Post tensioned slabs design fundamentals anas alakhras

Anas Malek Alakhras ‫م‬.‫اﻷخرس‬ ‫المالك‬ ‫عبد‬ ‫أنس‬
PE, MS.CEng, PMP
03-10-2020

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About lecturer
BSc. Civil engineering, Damascus University
MSc. SJSU, California, USA
Prestressed concrete teacher assistant
Member of ACI 423(Prestressed)Member of ACI 423(Prestressed)
Worked At ADAPT, CA
Registered professional Engineer in Texas and Maryland
Independent consultant in USA and Middle East
03-October 2020 ANAS ALAKHRAS CEANASS@GMAIL.COM 2

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Contents
Institutes
References
Software
Type of PT slabs
PT slabs and sustainabilityPT slabs and sustainability
PT design check steps
PT slabs and seismic
PT slabs and temperature
Details of PT slabs

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PT Institutes around the world
USA Australia
https://www.post-tensioning.org/

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PT Codes& standards around the world
USA UK& EN

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ACI & PTI

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PT references
https://ptstructures.com/technical-notes/

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PT references
http://www.senecastructural.com/

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PT references

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PT strands consumption in the world
U.S. prestressed concrete wire and strand market by
application, 2014 - 2025 (USD Million)

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PT strands consumption in the world
Global prestressed concrete wire and strand market, by region, 2016 (%)
Source: www.grandviewresearch.com

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PT system review

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PT system review
Each tendon has 3-5 strands
(PT slabs)
Each strand has 7 wires

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PT system review

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PT software-Adapt
https://risa.com/products/adapt-builder

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PT software-Adapt builder

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PT software-RAM Concept

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PT software-RAPT

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Normal PT slabs

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Waffle PT Slabs

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Voided PT Slabs
COBIAX PT- CREDIT TO COBIAX
Columbia University Medical Center

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Voided PT Slabs
CREDIT TO CCL

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Innovative PT
Moscone Convention center- San Francisco (83 m arches)

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Innovative PT
Falconhead Golf Course, TX.
Bonded post-tensioned slab (8 m long x 75 cm thick)

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Innovative PT
Olympic Oval, Canada(1987) Prestressed beams

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Innovative PT

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PT & Sustainability
Using PT slabs is consistent with Leed and Sustainability
requirements
Less Material(rebar/concrete)
Lower Carbon footprint
Higher building volumeHigher building volume
Lower construction cost
Faster construction
Lower height(less shadow)
Lower waste & Pollution

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PT design steps
Step1
• Draw Structural layout
• Determine Design code
• Determine Materials grade
Step 2
•Determine Required PT force
•Determine number of strands per tendons
•Determine tendon profile
• Assign external loads
Step 3
• Assign external loads
• Draw design strips/sections
Step 4
• Check service stresses
• Check deflection
• Check flexural adequacy
• Check shear (one way/punching)
Step 5
• If all is satisfied, determine required reinforcement

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Geometry

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PT Material properties

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Determine initial thickness of PT slabs/beams
Slab type Total
service
loads
(kN/m2)
L/t
(TR43/PTI)
L/t
for beams
Flat slab 2.5 40/45
5 36/40
10 30/3610 30/36
Flat slab
with
shallow
drops
2.5 44/48
5 40/45
10 34/40
Flat slab
with drop
beams
2.5 45/48 25/35
5 40/45 22/30
10 35/40 18/25
03-October 2020 ANAS ALAKHRAS CEANASS@GMAIL.COM 35Source: Aalami & Bommer (1999)

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Principle of load balancing
P
hc
Pe
Neutral axis
Load balancing for uniform distributed load
L1 L2 L3 Lc
Pe
h3h2h1
Pe
Balance 60% to 70% of DL for one- and two-way slabs

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Principle of load balancing
h4Pe
P4
P3P2P2
P1
EQ EQ EQ
Load balancing for concentrated load.
Pe
h3h2h1
L1 L2 L3 Lc

