1. TEACHING PRESTRESSED CONCRETE DESIGN
RICHARD A. MILLER, FPCI
PROFESSOR OF CIVIL ENGINEERING
UNIVERSITY OF CINCINNATI
CHAIR, PCI R&D COUNCIL

2. WHY TEACH PS CONCRETE?
Code is now “unified”. PS and RC are treated basically the same.
PS heavily used in bridges.
PS heavily used in structures – especially
Parking garages
Slabs
Small industrial/commercial
Panels

3. MAJOR DIFFERENCES BETWEEN PRESTRESSED AND RC
Load Factors:
The same for RC and PS
Analysis
PS is often easier as many PS structures are precast and are analyzed as simple spans.
RC and Post Tensioned tend to be continuous.
Due to prestressing, PS structures experience additional creep deformations which may affect load distributions.

4. MAJOR DIFFERENCES BETWEEN PRESTRESSED AND RC
Flexure
Service load
Service load stresses must be considered with PS at two states
Release of prestressing
Service loads
RC - only service load deflection is checked.
Ultimate
Basically the same (stress block)
Must calculate the stress in the PS steel.

5. MAJOR DIFFERENCES BETWEEN PRESTRESSED AND RC
Shear
ACI shear calculation for CONCRETE contribution in PS is completely different.
Vci and Vcw– Flexural and Web Shear Capacity
Vc – Combined Shear Capacity
Stirrup contribution is the same for RC and PS.

6. MAJOR DIFFERENCES BETWEEN PRESTRESSED AND RC
AASHTO LRFD uses Modified Compression Field Theory for both RC and PS.
As an alternate, AASHTO now allows the Vcw Vci method, used in ACI 318, to be used for PS concrete. This was the method used in the old Standard Specs. Will probably be removed in next edition of AASHTO.
AASHTO allows the simplified 2√fc’ for RC.

7. MAJOR DIFFERENCES BETWEEN PRESTRESSED AND RC
Torsion
ACI: can use same method for RC and PS.
Some formulae modified for PS members.
Not particularly accurate for PS Concrete
ACI: permits the use of the PCI method for PS concrete.
Found in the PCI Design Handbook.
AASHTO: Modified Compression Field Theory for both PS and RC

8. MAJOR DIFFERENCES BETWEEN PRESTRESSED AND RC
Bond/Development length
Equations for development of non prestressed steel are not changed by the presence of prestressing steel.
Separate equations for development length of prestressed strand or bar.
Loss of prestressing force
Unique to PS concrete.

9. MAJOR DIFFERENCES BETWEEN PRESTRESSED AND RC
Deflections
PS structures are usually uncracked under service loads, so deflections are easier.
Must account for camber due to prestressing
Must account for creep deformations caused by prestressing.
If the PS beam cracks, deflection is calculated using a bilinear function.

10. NICE DEMONSTRATION “Unreinforced” Concrete Foam block
Prestressed Concrete!
Add rubber band!
Even holds load!

11. There are two ways to prestress:
Pretensioning
Post-tensioning

12. PRETENSIONING

13. PRETENSIONING Pretensioning: Uses a bed. Strand is tensioned first.
Concrete is cast around the strand.
Strand is cut, transferring prestressing force by bond.
Some prestressing force is lost because the concrete shortens under load and the strand shortens along with it.

14. This slide shows construction of I girders
This slide shows construction of I girders. Here, the stirrups are already in place and the strands have been tensioned.

15. A raked finish is needed as these will be composite beams.

16. Workers detension the strand. Both ends must be cut at the same time
Workers detension the strand. Both ends must be cut at the same time. The strand must be cut symmetrically – from side to side. If all the strand on one side is cut first, the prestressing forces will cause the beam to bow sideways or “sweep”.

17. POST TENSIONED

18. POST-TENSIONING Post-tensioning No bed is required.
Concrete is cast with ducts.
Strand or bar is placed in the ducts.
Strand or bar is tensioned by jacking against the concrete. This requires plates to spread jacking forces.
May be jacked from one or both ends.
Strand/bar is anchored.
Loss due to shortening is less than pretensioning. There is additional loss due to friction.

