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Computer Aided Analysis of Hollow slabs

Presentation by… Thesis Guide and Supervisor,

Phani Krishan.B, Dr .N.V. Ramana Rao,M.Tech Structures, Professor of Dept. of Civil Engineering, Roll no: 05011D2016, JNTU College of Engg.,Kukatpally.

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Objectives of the Work

Computer Aided Analysis of Hollow Slabs of different block cross sections

under various loading conditions.

To Compare slab results modeled in the software with the manually

modeled one.

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INTRODUCTION

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Fig(a) Fig(b)

Fig(c)

Fig(d)

Slabs Where topping is considered to

Contribute to structural strength.

Slabs Where topping not considered to Contribute to structural strength

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Hollow “or “solid block” formers as per BS : 8110 and materials as per

ASTM -C 90-[24.80], ASTM- C 55-[24.88], ASTM -C 145-[24.87].

Table 13.1of BS 8110, Weights of hollow clay block floor construction with 40 mm topping

Overall weight (kN/m2)

Block size Wall Thickness Structural Depth 75 mm 100 mm 125 mm

(mm) (mm) (mm) rib rib rib

300x300x75 15 115 1.75 1.80

300x300x100 15 140 1.95 2.00

300x300x125 15 165 2.15 2.25

300x300x150 18 190 2.39 2.54

300x300x175 18 215 2.58 2.73 2.88

300x300x200 18 240 2.82 2.98 3.13

300x300x225 18 265 3.22 3.42

300x300x250 20 290 3.51 3.70

6Not more than 500 mm

Not more than 4bw

Structural topping

Bow

Not more than 4bw

Structural topping

Bo

Non structural topping

a0

Not less than a0 / 5

a0

Not more than 1500 mm

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Hollow slab with mud blocks.

Edges and Fire resistance.

Analysis:

Analysis for moments and forces due to ultimate design loads in hollow slabs may be found

as per solid slabs, alternately can done as continuous T-beams simply supported.

Shear: The shear stress v should be calculated as

v = (V / bv d)

Where ‘v’ is the shear force due to ultimate loads on a width of slab equal to the distance center

to center of ribs, and ‘bv’ is the average width of the rib and ‘d’ is depth of the slab..

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Guidelines against spalling (as per FIP considerations 1988 paper EN 1168).

(a) For the slab if spalling stress is generated on the strands for the section width or a whole must

satisfy the following condition.

(b) A fracture mechanics design using FEM prove that no spalling cracks develop ,using

characteristic values on fracture energy and tensile strength.

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Floor diaphragm action (as per Elliott, K.S., Davies, G. and Bensalem, K., Pre cast Floor Slab Diaphragm without Structural Screeds, Concrete 200- Economic and Durable Construction through Excellence, Dundee, sept 1993, pp 617-632)

The stability of pre cast concrete buildings is provided in two ways,

(a) the horizontal loads due to wind are transmitted to shear walls.

(b) the reaction forces resulting from the floor at each level are transmitted to the foundation.

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As well as to wind loading, the floor diaphragm may also be subjected to additional horizontal forces, such as

(a) Horizontal forces due to lack of verticality,

(b) Temperature and shrinkage effects,

(c) In-plane forces as a consequence of accidental loading, abnormal loading.

Floors under seismic action:

The forces transmitted to the structure are related to many parameters; depend both on ground

motion and on the structural behavior.

Ductility is the main feature preventing large damage during strong quakes..

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ADVANTAGES OF HOLLOW CORE SLABS: 

-Provides economical and efficient floor and roof systems.

-Provides excellent fire resistance. Depending on the strand cover it can endure up to 4 hours.

-The Underside can be used as a finished ceiling.

-The voids can be used for electrical or mechanical runs.

-Provides the efficiency of a pre stressed member for load capacity, span range and deflection control.

-Hollow core slabs can be used as diaphragms to transfer lateral loads.

-A verity of architectural finishes is available.

