Part 2: Calculation and structure of PT ​​slab

See part 1 here.

The smallest unit called tendon (Strand), commonly used in construction design, is a type of 7 steel strands together, 12.7mm in diameter, with a high intensity of 1860MPa. This type is also available on the market today, including the cheap Made in China and Western origin of Freyssinet or VSL. The reason this type of diameter is commonly used because according to the most used standards, ACI, the maximum distance of the tendon (8 times the slab thickness) and the average compression stress in the slab is at least 0.85MPa. Using 12.7mm yarn tendon allows to satisfy both criteria above to save the most tendon. Another reason is that the tension for a 12.7mm single tendon is a handheld type, light and easy to execute. Larger diameter tendon, 15.3mm,Structural engineers Often used for tensioned or bridge assembled structures, recently for PT beams and floors.

 

There are two types of cables used for the following PT structure are unbonded and bonded.

The tendon (tendon) does not bonded is a single fiber consisting of 1 tendon in plastic cover. Each single strand has its own anchor and is stretched separately. Characteristics of Structural design. There is no bonded between tendon and concrete along the length of the tendon. The tendon tension transmitted into the slab only through the two ends of anchoring into the previous force into the concrete there. The function of plastic cover is (i) Preventing the bonded to concrete, (ii) protects the tendon during the construction process, (iii) protects corrosion by moisture and chemicals from outside. Corrosion -proof layer is usually fat (i) reducing friction between tendon and cover, (ii) increasing the effect of corrosion resistance.

The bonded is more commonly used in Vietnam. Flat jealous tubes are usually structural engineers used for the slab and jealous tube is often used for beams and bridges. The tendon in a bundle of 1 anchor at each end but often stretched by clicks and anchores with each separate high similar to the unbonded tendon. The normal jealous tube shell is made from thin corrugated iron.

 

The conceptual design idea for adhesive cables is to create adhesive force with concrete along the length of the tendon by pumping mortar to fill the jealous tube after stretching and anchoring the cables. When the mortar binds, it locks the shift of the tendon in the jealous tube, so the front tension in the tendon becomes the function of the deformation of the concrete around it.

 

The role of pump mortar is: (i) creating continuous bonded between tendon and jealous tube, (ii) against corrosion, (iii) The alkaline environment of insulating mortar, anti -electrochemical corrosion for tendon. The role of jealous tube: (i) creates a space for the tendon in concrete before and during tension, (ii) transmits the bonded force between the mortar and the surrounding concrete, (iii) increases the anti -corrosion effect on the surface of the jealous tube. The main role of the anchor heads at the two tip of jealousy is to keep the tension until the mortar is simmer and work.

 

Note that both slab options with bonded and unbonded have advantages and disadvantages to compensate each other and can work well for the slab structure for all use purposes. tendon not bonded is used for most civil buildings in North America, in Vietnam, probably due to the technical characteristics of contractors and market factors, making the use more adhesive becomes more popular in Engineering consultants.

In terms of Design consultants There is no difference in the calculation process between these two types of cables. However, the stress consumption for the type has more bonded due to the larger friction between the tendon and the jealous tube.

Request tendon protection layer

There is no difference in the thickness of the protective concrete layer for two types of cables, both for corrosion resistance requirements and fire -proof requirements (2 hours).

Stress limit

Both types of cables have the same limit Design standard About the initial stress when stretching and when working, as well as the minimum level of tension and maximum.

tendon stress in TTGH 1

At the same initial tension stress and tendon trajectory, the type has a higher stress bonded in the tendon.

The minimum of reinforced steel content

There are currently no construction design standards that require minimum control of reinforced steel content to control cracks for bonded tendon, unbonded type required in ACI.

Redesement Moment by taking into account flexible joints

The ACI design standard allows to calculate the flexible joints and requires the minimum reinforcement content at the flexible joints. However, only the tendon does not adhere.

The ability to cut the slab of the slab 1 direction and beam, anti -puncture of the slab 2 directions

There is no difference between the two types of cables.

Wind load slab

There is no difference.