19. POST-TENSIONING Bonded Unbonded
The PT bars/strands are tensioned and the PT ducts are filled with grout.
Protects against corrosion
Unbonded
The PT bars/strands are tensioned and the PT ducts are NOT filled with grout.

20. Laterally post-tensioned box beam bridge

21. Grout tubes
Post Tensioning jack

22. POST-TENSIONING VS. PRETENSIONING
Pretensioned members are usually used as simple spans or “continuous for live load”
Spans are set as simple then connected into a continuous structure. Loads applied before connection are taken as simple span; after connection loads are taken as continuous.
Post-tensioned structures may be simple or, more often, continuous.
In PT continuous structures, PT force causes “secondary moments”.

23. POST-TENSIONING VS. PRETENSIONING
In pretensioned elements, the prestressing steel is all or part of the primary load resisting mechanism.
In post-tensioned structures:
The PT steel is often part of the primary load resisting mechanism.
In some applications, PT is used for other purposes:
PT concrete boxes laterally to improve load distribution and prevent joint cracking.

24. POST-TENSIONING VS. PRETENSIONING
At transfer of prestressing force:
Different allowable stresses for compression in the concrete and tension steel.
Limits on stresses in the concrete due to anchorage devices in PT.
At service loads – no difference
At ultimate load
A different formula is used for fps for unbonded vs. unbonded steel.
Otherwise, no difference.

25. POST-TENSIONING VS. PRETENSIONING
Shear design is the same
Torsion design is the same.
Bond and development length:
Differences between pre- and post-tensioning.
For PT, tendons may be unbonded.
For pretensioned members, must account for “transfer length” – the length it takes for the prestressing force to be transferred by bond.

26. POST-TENSIONING VS. PRETENSIONING
Losses
Elastic Shortening is different
There is a friction loss and an anchorage loss for PT
Creep and shrinkage losses are the same.
Relaxation losses are based on the steel used.

27. A BASIC COURSE ON PS
It is NOT necessary to require RC as a prerequisite.
For a basic course, there is a limited amount of overlap.
If a student has taken RC, 80% of the course will be new material.
Students who have not taken RC should be able to pick up the common material.
Strength of Materials and Structural Analysis would be the only prerequisites.

28. A BASIC COURSE ON PS Two options
Spend the entire course on prestressed concrete for buildings
Divide the course ½ buildings and ½ bridges.
For some students, this may be the ONLY exposure they get to bridge design.
One way to teach is to teach pretensioned first, then teach post-tensioned.
For post-tensioned, it would only be necessary to cover differences in detail.

29. A BASIC COURSE ON PS A basic course covers flexure.
Flexure is the most common usage.
There is enough subject matter to fill an entire course and then some.
Beams
Non-composite vs. composite
Straight vs. deflected strand
Slabs/Hollowcore

30. A BASIC COURSE ON PS - SUBJECTS
Introduction to prestressing
Uses
Fabrication
Materials
Concrete
Properties at application of prestressing
Long term
Prestressing steel
Hardware (inserts/chucks/jacks)

31. A BASIC COURSE ON PS - SUBJECTS
Basic concepts of prestressing – how it works
Release/Application of Prestress
Top tension
Control with mild steel
Deflected/Harped strands
Debonded strand (pretensioned)
Bottom compression
Service load behavior
Loss of prestress
Service level stresses

32. A BASIC COURSE ON PS - SUBJECTS
Ultimate Strength
Load Combinations
Stress in Steel
Tension Control
Minimum Reinforcement
Cracking moment
Shear
Deflection/Camber

33. RESOURCES PCI Design Handbook
Sold at reduced cost to students (7th Ed)
CD’s $25 with (free) student membership
Hard Copy at member rate
Professors can usually get free copy from PCI Chapters
PCI Image Library
Great pictures to illustrate the point

34. RESOURCES PCI Bridge Design Manual
Free copy to professor with permission to duplicate some sections
It is completely electronic!
Updated in 2011.
Contact William Nickas at PCI for more information.

35. PRESTRESSED IN A BOX A GREAT RESOURCE - READY MADE CLASS!
Most professors do not have time to create a new class.
Codes change and updating is real pain.
Most faculty members do not have access to some basic material
PRESTRESSED IN A BOX IS THE ANSWER!!!!!!

