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Welcome back to prestressed concrete structures. This is the second lecture on the module seven
on transmission of prestressed. In today’s lecture, we shall cover post-tensioned members.
We shall see how to design the end zone reinforcement for a post-tensioned member and also how to
design the bearing plate for a post-tensioned member.
Unlike in a pre-tensioned member without anchorage, the stress in the tendon of a post-tensioned
member attains the prestress at the anchorage block. There is no requirement of transmission
length or development length.
Previously, we have learnt that in a pre- tensioned member the stress at the end of
the tendon is zero. It develops to the effective stress over a length, which is called transmission
length. The stress needs to develop upto the ultimate value at the location of the maximum
moment. Unlike a pre-tensioned member, in a post-tensioned member the stress develops
right at the anchorage block because the strands are anchored by wedge. Hence, the stress at
the end is not zero, but it is equal to the pre-stress. In a post-tensioned member, we
do not talk about transmission length of the development length. This is one primary difference
between the transmission of prestress between the pre-tensioned member and the post-tensioned
member. In a pre-tensioned member, the prestress is
transferred to the concrete over a certain length whereas in a post-tensioned member
the prestress is transferred right at the end. The anchorage device and the bearing
plate transfers the stress in the concrete at the end.
The end zone (or end block) of a post-tensioned member is a flared region which is subjected
to high stress from the bearing plate next to the anchorage block. It needs special design
of transverse reinforcement. The design considerations are bursting force and bearing stress. Unlike,
in a pre-tensioned member, where the prestress is transferred gradually, in a post-tensioned
member, the stress is transferred at the end. Hence, the end region of a post-tensioned
member, which is called the end zone (or the end block) is subjected to much higher stress
concentration. To reduce the effect of stress concentration for an I section, the end is
made into a rectangular section by bearing the web, so that the thickness at the end
zone is much larger than the thickness of the web in the intermediate region. Thus,
the end zone of a post-tensioned member is usually a rectangular section. This part of
the rectangular section is carried over a certain distance within which there is a high
stress concentration. Beyond that end zone region, the width of the web is reduced and
for the intermediate region, it is narrowed down with the design width of the web.
The photograph for the end zone of a post-tensioned member shows the anchorage block to hold the
prestressing tendons. We observe, when the strands are stretched, the jack gets the reaction
against the member itself. This creates quite substantial amount of stresses in the end
region. The end region is rectangular, whereas in the span, the beam is an I section. This
is the end zone of a bridge I-girder. You can observe the anchorage blocks, which have
been used to apply the prestress from the tendon to the concrete.
This is another photograph of a bridge box girder. Here, you see that the anchorage blocks
have been placed at the end zone. This creates substantial amount of stresses in the end
zone and the strands develop the prestress at the anchorage block itself.
The stress field in the end zone of a post-tensioned member is complicated. The compressive stress
trajectories are not parallel at the ends, they diverge from the anchorage block till
they become parallel. Based on Saint Venant’s principle, it is assumed that the trajectories
become parallel after a length equal to the larger transverse dimension of the end zone.
This sketch helps us understand the effect of stress concentration, the cause and the
effect of stress concentration in the end zone region. The bearing plate next to the
anchorage block applies the concentrated stresses at the end of the member, yp0 is the dimension
of the bearing plate. After the stress is transferred to the concrete in this bearing
region, the compressive stress trajectories which are denoted by green lines, expand and
over a certain length they become parallel. It is assumed that the distance within which
it becomes parallel is equal to the larger dimension of the end zone. Thus, y0 is the
larger transverse dimension of the end zone within which the stress concentration effect
gets reduced. Beyond y0, the stress distribution is uniform, if the pre-stressing tendon is
concentric and we do not have the effect of stress concentration beyond the length y0.
Thus, the length of the end block is equal to the larger dimension of the end zone that
is the ransverse dimension.