Minimum distance between tendons

According to ACI is 8 times the slab thickness or 1.5m. Therefore, the tendon bonded to the larger size proved to be less effective than the unbonded type.

 

For example, 140mm thick slab, designed with a pre -compressive stress of 0.86Mpa, using a 12.7mm tendon with an effective tension (after except for loss) is 116KN. The distance of each tendon will be:

 

116/(0.140) = 960 mm

 

The maximum distance for tendon is 8*140 = 1120mm. So using a tendon without bonded 1 tendon can be placed at a distance of 960mm as calculated. If the tendon adheses the flat tube, at a distance of 960mm, it only needs a tendon in the tube. Or use 2 tendon in 1 tube, the distance is 1120mm. Thus, the tendon is not as effective as, because a tube along with anchor usually contains 4 to 5 tendon.

Construction

The tendon does not bonded and quickly spread the orbit, or break on the ground to avoid open holes. Using bonded tendon must add the merits and time to pump mortar as well as accept this work.

 

PT slab structure design often uses flat tendon with 4-5 tendon anchor, but each tendon is still stretched separately. With beams or use tube 5-12 to create tendon and use hydraulic stimulating a lot of tendon at once. The disadvantage is that this size is large, weighing more than 1 worker manipulates and must have a tower crane in the position.

 

The clear advantage of the bonded tendon is the construction time because the cables are cut from the tendon roll and the anchor is always on the construction site. With tendon that does not adhere to all this stage, it must be processed in the factory, so it is not significantly more active and time -consuming.

Structural durability

Both types of cables give in the reliability Structural design High. With unbonded tendon, contractor experience and poor quality materials cause more damage to the number of works. With outdoor buildings such as parking, nails, in areas with more corrosive or humid climates like in Vietnam, designers often use more adhesive cables. The tendon does not adhere to these environments that require high quality of tendon corrosion, tendon covers and high -tech construction. Used with bonded, the durability depends more on the quality and techniques of the mortar pump.

 

The quality of unbonded tendon must be mentioned throughout the tendon length and 2 anchor heads. Only 1 point with stress loss is the tendon does not work. The longer the tendon is broken, the more impact on the structure.

 

The bonded tendon is capable of transmitting and developing tension from 1 point about 50 times the diameter of the tendon. 1 point that is broken on the tendon will only be local. This 50D paragraph stress in the tendon remains the same, the tendon is still working. Therefore, the reliability of the tendon has a higher bonded in construction design.

Retrofit, repair

The tendon does not bonded more flexibly for repair. A broken tendon can easily withdraw the tendon, replace and stretch. The replacement is also more beneficial in stress, due to smaller losses than the construction tendon from the beginning. On the contrary, the tendon has an irreplaceable bonded due to the grouting mortar in the jealous tube.

 

In case design consultants Change the function, for example, a large opening. The tradition still concept that cannot be chiseled through the tendon, but with the current construction technique, this is possible and even easier for the tendon with bonded.

 

With unbonded tendons, when cutting open holes will cut the tendon, stretch and anchor at the edge of the open hole to use special construction techniques. tendon with bonded does not need to be tension and anchor because the pump mortar in the area is not cut will hold the tendon position.

When Structural engineer uses PT slab, there are 3 parameters that need to be decided from the beginning and will lead to different results of steel layout, unlike the slab usually only has 1 single answer for the problem. That is:

 

– Pre -compression stress (via tendon tension)

 

– Percentage of balance load

 

– tendon profile: shape and elevation

 

Because there are many answers for the problem of Structural engineer A lot of experience will quickly choose the most technical and economical guarantee plan. Saving here is a balance between the number of slab cables (through tension) and the smallest reinforcement, because the price of tendon is always much more expensive than normal reinforcement.

Average Precompression

This very important parameter is defined by the total tension divided by the section area perpendicular to the tension. ACI design standard 318-02 requires a minimum of at least 0.85MPa compressive stress (after deducting losses).

 

In the majority of cases of designing civil houses, the 0.85MPa value is chosen to start for the tendon problem. With roofs or garage is usually 1.0-1.4Mpa due to high requirements for control of waterproofing cracks. But remember that the increase in compression stress does not mean guaranteeing no cracks. In the slab 1 direction or beam, the pre -compressive stress is calculated on the entire cross section area.

