chapter 5 post-tensioned slab

Chapter 5 Post-Tensioned Flat Slab

GENERAL

Post-tensioned concrete has been used for more than 40 years in the United States in a wide

variety of construction projects. First used primarily in bridge construction, applications for

post-tensioning now extend far beyond bridges to include tanks, office buildings, hotels,

parking structures, pavement, masonry, seismic walls, single-family homes and more.

They can be designed as two-way spanning flat slabs, one-way spanning ribbed slabs, or as

banded beam and slab construction. Flat slabs are supported, without the use of beams, by

columns with or without column heads. They may be solid or may have recesses formed in

the soffit to create a series of ribs running in two directions (waffle or coffered slab). The

design principles of continuous flat slab floors are similar to those of two-way reinforced

concrete slabs. A strip of slab of unit width, continuous over supports, is analyzed as a

continuous beam. Prestressing of continuous slab results in secondary moments. If the cable

profile is concordant, secondary moments can be eliminated. Since 1955 a number of number

of continuous flat slab have been built in U.S.A, in which unbounded tendons are to be

preferred both from the point of view of ultimate strength requirements and easy

maintenance under adverse exposure conditions.

The design of a continuous flat slab floors involves the computation of maximum and

minimum moments for various load combinations and the determination of suitable cable

profiles so that the resulting stresses in concrete are within the safe allowable limits as per

codes. Shear stresses at the junction of the column and slab should be carefully controlled by

proper design and detailing of the critical shear zones.

5.1 POST-TENSIONING SYSTEMS

In the U.S. and Canada, post-tensioned buildings and parking garages are typically

constructed with seven-wire, 12.7 mm diameter, un-bonded single-strand (monostrand)

Design of Reinforced Concrete & Post-Tensioned flat slab using software 1

Chapter 5 post-tensioned flat slab

tendons. These tendons, with a typical strength of 1860 MPa, are also greased and sheathed.

One reason for the widespread use of the 12.7 mm diameter strand is the Code requirement

that the tendon spacing not be greater than eight times the slab thickness. The use of 12.7 mm

diameter, 1860 MPa strand permits 110 and 125 mm slabs to meet both the minimum 0.85

MPa average pre-compression and the maximum tendon spacing requirement. In addition,

the tendons and stressing equipment are light enough for workers to handle them efficiently

on site. Larger diameter 15.3 mm strands are primarily used in pre-tensioning and bridge

construction. Higher strength steels and smaller diameter strands are also available but are

not commonly used for new construction.

5.2 STRUCTURAL MODELING

Several methods of floor slab analysis and design

1. Direct Design Method (DDM)

2. Equivalent Frame Method (EFM)

3. Strip Method

4. Closed Form Solution and Approximations

5. Finite Difference Method (FDM)

6. Finite Element Method (FEM)

7. Yield Line Method (YLM)

8. Experimental Techniques

9. Strut-And-Tie Method

In both one- and two-way systems, specifying the structural model includes defining the

design strips, irrespective of whether an FEM or Equivalent Frame Method of analysis is

used. Column-supported floors generally qualify as two-way systems; beam- and wall-

supported slabs and beams generally qualify as one-way systems.

Design of Reinforced Concrete & Post-Tensioned flat slab using software. 2


The fixity of the connections must also be specified. In some instances, such as corner

columns in flat slabs, the assumption of full fixity does not yield a satisfactory design. For

structural analysis, such connections may be assigned partial fixity or may be assumed as

hinged connections (releases). Connections that are assumed to be hinged must be detailed in

the construction documents to allow rotation, while retaining the integrity of the joint by

limiting crack width and transfer of axial and shear forces through the joint. Another instance

where a hinge connection may be beneficial is for short gravity columns at split levels in

parking structures, which have a ramp on one side and a level floor on the other side.

5.3 DESIGN GUIDELINES

There is a major difference between the design of a post-tensioned member and the design of

a conventionally reinforced concrete member. Once the geometry, loading, support

conditions, and material properties of a conventionally reinforced member are established, a

unique solution of the required area of reinforcement, As, is given by a formula.