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Structural Modeling of Hollow Slabs (as per BS 8110):

- be made of concrete or burnt clay;

- have a character strength of at least 14 N/mm2, measured on the net section, when axially

loaded in the direction of compressive stress in the slab;- when made of fired brick earth, clay or shale, confirm to BS 3921,

BS 772-1, BS 772-3, BS EN 772-7.

Spacing and size of ribs:

- In - situ ribs should be spaced at centers not exceeding 1.5 m and their depth is excluding any topping, should not exceed four times their width.

 

WIDTH

Depth

75mm to 125mm

Plan of 300x300 mm

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LAYING THE FLOOR OR ROOF (as per IS:6061-part-1):

 

a. The pre cast reinforced concrete joists shall be placed in position at the designed spacing

so as to span between the supporting elements, such as walls and beams.

b. The hollow blocks shall be placed in between the joists with their

Ends resting on the’ projecting lips of the joists in a manner indicated in

Figure shown below.

c. Nominal reinforcement shall be provided for the structural topping

concrete slab as per IS : 456-1964. At least 0.15 percent reinforcement along the joists

and 0.20 percent reinforcement across the joists shall be provided for the

structural topping concrete slab. The spacing of reinforcement bars shall

not exceed 300 mm. The top reinforcement in the slab over the supports

(joists) should be tied to the stirrups projecting from the joists. Welded wire mesh

may be used for the reinforcement as an alternate to mild steel bars.

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Dimensions:

Dimension of slab: 5m x 5m

Thickness of slab: 290 mm

Minimum depth is = (l/35x0.8) = 178.5 mm , So provide a depth of 200 mm.

As per British code BS: 8110, providing depth as topping is (1/10) of clear distance of ribs is 30 mm, and taking

fire in to consideration, total cover of the slab finally is 290 mm. resistance and durability in to the

consideration provide a cover of 40 mm: so total depth of slab is 290 mm.

As per BS:8110 code table 13.1, use the blocks of 380x380x200 size and 100 mm wide ribs.

Loads:

Area of the slab for Dead Load = {Total slab area – Area of the voids)

= [ 5x0.29- 0.3x0.18x9] =0.964 m2 ,

Equivalent depth for Dead Load Calculation = ( 0.964/5 ) = 0.1928 meters,

Taking Unit Weight of Concrete as 25 kN/Sqm;

Self Weight of the Slab = (0.1928x25)

= 4.82 kN/Sqm

Imposed/ live load = 4.00 kN/sq m

Finishes = 1.00 kN/Sqm  

Total load = 9.82 kN/sq m

Total factored load = ( 1.5x 9.82) = 14.73 kN/Sqm

 

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Moment = M = (α. W. l2 ) / 8 = (0.5x14.73x25)/8 = 23.9156 kN m/m

Moment per each rib = 2.40kN m / rib

  Used 10 mm hence safe and spacing 200 mm.

Maximum shear force = Vu = 21.33 kN

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COMPARISON OF RESULTS:

Hollow slab with Hollow blocks and cross section

A

A

Section A-A

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Voided Slab and Cross section Model of size 5x5 m

L x=5m L y=5m

A

A

Section A-A

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Hollow slab with rectangular blocks and Cross Section Model of 5x5m

L x=5mL y=5m

A

A

Section A-A

20-5

-4

-3

-2

-1

0

1

2

3

Ribbed Slab EQ

Ribbed Slab LL

Ribbed Slab WL

X Direction Moments in kNm  

Slab Span(m) EQ LL WL

0 -3.487 -4.06 -3.4

0.48 -1.026 -1.4 -1.022

0.96 0.708 0.77 0.717

1.44 1.524 1.775 1.415

1.92 1.823 2.25 1.826

2.4 1.778 2.205 1.78

2.88 1.413 1.78 1.514

3.36 0.583 0.807 0.575

3.84 -0.988 -1.38 -1.006

4.32 -3.527 -4.215 -3.527

5 -3.6 -4.3 -3.6

Ribbed slab Middle X Strip Moments

Span

Moments

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Hollow Rectangular Middle X Strip MomentsX Direction Moments (kNm)  