 

The maximum pre -compressive stress value should be 2.0MPa for the slab and 2.5MPa for beams. Although ACI specifies a larger value, it is no longer economical.

Percentage of balanced load

ABCs on Structural design Pre-stress are to create an opposite effect with the direction of the load -effect load, most of which is weight, through the percentage of the loading static load is balanced.

 

With the slab, the figure is reasonable in the range of 60-80% static load. With beams of 80-110%, the reason for the hammock of the beams is more affected by the working system.

Choose tendon profile

There are some attention for the designer to choose a tendon trajectory appropriately, but first of all talk about the method of balancing the load to understand clearly because the tendon trajectory determines the percentage of the load percentage.

Speaking of PT ​​is referring to this method. A little bit of history, it was t.y. Lin introduced from 1961 and until 1963 was posted in ACI magazine. This method is a strong tool and simplifies the theory of designing the structural engineers that can apply practice in practical problems.

 

Figure 2.4.1 For example, a continuous beam is stressed in advance with constant tension P. The slab tendon has a familiar parabolic trajectory with 2 bending points in the middle and 1 bending point for the border, the lowest point in the middle of the beat. The work of the PPCBTT is as follows: Separate the tendon from the structure and replace it because the load as shown in Figure 2.4.2 is called “balanced load”. The balance load includes the upward and downward parts from the parabolic parts of the tendon trajectory (as shown in Figure 2.4.3) and the pre -compressive force P. The load in Figure 2.4.2 and 2.4.3 are the opposite equal balance.

The tendon separates itself is also a static structure system and only tensile. The beam is still the super -static structure system with super -static steps depending on the number of pillows.

Figure 2.4.5 Considering the balance of the cut beam in a paragraph equal to a left pillow. At this cross section, it is the effect of compressing the center P, Moment MP and VX cutting force generated by the equilibrium load as shown in Figure 2.4.2. MP is defined as a primary moment, which has a role in maintaining a balance for the balanced load system here.

 

The component of the force on the tendon and is calculated from the first tendon between the fruit anchor and the lowest point of the trajectory as shown in Figure 2.4.4

From Figure 2.4.5 and 2.4.6, $ m_p = PE $. It should be remembered that this primary moment does not depend on the boundary conditions of the pillow or the load -acting loads on the beam.

In construction design, also known as the super static Moment – Hyperstatic. This is a typical effect in the PT structure due to the effect of the pillows. Consider the example in Figure 2.4.7 about a stretched PT beam. The front tension causes the girder level as shown in Figure 2.4.7 (b) and it is due to the bending effect of the primary moment MP. It is necessary to have compression to win this rainbow before closing the beams into the pillows in the predetermined straight line. Therefore, at the pillow, the reactions arise as shown in Figure 2.4.8 (a) to keep this gong and are called secondary effects (hyperstatic). This secondary jet causes the moment on the beam as the chart in Figure 2.4.8 (b) called the secondary moment.

When structural design PT stretches later, the process is the opposite: The beam is fixed on the pillows when pouring concrete. The tendon tension after pouring concrete causes additional jets on the pillow due to the effect of free movement caused by the front compressive force of the pillows on the concrete structure. These jets are also secondary jets.

 

These secondary jets must balance each other: $Σr_ {sec} = 0 $.

 

Back to the previous example, consider any section on the beam as shown in Figure 2.4.9. There is Moment $m_ {sec} = ΣR_iX_i $ and secondary cutting force $V_ {sec} = ΣR_i $.

 

These forces are subject to internal force in concrete and tendon as shown in Figure 2.4.9 (b)

Considering the load ($M_d $) and the load ($M_L $), the structural design calculation combination for TTGH 1 according to ACI will be as follows:

 

$$1.2M_d+1.6M_l+ M_{sec}$$

 

The important conclusion is drawn: Construction design with TTGH1 (in terms of intensity) has only secondary effects, not considering the primary impact and balanced load. The secondary moment in the combination is not multiplied by the over -load coefficient because: its value is clear, not the statistical probability such as the static load and the load, and its effect is the opposite of the static and the loading, so the fact that there is no additional coefficient of overpass is safe.

