Prestressed Concrete - 8 Prestressing Anchorages

8/12/2019 Prestressed Concrete - 8 Prestressing Anchorages

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University of Western AustraliaSchool of Civil and Resource Engineering 2004

8. Prestressed Concrete :

Prestressing anchorages

Introduction

Post-tensioned anchorages

Pre-tensioned anchorages


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INTRODUCTION

What is Anchorage?

Anchorage is the term used to describe the method of permanently lockingtogether the concrete (in compression) with the tendon(s) (in tension).

The compressive force C in the concrete equilibrates the tendon force P .

In post-tensioning, force transfer occurs at anchor locations,

usually, but not always, at the ends of the member, for example:

exposed

anchorrecessed

anchorforce transfer

Po

}C

tendon force P = jacking force Po

high local

stresses

and pre-tensioning ? . . .


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In pre-tensioning, force transfer occurs by bondbetween tendon and concretethus:

fully bonded partly de-bonded

Stresses applied by

concrete on strands

Before transfer (while concrete hardens)

Af ter transfer (Release)

Anchor

abutments

Transmission

length Lp

Transmission

length Lp

Over this length, tensile

force in tendon equals

compressive force in

concrete, and is constant

Pre-tensioning system (diagrammatic):

Stresses applied by

strands on concrete

Value of L p?

. . .

Pre-tensioning


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Three sorts of critical stresses are caused in the concrete:

Bearing stressunder the anchor plate - very high, and requiresconfinement rebar to prevent crushing - the rebar provided for

bursting and spalling stresses is usually adequate;

Bursting stressesin the transmission zone;

Spall ing stressesat concrete surfaces near the anchorage.

Bearing stress Bursting stresses Spall ing stresses

Requires web

thickeningRequires confinement

stirrups

Requires surface

rebar

To cope with these stresses, enlargement of the section is often requi red . . .

POST-TENSIONED ANCHORAGES


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Extent of web thickening to ensure that stresses due

to prestress are properly dispersed into the I-section,

and that bearing stresses at the bearing plate are notexcessive; hence = transmission length or more.

Typical Web Thickening to accommodate end block :

Shown for an I-Beam section :

width of anchor block,

greater than web of

beam.

Similar web thickening is usual ly required for a T-beam.

Consider these stresses in more detai l . . . F irst, Bearing stress . .


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Bearing plate area = A1

Bearing stress = Po / A1

Bearing stress behind the bearing

plate Po / A1 is very high, and

crushing of the concrete couldoccur.

This concrete is highly confined

by adjacent concrete, so bearing

stress in excess of f c can be

tolerated.

But additional confinement rebar

is usually required.

This is needed when bearing

stress exceeds :

f 0.85 f c (A2 / A1)0.5 < f 2 f cusing f = 0.6

A1

A2 similar to

andconcentric

with A1

Next, Bursting stresses . .

Bearing Stress


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Longitudinalcompressive stresses

Stress trajectories(elastic)

Uniformpressure =

P /(hb)

Uniform

pressure

= P /(bD)

Consider now the spread of force from behind the bearing

plate to a section at which the pressure is uni form:

From the shape of the trajectories, there is a transverse compression

near the plate, but a transverse tension thereafter.

AND TENSION IS A CONCERN FOR US ! So . . .

Bursting Stress


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Potential cracking

Areas of tension include:

Bursting tensions in l ine with P, and

Spall ing tensions at sur faces of block.

We need to estimate these tension forces:

In-Line bursting forces

Consider this free body

block. I t needs Mb for

equil ibr ium . . .

Mb. . and this is provided by forces Cband Tb in the concrete, thus :

Cb Tb

oM = 0 : Mb + P/2 h/4 - P/2 D/4 = 0So Mb = PD/8 [ 1 - h/D]

This helps, but we really need Tb, and this requires the distance from Cbto Tb


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Research studies have shown that

the tr ansverse str ess yis of the

form shown thus:

Transverse stress distribution

. . and the integration for the

tensile force can be approximated

by a straight l ine thus:

Code approximation for Tb

So Tpis approximated by 0.25 P [1 - kr], where kris the

concentration ratio h / D.