36. PRESTRESSED IN A BOX A GREAT RESOURCE - READY MADE CLASS!
PCI teaches a one day seminar on basic prestressed concrete design.
Class is basically my notes from the UC PS course.
S. Brena from U Mass updated them.

37. PRESTRESSED IN A BOX A GREAT RESOURCE - READY MADE CLASS!
PCI changed their structural design seminar and had a lot of copies of the old (but still valid) seminar notes.
Bridge examples were available from PCI seminars.

38. PRESTRESSED IN A BOX A GREAT RESOURCE - READY MADE CLASS!
VERSION 2.0 IS UPDATED TO ACI !!!!

39. WHAT YOU GET
The basic one day “Introduction to Prestressed Concrete” seminar notes as PPT files.
The PCI Structural Design Seminar notes.
PPT files

40. WHAT YOU GET Two Bridge Examples (Need updating) Supporting Materials
The 7th Edition of the PCI Design Handbook.
Cost - $50
We are hoping that Producer Members and Regional Directors will help with costs.

41. RULES FOR USE Only not-for-profit institutions may use the material.
Institutions may only use the material for courses in a regular degree program.
May not be used for continuing education courses without PCI permission.
Institutions must protect the PCI Copyright.

42. RULES FOR USE May post PDF versions of the notes on SECURE web sites.
Professor may modify the notes to correct errors or add ‘local’ material.
Basically – PCI wants to help professors, but they don’t want people making money off PCI work.

43. THE BASIC PS COURSE Teaches through a design example.
12RB28 beam is designed.
Three designs are available
Straight strand with top steel to control top tension.
Straight strand with top strand and debonded bottom strand to control top tension.
Harped strand to control top tension.
Complete design of the member
Back up calculations/spreadsheets are provided.
Background information and theory modules are provided.

44. THE BASIC PS COURSE Introduction to Prestressing Materials
Fabrication video
Applicable Code Provisions (ACI )
PCI Suggested Practices
Loads/load combinations
Factored Load Combinations
Advice on service load combinations (not in ACI).
Explanation of Classes U, T and C prestressed beams.

45. THE PS COURSE Class U beam design. Choice of:
Straight strand
Top strand/bottom debonded strand
Harped Strand
Loss of prestressing calculation
Service load stresses (flexure)

46. THE PS COURSE Release stresses and control of top tension
Ultimate flexural strength
Calculation of steel stress with approximate equation
Determination of and explanation of tension and compression control in PS.
Ductility Limit (Minimum steel requirement)

47. THE PS COURSE Shear Development length/transfer length
Explanation of shear in concrete (compression field)
Vc equation
Vci and Vcw equations with derivation
Stirrup calculations
Development length/transfer length
Explanation of transfer length
Calculations
Bursting stirrups

48. THE PS COURSE Camber/deflection Design of a Class T beam
Initial camber
Growth in storage
Long term camber
PCI Camber Co-efficients
Design of a Class T beam
Existing design is modified for additional load and designed as Class T.

49. Sample slide Design the pretensioned interior 12RB28 beams
Consider the structural system shown below: 49

50. All slides are updated to PCI Design Handbook 7th edition.
Sample slide
Calculate the self weight of the beam:
From the PCI Handbook page 2-42 the section properties for a 12RB28 beam and strand pattern of 5 per 2 inches.
wsw = 350 plf 50

51. MOMENTS AND LOADS AT MIDSPAN
Sample slide
Analysis calculations are provided.
MOMENTS AND LOADS AT MIDSPAN
TYPE
MAGNITUDE
MMIDSPAN
Self Weight
350 plf
39.4 kft
Slab Weight
980 plf
110.3 kft
Live Load
2000 plf
225 kft
Total
3330 plf
374.6 kft
Note that the moment calculations are based on the center-to-center span length of 30 feet rather than beam length of 32 feet. 51

52. Sample slide Calculate the number of strands:
Recall that stress distribution in a generic prestressed concrete beam is as follows: 52