The tensile stress trajectories are also shown by the orange lines. Here also, you can see
that these lines are bent and gradually they become parallel as we move towards the end
of the end zone. Since the stress trajectories are not parallel, it generates tensile stresses
and compressive stresses within the end zone. If you look into an element at the level of
CGC, we observe that, axially there is a compressive stress whereas, in the transverse direction
we have a tensile stress that transfers tensile stress and denoted as sigmat. This is the
stress which we shall consider in designing of the end zone reinforcement. Thus, understanding
the stress trajectories is important to understand the reason of providing end zone reinforcement
in a post-tensioned member.
The end zone is divided into a local zone and a general zone. The local zone is a prism,
right behind the bearing plate, it is subjected to very high stress concentration and to the
tensile stresses sigmat, which we take into account in designing reinforcement for the
local zone. The region outside the local zone is denoted as general zone. In fact, the local
zone is considered to be a part of general zone. The general zone also has stress concentration,
but not as much as the local zone but it has some other effects, like spalling of concrete
in the region outside the bearing plate. The general zone is reinforced by the end zone
reinforcement to check the bursting effect of the tensile stresses.
Thus, the local zone is the region behind the bearing plate and is subjected to high
bearing stress and internal stresses. The behaviour of the local zone is influenced
by the anchorage device and the confining reinforcement.The general zone is the end
zone region which is subjected to spalling of concrete. It is strengthened by end zone
reinforcement. We do provide special reinforcement in both the local zone and general zone region.
The variation of the transverse tensile stress sigmat, at the level of CGC along the length
of the end zone is shown in the next figure. The stress is compressive for a distance 0.1y0
from the end. Beyond that it is tensile. The tensile stress increases and then drops down
to zero within a distance y0 from the end.
If you plot the variation of the transverse stresses at the level of CGC and along the
axis of the beam, we observe that right behind the bearing plate, the transverse stresses
are compressive. After a distance of about one tenth of the length of the end zone, the
stresses become tensile and it increases up to a maximum value then it decreases and becomes
negligible towards the end of the end zone. We are more concerned about the tensile stress
that occurs between the regions, 0.0y0 to y0. It is 90% of the length of the end zone
is of concern because of the transverse tensile stress. This transverse tensile stress acts
in a radial direction with respect to the axis, which means, it is neither vertical
nor horizontal but it acts in a radial direction with respect to the axis of the beam.The transverse
tensile stress is known as splitting tensile stress. The resultant of the tensile stress
in a transverse direction is known as the bursting force.
In our previous sketch, we have denoted the resultant of stresses by a force, which we
denote as Fbst and this term is referred to bursting force. This force creates horizontal
crack unless it is properly reinforced. This is called the splitting of the concrete. That
means, splitting of the concrete refers to the horizontal crack that generates due to
the stress concentration.
Compared to pre-tensioned members, the transverse tensile stress in post-tensioned members is
much higher. During our lecture on pre-tensioned member,
we observed that there is a transverse tensile stress in the pre-tensioned member. But, the
transverse tensile stress in the end zone of a post-tensioned member is much higher
as compared to the pre-tensioned member. Hence, the end zone of a post-tensioned member needs
special attention regarding the design of end zone reinforcement.
Besides the bursting force, there is spalling forces in the general zone. We not only have
the bursting force in the local zone and stress peel over to the general zone, but we also
have some other forces which create spalling of concrete and this is outside the bearing
plate region. This force which causes spalling of concrete is termed as a spalling force.
IS: 1343-1980, Clause 18.6.2.2 provides an expression of the bursting force Fbst for
an individual square end zone loaded by a symmetrically placed square bearing plate.
Thus, the expression that is given in IS 1343 is for an end zone whose cross-section is
squared and with the bearing plate is also squared. This bearing plate is concentric
with the end zone. That means the axis of the bearing plate is same as the axis of the
end zone. The expression of Fbst is equal to Pk times 0.32 minus 0.3 times yp0 divided
by y0. Here, Pk is the prestress in the tendon that means if you have a larger bursting force
in prestress and also the bursting force is a function of the ratio of the dimension of
the bearing plate to the dimension of the end zone. yp0 is the length of a side of bearing
plate that is parallel to Y0.