For a post tensioned member, there are a number of acceptable reinforcement designs

because there are several additional parameters that must be specified by the engineer. These

parameters may be grouped as follows:

Average pre-compression (prestressing force);

Percentage of load to balance (uplift due to tendon drape); and

Tendon profile (shape and drape).

From the many possible design solutions for a post-tensioned member, the one that meets

the Code requirements for serviceability and strength and is the least expensive to build is

usually the preferred solution. Generally, for a given slab dimension, loading, and

construction method, less material means a more economical design. Values for the three

parameters listed above must be established before the required amount of post-tensioning

can be determined. The amount of supplemental reinforcement as required for strength



design of the post-tensioning member is determined by the amount of the post-tensioning

reinforcement and the reinforcement profile. The typical ranges of spans for the

various forms of construction and their corresponding slab and beam depths

are shown here.

Fig. 5.1 Typical economical spans with different types of slab

Table 1 Typical slab and beam depths



5.3.1 AVERAGE PRE-COMPRESSION

The average pre-compression is the total post tensioning force divided by the gross cross-

sectional area normal to the force. ACI 318 requires a minimum 0.85 MPa effective pre-

compression (pre-compression after all prestress losses). In general, 0.85 MPa should be used

for the initial average pre-compression. For roofs and parking structures, use 1.0 to 1.4 MPa

if water tightness or cracking is a concern. however, an increase in pre-compression does not

guarantee water tightness and may not completely eliminate cracking. To avoid leakage, the

increased post-tensioning must be supplemented by other measures, such as a membrane

overlay. In one-way slab and beam construction, the member is defined as the beam and its

tributary slab area. Maximum pre-compression should be 2.0 MPa for slabs and 2.50 MPa for



beams; although the Code’s limit of maximum compressive stress is much higher, values

higher than these typically mean the design will be less economical.

Fig. 5.2 Tributaries used when computing average pre-compression

5.3.2 PERCENTAGE OF LOAD TO BALANCE

This is expressed as the ratio (percentage) of the dead load that is balanced. For slabs, it is

customary to balance between 60 and 80% of the dead load. For beams, this is usually

increased to between 80 and 110%. One reason for higher balanced loading for the beams is

that beam deflection is more critical to service performance of a floor system. To determine

the required post-tensioning force, start with the critical span. For the spans adjacent to the

critical span, a lower percentage of the dead load should generally be balanced because less

upward force in an adjacent span helps to reduce the design values of the critical span.

Balancing all the spans of a continuous member to the same percentage of dead load is not

always economical. In practice, tendon profiles are reversed parabolas; such example is

shown in Figure 2. Tendons thus exert both upward and downward forces in the same span.

In such cases and for the purpose of design, the percentage of dead load balanced is

considered as the sum of the upward forces divided by the total dead load (DL) on the span.

For the design shown in Fig. 4, this becomes: % of DL balanced = 100[(W2+W3)/DL]



Fig. 5.3 Post-tensioning tendon of reversed parabola shape, exert both an

upward and a downward force in the same span

5.3.3 TENDON PROFILE: SHAPE

For beam tendons and slab tendons in the distributed direction, a reversed parabola tendon

profile with inflection points at one-tenth of the span length (Fig. 5.4) is typically used. For

an exterior span, the tendon is at the mid depth of the slab at the slab edge and at its high

point (typically somewhat higher than mid depth) at the other end. Moving the tendon low-

point to 0.4L, results in a more uniform uplift over the exterior span.

Fig. 5.4 The tendon profile, reversed parabola with inflection



5.3.4 TENDON PROFILE: DRAPE

The high point of the tendon profile should be as close to the top surface of the member as

practical, allowing for clearance and reinforcement in the orthogonal direction, if necessary.

