Whether a Post-tensioned Slab (PT) is cost-effective or not depends largely on the skills of the Structural Engineer. Practice makes perfect. To quickly master it, increase productivity and quickly find the optimal solution, you can use ETABS structural design software from version 2016, which is familiar to Engineers. Basic knowledge can be found in the old topic on PT slab. Below is a summary of how to do it step by step:
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1️⃣Preliminary floor size
First, the design engineer chooses the floor thickness, column cap, beam, … based on experience. For example: Normal civil floor
Hs=L/(36-42) without drop panels
Hs=L/(40-48) with drop panels
Hcap = 1.75.Hs
Create a multi-storey building model as usual.
2️⃣Create a 2-way slab strips
On the Etabs model with all floors, draw the floor strips (Design Strip), note in both perpendicular directions. The width of the strips covers the floor area that needs to be calculated for PT.
Column Strip floor strip, connecting the column points with a width that hugs half of the column grid on each side. Use the Edit> Add/Edit Design Strips> Add Design Strips and Edit Strip Width functions to speed up drawing.
3️⃣Declare the parameters of PT in Etabs
– Define> Material Properties> Material Type: Tendon
– Define> Section Properties> Tendon Section 🗻Photo 3
– Define> Load Patterns> Prestress-Final, Prestress-Transfer 🗻photo 4
– Define> Load Cases> Hyperstatic🗻photo 5
🔍Definitions:
Tendon, Strand, Bonding Option, Prestress-Final, Prestress-Transfer, Hyperstatic,
4️⃣Cable model for each floor strip
A simple cable model in a strip is a single Tendon, the number of strands in this Tendon is equal to the total number of cables expected to be actually arranged within the width of that strip.
🔲Design verification problem:
The number of Strands is known, just enter the Number of Strands in the properties of each Tendon (🗻Image 6)
🔲Design case:
The design engineer needs to determine the number of Strands for Tendon in each floor strip, according to the percentage of balanced load.
Use the function Edit> Add/Edit Tendons> Add Tendons in Strips (🗻Image 7).
Enter the parameters:
Precompression Level, Self Load Balancing Ratio
Also declare the parameters:
– Cable trajectory 🗻Photo 8
– Jack from This Location
– Tendon Jacking Stress
– Tendon Loss Data 🗻Image 9
🔍Definitions:
Balanced load, Precompression Level, Self Load Balancing Ratio, Tendon Jacking Stress, Jack from one-End, Jack from Both Ends, Tendon Loss
5️⃣Slab design
– Select design standards: Design> Concrete Slab Design> View/Revise Preferences
– Create load combinations according to standards:
Define> Load Combinations> Add Default Design Combos> Concrete Slab Design
Design> Concrete Slab Design> Select Design Combinations
The reason ETABS is more accurate than SAFE: the effect of DUL, horizontal loads (wind, earthquake, …) on many floors at the same time.
– Copy Cables and floor strips for floors to be calculated:
Edit> Replicate
Design> Concrete Slab Design> Select Stories for Design
– Run! Start Design
Design according to TTGH 1: use Hyperstatic Load case for DUL
– Calculate normal reinforcement arrangement: Design> Concrete Slab Design> Display Flexural Design
– Check column cap punching: Design> Concrete Slab Design> Display Punching Check
Design according to TTGH 2: use Prestress-Final or Prestress-Transfer Load case for DUL
– Check internal stress conditions: newly tensioned stage, final stage when working.
– Crack width: Design> Concrete Slab Design> Display Flexural Design
6️⃣Arrangement of rebars on design drawings
The design of PT floors requires attention to the structural requirements of reinforcement. Although the calculation is not required, it is still necessary to arrange enough:
🔲Tendons
Arrange cables in 2 directions to ensure the total number of Strands in each floor strip as calculated. There are some arrangements such as 🗻Photo 10.
– Tendons are concentrated in a tape with a width of usually 1.2m, connecting vertically through columns and walls
– The arrangement in a band in one direction and the distribution in the other direction is the most advantageous in terms of design, because both directions have the largest cable height difference, so the balanced load is the largest, and there is also the least collision because the cable trajectory is Parabolic.
🔲Normal Steel – Upper Layer
Arrange at least 4 steel bars in the area around the column and wall, with a minimum length as in 🗻Photo 11
Small diameter steel should be selected because it is necessary to arrange 2 layers in 2 directions on each support. Small diameter is also more effective in controlling cracking.
