.4 Shear bearing capacity of the beams in civil and industrial buildings
9.10 Flexural bearing capacity of the oblique section
9.11 Example 9.4
9.12 Solution
   9.12.1 Parameters
   9.12.2 Verify the cross-sectional dimension
   9.12.3 Calculate and verify the shear bearing capacity
9.13 Example 9.5
9.14 Solution
   9.14.1 Parameters
   9.14.2 Verify the cross-sectional dimension
   9.14.3 Calculate and verify the shear bearing capacity
9.15 Example 9.6
9.16 Solution
   9.16.1 Parameters
   9.16.2 Verify the cross-sectional dimension
   9.16.3 Calculate and verify the shear bearing capacity
9.17 Torsion bearing capacity in the beams
   9.17.1 General concepts of torsional failure and torsional strength
   9.17.2 Ultimate strength of prestressed concrete members under pure torsion
   9.17.3 Ultimate strength of prestressed concrete members under combined bending,shear,and torsion
      9.17.3.1 Bearing capacity of prestressed concrete members under shear-torsion
      9.17.3.2 Bearing capacity of prestressed concrete members under combined bending, shear, and
                    torsion
9.18 Example 9.7
9.19 Solution
    9.19.1 Parameters
    9.19.2 Calculation and verification of bearing capacity
9.20 Bearing capacity of anchorage zone under local compression
    9.20.1 Failure mechanism of the local zone under local compression
    9.20.2 Compressive bearing capacity of the local zone
       9.20.2.1 Compressive strength of confined concrete under local compression
       9.20.2.2 Compressive bearing capacity of the local zone
    9.20.3 Tension bearing capacity in the general zone
       9.20.3.1 Calculation of tension force in the general zone of end anchor
       9.20.3.2 Calculation of tension force in the general zone of tooth anchor
Suggested readings

10  Design of prestressed concrete flexural structures

Contents

10.1 Outline for designing a prestressed concrete flexural structure
10.2 Durability design of prestressed concrete members
  10.2.1 Concrete durability
  10.2.2 Structural design
10.3 Section design for prestressed concrete flexural structures
  10.3.1 Sectional types
    10.3.1.1 Prestressed concrete hollow slab
    10.3.1.2 Prestressed concrete T-section
    10.3.1.3 Prestressed concrete I-section
    10.3.1.4 Prestressed concrete box section
    10.3.1.5 Prestressed concrete combined box section
  10.3.2 Section design
10.4 Area estimation for prestressing tendons
  10.4.1 Estimation based on the concrete stress limits during stretching and in the service period
  10.4.2 Estimation based on the ultimate strength limit state
10.5 Selection and layout of prestressing tendons
  10.5.1 Selection of prestressing tendons
  10.5.2 Reasonable position of the prestressing tendons
  10.5.3 Principles of the prestressing tendon layout
  10.5.4 Layout of prestressing tendons in the pretensioned members
  10.5.5 Layout of prestressing tendons in the post-tensioned structures
10.6 Requirements for reinforcing steels in design
  10.6.1 General requirements for reinforcing steels in design
  10.6.2 Design of reinforcing steels in the anchorage zone
10.6.2.1 Calculation of reinforcing steels in the anchorage zone
10.6.2.2 Layout of reinforcing steels in the anchorage zone
Suggested readings

CHAPTER 11 Analysis and design of tension and compression members

Contents

11.1 Analysis and design of tension members
  11.1.1 Stress and deformation of axial tension members
  11.1.2 Bearing capacity of tension members
    11.1.2.1 Bearing capacity of axial tension members
    11.1.2.2 Bearing capacity of eccentric tension members
11.2 Analysis and design of compression members
  11.2.1 General issues on the ultimate bearing capacity of eccentric compression members
    11.2.1.1 Failure patterns and characteristics of eccentric compression members
    11.2.1.2 Basic assumptions for calculating the bearing capacity of eccentric compression
                  members
    11.2.1.3 Distinguishing failure patterns due to small or large eccentric compression
    11.2.1.4 Stresses in prestressing tendons and reinforcing steels
    11.2.1.5 Increasing factor of eccentricity
  11.2.2 Ultimate bearing capacity of eccentric compression members
    11.2.2.1 Bearing capacity of rectangular section under eccentric compression
    11.2.2.2 Bearing capacity of the T-section under eccentric compression
    11.2.2.3 Bearing capacity of circular and annular sections under eccentric compression
    11.2.2.4 Section bearing capacity under biaxial eccentric compression
    11.2.2.5 Compression bearing capacity and stability of prestressed concrete members at transfer
11.3 Example 11.1
11.4 Solution
  11.4.1 Parameters 3
  11.4.2 Calculate the eccentricity increasing factor
  11.4.3 Judge the type of eccentric compression
  11.4.4 Calculate and verify the bearing capacity
Suggested readings

CHAPTER 12 Analysis and design of unbonded prestressed concrete flexural structures

Contents

12.1 General concepts on unbonded prestressed concrete flexural structures
12.2 Anchorage system for unbonded tendons
12.3 Flexural behavior of unbonded prestressed concrete structures
12.4 Calculation of stress in unbonded tendons
     12.4.1 Effective stress in unbonded tendons in the service period
     12.4.2 Stress change in unbonded tendons under loading
     12.4.3 Ultimate stress in unbonded tendons at flexural failure
12.5 Bearing capacity of the unbonded prestressed concrete sections
   12.5.1 Flexural bearing capacity of the normal sections
12.5.2 Shear bearing capacity of the oblique sections
12.6 Calculation and control of deflection and crack
12.6.1 Deflection of the unbonded prestressed concrete flexural structures
12.6.2 Crack width of the unbonded prestressed concrete flexural structures
Suggested readings

CHAPTER 13 Analysis and design of externally prestressed concrete structures

Contents

13.1 General concepts on externally prestressed concrete structures
13.2 External prestressing system and external cable assembly
    13.2.1 External prestressing system
    13.2.2 Anchorage system
    13.2.3 Steering devices
    13.2.4 Damping devices
13.3 Calculation of stress in external tendons
    13.3.1 Effective stress in external tendons in the service period
    13.3.2 Stress change in external tendons under loading
    13.3.3 Ultimate stress in external tendons at flexural failure
13.4 Bearing capacity of the externally prestressed concrete sections
    13.4.1 Flexural bearing capacity of T-section when the flange is in the compression zone
      13.4.1.1 When the neutral axis falls within the flange
      13.4.1.2 When the neutral axis falls within the web
    13.4.2 Flexural bearing capacity of the T-section when the flange is in the tension zone
     13.4.3 Shear bearing capacity of the oblique section
13.5 Stress analysis in externally prestressed flexural sections
13.6 Calculation and control of deflection and crack
13.6.1 Deflection of the externally prestressed concrete flexural structures
13.6.2 Crack width of the externally prestressed concrete flexural structures
Suggested readings