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When all sides of a post-tensioned (PT) slab are strongly supported by continuous walls or beams, the design process simplifies significantly due to enhanced structural continuity, load sharing, and reduction of critical stress points. The primary simplifications include lower deflection, reduced slab thickness, and improved crack control, which often allow for more streamlined calculation methods.
Post-Tensioning Institute +1
Here is how the design simplifies:
1. Reduced Design Moments and Deflection
Continuous Support Action: Continuous edge supports act as rigid boundaries, reducing the maximum positive bending moments at the center of the span.
Lower Tendon Requirements: Because the slab is "restrained" rather than free, the upward balancing load provided by the tendons is more effective, allowing for fewer cables or less drape to meet serviceability requirements.
Simplified Serviceability Check: Deflection, often the governing factor in long-span PT design, is drastically reduced because the edges are not allowed to "sag".
Post-Tensioning Institute +3
2. Enhanced Crack Control and Durability
Reduced Tensile Stresses: Strong edge constraints prevent the slab from lifting or curling at the edges, which means the concrete remains largely in compression, significantly reducing the risk of cracking.
Reduced Reinforcing Steel: With fewer tension cracks to control, less conventional "passive" reinforcing steel (rebar) is needed for crack control.
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3. Simplified Design Procedures
One-Way or Two-Way Analysis Simplification: Continuous support allows engineers to use simplified moment coefficient methods (such as those in BS 8110-1-1997 or Eurocode 2) rather than complex Finite Element Analysis for initial sizing.
Reduced Need for Thicker Sections: The improved stiffness allows for a higher span-to-depth ratio, meaning a thinner, more cost-effective slab can be used without risking excessive deflection or punching shear.
Coloscapes Concrete +1
4. Simplified Foundation/Slab-on-Grade Design
Elimination of Stiffening Ribs: In slab-on-ground applications, continuous perimeter walls allow the slab to act as a rigid mat, often allowing designers to eliminate stiffening ribs and use a uniform thickness slab.
Reduced Formwork Complexity: The edge constraints simplify edge formwork, as the walls already provide the necessary anchoring and support, reducing the need for specialized edge bracing.
Post-Tensioning Institute
Summary of Design Differences
Feature
Supported on 4 Sides
Free Edge/Columns
Slab Thickness
Thinner
Thicker
Deflection
Low (negligible)
Higher (governs design)
Rebar Quantity
Low
High (for crack control)
Tendon Profile
Lower drape required
Higher drape required
Calculation
Simplified (coefficients)
Complex (FEM)
Disclaimer: This information is based on structural engineering principles for post-tensioned design, and specific designs must be performed by a qualified professional.
How does post tension slab design simplify when all sides of the slab are strongly supported by continuous walls and beams?
Post-tensioned (PT) slab design simplifies significantly when all sides are strongly supported by continuous walls or beams because the system shifts from a complex "two-way" bending problem to a more predictable "one-way" or "clamped" behavior.
Structural Simplifications
Uniform Tendon Layout: Tendons can follow a simple grid rather than complex banded/distributed patterns.
Reduced Deflection: Strong perimeter support limits "dish-style" sagging, requiring less prestressing force.
Lower Punching Shear: Continuous walls eliminate the risk of columns "punching" through the slab.
Minimal Corner Torsion: Rigid supports absorb twisting forces that usually require extra steel in flat slabs.
Simplified Load Path: Loads transfer directly to the nearest wall or beam via short, clear spans.
Design & Execution Benefits
Thinner Slabs: The rigid support allows for higher span-to-depth ratios, saving concrete and weight.
Standardized Profiling: High and low points for tendon chairs become consistent across the entire floor.
Cracking Control: The continuous support provides a natural "restraint" that helps the PT force compress the slab more evenly.
Faster Detailing: Engineers can use simpler software models as the slab behaves like a series of simple beams.
An example slab, will say up and down is north south and left right is west east. The north south is a bit longer than west east so the banded (closely spaced) tendons run that direction. The little rectangles represent support columns. With my system the columns are actually wall beams that run the full length of the slab. I'm going to go through all the ACI 318 Code calculations to see how that elongated column phenomea works out.
With my system the slab thickness will be either 6" or 8" depending on how the slab is formed. It's six inches if formed on 2" thick support pavers or 8" if formed at the wall height, eliminating the pavers. The pavers are offered as an efficient method to give the tendons a 2" cover which would be a four hour (highest) fire rating.
So the center columns are 20" in the north south direction and 14" in the east west direction, while the end columns are 12" north south and the same 14" east west.
The spans using the 45 ratio span the slab thickness ratio yield choosing a 6.5" thickness.
Both unfactored and factored dead and live loads are used and kept separate.
The challenge in working the equations is knowing where the numbers come from. The math looks fancy and intimidating but it's really not complicated. I've found tracking down the source of the numbers is the challenge. For the example the factored dead load is 134 psf, unfactored 96, live load 40 psf and factored 68 psf. Total unfactored load 136 psf and factored 202 psf.
We'll see how and where these numbers pop up during the analysis. These are the loads used to be "balanced" by parabolic tendons.
The first number is Fpc = 175 psi. That is an assumed desired amount of compressive force to be imparted to the concrete through the squeezing (tightening) of the tendons. That 175 is between 136 unfactored load and the 202 factored load. It is 175/202 =
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