🔲Normal steel – Lower layer
It is possible to design a 2-way floor structure without normal reinforcement in the lower layer as long as the cable has ensured load-bearing capacity. If the tensile stress in the concrete is greater than the value specified in the standard, it is necessary to arrange the minimum amount of steel to control cracking, the minimum length as in 🗻Photo 11.
– The lower layer reinforcement in the cable arrangement direction according to the strip is placed within the width of the cable strip to ensure the minimum distance. According to the cable direction, the lower layer reinforcement is also evenly distributed. The reinforcement in the distribution direction is placed on top of the reinforcement in the cable strip direction.
– If the design engineer calculates that the lower layer of reinforcement must be arranged, it is necessary to extend at least 1 bar to the wall column:
+ Pull 1/3 of the bars at the edge span to anchor to the column
+ Pull 1/4 of the bars at the middle span to anchor to the column
🔲Shear and puncture steel
Shear steel for flat floors, according to the calculation of puncture when the concrete is not strong enough. J-shaped steel can be used quite economically.
🔲Structural steel at the cable anchor head
These details are typical and included in the drawing General notes
7️⃣ Handling common construction situations
In construction design, the following situations are common when constructing PT Slab structures:
🔲Cable elongation is not achieved
Insufficient elongation: when pulling 100% of the force, the elongation value of the cable bundle does not drift according to the design. Even though the measuring device has been tested and accepted to meet the required accuracy.
Possible causes and solutions:
– Due to increased friction between the cable and the duct due to long-term storage or due to the pipe being broken when compacting the concrete, the cement water seeps in. The solution is to pull the force up to 1.05 Ptk or pull the cable without load 3->5 times to reduce friction.
– Due to the cable not meeting the design specifications.
Normally, the average elongation is about 6.5 parts per thousand (with 12.7mm cable). The highest elongation is achieved with cables of about 15m or less (1 active anchor head), the longer the cable, the more difficult it will be to achieve the elongation, cables longer than 30m will have to use 2 active anchor heads. After stretching the cable, the elongation value of the cable reaches 0.95 to 1.1, the elongation of the cable when calculated is within the allowable limit.
🔲Tendon slippage during pulling
When the pulling force reaches 100%Po and then rebounds, the anchor foundation (anchor pin) slips and the cable cannot be held.
– If it is not possible to re-construct, the design consultant needs to recalculate the bearing capacity of the structure with the tensioned cable.
– If in that structure, 1 broken cable accounts for 1-2%, it must be discarded.
Can be handled as follows:
– Thread another cable.
– Punch out and re-anchor.
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🎁Definitions in Post-tensioned structure design (in alphabetical order):
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💎Bonding Option |
Bonding properties, including 2 types:
– Bonded has adhesive force to adhere to the concrete along the length of the cable by pumping mortar to fill the duct after tensioning and cutting the cable strands. This is a popular type in the Vietnamese market today for civil houses, often used by design consultants.
– Unbonded has no adhesive force between the cable strands and concrete along the length of the cable. The cable tension force is transmitted to the floor only through the 2 anchor ends to become a pre-compression force on the concrete there.
Stress loss for the bonded type is greater due to greater friction between the cable strands and the duct
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💎Design Strip |
It is a virtual beam to take internal force and calculate the design of the floor structure as a beam with width equal to the strip width, the main supports are wall columns. |
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💎Elongation |
Is the deformation of the cable caused by the cable tension force, minus the loss, on each cable.
When constructing, this value is measured as the basis for acceptance.
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💎Eurocode – Some limitations to note when designing floors according to EC2 |
– Compressive stress in concrete does not exceed 0.6fck (0.45fck in long-term combination)
– Tensile stress in cable does not exceed 0.75fyk
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💎Hyperstatic |
The super-static effect, characteristic of the design of the DUL structure, is the result of the effect of the supports of the floor (columns, walls). The tensioning of the cables after pouring concrete causes additional reactions on the supports due to the effect of preventing the free displacement caused by the pre-compression force of the supports. These reactions cause additional internal forces on the floor, so it needs to be considered during the working phase.
(see more in the post Basics of PT Slab Design) if you find it difficult to understand, don’t worry, Etabs will calculate it for you
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💎Jack from Both Ends |
Tendons jacked at both ends, actively anchored, by jack. Applicable for cable lines longer than 30m |
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💎Jack from one-End |
Tendons jacked at only one end, at the active anchor position, by jack. Applicable for cable lines shorter than 30m |
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💎Precompression Level |
1 important parameter when designing DUL slab structures. Equal to the total tensile force divided by the cross-sectional area perpendicular to the direction of the tensile force. Some standards specify a minimum value of 0.85MPa (ACI)
The maximum precompressive stress value should be 2.0MPa for slabs and 2.5MPa for beams. Larger values, meaning more cables, make the design uneconomical.