In Figure 2.4.9, PT cables are still kept in the diagram. In PP balanced load, the tendon is separated and replaced by a balanced load. Figure 2.4.10 shows Figure 2.4.9 after tendon separation. Thus the force acting on the beam includes equilibrium load and secondary jets. At the cross section of distance a from the left pillow, the forces acting are Moment balanced $M_b$, balancing force balance $V_b $ and tension P.

From the picture above, we see the balanced moment equal to the sum of the two primary and secondary effects.

 

According to TTGH2, the stress test is required in concrete to control the hammock and crack. The diagram calculated in Figure 2.4.10 is used to calculate the structural design according to TTGH2: The separation does not consider the tendon anymore, the Moment Mb and the P forces are subject to stresses in concrete and reinforced steel.

 

That is the use of PP balanced load in a simple work model for non -stress diagrams. The remaining calculation is carried out when designing normal reinforced concrete structures. The fact that this model is acceptable because the effect of the tendon on the hardness of the structure can be ignored.

 

A case common in construction design is a cross-sectional section or thickness, creating a jump to the neutral shaft of the structure as shown in Figure 2.4.11 (A). This should be considered when calculating the balanced load.

In this example, the tendon is continuous and anchored at the neutral axis of the two ends (N.A.) The balanced load as shown in Figure 2.4.11 (b), with the tension P at the two ends is not aligned. This force P can be replaced by pairs of forces and torent as shown (C).

 

Thus, the equilibrium load in the figure (b) must consist of 2 components that cause vertical force as shown in Figure 2.4.11 (d) and the ingredient that causes beams 2.4.11 (E).

Now we have understood the PP balanced PP and can continue to talk about the third parameter when the Structural engineer options for the PT slab: choosing a tendon trajectory (profile).

 

The common trajectory is the parabola form as shown in Figure 2.5.1 with a bending point at about 1/10 of the rhythm length. This trajectory gives equilibrium balanced load as shown in Figure 2.5.3 and is recommended to be used for beams and slab cables according to the equilateral distribution tendon. With the tendon focus on the column strip, the orbit should be used as shown in Figure 2.5.2 with a straight line on the pillow about 1.2m, with the purpose to have a perpendicular steel running space in a perpendicular direction.

The lowest point of the parabola is usually placed in the middle of the rhythm and this is more convenient for the construction positioning. If the most beneficial to the PT force, this point is about 0.4L in the border, because the load will be more evenly distributed. The lower the height will give the larger balance force.

 

The highest score of the tendon trajectory should try to put as close to the slab as possible to have room for steel often perpendicular.

 

In case of continuous design construction design, there are different spans in length or load. Arranging the above tendon height for a more dangerous pace, with a smaller rhythm can reduce tension by disconnecting the tendon or better than raising the lowest point to reduce the balanced load.

 

Talk about anchor. Single beams (without slab) will be anchored in the neutral axis, and T -beams (slab beams), in the neutral axis of the cross section, including the body of the beam and the width of the slab transmission as shown in Figure 2.5.4. Note that this width is different from the effective width when bending.

Effective tension is used to calculate, is the force after all stress loss. The number of tendon required will be calculated according to this effective tension. In most cases, the effective tension for a 12.7mm tendon is 120kn, provided that:

 

– The tendon length is less than 72m

 

– If the tendon length is greater than 36m, it must be stretched from both anchor.

 

If due to special conditions, the tendon is long but only one end is, the effective tension is determined after the Structural engineer calculates specific stress loss.

In the presentation of the PP balanced PP, the tension P in the feuding tendon is constant. In fact it decreases with tendon length and over time (long -term part). The calculation of stress loss is complicated and must use software. In the design of design or simplification consultants, with low tendon commonly used today, the total loss is about 10-15% of the initial tension stress.

 

The loss consists of 2 parts:

 

– Instant part, including (i) loss due to friction, (ii) loss caused by anchor deformation.

