Download pdf - POST-TENSIONED SLABS IN BUILDINGS

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Workshop - 27-29 November 2006, Varese, Italy

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POST-TENSIONED SLABS IN BUILDINGS

Increasing popularity /versus/

Lack of specific coverage by Euro codesby

Guy A. TABETLEBANON

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Post-tensioned Slabs in Buildings

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PRINCIPLE

OF POST-TENSIONED

CONCRETE

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Illustrative example

P

2 P cosα

For harped profile

ααP

Three-span post-tensioned beam

Tendon

P

V

PA

BW

Free-body diagram of a tendon section between its low point (A) and point of inflection (B)

w =For parabolic shapeL2

8P x sag

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WVdVa

P P

Free-body diagram of tendon

Free-body diagram of beam after removal of tendon

Force system between tendon and beam

P

Va W Vd

P

Illustrative example

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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

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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

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IN SLABStwo categories of PT systems are used :

Un-bonded system&

Bonded system

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• 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

Un-bonded Tendons

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• 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

Flat corrugated ductBonded system tendon detail

for beams & slabs

Strand position in a circular duct

Bonded Tendons

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Structural Forms

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Structural Forms

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• Preferred Option– Flat Slab

• Minimum Thickness• Flat Soffit

Structural Forms

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LOAD BALANCING

A comprehensive solution to Post-Tensioningby T.Y.Lin

Simple - General – Powerfulfor 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

Design Concept

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Load Balancing

Three-span post-tensioned beam

Tendon

WVdVa

P P

Design Concept

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Modeling of two way slab system

Methods available :– Equivalent Frame Method– Finite Element Method– ……….

Analysis of the Structure

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

• Plane Frame Model– Models a single sub-frame

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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

Equivalent Frame Method


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Typical slab frame


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STRUCTURE PERSPECTIVE

Finite Element Model

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ELEMENT MESH PLAN


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BANDED TENDON LAYOUT


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DISTRIBUTED TENDON LAYOUT


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TOP FIBER STRESSES

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BOTTOM FIBER STRESSES

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DEFLECTION

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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

Design Checks

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• Un-Factored Loads• Check Stresses• Maximum Tension• Maximum Compression• Check Deflections

Serviceability Limit StateServiceability Limit State

Design Checks

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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

Serviceability Limit State (Cont’d)

Design Checks

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Bending

SECTION FORCE RESULTANTS

Ultimate Limit StateUltimate Limit StateDesign Checks

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Non regular geometry easy to handle

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IDEAL SOLUTION

FOR TOWERS

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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 frameless slabs

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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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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.

Lack of coverage

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A need to addressThe increasing popularity of the use of Post-Tensioned 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.

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THANK YOU FOR YOUR ATTENTION