the design post tension is becoming
more and more popular globally
both in residential and commercial
spaces this is because structures can be
stronger
span further and be more efficient today
i'll be going through the basics of post
tension detailing and some of the
considerations you need to have
over a standard rc design
my name is Brendan your Structural engineer
based in Australia and i provide videos
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So why should we do a post-tensioned design
over standard rc design
post-Tensioning designs can generally span
further are thinner
or stronger so they're more efficient
all around this because of the two
primary actions apart from the post-tension
the first being a
pre-compression force
we all know that concrete is weakest
under tension so adding a
pre-compression means it needs a higher
tensile actions to overcome that
pre-compression
thus overcoming concrete's greatest
weakness there's a number of reasons why
you can see tensile forces inside the
structure these either being from
shrinkage or Restraint
flexural actions or strut and tie actions so
by adding that precompression means you
see higher
stresses inside that structure before
you get tensile cracking so this comes
to the second primary reaction to post
tensioning
and this is due to the tendon trying to
flatten out so when the tendon tries to
flatten out and inparts a
forced in the opposite direction to
which it way it's straight so for a
concave deflection it's trying to
flatten upwards so it's
provideing in it upwards force or if it's
convex there'll be a net downwards force
so what does this tell us
it means that we can move force from where it's most
critical say like the middle of a
structure
to a support line
so we want it to be lowest
where the deflections are the highest or
where the highest moments are and
highest where we have hogging moments
as we're moving the load from where
where it's impacting structure the most
to where it impacts the structure at
least
so from these two actions we're able to
overcome
some of the issues that we have with
concrete design understanding the
secondary actions of post tensioning is
important as well
this is most easily explained by the
three examples I have on the screen
so we have flat tendon above the neutral
axis on the neutral axis
and below the neutral axis
in this example we're just assuming
there is no other net forces imparted other
than the post tensioning themselves
so when is on the neutral axis the only
thing that happens is that it
shortens from each side
as there is no really net action top and
bottom there's relatively even
distributive load where it gets exciting
is where we have a tendon either above
or below the neutral axis
so let's look at above the netrual axis
what happens here
well the top of the slab will shorten
this causes the slab to deflect
downwards as you can see the curvature
is forcing the slope downwards
this is due to the action above the post
tensioning causing the top tendons to be
shorter more so than the bottom and the
inverse will happen as well
when it's on the bottom it'll cause a
hogging force
so from this we can apply this to when
we're applying drapes in the structure
now that we've gone through the primary
actions proposed tensioning let's look
at where our high points and low
points should be inside that structure
so where should they be
the easiest way i do this is to have a
look at the deflected shape of the side
of the structure
as this will show me where the column
strips are where the middle strips are
by looking at the deflected shape i can
see where my low points need to be is
where the structure is deflecting the
most
is where the tendon needs to be the
lowest this is generally where
also the highest tension is inside that
structure as well
and again where it's hogging the most is
where we want it to be high
so by balancing out our tendons
depending on on how the structure is
behaving
allows us a quick way to first do a
preliminary run on our post tension high
and low points and when we have band
beams
which is a beam inside the slab we
generally have a high point on either
side of that band beam
and this offers two benefits firstly it
increases the parabola with the drape
thus pulling the load
more efficiently to where we need it
which is on side that band
and also adds an even distributive load
right across that band beam
when you do this this is not only
important for band beams but also when
you've got a flat plate slab
so when you've got a column strip
running up and down the page it's worth
putting two high points on either side
of that column strip as we'll have the
same benefit that you have inside that
band beam by increasing
the parabola now how about cantilevers
this is where you may go wrong by
looking at the deflected shape
because if you have a look at the
deflected shape you would assume that
the tendon needs to be low
low at that point yes it will pull the
slab back up but also not be as
efficient as if it was above the neutral
axis due to the secondary effects from
the pre-compression force
so generally on cantilevers you want to
keep that tendon high to be able to pull
the drape back so this means that their
tendon needs to be
above the neutral axis and onto the
neutral at the far point
as this gives you the benefit of two
things it allows you
the most efficient way of pulling that
tendon up but also means that you
implying all the second reactions as
needed above
the neutral axis now they've gone through
where the high and low points are
how do you do with a fold in a slab this
is simple as trying to limit
how quickly actually diverge the tendon
so you want to try and
divert the tendon very slowly through a
slab fold so you roughly want a ratio of
about
10 times or eight times the actual step
so you've got a step of 100mm you