At the low point of the profile, it is best to place the tendons as close to the soffit of the

member as allowable, to take full advantage of the uplift and contribution to strength that the

tendon can provide. This arrangement is possible for the critical spans in a continuous

member, but may need to be adjusted for other spans. Maximum drape results in excessive

uplift in a span other than the critical span, the first choice should be to reduce the

prestressing force. Tendons should be anchored at the centroid of the slab even if there is a

transverse beam or drop cap/panel at the slab edge (fig. 5.5)

Fig. 5.5 Anchorage at exterior support

5.4 ANCHOR LOCATIONS

Tendons in stand-alone beams (beams not cast monolithically with the slab) should be

anchored at the centroid of the beam. Tendons in flanged beams such as in one-way slab and

beam structures should be anchored at the centroid of the combined beam stem and its

tributary. In the traditional load- balancing analysis used by most designers, the force in the

tendons, generally considered constant, is represented by an axial force, P, at a location that

results in “uniform pre-compression”, if a force is acting at the centroid of a member, it will

disperse in to a uniform compression at a distance “sufficiently far” from the point of

application of the force.



5.5 ADDITIONAL CONSIDERATIONS

5.5.1 COVER FOR FIRE RESISTANCE

When determining fire ratings, designers typically consider the end spans in column-

supported structures unrestrained. To achieve fire resistance equal to that of interior spans,

provide a larger cover for tendons at the low point of exterior spans unless the end support is

a wall or transverse edge beam. Only the first and last spans of tendons along a slab edge are

considered as “end spans”.

5.5.2 TENDON LAYOUT

The preferred tendon layout for two-way slabs is to concentrate the tendons over the supports

in one direction (the banded tendons) and distribute them uniformly in the other direction.

Place the distributed tendons in the orthogonal direction, parallel to one another, making sure

that a minimum of two tendons pass over each support as required by ACI 318-02.

5.5.3 TENDON STRESSING

Most engineers in North America design with final effective forces—the post-tensioning

forces after all prestress losses. The post-tensioning supplier determines the number of

tendons required to provide the force shown on the structural drawings, based on the

effective force of a tendon. The effective force of a tendon is a function of a number of

parameters, including the tendon profile, certain properties of the concrete, and the

environment. For typical designs, however, a constant force of 120 kN may be assumed for

12.7 mm. Un-bonded tendons shall meet the following conditions for stressing.

Tendon length (length between anchorages) shall less than 72 m.



Tendons less than 36 m long are stressed at one end; and

Tendons longer than 36 m but less than 72 m are stressed at both ends.

Tendons that do not meet these conditions may be used, as long as the assumed effective

force is lowered to account for the higher friction losses.

5.6 OTHER DESIGN CONSIDERATION

5.6.1 SEISMIC DESIGN

Although seismic design technology is not currently as well developed for post-tensioned

structures as for some other structural systems, a number of experimental research projects

have been completed which indicate that energy dissipation characteristics conforming with

accepted standards can be achieved by appropriate combinations of prestressed and non-

prestressed reinforcement. The preliminary report on the moment transfer tests at the

University of Washington sponsored by the Post- Tensioning Institute and the Reinforced

Concrete Research Council states: "It is apparent that prestressing could provide an excellent

means for tieing a slab together and ensuring ductile behavior for seismic loading. However,

reversed cyclic large edge deflection tests are necessary to validate that potential and develop

the rules necessary to ensure ductile behavior" (Fig. 5.6).



Fig. 5.6 Comparison of Lateral Load-Edge Deflection Relationships for Reinforced and

Prestressed Concrete Slab - Interior Column Specimens

Graph shows that after low intensity reversed cyclic loading one of the post-tensioned slab

specimens could still develop a lateral load - edge deflection relationship for unidirectional

loading paring very favorably with the same relationship for a similarly loaded reinforced

concrete slab with integral beam stirrups. For the prestressed slab, the cracking that

developed at the column face during the first cycle between maximum lateral loads of two

kips resulted in a permanent edge deflection for zero lateral load. However, for the second

and third cycles to the same maximum lateral loads, and even when the lateral loads were

increased to three kips, the hysteresis loops remained stable and spindle shaped. Further,

there was no degradation in stiffness with cycling. Use of post-tensioned flexural systems

with un-bonded tendons in areas of high seismicity has sometimes been questioned because

the tendons may not be stressed beyond the elastic range, even in a severe earthquake, and,

for this reason, the tendons do not dissipate much energy. This objection may be overcome



when the slabs are an integral part of the moment resisting frame by use of a combination of

un-bonded tendons and non-prestressed bonded reinforcement as discussed above. However,

in most post-tensioned structures in seismic zones the post-tensioned elements are not part of

the ductile moment resisting space frame, or the seismic resistance is provided by shear walls

or some other force resisting system. For such cases, Uniform Building Code 1976 Edition,