If you plot the variation of the bursting force normalized with respect to the prestress
in the tendon, we observe that the bursting force reduces as the size of the bearing plate
increases. The equation is the linear equation if have negligible plate, then the bursting
force is about 32% of the prestress. As the plate increases to the end zone dimension,
the bursting force drops down to about 2% of the prestressing force. Thus, we can observe
that if we increase the size of the bearing plate, the bursting forces are reduced.
In this figure, we are observing that for the same prestress member, if we have three
different sizes of the bearing plates: for one, it is a very small bearing plate, for
two we have a larger bearing plate, for three we have a bearing plate which covers the width
of the end zone. For these three cases, we observe that the bursting force is largest
for case 1, which has a small bearing plate and is least for case 3 which has the largest
bearing plate. Thus, one way to reduce the effect of bursting forces is to increase the
size of the bearing plate so that it applies a more uniform stress at the end of the post-tensioned
member.
For a rectangular end zone, Fbst is calculated from the previous equation for each principle
direction. That means, if the end zone and the bearing plate are rectangular, then we
apply the previous equation for the horizontal and vertical direction separately and we calculate
the two bearing forces, one in the horizontal direction and one in the vertical direction.
If the bearing plate is circular, an equivalent square loaded area is considered in the calculation
of Fbst. Thus, for a circular bearing plate, we consider an equivalent square bearing plate,
whose area is same as that of the circular bearing plate and then we apply the expression
that is given earlier. Again, the expression of the bursting force is a function of the
prestress in the tendon, it is a function of the ratio of the dimension of the bearing
plate to the dimension of the end zone and both these dimensions are in the same direction.
We observe that as the ratio of the dimension increases the bursting force comes down. If
you have more than one bearing plate then the end zone is divided into symmetrically
loaded prisms. Each prism is analysed by the previous equation.
As you have observed, we may have more than one bearing plate. In that case, we divide
the end zone into regions which are tributary to each bearing plate, the region for one
bearing plate is placed symmetrically about its center. Then, we apply this expression
for each region of the end zone separately. Next, we are moving on to the design of the
end zone reinforcement.
The transverse reinforcement is provided in each principle direction based on the value
of Fbst. We have calculated till now is the bursting force. If it is a square bearing
plate, with a square end zone, then the bursting force is same in both the horizontal and the
vertical direction. If it is the rectangular bearing plate and if the proportion of the
dimensions of the bearing plate to the end zone is different in the two directions, then
we shall have two values of the bursting force: one for the horizontal direction and another
for the vertical direction. We select the higher of the two and design the end reinforcement
for the bursting force. End zone reinforcement is also called anchorage zone reinforcement
or bursting links. The reinforcement is distributed within a length from 0.1y0 to y0 from an end
of the member. The end zone reinforcement is started from
a distance 0.0y0 because there the transverse stresses become tensile and the end zone reinforcement
is continued up to a distance y0 from the end. Beyond that, the transverse tensile stress
becomes negligible. Hence, the end zone reinforcement is placed in a distance of 0.9y0. This end
zone reinforcement is also called anchorage zone reinforcement or bursting links.
The amount of end zone reinforcement in each direction shall be denoted as Ast and can
be calculated from the following equation: Ast is equal to Fbst divided by fs. The stress
in the transverse reinforcement fs is limited to 0.87fy. When the cover is less than 50
millimeters, fs is limited to a value corresponding to a strain of 0.001. Thus, when we are designing
the end zone reinforcement, we are free to select the stress that we can allow in the
transverse reinforcement. The maximum value is 0.87fy. If the cover of the concrete to
the tendons is less than 50 millimeter, then the code recommends that we reduce the allowable
stress in the transverse reinforcement to a value which corresponds to a strain of 0.001.
Thus, fs will be equal to the modulus of the transverse reinforcement times 0.001. With
this value of fs we calculate the amount of transverse steel here which is denoted as
Ast.
The end zone reinforcement is provided in several forms some of which are proprietary
of the construction firms. The forms have closed stirrups, mats or links with loops.
A few types of end zone reinforcement are shown in the following sketches.
