Post-Tensioned Slabs on Grade

2.2 Post-tensioned slabs on grade Rhys Rogers Structural Engineer – R&D and Design BBR Contech

Specification and design of commercial concrete slabs on grade

Post-tensioned slab on grade • Definition, applications & advantages • • • •

Typical layouts Elements of a PT slab PT slab design for mobilisation PT slab design for loadings (thickness)


Post-tensioned slab on grade


Post-tensioned slab on grade


Post-tensioned slab on grade • PT stress puts concrete in compression – PT stress prevents shrinkage cracking by allowing slab to shrink as one unit – Enhances load bearing capacity

– Causes any cracking that does occur to tend to remain narrow or to close up Specification and design of commercial concrete slabs on grade

Post-tensioned slab on grade • PT provides resilience and robustness – Allows slab to recover from minor overloads – Causes any cracking to tend to remain narrow or close up

• Can accommodate moderate levels of differential settlement, and deformation • Minimises interference with pouring and finishing – Gives placers best opportunity to achieve finish & flatness requirements


Why select a PT slab? • Increased joint spacing – Construction joints only, no sawcuts

• Minimises shrinkage and flexural cracks • Lower life-cycle cost – Fewer joints to maintain – Better durability

• Enhanced serviceability

– Minimum down-time for joint repair/maintenance ACI 360R-10 Guide to design of slabs-on-ground Specification and design of commercial concrete slabs on grade

Why select a PT slab? • Better preservation of floor flatness by minimising joints • Decreased slab thickness • Increased load strength • Resilience and recovery capability from overloading

ACI 360R-10 Guide to design of slabs-on-ground Specification and design of commercial concrete slabs on grade




Typical layout of PT slab • Objective is to minimise joints – Fewer joints results in better operational productivity and lower life cycle maintenance

• Primary limitation on joint spacing is max. pour size – single pour usually <≈ 2500-3200m2

• No sawcuts or joints required within each pour Specification and design of commercial concrete slabs on grade

Typical layout of PT slab • Multiple pours can be post-tensioned togeth • Day joint between 2 slabs (allows up to 6000m 2) • Coupled joints can join more than 2 slabs

• Creates tight/closed joints – Good durability, minimal impact on forklifts – No joint armouring required

• Allows very large slabs with no opening join – Shrinkage movements restricted to slab edges


Multiple pours post-tensioned as one slab (Day joint) Day 1 Pour

Day 2 Pour PT tendons

PT tendons stressed after second pour


Multiple pours coupled together Pour 3

Pour 1

Stress 1 Stress 3 and 4 Pour 4

Pour 2

Stress 2


Tight construction joints • No armouring • Durable joint • Minimal impact on forklifts operations • Clients should expect some minor cracking around joints, these don’t usually affect slab performance





Elements of a PT slab 

Edge Reinforcement

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Casting

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Strand Onions

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Strand

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Grout Vents

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Spiral reinforcement

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Ducting

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Duct Chairs

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Barrels & Wedges


Elements of a PT slab






Stressing access: Infill strips

• Nominally 1m wide infill strip provides access for stressing • Most flexible way to provide access • Usually tied to slab with rebar so opening joint is at wall • Adds another tight joint, but usually hidden by racking Specification and design of commercial concrete slabs on grade

Stressing access: Pockets

• 300x110mm pockets cast into wall panels • PT Slab extends to wall • Must isolate slab from panels and columns • PT slab design required before PC panel production begin Specification and design of commercial concrete slabs on grade

Stressing access: Pockets


PT slab design concepts • Design for mobilisation (concrete shrinkage – PT design – Detailing – Early shrinkage & Relative shrinkage

• Design for loading – Design methodology – Types of loading – Sensitivity to different types of load Specification and design of commercial concrete slabs on grade




PT design for mobilisation • Avoidance of Shrinkage cracks – The PT is designed to be sufficient to overcome subgrade friction and allow the entire slab to shrink as one unit – Restraint of this movement will result in cracking (detailing critical) – Concentrates shrinkage gaps at slab edges (can be large for long slabs) Specification and design of commercial concrete slabs on grade

PT design for mobilisation • Shrinkage starts when concrete begins to harden • Nothing to prevent cracking before PT is applied • Rate of shrinkage drops off quickly with age – Our observations indicate shrinkage movement occuring up to 2 years age – Minimal shrinkage occurs after 2 years – Restraint over first six months most likely to cause problems Specification and design of commercial concrete slabs on grade