 

– The long -term part, including (I), is damaged by shrinkage, (ii) due to elastic shorts (elastic shortening) of concrete, (III) due to the variable of concrete, (IV) due to relaxation.

 

Figure 2.7.1 (C) shows the loss of the tendon when the wedge at the anchor is locked. Max is achieved at the distance of XL from anchor. The max allows immediately after cutting the tendon and the wedge lock is $ 0.7F_ {Pu} $.

 

The tendon tension in anchor must raise the stress here and will last up to the right between the tendon length as shown in Figure 2.7.2 (d)

 

The average stress of this whole chart at the time of cutting the tendon is the value used in the design for the Transfer Stage.

 

Figure 2.7.2 (F) shows stress distribution after all losses, including long -term loss over time.

2.7.1. Losts due to friction

The stress of the tendon is related to the tension stress at the active anchor according to the formula: $$P_S=P_Xe^{(\mu\alpha+KX)}$$

 

In there:

 

$P_s $: stress at anchor

 

$P_x $: at distance x from anchor

 

α: Radian angle (radian) from active anchor to point x

 

K: Oscillation coefficient of friction on a unit of tendon (wobble coefficient)

 

μ: Angel FRAY FRACTION COEFICIENT

 

2 The k and μ coefficients are the mechanical indicators of steel materials to create tendon, often must be specified in the construction design dossier to compare with the origin of the contractor material used.

2.7.2. Loss caused by anchor deformation

This loss occurs during the cut and anchor the tendon after stretching. The formula is as follows:

$$A = (1/E_s)\int {(Last stress – initial stress) dx}$$

 

A: The seasoning space (usually A = 6mm)

 

$E_s $: tendon elastic module

 

The integral is taken on the segment XL or XR (Figure 2.7.1 and 2). The meaning of it on the chart is the blocking area by the previous two stages and right after cutting the tendon divided by the elastic module of the tendon, as shown in Figure 2.7.3

2.7.3. Loss caused by elastic shrinkage (ES)

The general formula is as follows, with the coefficients will vary from the tendon and not bonded:

 

$$ES = k_ {es} * (e_s/e_ {ci}) * f_ {cp} $$

 

With:

 

$K_ {es} = 0.5 $

 

$E_s $: tendon elastic module

 

$E_ {ci} $: The elastic module of concrete at the time of tendon tension

 

$f_ {cpi} $: With unbonded tendon is the first compressive stress in concrete right after the tendon tension at the tendon focus point (note that this value is greater than the average compression before the average on the strip section)

 

If the tendon bonded, use $f_ {CIR} = k_ {Ci} .f_ {CPI} – f_g $

 

$K_ {ci} = 1 $ with posterior structure, $k_ {ci} = 0.9 $ with a stretched structure

 

$fg $: The stress in concrete caused by weight is also at the tendon focus point

2.7.4. Loss caused by variables (CR)

$$CR = K_{cr}* (E_s/E_c) * f_{cpi}$$

With:

$K_ {cr} = 1.6 $ with unbonded tendon. With bonded tendon, $k_ {cr} = 2.0 $ for posterior tension and 1.6 for first tension

 

$EC $: concrete elastic module at the age of 28 days

 

$f_ {CPI} $ and the meaning of ES when using tendon without bonded. In case of bonded using $ value (f_ {CIR} -f_ {cds}) $ $

 

$f_ {CDS} $: In concrete at the tendon center point due to additional loads in addition to the weight of the structure.

2.7.5. SHATPS (SH)

$$sh = 8.2e -6 * k_ {sh} * e_s * [1 – 0.06 * (v/s)] * (100 – rh) $$

 

With

 

$K_ {sh} $ defined over time as follows

 

Day 1 3 5 7 10 20 30 60

 

$K_ {sh} $ = 0.92 0.85 0.80 0.77 0.73 0.64 0.58 0.45

 

After 60 days still take $k_ {sh} = 0.45 $

 

V/s: The ratio between the volume and surrounding area is exposed to the environment of the structure

 

Rh: Average annual average air humidity (%)

2.7.6. Lagoon loss (Re)

$$RE = \left[K_{re} – j* (SH+CR+ES)\right] * C$$

 

With $k_ {re} $, j and c are table check coefficients.

