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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.
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⚠️ Critical Watchpoints
While the design is simpler, you must account for Restraint to Shortening. Because the walls and beams are "strong" and "continuous," they can prevent the slab from shrinking during tensioning, which may lead to cracking at the joints.
If you are working on a specific project, let me know:
The span lengths between the walls?
Is it a residential or heavy industrial load?
Are you using bonded or unbonded tendons?
I can help you determine the optimal tendon spacing or slab thickness.
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design a 22' x 18' post tensioned slab 6" thick. The unfactored dead load is 80 psf and unfactored live load is 75 psf. The slab is continuously supported on all 4 sides with spandrel beams.
To design this post-tensioned (PT) slab, we will assume a one-way design approach in the long direction, as the strong perimeter support from spandrel beams allows for simplified load paths. We will follow ACI 318 guidelines for serviceability and strength.
1. Identify Material and Section Properties
We assume standard values for a typical PT slab:
Concrete Strength ():
PT Strand (
): (unbonded)
Effective Prestress (
):
Slab Thickness (
):
Self-weight (
):
2. Determine Total Gravity Loads
Sum the dead and live loads to find the total service load:
Dead Load (
):
Live Load (
):
Total Service Load (
):
3. Calculate Required Prestressing Force
We aim to balance approximately of the self-weight to control deflections:
Balanced Load (
):
Maximum Sag (
): For a slab with cover, the drape is ().
Force per foot (
): Use the formula
4. Spacing of PT Strands
Calculate the number of strands needed based on a standard diameter strand ():
Force per Strand:
Spacing: on center.
5. Check Serviceability Stresses
The average precompression () should typically fall between and to prevent cracking:
: (Slightly high, but acceptable for heavy loads).
✅ Result Summary
The design for a slab requires diameter unbonded tendons spaced at on center in the long () direction to support the specified loads while maintaining deflection control.
If you'd like to refine this further, let me know:
The concrete strength () you plan to use?
Any fire rating requirements (this affects cover)?
If you need a bill of materials for the tendons?
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Dec 30, 2025 — Example 8.1 For the prestressed beam shown in figure and knowing that the beam is fully prestressed determine, 1. The required for...
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concrete strength = 4,000 psi
Designing with concrete slightly adjusts the allowable tensile stresses but maintains the overall structural efficiency of the slab. Given the strong continuous support on all four sides, we can proceed with a one-way design for the primary span of .
1. Calculate Gravity Loads
Self-Weight (
):
Dead Load (
):
Live Load (
):
Total Service Load (
):
2. Required Prestressing Force (
)
To balance of the self-weight () with a tendon drape (
) of (assuming cover at top and bottom):
3. Tendon Spacing
Using standard diameter unbonded tendons ( effective force):
Spacing: on center.
Check Precompression: . This falls within the recommended range.
4. Stress Checks at
Allowable Tension: .
Total Service Moment (
): .
Net Stress: . With balanced loads, the tension is significantly reduced, keeping the slab "class U" (uncracked).
✅ Result Summary
For a slab using concrete, use unbonded tendons spaced at on center in the span direction. This provides a balanced load of and an average precompression of , which is ideal for crack control and deflection.
If you are ready to move to the next phase, I can help with:
The secondary tendon layout for the direction?
Calculations for minimum bonded reinforcement (rebar) at supports?
A cost estimate for the PT materials?
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yes, all of the above
1. Secondary Tendon Layout (18' Direction)
In the 18' direction (shorter span), the tendons act primarily as temperature and shrinkage (T&S) reinforcement.
Design Objective: Provide a minimum average precompression () of at least as per ACI 318 to control cracking.
Required Force: For a 6" slab, requires of force per foot.
Spacing: Using 1/2" unbonded tendons ( effective force), the required spacing is:
Layout Detail: Place these tendons in a single layer, perpendicular to your main tendons. They should be centered in the slab thickness (3" from the bottom) unless they need to provide flexural capacity at midspan.
2. Minimum Bonded Reinforcement (Rebar)
Even with PT, ACI requires bonded rebar to ensure ductility and control surface cracking, especially at support regions.
At Supports (Top Bars): Place top rebar over the spandrel beams to resist negative moments.
Quantity: Minimum area , where
is the cross-sectional area of the slab.
Calculation: total.
Placement: Use #4 bars at 12" on center extending of the span into the slab from each support.
In Span (Bottom Bars): If tensile stresses exceed , bottom rebar is required.
Requirement: For your loads, provide #4 bars at 18" on center in both directions as a bottom mat for basic robustness.
3. Material Cost Estimate (Approximate)
Prices fluctuate based on current market rates for concrete and steel.
Item
Quantity
Rate (Est.)
