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Post-Tension Slab Analysis & Design
What is Post-Tensioning?
Post-tensioning is a technique for reinforcing concrete. Post-tensioning tendons, which are prestressing steel cables inside plastic ducts or sleeves, are positioned in the forms before the concrete is placed. Afterward, once the concrete has gained strength but before the service loads are applied, the cables are pulled tight, or tensioned, and anchored against the outer edges of the concrete.
Post-tensioning is a form of prestressing. Prestressing simply means that the steel is stressed (pulled or tensioned) before the concrete has to support the service loads. Most precast, prestressed concrete is actually pre-tensioned-the steel is pulled before the concrete is poured. Post-tensioned concrete means that the concrete is poured and then the tension is applied-but it is still stressed before the loads are applied so it is still prestressed.
ADVANTAGES & APPLICATIONS OF POST-TENSIONING
* It reduces or eliminates shrinkage cracking-therefore no joints, or fewer joints, are needed.
* Cracks that do form are held tightly together.
* It allows slabs and other structural members to be thinner.
* It allows us to build slabs on expansive or soft soils.
* It lets us design longer spans in elevated members, like floors or beam.
Post-Tension Type
(a) Bonded Post-Tensioning
It is used for large structural elements such as beams and transfer girders, design advantages include increased span lengths and load carrying capacity and reduced deflection.
(b) Unbonded Post-Tensioning
It is typically used in new construction for elevated slabs, slabs-on-grade, beams, and transfer girders, joists, shear walls, and mat foundations. Light and flexible, the unbonded mono strand can be easily and rapidly installed &#; providing an economical solution.
Strength of Prestressing Steel
Step Immediately after prestressing After anchoring Tension Stress Min[ 0.94 fpy, 0.80 fpu ] 0.70 fpu
Diameter Aps
(mm2)
fpu (Mpa) fpy (Mpa) fpe (Mpa) Fst (kN) Fse (kN)12.7mm
98.71 1,860 1,674 1,200 146 118.4 15.2mm 138.7 1,860 1,674 1,200 205 166.4
Aps : Area of prestressing steel
fps : Stress in prestressed reinforcement at nominal strength
fpu : Specified tensile strength of prestressing steel
fpy : Specified yielding strength of prestressing steel (0.90* fpu= 0.90*1,860Mpa = 1,674Mpa)
fpi : Initial prestress stress of prestressing steel
fpe : Effective prestress stress of prestressing steel (0.65* fpu= 0.65*1,860Mpa = 1,200Mpa)
Fst : Max. prestress force ( Min[ 0.94 fpy, 0.8 fpu ] *Aps = Min[ 1,573 or 1,485 ] *138.7 = 205kN )
Fse : Effective prestress force ( fpe*Aps = 1,200Mpa*138.7 = 166.4kN )
Fps : Ultimate prestress force
Design Steps
(a) Post-tensioned member (b) Tendon removed
Step 1: Jacking Stage (Fst)
Step 2: Transfer Stage (Fpi)
(c) Service condition (SLS) (d) Strength condition (ULS)
Step 3: Service Stage (Fse) Step 4: Ultimate Stage (Fps)
After Jacking Stage
&#; Activity of anchorage device
&#; Tension force loss due to friction
&#; Tension loss due to elastic shrinkage of concrete
AfterTransfer Stage
&#; Tension loss due to creep
&#; Tension loss due to shrinkage
&#; Tension loss due to strand relaxation
Loading Conditions
Transfer Stage
&#; Using Prestress Force &#; Fsi (before short/long-term tension loss occurs, Max. prestress)
&#; Using Concrete strength : fci (compressive strength of concrete when prestress is introduced, Min. strength)
&#; Loading : only Self-weight (before adding a finishing and live loads)
&#; Checking item : Tensile cracking and crushing of concrete, failure of anchorage part.
Service Stage
&#; Using Prestress Force &#; Fse (Effective tension after short/long-term tension loss occurs)
&#; Using Concrete strength : fck (Max. design strength)
&#; Loading : All design load (Unfactored Load)
&#; Checking item : Deflection, Crack Width.