 

 

@@

 

In general, use construction design software to accurately calculate losses. It is necessary to determine the exact figures in case the designer needs to compare his calculation with the measured values ​​when executing and during the use of the project if any changes in use of the investor.

In PP balanced load, the tendon is separated from the structure to simplify the model. In fact, the tendon also contributes to the load as the section as a regular reinforcement. The PTHH PP is used through software that allows the tendon model as a separate element linked to concrete. The stress loss is also automatically calculated without having to calculate separately and then deducted as before.

 

In Figure 2.8.1, the comparison description between these two methods. Notes on the figure (D) belongs to the CBTT PP, the initial tension in the tendon transmits to the neutral axis of the element. These forces are considered constant. The effect of long -term losses is calculated in the calculation step afterwards.

In contrast, in the PTHH PP, the tendon is discrete and remains in the element model. Each separate tendon element is subject to the effect of displacement and stress change due to the displacement of the concrete element containing it. Each tendon element is assumed that the original internal force has deducted the loss. Any distinctive discharge of the concrete element as shown in Figure 2.8.1 (g) also causes the corresponding deformation on the tendon element in the assumption of compatibility and the flat deformation hypothesis of the sections (Figure 2.8.2). Transferring tendon element button at the edge of the concrete element will cause the internal force change of that tendon element.

The way this model has included the interaction between the deformation of the concrete element and the force in the tendon, independent of the cause of the deformation of that element. Therefore, the Structural engineer does not need to calculate the effect of long -term losses on the deformation of the tendon element. All automatically mention in the equilibrium equations of this finite element.

 

From the above example can be inferred to the 3 -dimensional problem used in construction design software such as Safe, Adapt slab Pro … as shown in Figure 2.8.3

Most floors in the actual work in 2 directions. However, the work of 1 or 2 directions is closely related to the concept of the lines of the load, this is the line where the load is received and transmitted to the pillow. Structural engineers As the one who chooses the transmission line and therefore there may be many different transmission lines for the structure.

 

See examples in Figure 2.9.1 (A), simple beams transmit F weight to pillow A and B through the moment and cutting force on beam sections. The structural system works in 1 direction, vertical AB.

In Figure 2.9.1 (b), there are 2 perpendicular beams with loads F. On the cross section of the beam system in both AB directions, CD has moment and cutting force as a means of transmission. This system works in two directions. Sharing between 2 directions in reality to transmit F force depends on: 2 -beam hardness before cracking appears, the reinforced content of steel work after cracking. The main problem is to choose the appropriate transmission line on the basis of considering the possible transmission lines that can be applied in the magnitude of the load of F. The construction designer can completely choose and structure the reinforced line according to the transmission line above only one CD, and considering that direction to transmit the entire load F. Of course that plan is unreasonable. The transmission line should be 2 directions according to some options as shown in Figure 2.9.2.

Now consider a pitcher P on the middle of the box to 4 pillows in the corner as shown in Figure 2.9.3. There are 2 ways to assign the transmission line. In the slab tape model, the P load is transmitted from the CD-AB tape to 2 bands AB and CD. Looking at the vertical face, the tape in each direction has to bear the full load P. Similarly infer for the slab method. Each strip in one direction must be transmitted ½ load P as shown.

 

Thus, when dividing the strip for the 2 -way slab, it must be divided in 2 perpendicular directions and each direction is full of the load, not each direction to bear 1 part of the slab load as we think naturally.

For concrete structure, many factors affecting the transmission line: geometry, reinforcement, PT tendon, distribution and magnitude of the load. The transmission line applies to the structure that may change after cracking and mobilization of steel work. And usually the actual transmission line of the slab is different from the discharged line assigned by the Structural engineer as well as there are several possible transmission lines on the pillows. Therefore, the work of 1 or 2 directions is sometimes more designed by the concept of design than the natural nature of the slab.

 

Consider the influence of the beam system on the transmission of the slab. The beam is considered as part of the slab that is thickened between the pillows (columns, walls), playing a pillow role for the slab through its large anti -bending hardness. In PT beam slab, it also plays a role in providing more space to place tendon.