Section 2314 states: " framing elements not required by design to be part of the lateral force

resisting system shall be investigated and shown adequate for vertical load carrying capacity

and induced moment due to 3/K times the distortions resulting from the Code required lateral

forces." K is the horizontal force factor. It has been shown that under reinforced prestressed

concrete members can meet the ductility requirements of the above Uniform Building Code

provision. Also suggests" that in the range of seismic disturbances slightly greater than

moderate, prestressed concrete can provide the necessary deformability and still respond

almost elastically." The elastic response results from the fact that it is not possible for the

stress in an un-bonded tendon to reach the yield point within the deformation range

anticipated in a moderately severe earthquake. A significant practical benefit of this is that

permanent structural damage to the floor system will be greatly reduced in comparison to

other structural systems.

Anchorage systems used for un-bonded tendons are required to meet static and dynamic test

requirements much more severe than the loadings that would be anticipated in an earthquake

of high intensity. These specifications also require the anchorage system to withstand,

without failure, 500,000 cycles from 60 to 66 percent of the minimum specified ultimate

strength of the tendon material.

In addition to the satisfactory performance of post-tensioned specimens subjected to

earthquake loadings in laboratory research projects, post-tensioned structures have responded

well in numerous earthquakes in the United States and in other countries. Many post-

tensioned structures have been built in areas of 'high seismicity and many have been

subjected to earthquakes of significant magnitude. A post-tensioned ductile moment resisting



space frame with un-bonded tendons in combination with bonded non-prestressed

reinforcement, as well as other post-tensioned buildings, performed very well in the 1971

San Fernando earthquake in California. In summary, both test results and performance in

earthquakes indicate advantages for the use of un-bonded tendons for structures in areas of

high seismicity, particularly when used in conjunction with shear walls or other lateral force

resisting elements.

5.7 SELECTION OF NON-PRESTRESSED REINFORCING

5.7.1 BAR SIZE

To take full advantage of the maximum lever arm for reinforcement in both directions, the

top bar diameters should match those of the adjacent tendons. Thus, it is reasonable to use 16

mm bars over the supports, a sheathed 12.7 mm diameter strand is slightly larger than a 16

mm bar. For bottom bars, it is better to use smaller bars, such as 12 mm bars, for the

distributed tendon direction because these are distributed uniformly among the tendons, and

larger bars for the banded tendons because bars for the banded direction are normally

grouped together and placed within the band width.

5.8 ANALYSIS TOOL

For design and analysis of Post-tensioned flat slab, ADAPT-6.15 software is used. Three

span continuous two-way flat slab geometry is used for the analysis. Following points and

values of various parameters were used for the analysis and design with ADAPT software.

Clear span (from face of support) is used to reduce moments.

Equivalent frame modeling is used for analysis and design.



Including self weight of slab, 2 kN/m2 floor finish load and 5 kN/ m2 live load is

taken.

5.8.1 MATERIAL

28 days compressive strength at is 30 N/mm2 :- M30

Ultimate creep co-efficient :- 2

Steel reinforcement grade :- Fe415

For post-tensioning tendon, 12.7 mm diameter – 7wires strand is used.

Ultimate strength of tendon :- 1860 N/mm2

Effective stress of tendon :- 1200 N/mm2

Minimum strand cover from top fiber 25mm

Minimum strand cover from bottom fiber 25mm

5.8.2 Allowable stresses

Initial tensile stress of top fiber at time of jacking (transfer) :- 0.25√ f ci'

Final tensile stress of top fiber at time of service load :- 0.5√ f c'

Initial tensile stress of bottom fiber at time of jacking (transfer) :- 0.25√ f ci'.

Final tensile stress of bottom fiber at time of service load :- 0.5√ f c'

Initial compression stress of top fiber at time of jacking (transfer) :- 0.6f ci'.

Final tensile stress of top fiber at time of service load :- 0.45f c'.