Slab Span(m) EQ LL WL

0 -3.527 -3.7 -3.48

0.48 -1.022 -1.3 -0.981

0.96 0.684 0.8 0.681

1.44 1.511 1.67 1.513

1.92 1.82 2.032 1.823

2.4 1.78 2.006 1.781

2.88 1.146 1.62 1.434

3.36 0.609 0.756 0.607

3.84 -1.036 -1.02 -0.97

4.32 -3.501 -3.9 -3.473

5 -3.6 -3.95 -3.5

-5

-4

-3

-2

-1

0

1

2

3

Hollow Rect "EQ"

Hollow Rect"LiveLoad"

Hollow Rect"WL"Span

Moments

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-6

-5

-4

-3

-2

-1

0

1

2

3

4

0 0.48 0.96 1.44 1.92 2.4 2.88 3.36 3.84 4.32 5Voided "EQ"

Voided "LL"

Voided "WL"

Voided slab Middle X Strip Moments

X Direction Moments(kNm)  

Slab Span(m) EQ LL WL

0 -3.284 -5.55 -3.267

0.48 -1.1 -1.999 -1.101

0.96 0.623 1.042 0.638

1.44 1.5 2.45 1.483

1.92 1.801 3.03 1.802

2.4 1.78 2.33 1.784

2.88 1.45 2.423 1.434

3.36 0.64 1.113 0.661

3.84 -1.07 -1.78 -0.87

4.32 -3.3 -5.467 -3.3

5 -3.34 -5.5 -3.35

Span

Moments

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-5

-4

-3

-2

-1

0

1

2

3

0 0.48 0.96 1.44 1.92 2.4 2.88 3.36 3.84 4.32 5Ribbed EQ

Ribbed LL

Ribbed WL

Ribbed Slab Middle Y Strip MomentsY Direction Moments(kNM)  

Slab Span(m) EQ LL WL

0 -3.483 -4.046 -3.447

0.48 -1.066 -1.105 -1.058

0.96 0.683 0.772 0.575

1.44 1.525 1.852 1.532

1.92 1.82 2.235 1.815

2.4 1.781 2.204 1.78

2.88 1.413 1.8 1.431

3.36 0.624 0.801 0.613

3.84 -0.96 -1.03 -0.98

4.32 -3.43 -4.15 -3.421

5 -3.5 -4.16 -3.5

Span

Moments

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-5

-4

-3

-2

-1

0

1

2

3

Hollow Rect "EQ"

Hollow Rect "LL"

Hollow Rect "WL"

Hollow Rectangular Slab Middle Y Strip Moments

Y Direction Moments(kNm)  

Slab Span(m) EQ LL WL

0 -3.527 -3.7 -3.48

0.48 -1.022 -1.3 -1.028

0.96 0.684 0.8 0.688

1.44 1.511 1.67 1.537

1.92 1.82 2.032 1.825

2.4 1.78 2.006 1.77

2.88 1.146 1.62 1.431

3.36 0.609 0.756 0.66

3.84 -1.036 -1.02 -0.968

4.32 -3.501 -3.9 -3.42

5 -3.6 -3.95 -3.48

Span

Moments

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Voided Middle Y Strip Moments

-6

-5

-4

-3

-2

-1

0

1

2

3

4

0 0.48 0.96 1.44 1.92 2.4 2.88 3.36 3.84 4.32 5Voided "EQ"

Voided "LL"

Voided "WL"

Y Direction Moments(kNM)  

Slab Span(m) EQ LL WL

0 -3.284 -5.55 -3.264

0.48 -1.1 -1.999 -1.093

0.96 0.623 1.042 0.643

1.44 1.5 2.45 1.485

1.92 1.801 3.03 1.803

2.4 1.78 2.33 1.797

2.88 1.45 2.423 1.443

3.36 0.64 1.113 0.658

3.84 -1.07 -1.78 -0.875

4.32 -3.3 -5.467 -3.217

5 -3.34 -5.5 -3.3

Span

Moments

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Contour Representation of the Moments in Voided Slab

Ly=5m

Lx= 5 m

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Comparison

0

0.5

1

1.5

2

2.5

3

3.5

Actual Ribbed Hollow voided

Comparison

Manual (Actual) Ribbed Hollow voided

2.400 2.25 2.032 3.03

Comparison of All Slabs with Manually Modeled Slab

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CONCLUSIONS

  

When the Live load, earthquake load and Wind load are applied on group of hollow block slab, voided

slab and hollow rectangular slab, it has been observed that there is considerable increase in moments

and shears, voided slabs has more moments than ribbed slabs and then Hollow rectangular moments.