 

2.9.1. slab beam system 1 method

As shown in Figure 2.9.4, the beam rhythm is 3-4 times the slab rhythm. The 1 -way working slab is the main direction of the tendon, which can be placed for the remaining tendon to prevent and crack due to shrinkage and temperature. The beam is also a 1 -directional system, bearing the load from the slab transmission to it but the T -wing mentioned in the bending with a smaller width.

2.9.2. 2 -way slab beam system

This is a 2 -way working system and is often commonly used for the slab than PT slab. (Figure 2.9.5)

 

The beam is calculated independently in one of the two models as in the picture with the transmission of the same cross -brick bowl on the slab. The trapezoidal beam or triangle is transmitted and includes the T -shaped wing with a bending with a smaller width or equal to the maximum width of the transmission. If the structural design is calculated according to the equivalent frame PP, the beam model and the slab work together in the transmission area, the width of the T -shaped wing is effective and may be larger than the transmission. Of course, the second case will produce more steel.

2.9.3. 1 -way flat beams

This is a more economic plan for PT slab with 2-way column grid with a ratio of 1.5-2.5 (Figure 2.9.6)

 

The flat beam is considered a slab tape with a larger thickness that passes through the column in a large pace. The thickness of the slab only needs to choose according to the baby’s beat. Note that this is the 2 -way working system in both TTGH1 (after cracking) and TTGH2. Often calculated by the equivalent frame PP.

2.9.4. Flag slab

Recently, the unit introduces this slab plan in Vietnam with pre -made plastic formwork, for example, Figure 2.9.7. Due to the equal structure of the slab tendon in 2 directions, the slab works in 2 directions and like a slab with equivalent thickness (similar to the design of other hollow slab types such as 3D slab or glossy slab).

 

2 -way slab tendon can walk in the ribs. In the column area, the column is still structured and the slab tape is thick and calculated as a column hat or beam when calculated as normal floors with the same thickness.

There are several tendon layout on the ground that are applied effectively in practice as shown in Figure 2.10.1. tendon in each direction can be arranged evenly, concentrated in the tape or mixture of 2 ways.

The tendon is concentrated in a band on a width of usually 1.2m along the lines of loading through the pillows. According to the tendon distribution method is spread evenly.

 

Because PT structural design only is important, the number of cables on the range and its distribution in the slab strip does not affect bearing. The arrangement in what way is to be most convenient for construction, so that the 2 -way tendon is at least touched by coinciding with orbit.

 

The layout of the 1 -directional tape and the remaining direction is as shown in Figure 2.10.1 (a) is the most beneficial in terms of design, because both directions have the largest tendon difference, so the balanced load is the largest, but the least touched. (Figure 2.10.2)

tendon distance

Repeat, the maximum distance of the tendon is 8 times the slab thickness or 1.5m, not applicable to the layout of the tendon tape.

 

The minimum distance given on Figure 2.10.3

 

 

Minimum number of tendon

ACI 318 standard requires a minimum of 2 cables each going directly through the column, regardless of how many tendon tendon in each tendon.

 

Other construction design standards seem more reasonable. For example, Canadian standard requires a minimum steel content on the column.

Break the tendon on the ground

In case of bending as shown in Figure 2.10.4, there are a few controls. tendon curling when the column is not aligned or to avoid the hole open the slab. This causes the risk of tendon that is exposed when stretched, so it must be controlled as shown in the picture. If you want a greater curvature, the tendon brace is required as shown in Figure 2.10.4 (C). This drawing gives me a 12.7mm tendon and a horizontal stress due to bending steel on concrete not exceeding 3 MPa. The minimum curved radius is 3m.

 

Another point is to bend the tendon that may arise in the tendon. With the tendon without bonded to control the smallest curved radius is 20 times the diameter of the tendon.

tendon

The millet has the effect of ensuring the height of the tendon in accordance with the design trajectory. Often use steel φ12a1200. Do not use the distance exceeding the A1500.

tendon tolerance

According to the vertical direction of 6mm for the slab thickness ≤200mm, 10mm for the slab from 200 to 600mm and 12mm for thickness greater than 600mm.

