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.