5.8.3 VALUES FOR POST-TENSIONING

Minimum average pre compression :- 0.86 N/mm2

Maximum average pre compression :- 2.07 N/mm2

Minimum percentage of dead load to balance :- 25%



Maximum percentage of dead load to balance :- 100%

5.8.4 VALUES FOR CALCULATION OF FRICTION STRESS LOSSES

Ratio of jacking stress to ultimate stress :- 0.8

Strands modulus of elasticity :- 2 x 10^5 N/mm2

Angular coefficient of friction Mu :- 0.07 /rad.

Wobble co-efficient of friction k :- 0.0046 rad/m

Anchor set :- 6 mm.

5.8.5 CALCULATION OF LONG TERM STRESS LOSS

Age of concrete at stressing :- 5 days.

Concrete modulus of elasticity :- 20000 N/mm2

5.8.6 LOAD COMBINATIONS

Service combination factors for DL, LL and prestress ( balanced loading) :-

1 DL + 1 LL + 1 prestress.

Strength combination factors for DL, LL and hyperstatic (secondary) actions:-

1.5 DL + 1.5 LL + 1 hyp.

Analysis and design is done by ADAPT-6.0 software with the use of design code ACI 318.

Here explanation of software shows, how input data are to be entered to the software. At

starting of software window, it asks general settings of title. Two way slab structural system

is used for the analysis. equivalent frame modeling is used for design. After giving structural

system and design settings the next window will be of span geometry (fig. 5.7), this screen is

used to enter the cross-sectional geometry of the slab at mid span. All dimensions are defined

in the legend at the top of the screen and illustrated in the appropriate section figure. The



section span can be changed by clicking on the section column. We can use the “Typical”

input row to enter similar dimensions. Type the values in to the appropriate cell in the top

row and then press enter. The typical value will be copied to all the spans.

Fig. 5.7 Window showing input data of span geometry in software



Fig. 5.8 Window showing input data of support geometry in software

As shown in fig. 5.8. This screen is used to input Column/wall height, widths and depths.

After entering support condition the next window will be of boundary condition. Design of

post-tensioned flat slab is done with no end support fixity. Boundary condition for the

column is assumed as upper and lower columns are fixed. For the input of loading

information, software gives the various types of loading pattern which we can directly entre

the value of loading by simply dragging the loading type indicated with graphics icon

(fig.5.9).



Fig. 5.9 Window showing input data of loading in software

It is required to provide the material property for concrete as 28 days compressive strength of

concrete for slab as well as for column and also and ultimate creep coefficient. Then it is also

necessary to input the material property of reinforcement, post-tensioning system whether

bonded or un-boned, area of tendon, allowable stresses and post-tensioning values to the

software as listed above. Software will ask to specify the tendon profile among three types,

reversed parabola, partial parabola and harped parabola (Fig. 5.10). X1/L and X3/L are the

inflection points.



Fig. 5.10 Window showing criteria of tendon profile in software

Then specify minimum covers for post-tensioning tendons and mild steel reinforcement, also

specify minimum bar length and bar extension of mild steel reinforcement and load

combinations. Finally we can see the 3D model view of strip of slab of input data as shown

in Fig. 5.11, Fig. 5.12 and Fig. 5.13.



Fig. 5.11 3D view of interior panel of Post-Tensioned flat slab

Fig. 5.12 3D view of exterior panel of Post-Tensioned flat slab



Fig. 5.13 3D view of interior panel of Post-Tensioned flat slab with drop cap

Fig. 5.14 Graphs showing tendon profile, tension and compression stresses and required and

provided Post-Tensioning forces

Fig. 5.14 displays the top diagram, the tendon height diagram shows the elevation of tendon

profile. The second diagram, stress diagrams, plots the maximum compressive and tensile

stresses at the top and bottom face of the member. The third diagram, Post-Tensioning

diagrams shows the required and provided post-tensioning force at 1/20 th points along each

span. The vertical line represents the required post-tensioning and the horizontal line

represents the provided post-tensioning at that section. The program also gives the required



non-prestressed reinforcement and stress ratio for punching shear which shall be below 1

otherwise shear reinforcement is require near column.


chapter 5 post-tensioned slab

Documents

slab construction

strip of slab

slab thickness

coffered slab

twoway spanning flat

continuous beam

bridge construction

tensioned buildings