want somewhere between 800mm to a meter
that that the diversions actually occurs
over you also
also want to ensure that the tendon is
diverging all the way through that fold
so you don't diverge it
before you get to the fold and you've
stopped the versions up
before you get to the end of that fold
as well so why do you do this
is because when you're actually draping
the tendon symmetry properly you'll have
a net force upwards or downwards
depending which way the tendon is
actually bending so you want to ensure
that you're actually bending it
in the deeper section of the slab not
not the shallower section as you could
cause a net thrust downwards
and in extreme cases actually force the
tendon outside the slab so it's just
something to be cautious of
now that we've also talked about
diverging slabs around steps and folds
how about voids divergent sideways will
also cause that same lateral force
sideways
so you just want to make sure that you
don't diverge the strut too much
or too steeply otherwise you'll have a
great force going back the other
direction
so you try and limit the amount of
diversions to about one to one and a
half meters
and keep it as as shallow as possible so
if you can keep the similar ratio to
what you had in the step
however again you try and diverge this
tender before you actually get to the
void
so you're not actually imparting your
force sideways at that void
we've gone through both where the high
points and low short points should be
now we need to locate where our dead end
and live ends are
so what are dead ended live ends well a
live end is an end that we stress the
tendons from that be generally a jack
approach to the tendons on inside that
structure that we stretch up to impart
the tension forces
with inside that beam structure or slab
and dead end is the end that we're
anchoring it from
so generally they splay out and it's an
anchorage zone in both these zones
there's generally bursting forces
imparted inside the structure so
generally we have spiral structures
around around those areas to
resist those bursting stresses and you
want to make sure that the tendons are
not really close to either surface
so generally you want to make sure that
either wherever preferable to be inside
the center of the beam to give as much
concrete around it
but wherever it's not possible to be
with inside 100mm of either surface
this is generally where you want to
locate you'd live in dead ends
there's also two types of live ends this
either an edge stress which is
preferable
or a pan stress now what is an
edge stress it's where the
live end goes right to the edge of the
slab and you stress off that edge of
that slab now this is not always
possible
as you may have issues where you don't
have scaffolding the edge of the slabs
therefore you don't have access
to stress it or you may be stressing
adjacent core obviously you can't stress
on the other side of the core as there
is a wall in the way
so you therefore you need to do a pan
stress generally with pans you generally
need to make sure that you at least 500
to a meter away to give enough clearance
to apply the jack to that structure
and when you're putting your pan in
you need to make sure there's additional
reinforcement in the slope locally in
that area
to overcome the shortfall from the
post-tensioning pulling short
when stressing at the edge of a slab an
area watch out for
is the loss of post tensioning locally
between the post tension tendons
so when you stress a tendon at the edge
of a slab there will be a zone of about
45 degrees between those tendons where
there will be no P on A
thus will not be resisting the cracking
or loads in this area
so therefore you need to have edge
reinforcement so how much post tension
do we need inside our structure
there's two ways that i do to work this
out this is the P on A
and the load balancing required the a is
really to do with crack control
so you'll need a low degree of crack
control moderate crack control
or high degree of crack control and
these are applied depending on
what degree of crack control when you
inside our structure so low degree crack
control is
roughly about 0.7 mpa and this is
generally used in areas where we're
not too concerned about shrinkage
cracking so if we've got carpeted
surfaces
inside a car park or other areas where
minor degrees of cracks are not really
concerned inside our structure
moderate of crack control this is
typically where you are in most
residential or commercial spaces
as there is some concern with cracking
so this is roughly about 1.4 mpa
this means that you should not really
see too many shrinkage cracks
and this is generally where we are most
of the time then high degree of crack
control is generally where you've got a
wet deck
and this is roughly about 2.5 to 3 mpa
this is where you can't have the
cracking is that cracking will degrade
the structure greatly
to increase your amount of P on A inside
your structure to overcome those
shrinkage restraints
now how about load balancing as you
remember earlier i said that the tendons
and part
net upwards force on our structure
or downwards force depending on which
way the tendon is going
when we're designing our post tensioning
we want to make sure they're not
balancing any more than about 80 percent
this is similar to the pre-camber of
steel beams so why do we do this
is because if we over balance the
structure we could have a net hogging
force across
the structure which would be detrimental
to our design so generally we want to
make sure we're about 80 percent
now balancing of the side of the
structure has two aspects to it
has the amount of P on A we have inside
that structure and how much drape we
have
so depending on which way it's going to
be governing potentially P on A governs
therefore we may need to pull up that
tendon a bit more or we may need to