End zone reinforcement can be of several types and are usually designed by the post-tensioned
firms and they have proprietary designs. A few of them are shown; on the left, we can
observe a mat of reinforcement and here you see that we are providing both horizontal
reinforcement and vertical reinforcement. We can also provide the reinforcement in the
form of links, instead of providing individual horizontal or vertical reinforcement, we can
provide the reinforcement by having links in them. The simplest form of the end zone
reinforcement is to have closed stirrups, so as to confine the concrete of the end zone.
The local zone is further strengthened by confining the concrete with spiral reinforcement.
Performance of the reinforcement is determined by testing end block specimens. The following
photo shows the spiral reinforcement around the guide of the tendons.
As I mentioned before, the local zone is subjected to severe stress concentration. In order to
increase the strength of the concrete, confining reinforcement is placed in the local zone
in the form of spirals or helical reinforcement. Most of the reinforcement is proprietary of
the firms manufacturing the anchorage blocks and the end devices. Performance of this type
of reinforcement is usually determined by test of the end blocks. In this photograph,
you can observe that the prestressing strands after it has passed to the guides, has been
anchored at the end block through the wedge and anchorage block. A part of the guide has
been cut open to show the strands which passed through the guide to the anchorage block and
outside the guide a spider reinforcement has been provided to confine the concrete to increase
its strength, so as to resist the internal stress concentration. There is also a pipe
for the grouting of the ducked after the post tensioning operation has been done. Thus,
this type of special confining reinforcement is provided in the local zone so as to reduce
the effect of the stress concentration. The end zone may be made of high strength concrete.
Use of dispersed steel fibres in the concrete reduces the cracking due to the bursting force.
Thus, we may have special type of concrete for the end zone, one option is a high strength
concrete. We can also have fibre reinforcement concrete, where steel fibres are dispersed
within the concrete in the end zone. This helps to check the growth of cracks in the
end zone. Pertinent designs have been made for the concrete in the end zone region.
Proper compaction of concrete is required at the end zone. Any honey comb of the concrete
leads to settlement of the anchorage device. Thus, during concreting, attention has to
be paid towards the quality of casting, proper compaction has to be done in the end zone.
If there is any honey comb left, that will lead to the sinking of the anchorage block
and that may also lead to any accident during the post-tensioning operation. Thus, the post
tensioning operation is a testing time to make sure that the post-tensioned beam has
good quality concrete. Especially, the end zone has a concrete which is sufficient to
sustain the stress concentration in the end zone.
If the concrete in the end zone is different from the rest of the member, then the end
zone is cast separately. The following photo shows separate casting of the end zone. For
this bridge girder, you can observe that the end zone has been cast prior to the casting
of the rest of the member. The end zone is a high strength concrete and there was strict
quality control during the casting of the end zone concrete. Thus, this will ensure
that the effect of the stress concentration will be reduced and the end zone will be able
to sustain the stresses which arise during the post tensioning operation. Observe that
the tendons will pass through these ducts and they will be fixed by anchorage blocks
behind these bearing plates. The next important aspect is to design the
bearing plate for the end zone. In this lecture, we are not designing the
thickness of the bearing plate which is based on the conventional steel design. We are more
interested to design the dimension of the bearing plate, the height and the width so
that the effect in the concrete is minimized. The design of the bearing plate refers to
designing the length and the width of the bearing plate such that the bearing stresses
in the concrete are within the allowable value.
High bearing stress is generated in the local zone. You can observe from this figure that
when the bearing plate is resting against the end zone and the post-tensioned is applied,
substantial bearing stress is applied in the local zone of the end zone and we need to
check the failure of concrete due to the bearing.
The bearing stress which is denoted fbr is calculated from the following equation: fbr
is equal to Pk divided by Apunching, where Pk is the prestress in the tendon with one
bearing plate and Apunching is the punching area which is the area of contact of bearing
plate. Thus, the bearing stress is the ratio of the prestressing force in one particular
tendon within single bearing plate divided by the area of the bearing plate. We are assuming
a uniform bearing stress to occur over the bearing area.
As per clause 18.6.2.1 of IS 1343-1980, the bearing stress in the local zone should be
limited to the following allowable bearing stress, which is denoted as fbr,allowable.
