Post-Tension Slab Analysis & Design

October 26, 2022
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Post-Tension Slab Analysis & Design


Please fill out the Download Section (Click here) below the Comment Section to download the Structural Design Guide for Prestressed Slabs.

 

 

 

Table of Contents 

 

What is Post-Tensioning?

 

 


 

 

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

 

 
Post tension analysis & design_1
 
                  * 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

 

bonded pos-tensioning and nbonded post-tensioning

 

(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

 

 

 

 

pt slab jacking stage and service stage

Figure 1: Wheel load dispersion; hc < 2 ft) - Source: AASHTO LRFD
 

 

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

 

 

PT SLAB Design Step

 

post-tension member and tendon removed

Figure 3: Wheel load dispersion (Overlapping dispersion area); hc > 2 ft - Source: AASHTO LRFD

 

         (a) Post-tensioned member                                               (b) Tendon removed

                                                                                                                                 Step 1: Jacking Stage (Fst)

                                                                                                                                 Step 2: Transfer Stage (Fpi)

 

 

service codition and strength condition

 

 

                                        (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

 

Loading Conditions-1

 

 

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

 

primary moment

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

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 :  

이미지 49

secondary moment

 

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 :  𝑀𝑆𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝐵=(3𝑃𝑒/2𝑙)×𝑙=3𝑃𝑒/2

MNet : Net final Moment = M1 + MSecondary : Moment acting on the actual continuous beam by prestressing.

In example 1 : 𝑀u 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝐵=−𝑃𝑒+(3𝑃𝑒/2)=𝑃𝑒/2

 

 

Thickness or Depth of Section

 

PT SLAB

<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

intalling slab formwork

Step 02 : Installing slab rebar

installing slab rebar

 

Step 03 : Placing bar chair by profile height

placing bar chair by profile height

 

Step 04 : Placing tendon on the bar chair

Step 04  Placing tendon on bar chair

Step 05 : Add extra rebar

Step 05  Add extra rebar

Step 06 : Pouring concrete

Step 06  Pouring concrete

Step 07 : Insert block and jaws bar chair

Step 07 Insert block and jaws bar chair

Step 08 : Stressing and measuring elongation

Step 08  Stressing and measuring elongation

Step 09 : Grouting

Step 09  Grouting

 

 

 

Design Flow Chart for Post-Tension

 

 

Design Flow Chart for Post-Tension

 

1. Choose Tendon force and profile

Tendon Profile Type

Tendon Profile Type

How to arrange tendon of parabolic shape

How to  arrange tendon of parabolic shape_1

 

How to  arrange tendon of parabolic shape_2

 

After Transfer Stage

 

How to  arrange tendon of parabolic shape_3

 

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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About the Author
Young-il Seo | Principal Structural Engineer

Young-il has over 13+ years of experience in building design, especially high-rise buildings with column reduction analysis, plant structures, pushover analysis, health monitoring, and vibration control projects. Since 2016, he is planning and providing technical supports for midas building products such as midas Gen, nGen, and Design+.

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DOWNLOAD Structural Design Guide
for Prestressed Slabs

Chapter 1. What is post-tensioning
Chapter 2. Design Flow for Post-Tension
Chapter 3. Post-Tension Design Tip and Example
Chapter 4. Tutorial forPost-Tension Beam

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