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Tendon profiles
Tendon Layout Over and Adjacent to a Wall
SLAB/BEAMCONTROL POINT
(a) ELEVATION AT COLUMN
L
(b) ELEVATION AT WALL
SLAB/BEAM
WALL
TENDON
CONTROL POINT
(a) ELEVATION AT COLUMN
Source: B. Aalami

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Tendon profiles
Tendon Layout Over and Adjacent to a Wall
<
COLUMN
WALLTRIBUTARY
(a)
1.5m (5') L/4
REGION OF
DISTRIBUTED DIRECTION
(c) PARTIAL PLAN OF SLAB
TENDONS
STRAIGHT
<
(b)
(a)
1.5m (5') L/4
Source: B. Aalami

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Tendon profiles
Tendon Profile and Anchorage at Exterior Support
SLAB/BEAM
PARABOLA
STRAIGHT (OPTIONAL)
Source: B. Aalami
CENTROID
(a) SLAB/BEAM AND EXTERIOR WALL
TENDON
WALL

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Tendon profiles
Tendon Profile and Anchorage at Exterior Support
AXIS
Source: B. Aalami
TENDON
(b) ANCHORAGE AT EXTERIOR SUPPORT
h/2

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Tendon profiles

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One-end and Two-end Stressing
10m (33 ft)
10m (33 ft) SLAB
36m (120 ft)
10m (33 ft)
STRESSING END
DEAD END
36m (120 ft)
Source: B. Aalami

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Tendon layout in plan
Tendon fully banded in one direction and uniformly distributed in the other direction
Source : Suncoast Post-tension

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Tendon layout in plan
Uniformly distributed tendon
Source: TR43

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Determine amount of PT
ACI 318- 2011

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Determine spacing of PT tendons
ACI 318- 2011

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Too much PT?
High
Cracking
due to
restraints
Slab
shortening
Increase
PT losses
High
P/A
Problem of
bursting
anchorages
Congestion
of PT

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Concrete strength at time of stressing
ACI 318- 2011

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Design load combinations
Source : ADAPT software manual

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Calculate service stresses after all losses
Top fiber stress
The bending moments calculated from the critical loading conditions given, including the
tendon effects, provide the serviceability stresses at each section using:
Bottom fiber stress
tc
t
z
M
A
P
f 
MP
f 
Bottom fiber stress
bc
b
z
M
A
P
f 
Where: zt = the top section modulus e = eccentricity of tendons, taken as positive below
zb = the bottom section modulus MA = applied moment due to dead and live loads
M = the total out of section moment MS = moment from prestress secondary effects
SA MPeMM 

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Allowable service stresses-ACI 318-11
The intent is to control crack formation and probable crack width

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The intent is to control excessive creep deflection

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Permissible stresses in prestressing steel

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Long term deflection load combination
Source : TR-43

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Moment capacity
ØMn = Ø {Aps*fps(dp–a/2) + As*fy(dr-a/2)}

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Moment capacity
ØMn = Ø {Aps*fps(dp–a/2) + As*fy(dr-a/2)} > 1.2 Mcr

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Shear capacity

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Drop panel size?

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PT losses
Immediate loss of stress
 Friction loss
 Seating loss (draw-in)
Elastic shortening
Long-term losses
 Relaxation in prestressing
Long-term losses
 Relaxation in prestressing
 Shrinkage in concrete
 Creep in concrete
Others, such as
 Change in stress due to flexing of
member under applied loading
 Aging of concrete
 Temperature

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PT losses

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PT secondary effect(Hyperstatic)

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Code minimum reinforcement-ACI318-11
ACI 318-11
Strip for placement of minimum
bonded top reinforcement
Source: Aalami (2001)

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Code minimum reinforcement-ACI318-11
Positive bending
ACI 318-11

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Code minimum reinforcement-ACI 318-14
ACI 318-14

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Minimum rebar/PT for temperature and shrinkage

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Temperature effect on buildings
The distribution shown in Fig. 2-3
assumes that the frame will
respond elastically and there is no
cracking. In practice, minute
cracks are likely to develop at the
floor connections to its supports,
and along the columns and walls.
Source : B. Aalami(TN463, 2016)
and along the columns and walls.
These cracks relieve the
temperature-generated forces so
that concrete structures are rarely
subjected to the level of internal
stresses that are calculated from a
non-cracked elastic analysis

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Temperature effect on buildings
Figures show the effects of
Source : Guo at al (PTI, 2009)
Figures show the effects of
restraint on the structure when
floor shortening attempts to
occur, as
simulated by a uniform
temperature decrease.