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💎Prestress-Final |
Loads exerted by cables on the structure.
at the working stage, all stress losses in cables have been deducted
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💎Prestress-Transfer |
The load exerted by the cable on the structure,
at the stage of newly tensioning the cable, begins to transmit the load to the concrete, minus the short-term stress loss. The general principle is that the tension force of the cable after anchoring is transmitted as a compressive reaction force into the concrete according to Newton’s 3rd law.
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💎Profile |
Cable curve shape on the floor cross-section. Each trajectory shape gives a corresponding type of balanced load. The most common is the Parabolic trajectory for evenly distributed balanced load. 🗻Photo 13 |
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💎PT |
Post Tension: Post-tensioning, pouring concrete before stressing tendons. Distinguished from prestress, stressing and anchoring strands before pouring concrete, often found in prefabricated structures.
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💎Strand |
🗻image 12
 The smallest unit of wire rope, commonly 7 high-strength steel wires woven together like rope, diameter 12.7mm. Strand has a larger diameter, 15.3mm, often used for pre-tensioned prefabricated structures or for bridges, for DUL beams and transfer floors. |
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💎Balanced Load |
Load in the opposite direction of the floor weight. The floor calculation diagram now removes the cable and replaces it with the balanced load. The load on the structure is equal to the floor load minus this balanced load.
🗻Photo 13
Experience in designing civil floor structures, the reasonable number is 60-80% dead load balance. With beams, it is 80-110%.
This is the parameter that determines the number of cables.
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💎Tendon |
🗻Image 12
The cable unit used in the calculation diagram, consisting of many Strands. The tension force on the Tendon is equal to the tension force of 1 strand multiplied by the number of strands in the Tendon
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💎Tendon Jacking Stress |
Stress equals cable tension at anchor divided by cable area |
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💎Tendon Loss |
The design of PT structures must always take this into account. The losses include 2 parts:
– Short-term part (Stressing Losses), including (i) losses due to friction, (ii) losses due to anchor deformation, (iii) due to elastic shortening of concrete.
– Long-term part (Long Term Losses), including (i) losses due to shrinkage, (ii) due to concrete creep, (ii) due to stress relaxation.
🗻Photo 14
The tension in the cable must be minus the loss to calculate the balance load. It is recommended to let Etabs calculate automatically. Parameters entered into the software:
– Curvature Coefficient, Wobble Coefficient: to calculate the loss due to friction, taken from the Catalogue of the cable type used.
– Anchorage Set Slip: to calculate the loss due to anchor deformation, usually 6mm
– Elastic Shortening Stress: stress loss due to elastic shortening of concrete
– Creep Stress: stress loss due to creep
– Shrinkage Stress: stress loss due to shrinkage
– Steel Relaxation Stress: stress loss due to stress relaxation
Independent software such as ADAPT FELT can be used to accurately calculate the stress losses and elongation of the cable.
In the first step of choosing the number of cables, it is assumed that the total stress loss accounts for 15-20%, of which the long-term part is about 10%. Doing it many times will assume this number is more accurate.
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🎁Summary:
– Designing a PT slab structure has become simpler because the calculation software is automatic. The only difference is that there are more parameters than conventional reinforced concrete for engineers to pay attention to.
– Choose any design code, ACI, Eurocode, … then the load, material strength, allowable limit, … are synchronized according to that code.
– If you find the article too long and difficult to understand, then read each step. At other times, when you are calmer and more relaxed, read the Blog, documents, to clearly understand the nature of the parameters, create confidence when going out to communicate, protect your products.
– Unlike conventional reinforced concrete, the DUL problem has many answers about reinforcement on the same concrete size solution. Choose many cables (more balanced load) then less conventional steel and vice versa. The more familiar the skill is, the easier it is to find the optimal problem about cable and steel mass, saving for Society.
For example, for a residential floor, for 1m2 of floor, a reasonable design is about 5kg, and regular steel is 15kg. If you calculate more, try to do it over and over again to gradually optimize.
Wishing all engineers to apply it successfully, quickly improve their capacity, and have many useful design and construction projects for life 🎉
Reference source: Prof. Alaami – founder of ADAPT corporation