The moments obtained Under live load in voided slab are more when compared with the hollow block

slab and hollow rectangular slab than under Earth quake load and then Wind load.

 

Hollow block slabs show less deflection than hollow rectangular slabs, Voided slabs show more

deflection.

 There is a reduction obtained in the torsional moment with horizontal restraints. This however has

further implications; rigid supports are highly undesirable as they would be creating restraining forces,

for example shrinkage and thermal movement within the unit.

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Recommendation to Further Study

The slabs are modeled and analyzed using the Staad Pro software this work also be done using

the other soft wares like SAP and Ansys.

In the present thesis Hollow slab with rectangular hollow blocks, hollow slab with hollow

blocks and voided slab are modeled, in the software same slabs can be modeled using other

blocks like trapezoidal shaped blocks, oval shaped blocks and square blocks and rectangular

blocks with edges semicircular.

The loading used in the present work are live load, seismic load and temperature loads, and

there is a scope for future work as can use other type of loads and their combination.

Same slab can be analyzed by changing dimension and by using the stabilized mud blocks or

block type bricks.

 

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REFERENCES  Walraven, J.C, Diaphragm Action in Floors, Pre fabrication of concrete Structures

International Seminar, Delft University of Technology, Delft University Press, Oct. 1990, pp 143-154.

Menegotto.M, Seismic Resistent Extruded Hollow Core slabs, International Symposium on Noteworthy Developments in Prestressed and Pre cast Concrete, Singapore, November 1989.

De Roo, A .M. Straman, J.P., Krachtsverdeling in en Vormverandering van een inSynvlak Belaste Prefab Vloerconstructie, PhD thesis, Delft Precast Concrete Institute, Delft University oof Technology, 1991.

Svensson.s,Skivverkan I Elemenybjlklag, Publication 88:1, Chalmers Technical University, Goteborg, Sweden, 1988.

Elliott, K.S., Davies, G. and Bensalem, K., Pre cast Floor Slab Diaphragm without Structural Screeds, Concrete 200- Economic and Durable Construction through Excellence, Dundee, sept 1993, pp 617-632.

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P.Purushothaman, “Reinforced concrete structural elements behavior, analysis and

design” 

BS: 8110 Code of Practice.  

Jain, “Reinforced concrete” 

IS: 456-2000, Plain and Reinforced Concrete-Code of Practice,

Bureau of Indian Standards, New Delhi.

10. Pajari M & Koukkari H, (1998) ‘Shear resistance of PHC slabs supported

on beams I: Tests’. Journal of structural engineering, No. 9, 1050-1061

Joris Fellinger, TNO Centre for Fire Research, Delft, the Netherlands

11. Jan Stark, Delft University of Technology, Fac. of Civil Engineering and

Geosciences, Delft, the Netherlands

12. Joost Walraven, Delft University of Technology, Fac. of Civil

Engineering and Geosciences, Delft, the Netherlands.on Vol. 28 – No. 3.

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13. ENV1992-1-2 ( 1995), ‘Eurocode 2: Design of concrete structures, Part

1.2: General rules, structural fire design’, Brussels: CEN

14. Walraven, J.C., P. Mercx (1983), ‘The bearing capacity of prestressed

hollow core slabs’, Heron Vol. 28 – No. 3.

15. Breunese, A.J. (2001) ‘Tensile properties of concrete during fire’,

Rijswijk,

TU Delft – TNO, Centre for Fire Research report 2001-CVB-R04634.

16. Production and Use of Hollow Interlocking CSEB for Disaster

Resistance, 2005-25p,Auroville.

17. Sp-24,“Explenatery Hand Books Pre stressed concrete” 

18. STAAD pro- Getting Started ,Examples and reference manual.

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