It is equal to 0.48 fci times root over Abr divided by Apunching. The allowable bearing
stress should be limited to 80% of fci.
In this equation, Apunching is the area of contact of the bearing plate which is shown
as the gray shaded area and Abearing is the bearing area which is equal to the maximum
transverse area of end block that is geometrically similar and concentric with the punching area.
We shall explain the A bearing in the subsequent slide. Before that, let us mention that fci
is the cube strength at transfer. This is sketch of the end view showing the bearing
plate resting against the post-tensioned member. Thus, the code recommends are limiting bearing
stress and this bearing stress is a function of the cube strength at transfer. It is the
function of two areas: one is the punching area, which is the area of the bearing plate
and another is the bearing area, which is the area in the concrete that is similar to
the punching area and concentrically located with the punching area. If we have to reduce
the bearing stress, or in other words if you are trying to increase the allowable bearing
stress, then we should have adequate concrete strength. The post-tensioning operation can
be done only when the concrete achieves the minimum strength as specified in the design
calculations. Only then we shall have a high value of fci which will give a high value
of the allowable bearing stress. If the ratio fbr divided by Apunching increases, then we
can increase the allowable bearing stress. Now, let us try to understand the concept
of the Abr which is the bearing area in the concrete resisting the bearing stress.
The previous expression of allowable bearing stress takes advantage of the dispersion of
the bearing stress in the concrete. Apunching is the area where the bearing stress is applied
and after that the bearing stress gets dispersed in the end zone to an area which can be placed
within the end zone, this is geometrically similar to Apunching. Thus, Abr and Apunching
are the two ends of a frustum which can be placed within the end zone. The purpose of
having a larger Abr as compared to Apunching is that the bearing stress gets dispersed
in the concrete which has been adequately strengthened by providing end zone reinforcement.
Thus, if the end zone reinforcement is there, we are taking advantage of the dispersion
of the bearing stress and considering of factor which is larger than one, this helps us to
increase our allowable bearing stress.
The performance of anchorage blocks and end zone reinforcement is critical during the
post- tensioning operation. The performance can be evaluated by testing end block specimens
under compression. The strength of an end block specimen should exceed the design strength
of the prestressing tendons. As I mentioned before, the post-tensioning operation itself
is the testing time for a post-tensioning member. The anchorage block and the end zone
have to perform during the post-tensioning operation. Now, these regions are tested separately
in a laboratory to check their capacity and the capacity of an end zone should be larger
than the maximum prestressed that is coming in the tendon. Hence, we ensure that there
will not be failure in the end zone and the stress will be transferred to the post-tensioned
member. The following photos show the manufacturing
of an end block specimen.
This is the end zone reinforcement for an end block specimen. For this reinforcement,
the anchorage block will be coming on the right side. Observe that the end zone reinforcement
is larger sized and closely spaced towards the end of the post-tensioned member. The
end of the post-tensioned member will be on the right side and the reinforcement is of
a smaller size and is largely dispersed, as we are moving out from the ends of the end
zone. Thus, the end zone reinforcement is not uniformly placed along the length of the
end zone. There is more reinforcement towards the end of the end zone near the anchorage
block and there is less reinforcement toward the other half of the end zone. This is a
more efficient way of placing the end zone reinforcement in the end block specimen.
In this photo, we observe the guide through which the prestressing tendon will pass and
the anchorage block where the prestressing tendons will be attached.Once, this guide
is placed within the reinforcement gauge, the concrete will be cast. We shall have a
specimen as shown in this photograph.
This is an end block specimen which will be tested to check its capacity. Here, you can
observe that this is the bearing plate which is also a part of the guide and the space
will provide us the requisite space to put the tendons. Once the tendons are placed,
the anchorage block will be placed where the tendons will be attached. This type of specimen
can be tested under compression to simulate the compression due to the anchorage blocks
or it can also be tested for fertig to check the performance of the whole anchorage systems
under varying load.