Ultimate Stage
&#; Using Prestress Force &#; Nominal Strength
&#; Using Concrete strength : fck (Max. design strength)
&#; Loading : All design load (Factored loads)
&#; Checking item : Flexural failure or compression stress under flexural behavior.
Definition of Member Forces
Example 1: Continuous Beam
MS : Moment due to own weight of concrete section.
MO : Moment due to other applied loads.
M1 : Primary moment &#; Moment by the distance between the section center and the prestressing point.
In example 1: M = Prestressing force x Eccentricity distance = P x -e = -Pe
Δ : Deflection by M1 &#;Deflection at point B when considered as a simple beam.
In example 1 : "Δ"=(Mol2 )&#;8EI= (Pe(2l)2 )&#;8EI=(Pel2 )&#;2EI
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R : Reaction by Δ &#; Point B should not be deflected by the support, so a reaction force is generated so that deformation as much as (-)Δ occurs.
In example 1 :
MSecondary : Secondary Moment &#; Moment caused by R
* MSecondary means the moment created by the reaction force that restrains the deformation caused by M1.
In example 1 : &#;&#;&#;&#;&#;&#;&#;&#;&#;&#; &#;&#; &#;&#;&#;&#;&#; &#;=(3&#;&#;/2&#;)×&#;=3&#;&#;/2
MNet : Net final Moment = M1 + MSecondary : Moment acting on the actual continuous beam by prestressing.
In example 1 : &#;u &#;&#; &#;&#;&#;&#;&#; &#;=&#;&#;&#;+(3&#;&#;/2)=&#;&#;/2
Thickness or Depth of Section
<Thickness-span correlation by each slab system>
&#; RC Member
Span/Depth Continuous span Simple span Beam 21 16 2-way slab 30 - 1-way slab 28 20
&#; Post Tension Member
Span/Depth Continuous span Simple span Roof Not Roof Roof Not Roof Beam 60% 70% 53% 62% 2-way slab 63% 71% - - 1-way slab 56% 62% 44% 50%
&#; Reduction ratio of thickness or depth when PT is applied
RC/PT (%) Continuous Span Simple span Roof Not Roof Roof Not Roof Beam 60% 70% 53% 62% 2-way slab 63% 71% - - 1-way slab 56% 62% 44% 50%
The thickness is reduced by 30-50% compared to the RC member. Alternatively, an economical design can be made by reducing the amount of rebar or tendon required for the same thickness.
Post-Tension Slab Procedure
Step 01 : Installing slab formwork
Step 02 : Installing slab rebar
Step 03 : Placing bar chair by profile height
Step 04 : Placing tendon on the bar chair
Step 05 : Add extra rebar
Step 06 : Pouring concrete
Step 07 : Insert block and jaws bar chair
Step 08 : Stressing and measuring elongation
Step 09 : Grouting
Design Flow Chart for Post-Tension
1. Choose Tendon force and profile
Tendon Profile Type
How to arrange tendon of parabolic shape
After Transfer Stage
2. Check final stresses and Check initial stresses
Allowable stress for Concrete unit : (MPa)
Checking Stage Conditions Allowable stress under Initial Service Load (Initial) 1. Extreme fiber stress in compression pci = 0.60 fci 2. Extreme fiber stress in tension pti = 0.25 fci0.5 3. Extreme fiber stress in tension at ends of simply supported members pti = 0.50 fci0.5 under Service Load (Final) 1. Extreme fiber stress in compression (at Long-Term Service Load) pcf = 0.45 fck 2. Extreme fiber stress in compression (prestress + total load) pcf = 0.60 fck 3. Extreme fiber stress in tension ptf = 0.50 fck0.5
Allowable stress for Tendon (Strand) unit : (MPa)
Checking Stage Conditions Allowable stress During Stressing - Max [0.94 fpy, 0.8fpu] Immediately after stressing - 0.70fpu
Please download the white paper of Structural Design Guide for Prestressed Slabs below to see the full contents.
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