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PT Slab design for temperature
Distribution of axial stress from a drop of 20 C in ambient temperature.
Stresses shown are in MPa. Tension is shown positive.
The axial stresses shown are additive to those from gravity and other loads.
Source : Aalami TN 463-2016

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(a) Axial stress for service condition (b) Axial stress for service condition; drop in
temperature
The values shown are the stresses along the support lines of the design strips for the
sustained service (quasi permanent) load combination plus 20o C drop in ambient
temperature. Stresses shown are in MPa.

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Ho w much rebar is required for temperature ?
1- In Y direction, no need since the slab is still under
compression
2- In X Direction, the slab was compressed without
thermal effect then got tension due to temperature,
thermal effect then got tension due to temperature,
hence rebar is required
To calculate how much rebar is required, use the
following equation :
As= Axial stress due to temp X Cross sectional area/fy
As= 1.69 (MPa) x 220mmx 1000xx/420 MPa =885 mm2
Use 5T16/m

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Ho w much rebar is required for temperature ?
Option-2
Use ETABS model output for Moment and axial force
due to gravity+ temperature
due to gravity+ temperature
Take similar strip from PT slab including all PT and
rebar in it
Design the strip as a column under P-M loads and
calculate how much additional rebar required

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PT Floor shortening
PT slab should be free to
shorten, however the
below elements affect the
overall slab shortening
1- Elastic shortening
(immediate )
DESCRIPTION PERCENTAGE
%
SHRINKAGE(SH)
CREEP (CR)
66
11
(immediate )
2- Creep shortening (long
term)
3- Shrinkage shortening
(LT)
4- Thermal
CREEP (CR)
ELASTIC SHORTENING (ES)
TEMPERATURE (ES)
TOTAL
11
7
16
100

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Effect of support restraint on PT
Source: B.Aalami, OCT2017, Structuremag

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Effect of support restraint on PT
•Restraint cracks are most pronounced at
the first level of a concrete structure, due
to the restraint from the foundation.
There is less cracking at higher levels.
• Restraint cracks are often long in
comparison to span lengths; they
typically extend beyond the length of a
Source: B.Aalami, 2017, Structuremag
typically extend beyond the length of a
panel and through the entire depth of the
member.
•They occur at points of weakness, such
as where non-prestressed reinforcement
is reduced or terminated, or where there
is a reduction in the member’s cross-
sectional area.

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Effect of restraint on precompression
•P/A will be reduced due to
support restraints
•This will reduce the capacity
of slab to resist cracking
Source: Aalami

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Restraint rebar
Source: TR43-2005

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Crack mitigation due to restraints-Pour strips
Bonded reinforcement
through the pour strip must
through the pour strip must
be designed to resist all
tensile, shear, and flexural
forces alone, as post-
tensioning is interrupted
Source: Guo et al-PTI journal

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Pour strips
Source: B.Aalami(TN451-2014)

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Location of Pour strip
Option-1

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Option-2

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Propping the Pour strip

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Creep and Shrinkage effect with time

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Pour strips guidelines

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PT Slab modifier for seismic
ASCE 41-13

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PT Slab diaphragm

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Reversed moment due to lateral loads
Source : Aalami(2014)
Add normal reinforcement where slab is deficient

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Detailing-Openings

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Detailing

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Detailing-Steps
Source : Aalami

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Detailing-Steps
Source : Don Kline

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Recommended PT Design sites
https://ptstructures.com/technical-notes/

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Recommended PT Design Theory lectures

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Future subjects
Condition assessment, Repair /strengthening of PT slabs
Strengthening with external prestressing

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Future subjects
Strengthening with FRP
Condition assessment and Strengthening of Bridges
CEANASS@GMAIL.COM
https://www.linkedin.com/in/anass1/

Post tensioned slabs design fundamentals anas alakhras

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