Let us now try to understand the design of the end zone reinforcement and the bearing
plate by an example. Design the bearing plate and the end zone reinforcement for the following
bonded post-tensioned beam. The strength of concrete at transfer is 50 Newton per millimeter
square. A prestressing force of 1055 Kilonewtons is applied by a single tendon. There is no
eccentricity of the tendon at the ends.
This section is as follows: in the span region, it is an I section which is 400 millimeter
wide flanged. The depth of the flanges is 100 millimeter and it is a section which is
symmetric about a horizontal axis. The tendon has an eccentricity with respect to CGC in
the intermediate region. The width of the web is 100 millimeters and the total depth
of the section is 600 millimeters. Now, when we are coming to the end, the width of the
web has been flared so that we have an increased width of the end zone. The width of the end
zone has been made equal to the width of the ***. That means, the end zone is of uniform
width which is 400 millimeters and the depth of the section is 600 millimeters. Thus, the
end zone is a rectangular section, where as the section in the span region is an I section.
Again, the purpose of flaring the end zone is to reduce the effect of the concentrated
stresses.
For this problem, there is only one tendon which does not have eccentricity at the end
and the strength of the concrete at transfer has been given, which is 50 Newton per millimeters
square. We can observe that this is substantially high value of the concrete strength. Now,
before designing the end zone reinforcement, we are calculating the bearing stress that
will come in the end zone. For that, we need to have a trail bearing plate and for this
problem, we are selecting a bearing plate which is geometrically similar to the end
zone section, its width is 200 millimeters which is half of the width of the end zone.
The height of the bearing plate is 300 millimeters which is again half of the height of the end
zone. We shall place the bearing plate concentrically with the end zone. The bearing stress is calculated
by the following equation: fbr is equal to Pk, which is the prestressing force coming
in the tendon divided by the Apunching, which is the area of the bearing plate. The value
of Pk is given as 1055 Kilonewtons, which is 1055 times 10 to the power 3 Newton divided
by Apunching is equal to 200 times 300 millimeter square. Thus, we get a uniform bearing stress
of 17.5 Newton per millimeter square in the local zone of the end zone of the post-tensioned
member.
The allowable bearing stress as per the code is 0.48 fci times root over Abr divided by
Apunching. fci is given as 50 Newton per millimeter square and Abr is a geometrically similar
area in the end zone which can be placed. Since we have selected a bearing plate, which
is geometrically similar to the cross-section of the end zone, we are able to utilize the
full cross-section of the end zone as Abr. Thus, Abr is equal to 400 times 600 and Apunching
as before it is 200 times 300. We get the allowable bearing stress as 48 Newton per
millimeter square. But we have to check the other limit of the allowable bearing stress.
The allowable bearing stress should be limited to 80% of fci, which is 0.8 times 50 which
is equal to 40 Newton per millimeter square. The bearing stress which we calculated earlier
is less than fbr allowable and hence it is okay. Thus, what we have found, the allowable
bearing stress is governed by the second provision that it can be maximum of 80% of the cube
strength during transfer. Based on that, we found out that the allowable bearing stress
is 40 Newton per millimeter square. Earlier, we had found out the bearing stress to be
17 Newton per millimeter square, which is less than the allowable value. Hence, the
bearing plate is of adequate dimension which will help to have a stress which is within
the allowable bearing stress of the concrete.
Second, we are calculating the bursting force. Since it is a rectangular section, we are
calculating the bursting force in two directions: one in the vertical direction and one in the
horizontal direction. For the vertical direction, Fbst is equal to Pk times 0.32 minus 0.3 times
yp0 divided by y0 and the values of yp0 and y0 are the directions that are under consideration.
Pk is equal to 1055 Kilonewtons, yp0 in the vertical direction is 300 millimeters, which
means the dimension of the bearing plate in the vertical direction is 300 millimeters,
y0 is the dimension of the end zone for the vertical direction which we have as 600 millimeters.
Once, we substitute the values of yp0 and y0 in this expression, we get Fbst is equal
to 179.3 Kilonewtons. Thus, there is a bursting force of 179 Kilonewtons acting at the level
of CGC in the vertical direction.
