TEACHING PRESTRESSED
CONCRETE DESIGN
RICHARD A. MILLER, FPCI
PROFESSOR OF CIVIL ENGINEERING
UNIVERSITY OF CINCINNATI
CHAIR, PCI R&D COUNCIL
1
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
2
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.
3
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.
4
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.
5
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.
6
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
7
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.
8
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.
9
NICE DEMONSTRATION
“Unreinforced” Concrete
Foam block
Prestressed Concrete!
Add rubber band!
Even holds load!
10
There are two ways to
prestress:
Pretensioning
Post-tensioning
11
PRETENSIONING
12
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.
13
14
15
16
POST TENSIONED
17
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.
18
POST-TENSIONING
• Bonded
– 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.
19
Laterally post-tensioned box beam bridge
20
Grout tubes
Post Tensioning jack
21
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”.
22
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.
23
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.
24
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.
25
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.
26
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.
27
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.
28
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
29
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)
30
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
31
A BASIC COURSE ON PS SUBJECTS
• Ultimate Strength
– Load Combinations
– Stress in Steel
– Tension Control
• Minimum Reinforcement
– Cracking moment
• Shear
• Deflection/Camber
32
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
33
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.
34
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!!!!!!
35
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.
36
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.
37
PRESTRESSED IN A BOX
A GREAT RESOURCE READY MADE CLASS!
VERSION 2.0 IS UPDATED TO
ACI-318-14!!!!
1.38
WHAT YOU GET
• The basic one day “Introduction to
Prestressed Concrete” seminar notes as
PPT files.
• The PCI Structural Design Seminar notes.
– PPT files
39
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.
40
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.
41
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.
42
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.
43
THE BASIC PS COURSE
– Introduction to Prestressing
– Materials
– Fabrication video
– Applicable Code Provisions (ACI 318-14)
– 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.
44
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)
45
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)
46
THE PS COURSE
– Shear
• 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
47
THE PS COURSE
– Camber/deflection
•
•
•
•
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.
48
Sample slide
Design the pretensioned
interior
12RB28
beams
Consider the
structural
system
shown below:
49
All slides are updated to
Sample slide
PCI Design Handbook 7th
edition.
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 row @ 2
inches.
wsw = 350 plf
50
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-tocenter span length of 30 feet rather than beam length of 32 feet.
51
Sample slide
Calculate the number of strands:
Recall that stress distribution in a generic prestressed
concrete beam is as follows:
52
Basic prestressing
equations are
illustrated.
Sample slide
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):
P Pey

 fcbl  7.5 fc '
A
I
P
P(11 in)(14 in)
7.5 5000 psi


2.87
ksi


ksi
336 in2
21952 in4
1000
P  234 kips
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
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:
kips
Pstrand  0.75(270 ksi)(1.0 - 0.2)(0.153 in )  24.8
strand
P
234 kip
# strand 

 9.44 strands  Use 10 strands
kip
Pstrand 24.8 strand
2
54
Sample slide
Loss of prestressing force – Total Loss:
TL  RE  ES  CR  SH
TL  3.31 ksi  16.6 ksi  20.5 ksi  5.24 ksi
TL  45.6 ksi
45.6 ksi
LOSS 
(100%)  22.5%
0.75(270 ksi)
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.
fse  Pi - TL  0.75(270 ksi) - 45.6 ksi  156.9 ksi
Peff  10 strands(0. 153 in2 )(156.9 ksi)  240 kips
55
Graphic explanations are
provided.
Sample slide
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
Sample slide
The Excel file is
provided.
Transfer stress in a harped strand beam:
Stress at Bottom
3
fallowable= 2.4 ksi
2.5
Stress (ksi)
2
1.5
1
0.5
0
0
4
8
12
16
20
24
28
32
Length (ft)
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
Sample slide
Transfer stress in a harped strand beam:
Stress at Top
0
0
-0.1
4
8
12
16
20
24
28
32
fallowable= 0.19 ksi
Stress (ksi)
-0.2
-0.3
-0.4
fallowable= 0.38 ksi
-0.5
-0.6
-0.7
Length (ft)
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
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.
Harped Strands
2.5
Top – All loads
2.0
Stress (ksi)
1.5
1.0
Top – Dead loads
0.5
0.0
0
5
10
15
20
25
30
-0.5
Bottom – All loads
-1.0
Length (ft)
59
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
60
Sample slide
Check ultimate strength:
For prestressed concrete, the definition of
ultimate moment is exactly the same as for
reinforced concrete.
61
Sample slide
Check ultimate strength:
fps
 γ p  fpu d
 
 fpu 1  ρ p
 (ω - ω' ) 
 β1  fc ' dp
 
Valid only if f se  0.5fpu
Handbook and Code
references provided!
PCI Design Handbook Section 4.2.1.6.
ACI 20.3.2
62
Sample slide
For the harped strand configuration, ignore the mild
top steel (conservative):
 p  0.0051
f c '  5000 psi
1  0.80
γ p  0.28 (low relaxation strand)
 γp
f ps  f pu 1  1
f pu  

 p

f
'
c 

 0.28 
270 ksi  
f ps  (270 ksi)1 
0.0051
  244 ksi


5 ksi  
 0.80 
63
Sample slide
Find the capacity of the beam:
Check ultimate strength:
(1.53 in 2 )(244 ksi)
a

 7.32 in
0.85fc ' b (0.85)(5 ksi)(12 in)
7.32 in 

2
Mn  (1.53 in )(244 ksi)25 in 2 

 7967 kip in  664 kip ft
A p fps
ΦMn  0.9(664 kip ft)  597 kip ft
The capacity at midspan length of the beam is
597 kip ft.
64
Sample slide
125
F Vcw
100
F Vci
75
Shear (k)
F Vc
50
Vu
25
Center of Bearing
Midspan
0
0
3
6
9
12
15
Length (ft)
Comparing Vc with Vcw and Vci .
65
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
Sample slide
Camber :
The equations of deflection for straight
prestressing strands and self weight are:
Due to self weight of the beam
δ sw
5 wL4

384EciI
Due to initial prestressi ng force
δps
ML2 Peff eL2


8EciI
8EciI
Equations for deflection (camber) are found in the
appendix of the PCI Design Handbook.
67
Sample slide
The situation is a little different when strands are
harped. The equation used for harped strands is:
Equations for various cases of
P0 e eL P0 e'  L2 a 2 
deflected strand are found in the
  


appendix of the PCI Design
8EciI
EciI  8 6 
Handbook.
Where :
P0 is the initial pull of the prestressi ng
2
e e is the eccentrici ty at midspan
e' is the eccentrici ty at the end
L is the length of the beam
a is the distance from the end to the harp point
Eci is the initial modulus of elasticity
I is the moment of inertia of the beam
68
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
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
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
SUMMARY
• Additional subjects
– Torsion
– Composite structures
– Camber and deflection
– Nonlinear deflection/Class “T” members.
72
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!
73