PT design for mobilisation • At any given section: F >= F PT friction • Friction force prop. to weight of slab and applicable loadings • PT force varies along length of tendon

d n E s s e tr S

d n E d a e

D


PT design for mobilisation • Mobilisation equation at given section ntendons * Ftendon >= Aslab to be mobilised * μsubgrade * (UDLslab weight + UDLapplicable loads)


PT design for early shrinkage • Initial PT force must be applied ASAP – Must prevent shrinkage cracking from starting (<=24 hrs after pour)

• Allowable PT force is limited by early concrete strength – cylinders required for initial stress and final stress

• Initial PT force must be sufficient to overcome subgrade friction and allow slab to shrink as one unit • Only need to mobilise slab weight (no loads)


PT design for early shrinkage • At application of initial PT force – No load on slab, friction due to slab weight only – Friction coefficient is large • Friction coefficient tends to reduce as shrinkage movement occurs, worst case is for initial movement

– Initial load varies with slab size and layout, usually about 1/3 to ½ of final PT force


PT design for mobilisation (medium to long term) • More variables to consider – Greater PT stress available to mobilise – Must mobilise slab & realistic proportion of loading

• Long term, slab movement must not be restrained to allow thermal movements


PT design for mobilisation (medium to long term) • Med-long term mobilisation is usually not critical • Should consider when the following coincide: – Long slabs or multiple coupled slabs (>≈120m) – Early application of heavy UDLs (<≈ 6 to 12 months) – Limited load cycling is expected


PT design for mobilisation (medium to long term) • When we do consider med/long term mobilisation, we need to get an accurate picture of loading – Full UDL unlikely to apply to full floor area

• Unloaded aisles and forklift manoeuvring areas • What proportion of full UDL is realistically expected in loaded areas?

– True UDL can be as low as 50% of design UDL

• Will the load be cycled? – Shrinkage movement can occur piecemeal when loads are low Specification and design of commercial concrete slabs on grade

PT design for mobilisation (medium to long term) • Design options – Increase PT stress • More PT gives a more resilient slab over all • Greater PT can allow thinner slab – Reduces friction force and increases PT force

– Divide the slab with armoured opening joints • Limits slab length and required mobilisation force • Also reduces magnitude of shrinkage movement – Easier to detail for gaps at slab edges and doors Specification and design of commercial concrete slabs on grade

Differential shrinkage


Differential Shrinkage • Slab 1 is poured & begins to shrink • Slab 2 is poured & wants to shrink faster/further • Slab 2 is restrained by contact with slab 1


Differential Shrinkage • Total shrinkage for each slab will be the same • Say 20% of shrinkage occurs before slab 2 is poured • The 20% differential is permanent at the joint • 0.2*750με = 150με = 0.15mm/m = sum of crack widths /m


Layout and sequence 1. Layup slabs 1A & 1B 3. Pour 1B (day after)

5. Layup slab 2

4. Initial stress 1A & 1B 6. Final stress 1A & 1B 8. Initial stress 2 9. Final stress 2 2. Pour slab1A

7. 2 1B) (2 Pour weeksslab after


Differential shrinkage Slab 1A

Slab 1B 4 week differential shrinkage

Slab 3A

Slab 3B

l ia t n e r e g e f a fid k e e w 2

l a ti n e r e ffi d k e e w 2

n k ir h s

Slab 2A

Slab 2B

4 week differential shrinkage e g a k irn h s

Slab 4A

Slab 4B


Differential Shrinkage • Expect some cracking on coupled joints • Aim is to end up with many narrow cracks – Good detailing, construction programming, concrete, curing, PT processes required

• Mitigate risk of undesirable cracking by: – Limit time between adjacent pours – Use concrete with low early age shrinkage properties – Apply PT stress before shrinkage begins so that joint remains tight – Detailing

• PT couplers must transfer PT stress all the way to edge of first slab • Rebar in relevant locations to maintain small crack widths





PT slab design for loading • Loading design concepts • How to consider common loading types – Rack loading – Axle loads

• Key design information / Sensitivity


PT slab design concepts • Design objective: – Slab remains crack free during normal operation (governs design)

• Slab is allowed to crack under minor overloads – SLS EQ or SLS overload cases – PT maintains small crack widths which close up when load is removed Specification and design of commercial concrete slabs on grade

PT slab design concepts • Not designed as a “crack free slab” – Client expectation is often greater than reality • Need to manage this to avoid disappointment • PT slabs designed for water tightness have 2-3 times more PT stress than average PT slab on grade • Minor cracking at interfaces due to mobilisation and differential shrinkage can’t be prevented by more PT


PT slab design concepts • NZS1170 limit states don’t directly apply – ULS

• On the ground so slab can’t collapse • Must maintain integrity to prevent racking collapse – Resilient nature of PT slabs maintains bearing ability – Uplift forces restricted by yielding baseplates

– SLS • Cracking is permitted under NZS1170 SLS cases • PT Slab designed not to crack under normal operatio • Small crack widths under SLS EQ/overload Specification and design of commercial concrete slabs on grade

PT slab design concepts

“Avoid the use of multiple factors of safety. Post-tensioning provides reserve capacities, and factors of safety greater than those for nonprestressed slabs should not be used. Cracking under the concentrated load is permissible for post-tensioned slabs, and it can be taken into account by using structural design requirements of ACI 318.”

