Optimal Design of Hollow Core Panels

7/28/2019 Optimal Design of Hollow Core Panels

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The voids in hollow core slabs provided to reduce weight and cost moreover to use

them as ducts for services furthermore the other side benefits like fire resistance or

sound insulation. Span length of hollow core slab reach up to (18m) without columns

or any supporting. Using hollow core slab will reduce the manual labors and

eliminate the formwork where that surly will reduce the constructionperiod.

Introduction

Hollow core panel is a precast prestress concrete member with continuous

voids as shown in Figure


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Hollow core slab fast started for spreading where currently becomes widely in use forall the world as shown in figure below:-


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This 31-storey apartment building is the tallest totally precast concrete building

in Canada. The building was constructed using precast concrete interior and

exterior shear walls and hollow core floors.

Hollow core slab is used in any kind of building regardless of the building size, height

of building or the function of building, figures below show different kinds ofbuildings that used that technology


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Only by using a precast

solution could this six-storey

building's structure be

completely installed and turnedover to the client in less than

six weeks. The entire structure

was built using precast,

prestressed concrete hollow

core slabs, balcony slabs and

precast load bearing walls.


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Hollow core Analysis and design

It's important for any optimization problem is to take all the related equations

that are governed the problem to formulate the objective functions furthermore

its constraints. So, at the beginning, a review about analysis will be submitted:-

"precast/prestressed concrete institute (PCI)" deals with the hollow core slab as a

simply supported beam therefore a study is done in this part to take an idea about

its behavior.


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1- Analysis according to (PCI)

PCI deals with the hollow core slabs as a simply supported beam:-

2- Analysis of simply supported isotropic plate

According to Levy solution and for square plate with =0.3 , the result


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3- Analysis of simply supported anisotropic plate

The same previous procedure and information was used for anisotropic platewhere an approximate equivalent plate that adopted by Edward Venstel was

used in presnt study as shown in below figure:-

Equivalent of flat plateEquivalent of H.C. slab


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According to the previous approach, the results are briefed below

Finally, it's normally in optimum design of hollow core slabs to use (PCI

analysis) because the difference among the previous three studies is not so

large moreover that there is tendency in optimization to fix most of the

parameter to see the behavior on the focusing plate


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Optimization is done for any case according to the purpose that is required in the

field. Engineers tend to get the best specification, cost and time and they take

many technical or administration decisions to minimize the efforts or maximize

the benefits .These decisions need to be in a good sequence to reach for the aim,

that concept is represented by the optimization, so many mathematical

programming are produced to deal with that idea. The present work adopts three

cases of optimization as shown below:-

1-minimum weight of hollow core slab2-minimum cost of hollow core slab

3-maximum allowable live load

The objective function with its constraints for any case can be briefed in tables

below:-Minimum weight


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Minimum cost


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Maximum live load


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The optimum weight can be gotten by using the first and second curve,

the same procedure is used for any other data.

Applications

Concern the optimum weight of hollow core slab where the diameter of

voids equal to (0.1) m and number of void equal to (7), it's found that:-

Optimum thickness Optimum width

Optimum weight


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Regarding the optimum cost, it's found that:-

Optimum area steel Optimum thickness

Optimum void diameter Optimum number of void-length relation


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About the maximum allowable live loads

Here, the maximum allowable live load for different cases of lengths and areas of steel

Maximum live load due to flexure

* Dashed curves related to the hollow core slabs without topping

Without topping With topping


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Maximum live load due to shear



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Maximum live load due to deflection



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Maximum live load due to stresses



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Unique table is prepared where it covers all the above cases (flexure, shear,

deflection and stresses), so the maximum live load for different cases of length

and prestress reinforcement is clarified below:-

Maximum live load due to all condition (case without topping)

H.C.Sprecast, prestress / (0.15 cm) thickness, (1.2 m) width, (8) voids/ (0.105m) diameter

Maximum live load (kN/m2)..due to flexure, shear, deflection and stresses

As (mm2) 187 261.8 299.2 361.2 412.8 487.9 557.6 651 744 837

Span (m)

2.5 19.54 22.12 22.49 23.11 23.63 24.38 25.07 26.01 26.93 27.86

3 13.06 18.37 18.68 19.20 19.64 20.27 20.85 21.64 22.42 23.20

3.5 9.16 13.28 15.30 16.36 16.73 17.28 17.78 18.46 19.14 19.81

4 6.62 9.77 11.32 13.73 14.52 15.00 15.45 15.99

4.5 4.88 6.18 6.77 7.75 8.56 9.75 10.85 12.28

5 1.57 2.52 3.01 3.80 4.46 5.42 6.31 7.51 8.69 9.63

5.5 1.09 1.63 2.43 3.16 4.15 5.13 6.12

6 0.89 1.72 2.54 3.37

6.5 0.62 1.32

* Shadow cells means that increasing the reinforcement is considered non informative due

to the limitation of steel index.