We must provide stir rup reinf orcement to resist Tp


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Extra rebar in loaded

face to cope with

spalling stresses

DESIGN FOR IN-LINE BURSTING

IN VERTICAL PLANE

DESIGN FOR IN-LINE BURSTINGIN HORIZONTAL PLANE

a

D

D

b

Closed stirrups designed for full burstingforce Tb over 0.8 D, at 150 MPa, and

extended over 1.0 D

Total

burstingforce Tb =

0.25P(1-kr)

where

kr= a/D

Total

bursting

force Tb =

0.25P(1-kr)where

kr= a/b

Closed stirrups designed for full bursting

force Tb over 0.8 b, at 150 MPa, and

extended over 1.0 b

Design for Bursting Stress


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PRE -TENSIONED ANCHORAGES

Entirely different from post-tensioning anchorage.

Our interest is to estimate the length over which the

tendon (wire or strand) transmits its stress to the concrete

section.

The length Lp is dependent on the strength of the concrete

at transfer f cp

Note that the tendon has no stress at the members end!

Lp

is estimated on the basis of empirical evidence.

AS3600 suggests as follows . . .


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Transmission Length Lp:

Type of tendon Lp for gradual release:

fcp >= 32MPa fcp < 32MPa

Indented wire 100 db 175 db

Crimped wire 70 db 100 db

Strand 60 db 60 db

Tendons must

be free of

grease and oil ,otherwise

MUCH greater

L pis required.

stress in

tendon

Length from

end of memberLp

0.1 Lp

as tested

as assumed

in design

This has

importantinf luence on

shear strength

of beams on

narrowsupports !db is nominal diameter of wire/strand


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Postscript 1:

Relaxation of constraint on

tensi le strength at working load:Where reinforcement or tendon are

used near a tensile surface, the

permissible stress at working load may

be increased from 0.25 (fc)0.5 thus :

For beams, to 0.6 (f c)0.5

For slabs, to 0.5 (f c)0.5

This recognises the control offered by

rebar or tendon to surface cracking.See AS3600 cls. 8.6.2 and 9.4.2.

For members deeper than 750 mm, such

rebar or tendon is required anyway, for

other reasons.

s a >= - 0.6 (f cp)0.5

s b >= - 0.6 ( f c)0.5


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Postscript 2:

Strategies for avoiding excessive

tensile stress near supports in pre-

tensioned members:

Pre-tensioned members with straight

tendons may develop excessive tensile

stresses near supports:

s a = P/A - Pe/Z + Mswt/Zsa = P/A - Pe/Z since Mswt = 0

Two options:

1. De-bonding of some strands:

For example, introduce

de-bonding sleeve around

some strands for

calculated length from end

of member.

Care with shear strength near

ends !

2. Introduce top strands:For example, two top

strands negate

tension in top of

member - often used

in small pre-tens.

beams.


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Postscript 3:

Magnels Diagram:

In 1954, Gustav Magnel observed that

the constraints on extreme fibre stresses

can be represented on a single diagram

in which 1 / Pi is plotted against

eccentricity of tendon e.

Initial,

M swt

Effective,

M total

sa >= - f ti

sb


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Eccentricity e

1 / Pi

1 / Pi > 0

e >= 0

e


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SUMMARY

Post-tensioninganchorages require attention to bearing,

burstingand

spallingstresses.

Enlargement of the ends of thin webbed members is

usually required to accommodate the anchor plate,

and to reduce stresses.

Closely spaced stirrups, designed for 150 MPa, togetherwith longitudinal rebar, control these stresses.

Guidance on design procedures is provided in Section 12

of AS3600.

Pre-tensioninganchorage is achieved by transmission

length Lp from member ends.

Care to observe restrictions on application of Lp, and on

shear strength at member ends.

Prestressed Concrete - 8 Prestressing Anchorages

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