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

A_ps : Area of prestressing steel
f_ps : Stress in prestressed reinforcement at nominal strength
f_pu : Specified tensile strength of prestressing steel
f_py : Specified yielding strength of prestressing steel (0.90* f_pu= 0.90*1,860M_pa = 1,674M_pa)
f_pi : Initial prestress stress of prestressing steel
f_pe : Effective prestress stress of prestressing steel (0.65* f_pu= 0.65*1,860M_pa = 1,200M_pa)
F_st : Max. prestress force ( Min[ 0.94 f_py, 0.8 f_pu ] *A_ps = Min[ 1,573 or 1,485 ] *138.7 = 205kN )
F_se : Effective prestress force ( f_pe*A_ps = 1,200M_pa*138.7 = 166.4kN )
F_ps : Ultimate prestress force

Design Steps

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

                                                                                                                                                         Step 1: Jacking Stage (F_st)

                                                                                                                                                         Step 2: Transfer Stage (F_pi)

                                          (c) Service condition (SLS)                                                  (d) Strength condition  (ULS)

                                           Step 3: Service Stage (F_se)                                                     Step 4: Ultimate Stage (F_ps)

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 → F_si (before short/long-term tension loss occurs, Max. prestress)
• Using Concrete strength : f_ci (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  → F_se (Effective tension after short/long-term tension loss occurs)
• Using Concrete strength : f_ck (Max. design strength)
• Loading : All design load (Unfactored Load)
• Checking item : Deflection, Crack Width.

Ultimate Stage

• Using Prestress Force → Nominal Strength
• Using Concrete strength : f_ck (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

M_S : Moment due to own weight of concrete section.
M_O : 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"=(M_ol² )∕8EI= (P_e(2l)² )∕8EI=(P_el² )∕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 :  

M_Secondary : Secondary Moment → Moment caused by R
* M_Secondary means the moment created by the reaction force that restrains the deformation caused by M1.

In example 1 :  𝑀_{𝑆𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦} 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝐵=(3𝑃𝑒/2𝑙)×𝑙=3𝑃𝑒/2

M_Net : Net final Moment = M₁ + M_Secondary : 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

<Thickness-span correlation by each slab system>

• RC Member

• Post Tension Member

• Reduction ratio of thickness or depth when PT is applied

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 : (MP_a)

Allowable stress for Tendon (Strand)                                                                                                                                                         unit : (MP_a)

Please download the white paper of Structural Design Guide for Prestressed Slabs below to see the full contents.