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In case there is topping slab (50 mm), the result is shown below:-

H.C.Sprecast, prestress / (0.15 cm) thickness, (1.2 m) width, (8) voids/ (0.105m) diameter

Maximum live load (kN/m2)

As (mm2) 187 261.8 299.2 361.2 412.8 487.9 557.6 651 744 837

Span (m)

2.5 27.41 30.02 30.53 31.38 32.09 33.11 34.07 35.35 36.61 37.89

3 18.25 24.99 25.42 26.14 26.73 27.60 28.41 29.49 30.56 31.64

3.5 12.73 18.64 21.55 22.29 22.80 23.56 24.25 25.19 26.12 27.05

4 9.15 13.67 15.90 19.35 19.80 20.46 21.08 21.90 22.73 23.55

4.5 6.69 10.26 12.03 14.91 17.27 18.03 18.57 19.30 20.05 20.78

5 4.93 7.83 9.25 11.59 13.50 16.05 16.55 17.22 17.88 18.55

5.5 3.63 6.02 7.20 9.13 10.67 11.84 12.92 14.37 15.81 16.70

6 2.64 4.51 4.99 5.80 6.48 7.46 8.36 9.58 10.80 12.01

6.5 0.90 1.73 2.15 2.84 3.41 4.25 5.01 6.06 7.09 8.13

7 0.62 1.11 1.83 2.50 3.40 4.29 5.18

7.5 0.56 1.34 2.12 2.89

8 1.09

Maximum live load due to all conditions (case with 50 mm topping)

* The same procedure can be gotten for any other given data.

* The work was certificated by comparison the results with hand calculation, PCI handbook

and finite element method.


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The conclusions of lecture1-Precast / prestressed concrete institute (PCI) uses the coefficients that are related to

the beam analysis for analysis the hollow core slabs while the present study found by

using Levy's method for analysis isotropic plate :-

a-Twenty cycles in Fourier expansion is fair enough to be near the exact value.

b-The average differences percent between Levy and (PCI) is about (0.6%, 23%,

2.7%) for moment, shear and deflection respectively. Take into consideration it's

normally to use (PCI) coefficients in optimum design of hollow core slab.


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2- Increasing shear capacity of hollow core slab can be done by reducing the

number of void where it's found that decreasing the void percent (1%) causes

increasing in shear capacity about (2.5% - 5%).3- Void shape affects on the capacity of hollow core slab where the best shape is

the mix shape between the triangular and circular shape. Mixing shapes create

improved section where good properties are taken from each of them.

4- The average of void percent to get minimum weight is about (50%) where the

minimum weight of hollow core panel is obtained by depending on the voiddiameter where the thickness of hollow core panel will be a little bit larger than

the diameter (for just satisfying the practical and geometrical consideration

which is equal to 2.75 cm in each face), from another side the width will be a

little bit larger than the diameter of void multiplying by its number (min distance

between two voids is 2.75 cm). In addition to that, its recommended to usewidth less than (1.2m) in spans less than (5 m) to get minimum weight.


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5- It is found from optimum cost of hollow core slabs that:-

a-General charts can be used for finding the optimum design variables to get theoptimum cost.

b-The average of void percent is about (41%) where the diameter of void tend

to be less than the thickness by a little bit distance

c-In General, thickness, area prestress and diameter of void tend toward

increasing along increasing the length and live load while the number of void is

decreased.

6- Modified Hook-Jeevs method is considered very suitable method for the

problems that have large number of constraints where it's very easy for

programming and for connecting the constraints with the problem. From another

side the method is not able to move along the constraints and it converges on the

first point on the constraints that it is located during the progress of solution sosearching along the initial variables has to be done to avoid that problem.


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7- Concerning, finding the maximum live load, three main points are recorded:-

a-Many tables for available productions have been prepared to be informative

for any work or study, the tables have been covered all the requirements (flexure,

shear, deflection, stresses).

b-The governing equation for the last three rows for all the tables of max live

load is the deflection, from another side the deflection restricts the span lengthnot less than (60%) for any table of any section of hollow core slab.

c-Adding topping slab (5cm) increases the spans lengths in the tables where

adding topping for thickness of hollow core slab (15-22)cm(25-32)cm(40-

50)cm increases the span length about (16% -20%)(8%-14%)(3% - 8%)respectively.


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8- About the special design considerations, the main concluded points are:-

a-When there is concentrated load, line load or opening, a carful look has to be

taken into consideration for the keyways among the panels for creating slabsystem to transfer the additional load across effective width.

b-The using of the prepared tables for the maximum uniform live load is still in

use (informative) for the concentrated and line load or even for hollow core slab

with opening.

c-Adding top tendon in continues hollow core slab is absolutely considered noteconomical.

9- Regarding the analysis of hollow core slab by finite element method

(ANSYS- release 11), it's found:-

a-Solid modeling is considered very suitable method for modeling the hollow

core slab while the direct generation method is very difficult.b-Mesh hollow core slab by sweep is the only choice due to the complex in

topology.

c-Representation of prestress by giving Link 8 an initial strain reflects good

agreement.


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Optimal Design of Hollow Core Panels