Next, we are calculating the bursting force in the horizontal direction: For that, Pk
remains the same, whereas yp0 is now 200 because the horizontal dimension or the width of the
bearing plate is 200 millimeter and Y0 which is the width of the end zone is 400 millimeters.
Since, we have cleared the end zone, we are having a uniform width of the end zone as
400 millimeters. Once, we substitute the value of yp0 and y0 we get the same value of Fbst
179.3 Kilonewtons. The values of the bursting force in the horizontal and the vertical directions
have come out to be same because we had selected a geometrically similar bearing plate with
respect to the cross-section of the end zone. The cross-section of the end zone was 400
by 600 and our selected bearing plate was 200 by 300. Since, the ratio of the dimension
of the bearing plate and the end zone was same for both the horizontal and vertical
directions. We have got the same value of the bursting force for the two directions.
Thus, design bursting force is 179.3 Kilonewtons.
Next, we are calculating the end zone reinforcement: Ast is equal to Fbst divided by 0.87 fy. Since,
we have adequate cover around the tendon, we are selecting the maximum allowable stress
which is 0.87 fy so as to reduce our end zone reinforcement. We find that Ast is equal to
179.3 times 10 to the power 3 Newton divided by 0.87 times 250, which is the selected grade
of end zone reinforcement and we find Ast is equal to 824.6 millimeter square. Thus,
we have to provide confining reinforcement in the end zone which has an area of 824.6
millimeter square.
In order to design the end zone reinforcement, we are providing two third of Ast in the first
half of the end zone. Thus, two third of Ast is equal to two third times 824.6 which is
550 millimeter square. This much of reinforcement we are placing within 0.1y0 which is equal
to 60, here y0 is the larger dimension of the end zone and 0.5 y0 which is 300 millimeters
from the end. Thus, within the distance of 60 millimeters and 300 millimeters from the
end, we are providing two third of Ast which is 550 millimeter square. Select 6 number
of 2 legged 8 millimeter diameter stirrups. Provide the rest one third of Ast, which is
one third of 824.6, gives us 275 millimeter square within a distance 0.5y0 which is 300
millimeters and y0 which is equal to 600 millimeters from the end. Thus, we are providing the rest
one third of the end zone reinforcement in the second half of the end zone, which is
a distance from 300 millimeters to 600 millimeters from the end of the post-tensioned member.
Select 5 number of 2 legged 6 millimeters diameter stirrups. We observe that in the
first half of the end zone which is closer to the bearing plate, we are selecting a larger
diameter bar size and more number of bars, the spacing will also be closed, whereas for
the second half of the end zone the bars size is smaller, the number is smaller and hence
the spacing will also be larger for the second half.
This is the design section for the bearing plate. The dimension of the bearing plate
is 200 by 300 and it is placed concentrically with the end zone.The end zone reinforcement
is provided by closed stirrups. For a region from 60 to 300, from the end of the specimen
we are providing (6) 8 millimeter diameter stirrups and these are closely spaced whereas,
beyond 300 millimeters we are providing (5) 6 millimeter diameter stirrups that is up
to a distance of 600 millimeters from the end. This end zone reinforcement is in addition
to other shear reinforcement that we needed in the end zone region.
Since the end zone is substantially wide, the shear reinforcement recommend will be
small as compared to the part with the reduced thickness of the web.
Thus in today’s lecture, we talked about the transmission of prestress for a post-tensioned
member. Unlike a pre-tensioned member, in a post-tensioned member the stress in the
tendon develops right at the anchorage block and the prestress is transferred to the concrete
by the bearing plate. In doing so, there is a huge amount of stress concentration at the
end zone of the post-tensioned members which needs to be properly addressed to check the
splitting of concrete at the horizontal plane and the spalling of concrete in the vertical
surface which is outside the bearing plate region. We discussed about the bursting force
and the design of end reinforcement to check the cracking due to bursting force. Then,
we discussed about the bearing stress and how to design a bearing plate with adequate
area such that the bearing stress is less than the allowable bearing stress for the
concrete. In order to reduce the effect of bursting force, you should have a large bearing
plate and we should transfer the prestress when the concrete has attained substantial
strength. With this we are ending the module of transmission of prestress. Thank you.