53. Sample slide Basic prestressing equations are illustrated.
Calculate the number of strands:
Assume that the prestressing tendons will be 3 inches from the bottom of the girder. Thus the eccentricity is:
e = 14 in – 3 in = 11 in
The MINIMUM prestressing force is (tension is negative):
Again, tension is negative. Thus the greater than sign is correct for negative numbers
Note that P must be GREATER than 234 kips, so round the number of strands UP! 53

54. Sample slide Calculate the number of strands:
As will be explained in the next section, over time prestressing strands lose force. This loss must be calculated, but it can’t be calculated at this time because the number of strands is not known. A loss of 20% is assumed. For 0.5 inch, Grade 270, low relaxation strand, initially stressed to 0.75 fpu, the stress per strand after loss is assumed as: 54

55. Sample slide Loss of prestressing force – Total Loss:
Initially the loss was assumed to be 20%, but 10 strands (rather than 9.44) were used. Try 10 strands to see if it works. 55

56. Sample slide Graphic explanations are provided. Development Length:
It is assumed that the stress in the strand increases linearly over the transfer length from zero at the end of the beam to full effective stress at the end of the transfer length. 56

57. Sample slide The Excel file is provided.
Transfer stress in a harped strand beam:
fallowable= 2.4 ksi
A plot of the stress distribution along the length of the bottom of the beam is shown. The bottom of the beam is now OK 57

58. Sample slide Transfer stress in a harped strand beam:
fallowable= 0.19 ksi
fallowable= 0.38 ksi
A plot of the stress distribution along the length of the top of the beam is shown. The top of the beam is generally overstressed, so add steel. 58

59. Sample slide Check service level stresses:
The plot shows the service level stresses for the harped strand configuration. The stresses in the bottom of the beam are almost exactly the limit stresses.
Top – All loads
Top – Dead loads
Bottom – All loads 59

60. EXCEL FILES PROVIDED The original Excel files are provided.
They are not intended to be given to students, but can be if protected.
By looking at these files, instructors can see how the calculations are performed.
The original graphs are provided.
Can be modified to make additional points.
Instructors can make a copy of the Excel files and then use that as a basis for the new problems
Homework
Exams

61. Sample slide
Check ultimate strength:
For prestressed concrete, the definition of ultimate moment is exactly the same as for reinforced concrete. 61

62. Sample slide Check ultimate strength:
Handbook and Code references provided!
PCI Design Handbook Section
ACI 62

63. Sample slide
For the harped strand configuration, ignore the mild top steel (conservative): 63

64. Sample slide Find the capacity of the beam: Check ultimate strength:
The capacity at midspan length of the beam is 597 kip ft. 64

65. Sample slide
Comparing Vc with Vcw and Vci . 65

66. Sample slide Photos provided for clarification. Bursting stirrups :
Additional stirrups are required at the end of the members to prevent bursting when the tendons are released. 66

67. Sample slide
Camber :
The equations of deflection for straight prestressing strands and self weight are:
Equations for deflection (camber) are found in the appendix of the PCI Design Handbook. 67

68. Sample slide
The situation is a little different when strands are harped. The equation used for harped strands is:
Equations for various cases of deflected strand are found in the appendix of the PCI Design Handbook. 68

69. PRESTRESSED IN A BOX Bridge design examples
Single span prestressed box.
Middle span, interior girder of a continuous for Live Load Girder.
Information on this in the Bridge part of this seminar. 69

70. SUMMARY
Prestressed concrete is widely used. It should be given the same importance as reinforced concrete or steel design in the curriculum.
Prestressed concrete can be taught as a separate course or as part of an RC course.
If taught as part of an RC course, it can be a separate module, or it can be integrated into the RC course. 70

71. SUMMARY Subjects to teach are: Materials/Fabrication
Loads/Load Factors
Flexure
Release
Service (includes loss of prestressing force)
Ultimate strength
Minimum reinforcing
Shear
Development length 71

72. SUMMARY Additional subjects Torsion Composite structures
Camber and deflection
Nonlinear deflection/Class “T” members.

73. Available to you! PRESTRESSED IN A BOX CLASS NOTES (ACI 318-14!)
BASIC THEORY
BUILDING EXAMPLES
BRIDGE EXAMPLES
BACK UP SPREADSHEETS!
PCI DESIGN MANUAL!
PCI STRUCTURAL SEMINAR!