ACI 360R-10 Guide to design of slabs-on-ground Specification and design of commercial concrete slabs on grade

Loading design methods • Westergaard method • Other design approaches – Graphical methods (based on Westergaard) • PCA (Portland Cement Association) • WRI (wire reinforcement institute) • COE (Corps of Engineers)

– Finite Element Modelling – can be sensitive to interpretation/experience (rubbish in rubbish out!) – Proprietary slab design software Specification and design of commercial concrete slabs on grade

Westergaard slab design • Westergaard model is most common – design standards suggest this approach – Most CCANZ design guidance is available – Relatively simple to automate in a spreadsheet – Based on un-reinforced slab design • PT stress is added to the tensile strength of concrete • Design variables: Slab thickness & PT stress


Westergaard slab design Flexural stress from loading <= Flexural tensile strength of concrete • Accounts for fatigue and time to loading with factors on flexural tensile strength


Westergaard slab design • Considers subgrade as a winkler spring bed – Modulus of subgrade reaction = k • Often given as N/mm 2/mm or MN/m3 (misleading) • Measure of pressure per unit displacement (kPa/mm • Usually have to convert from CBR which can be inaccurate • Ideally Geotech engineers should do conversion – Provide k value for design, – Benkelman beam test targets for construction


Westergaard design for loads • UDL loads not usually critical – Evenly loaded floor has no flexural stress in slab – Aisle loading rarely governs

• Westergaard formulae deal with point loads – Equations for interior, edges and corners – Stresses from multiple loads must be combined


Westergaard PT slab design • Stress due to interior load

P

l is dependant on slab depth, typically 0.5 to 1m Specification and design of commercial concrete slabs on grade

Westergaard PT slab design • Stress due to single point load depends on: • • • • •

P = Load magnitude h = Slab depth (cubed, big influence) k = Modulus of subgrade reaction μ = Poisson ratio of slab (0.15 static, 0.2 dynamic) b = loaded radius

Loaded radius is calculated based on post area for rack loads. Baseplates are too thin to spread load


Westergaard PT slab design • Combination of loads – When two loads are close together (<2h) • combine loads (2*P) • Increase loaded radius (r)

– When two loads are further apart (>2h) • combine stresses in x & y directions at critical point using graph


Loading types • Rack loading • Forklifts (MHE) • Other types of loading – Container loads / Swinglifters – Truck loading


Back to back rack loading 300mm B2B rack Aisle

Large B2B spacing Feet considered separately (1xP) Less severe load case

200mm B2B rack Aisle

Small B2B spacing Feet combined (2xP) More severe load case

Edge rack Specification and design of commercial concrete slabs on grade

Back to back rack loading

Aisle

Sensitive to: 1.

Post load

2. 3. 4.

B2B spacing Post size Short leg spacing

Aisle


Double deep racking Aisle

Double deep B2B racking

Aisle More Critical than B2B racking Specification and design of commercial concrete slabs on grade

Shuttle Racking • Approximately square grid, 1.1-1.6m spacin • Generally less critical than B2B racking • No B2B posts


Rack loadings • Slab design & thickness is sensitive to: – Post load – Racking type (B2B, double deep, shuttle) – Back to back rack spacing (clear spacing) – Short direction post spacing (c/c or outside dim?) – Post size (not baseplate size) – Modulus of subgrade reaction (k)


Forklift Loadings


Forklift loadings • Machine + load weight balanced on front axle • Reasonable factor for impact and uncertainty


Forklift loading • Loaded radius based on tyre pressure – Pneumatic tyres – Solid “Cushion” tyres

(700-1000 kPa) (1200 to 1600kPa)

– Solid rubber tyres (1700-1800kPa) – Solid polyurethane wheels (>6900kPa)


Forklift loading • Slab design and thickness is sensitive to: – Axle load / rated capacity of forklift – Axle width – Single or double wheeled axle – Tyre type / pressure – Modulus of subgrade reaction (k)


Post-Tensioned Slabs on Grade

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