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POST-TENSIONED SLABS IN BUILDINGS Increasing popularity /versus/

Lack of specific coverage by Euro codes by Guy A. TABET LEBANON

Workshop - 27-29 November 2006, Varese, Italy

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Post-tensioned Slabs in Buildings

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Workshop - 27-29 November 2006, Varese, Italy

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PRINCIPLE OF POST-TENSIONED CONCRETE

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Illustrative example

Tendon Three-span post-tensioned beam 2 P cos α P

α α

V P

P W

B

For harped profile P A For parabolic shape w =

8P x sag 2

L

Free-body diagram of a tendon section between its low point (A) and point of inflection (B) Workshop - 27-29 November 2006, Varese, Italy

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Illustrative example W Va

Vd P

P

Free-body diagram of beam after removal of tendon Va

Vd

W

P

P

Free-body diagram of tendon Force system between tendon and beam Workshop - 27-29 November 2006, Varese, Italy

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Benefits of Post-Tensioned slabs • Longer Spans • Flat Soffits • Flexibility of Layout & Services • Deflection & Crack Control • Thinner Slabs • Reduced Storey Height • Lighter Structure • Fast Construction • Cost Saving Workshop - 27-29 November 2006, Varese, Italy

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Who Benefits ?

• Clients – More clearance & More Flexibility – Less Columns, Larger Open Spaces

• Architects – Easier Internal Planning – More Elegant Structure

• Structural Engineers – More solutions – Better Structural Performance

• Contractors – Quicker and Easier Construction Workshop - 27-29 November 2006, Varese, Italy

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IN SLABS two categories of PT systems are used :

Un-bonded system &

Bonded system

Workshop - 27-29 November 2006, Varese, Italy

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Un-bonded Tendons

• Single strand coated with corrosion inhibiting grease and encased in polyethylene sheathing • PT force is transferred to the concrete by the anchors provided at the ends

Workshop - 27-29 November 2006, Varese, Italy

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Workshop - 27-29 November 2006, Varese, Italy

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Bonded Tendons

Flat corrugated duct

Strand position in a circular duct

Bonded system tendon detail for beams & slabs

• Bond is achieved throughout the length of the tendon by a cementitious matrix called grout • PT force along the tendon is a function of the deformation of the concrete Workshop - 27-29 November 2006, Varese, Italy

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Workshop - 27-29 November 2006, Varese, Italy

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Structural Forms

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Structural Forms

Workshop - 27-29 November 2006, Varese, Italy

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Structural Forms • Preferred Option – Flat Slab • Minimum Thickness • Flat Soffit

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Design Concept LOAD BALANCING

A comprehensive solution to Post-Tensioning by T.Y.Lin

Simple - General – Powerful for analyzing simple & complex PT structures

Principles – Remove the PT tendons from the structure & replace it with all the forces that it exerts on the structure when in place – Analyze the structure under this given set of equivalent loads Workshop - 27-29 November 2006, Varese, Italy

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Design Concept

Load Balancing

Tendon Three-span post-tensioned beam

W

Va P

Vd P

Workshop - 27-29 November 2006, Varese, Italy

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Analysis of the Structure

Modeling of two way slab system Methods available : – Equivalent Frame Method – Finite Element Method – ……….

Workshop - 27-29 November 2006, Varese, Italy

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Analysis of the Structure

• Plane Frame Model – Models a single sub-frame

• Finite Element Model – Models a whole Floor – Actual Tendon Locations

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Analysis of the Structure

Equivalent Frame Method

Most common modeling of gravity loading and post-tensioning: – Slab systems are modeled as rows of intersecting two dimensional slab frames. – A single story slab frame consists of a line of column supports bounded by its tributary – Floor levels are treated each separately

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Analysis of the Structure

Typical slab frame

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Finite Element Model

STRUCTURE PERSPECTIVE

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Finite Element Model

ELEMENT MESH PLAN

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Finite Element Model

BANDED TENDON LAYOUT

Workshop - 27-29 November 2006, Varese, Italy

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Finite Element Model

DISTRIBUTED TENDON LAYOUT Workshop - 27-29 November 2006, Varese, Italy

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Finite Element Model

TOP FIBER STRESSES Workshop - 27-29 November 2006, Varese, Italy

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Finite Element Model

BOTTOM FIBER STRESSES Workshop - 27-29 November 2006, Varese, Italy

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Finite Element Model

DEFLECTION Workshop - 27-29 November 2006, Varese, Italy

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Design Checks

Design Criteria exist in most Codes: • British Standards (BS8110 Part 1) • ACI 318 (Chapter 18) • ACI 423 for un-bonded tendons • CAN3 – A23.3 • Euro Codes • Concrete Society Technical Report 43

Workshop - 27-29 November 2006, Varese, Italy

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Design Checks

Serviceability Limit State • Un-Factored Loads • Check Stresses • Maximum Tension • Maximum Compression • Check Deflections

Workshop - 27-29 November 2006, Varese, Italy

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Design Checks

Serviceability Limit State (Cont’d) Allowable Stresses – Design Classes • Class 1 - No Tension Allowed • Class 2 - Limited Tension (No Cracks) • Class 3 - More Tension allowed (Crack Width 0.1 to 0.2 mm)

Check at Critical Sections

Workshop - 27-29 November 2006, Varese, Italy

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Design Checks

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Ultimate Limit State Bending

SECTION

FORCE RESULTANTS

Workshop - 27-29 November 2006, Varese, Italy

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Non regular geometry easy to handle

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IDEAL SOLUTION FOR TOWERS

Workshop - 27-29 November 2006, Varese, Italy

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PROBLEM…..?!?....... How to get all the potential benefits of flat frameless PT slabs, AND still provide suitable resistance to lateral actions? Typical slab/column joint in PT slabs Æ frameless slabs Workshop - 27-29 November 2006, Varese, Italy

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Slab to act as diaphragm transferring lateral actions to shear walls

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Frameless PT slabs acting as diaphragm only, for lateral loads resistance

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Numerous walls for increased lateral resistance, if necessary

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Lack of coverage Although Euro codes address pre-stressed concrete structures in general and flat slabs in another separate chapter, YET Post-Tensioned flat slabs are not specifically covered and very little is said concerning their detailing and mostly their behavior with respect to seismic actions. Workshop - 27-29 November 2006, Varese, Italy

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A need to address The increasing popularity of the use of PostTensioned slabs in buildings should be enough reason for properly regulating their design in the Euro codes up to the level of other national current codes as in the ACI where a specific chapter is dedicated for this technique.

Workshop - 27-29 November 2006, Varese, Italy

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THANK YOU FOR YOUR ATTENTION

Workshop - 27-29 November 2006, Varese, Italy