increase the amount of
tenders we have inside our structure if
we're not balancing it enough
so sometimes we may increase the P on A
inside that structure to make sure we're
balancing out that structure more now
they've gone through
the p on A and the load balancing let's
have a quick look to see whether
oversized that structure
i do this through a factor called k now
k is derived from the euro code which is
m on b d squared and it works out the
relative stresses inside that cross
section
so from this we can work out the
relative steel stresses to work out our
structure is going to be over reinforced
or under reinforced
for a beam to be lightly reinforced you
roughly want to see it about five
this makes for an efficient structure
for a beam structure for a slab you want
to see about three
now why threee this is generally because slabs
are normally governed by deflection not
by strength
so this is why you see a relatively
lower k another area we can get tripped
up on is having tendons that are either
too long
or too short if the tendon is too short
you cannot effectively stress it that's
not imparting the P on A
inside your structure if a tendon is too
long there's too much friction forces
lost along that tendon
thus making it inefficient so how short
is too short
roughly around six metres is really the
shortest you want to go
anything less than this you cannot
effectively stress it through the
elongation of the tendon
and how long is too long well that's
roughly around 40 meters
if you're getting up around 40 meters
you need to make sure you're you're
flipping live and dead ends to evenly
distribute the P on A across that structure
any more than that really becomes really
inefficient and you're only
utilizing the steel of the post
tensioning instead of the P on A where it's
highly
effective rough tendons you want to keep
them around
12 to 24 meters wherever possible this
is really where you see the biggest
benefit from post tensioning
as not only do you get the continuity of
the slab you also get effective P on A
inside your slab as well the bane of any
post tensioning design
is restrained there's many reasons why a
slab can be restrained
these can either be blade walls cores
retention systems
even ramps so when we're looking at a
design we make sure as little restraint
as possible
what is the best way to do this is to
look at a general arrangement plan which
is a plan
looking down outside the structure and
marking all our restraint locations
and from this we can see which way the
slab is going to want to shrink
therefore then we can break up the slab
in the locations of where
the restraints are to ensure there's
only one point of restraining wherever
possible
when you're locating the pull joints you
need to consider a couple of things
firstly are you going to have permanent
or temporary movement joints or just a
construction joint
how much can actually pour in a single
day so how big a pour can you do when
you're breaking up your slab
what is the construction methodology
where your pt tendons are
to accommodate them so making sure that
you've got an even spacing across the
slab
where your band beams are where do they
clash with other walls so making sure
that they align up in logical places
throughout your whole structure
so these joints roughly need to be
somewhere space between
50 to 70 meters and then you need to
have a discussion with
how that affects the structure and what
other aspects you may need to have
in that location as there will be
movement there the architect just needs
to consider
jointing things like tiles for example
there's a couple of ways you can get
tripped up like this and as you can see
in the example up on the page
we have either one example where it's
broken up one way and
another example is broken up the other
as you can see here with the example on
the left
if it was to shrink it would lock up due
to this keying action
so what you might want to make sure is
that your keying action
is not going to lock up from each other
it's going to move apart from each other
just something that can trip you up most
labs have a lot of penetrations through
them to help service the structure so
whether you've got mechanical ducts
electrical ducts hydraulics or even
communications
so it's good to know where the good
places are to put these and where the
bad places are
now you can't always control this by
providing something like this to the
architect they can try and impart them
where it's going to be
impact the structure the least so i've
broken this up based on a two-way slab
where your support lines are your column
strips as you can see here
and your green area is your middle strip
as the green area is not supporting
anything else you can have as big
embedded interactions as they would like
as it does not support
affect the support lines where on the
orange and red strips there is a support
line through there so we need to be
careful with our design
so when we put a penetration in those
locations we're going to try and limit
it as much as possible or space them out
as much as we can
we also need to make sure we carefully
design them inside these locations
so inside the orange areas is our
preferred location for those
those penetrations where in the red is
where we really want to try and void
the red is where you have the higher
stresses in two directions so it's
harder to locate that penetration
it's also the punching zone around that
column so it will reduce our punching
perimeter which is critical for any
two-way slab design
so by giving this to the architect that
allows them to easily locate those
penetrations early on
in locations that are more efficient
inside that structure wherever possible
please comment below if you have any
other tips for any structural engineers
for post-tensioned design
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