Total Cost
Concrete (4k psi)
PT Tendons
Bonded Rebar
Anchorages/Chairs
1 Set
Flat Rate
Total Material
—
—
Note: This excludes labor, formwork, and shipping. Total installed costs typically range from $6 to $12 per square foot.
✅ Final Design Summary
Slab: ( concrete).
Primary Tendons ( span): unbonded, O.C. (High chair at supports, low at midspan).
Secondary Tendons ( span): unbonded, O.C. (Mainly for T&S).
Bonded Rebar: #4 at 12" O.C. (Top, over beams) and #4 at 18" O.C. (Bottom mat).
Would you like a more detailed tendon profile (chair heights) for the spans, or a full breakdown of the rebar lengths needed for ordering?
1 site
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...
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yes
To finalize your design, here is the exact geometry for your tendon profiles and a specific cut list for your rebar.
📍 Tendon Profile (Chair Heights)
The "drape" of the cable is what creates the upward force to balance the weight. Heights are measured from the bottom of the slab to the center of the tendon.
Location
Primary Tendons (22' Span)
Secondary Tendons (18' Span)
At Support (High Point)
5.0" (1" clear cover)
4.25" (Placed under primary)
At Midspan (Low Point)
1.0" (1" clear cover)
1.75" (Placed over primary)
Profile Shape
Parabolic
Parabolic
Tendon Quantity:
Long Direction (): 8 Tendons (at )
Short Direction (): 8 Tendons (at )
🏗️ Rebar Cut List (Bonded Reinforcement)
This reinforcement handles the "negative" moments at the walls/beams and provides a safety net for ductility.
Top Bars (Over Spandrel Beams)
Place these centered over the beams, perpendicular to the wall.
Long Walls ( sides): 44 pieces of #4 rebar, . (Space at )
Short Walls ( sides): 36 pieces of #4 rebar, . (Space at )
Note: length provides of embedment into the slab on each side of the beam centerline.
Bottom Mat (Shrinkage & Robustness)
A "checkerboard" grid placed on bolsters (chairs).
Direction 1: 13 bars of #4 rebar, . (Space at )
Direction 2: 15 bars of #4 rebar, . (Space at )
💡 Installation Tips
The "Basket": Weave the tendons. In the middle of the span, the tendons are on the bottom. At the supports, the tendons are on top.
Clearance: Ensure no rebar is within of a PT anchor to avoid "honeycombing" (voids) when pouring.
Elongation: When stressing the tendons, expect them to stretch approximately . Record this for your engineer's review.
📋 Bill of Materials (BOM)
Material
Spec
Quantity
PT Tendons
PT Anchors
Standard S-Anchors
Top Rebar
#4 Grade 60
Bottom Rebar
#4 Grade 60
PT Chairs
High/Low Plastic Chairs
Do you need a stressing sequence (which cables to pull first) or a pour sequence recommendation for the concrete?
yes
To ensure the slab stays balanced and doesn't crack during the tensioning process, follow these sequences for pouring and stressing.
🌊 Pouring Sequence
Since your slab is relatively small (), it should be placed in a single, continuous pour to avoid cold joints.
Start Point: Begin at one of the short walls.
Direction: Advance the concrete along the length.
Vibration: Use a pencil vibrator extensively around the PT anchors (the edges).
⚠️ Warning: Voids behind the anchor (honeycombing) will cause the concrete to "blow out" when you apply pressure later.
Finishing: Ensure the top surface is level, especially over the spandrel beams, to maintain the top cover for the rebar.
⚡ Stressing Sequence
Do not stress the tendons until the concrete cylinders reach the required "transfer strength" (typically for a mix).
Stage 1: Short Direction ( Tendons)
Stress these first.
Start from the center tendon and work outward toward the edges (alternating sides).
This "pre-compresses" the slab and stabilizes it for the longer span.
Stage 2: Long Direction ( Tendons)
Again, start with the center tendon.
Work in a "staggered" pattern (e.g., skip one, then go back) to distribute the force evenly.
Pressure: Pump to approximately (initial) to achieve a final effective force of after losses.
📏 Quality Check: Elongation
For every tendon, you must measure how much it stretches.
Span
Expected Stretch (Approx.)
Span
Span
If the stretch is less than of these values, the tendon might be snagged.
If it is more than , the concrete may have crushed or the anchor slipped.
✅ Final Verification
Do not cut the tails (the extra cable sticking out) until the engineer approves the elongation records.
Patch the pockets with high-strength, non-shrink grout immediately after cutting the tails to prevent corrosion.
Would you like me to explain the safety protocols for the stressing day (like the "No-Go Zone" behind the jack) or help you with the grout specs for the anchor pockets?
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