 

In the slab plane, the slope due to errors must not exceed 1/12.

Steel reinforcement in PT slab construction design has the effect:

 

-Please the load with the tendon

 

-The regulations on the minimum steel content to control cracks.

2.11.1. Upper steel

Quantity

With unbonded tendon, arrange at least 4 upper steel bars at a flat slab pillow.

Location

The above steel must be placed on each pillow pillow in the width of 1.5 times the slab thickness as shown in Figure 2.11.1

Overlapping reinforcement

This is an issue that needs special attention in construction design for reinforcement at the pillow. The use of baby steel diameter increases the bending arm for thin slab and avoids reducing the effective height of the cables in the perpendicular direction going under the upper layer reinforcement. The total reinforcement area of ​​the upper layer in the column in each direction should not exceed 4200mm2, so that the security concrete is more effective and easier to execute. This figure is equivalent to the maximum steel of 21 φ16 for reinforced tape on the column.

Length

The above reinforcement extends from the column of a minimum of 1/6 of the length of the pine rhythm of each direction, as shown in Figure 2.11.2. Notes in LD Figure is the minimum anchor length (rather than the length of stress transmission to concrete through adhesive force – Development Length).

Steel diameter

Design consultants should choose small steel diameter because they must arrange 2 layers in 2 directions on each pillow. Small diameter is also more effective in controlling cracks.

2.11.2. Lower layer steel

Minimum quantity

It is possible to design a 2 -way slab without regular reinforcement as long as the tendon has guaranteed bearing. In case the tensile stress in concrete is greater than the value specified in the standard, the steel content is required to minimize the cracking of cracks. Can use 120x120x3mm welding welding mesh if you want to be more secure.

Location

The lower layer reinforced steel is placed within each slab range, and how it is not important. However, to facilitate the construction of design consultants, some things about location should be noted. The lower reinforcement in the tendon layout is placed within the tendon width to ensure the minimum distance. According to the tendon equilateral distribution of the lower layer reinforcement is also evenly distributed. The reinforcement of the direction is stacked on the reinforcement in the tendon ice.

Long mat

In case of construction design, it is necessary to put the lower layer structure due to the large tensile stress, the minimum length is 1/3 of the pine rhythm as shown in Figure 2.11.2, no need to pull into the pillow.

 

The reinforcement by calculation also controlled the minimum length, and added the regulation of some bars to the pillow as follows:

 

– Pull 1/3 of the bars in the anchor rhythm into the column

 

– Pull 1/4 of the number of bars in the middle of the anchor into the column

2.11.3. Reinforcement

The steel structure is required to be anti -cracked due to shrinkage and temperature when the Average Precompress is less than 0.7MPa. Most PT structural design situations choose a minimum compressive stress before 0.85MPa, so there is no need to put steel in the tendon in the direction.

 

If the tendon is placed in the tape, it is necessary to make a normal steel structure between the two tendon bands into a triangle as shown in Figure 2.11.3.

2.11.4. Shear bars

The cutting steel for flat floors is the anti -puncture steel placed around the column. Because the slab does not place the belt as the beam, the welding (shear student) is as shown in Figure 2.11.4.

The number of welding nails on a perimeter of perforation is calculated. Nail hat acts as a Development Length to develop the largest stress in the body of the nail.

 

If the design consultant uses a gasket as shown in Figure 2.11.4 (a), the minimum of the gasket area is 10 times the body of the nail.

2.11.5. Rebars at anchor

Design engineers can refer to the details of VSL, about reinforcement is usually made at the active and passive anchor. These steels are usually added to the general notes and will deploy the Drawing shop outside the construction site.

 

Many construction design documents have guided the calculation of these reinforcement with local compressive stress at anchor position, which can be made according to the virtual system. Here please do not present.

 

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Source of reference: “ADAPT-PT Version 7.0 for Analysis and Design of Post-Tensioned Buildings Beams, Slabs, and Single Story Frames – Volumn I: Description and Background” by Dr. Bijan O.Aalami