Engineering Manual Issue 2010
© 2010 Cobiax Technologies AG All rights reserved International patents Version 1.0-2010-EC
Provided by: COBIAX TECHNOLOGIES AG Oberallmendstrasse 20A 6301 Zug Switzerland +41 41 767 00 00 www.cobiax.com
[email protected]
Engineering Manual 1.
INTRODUCTION
Cobiax slabs differ in three ways from traditional solid flat plate slabs: •
Reduced dead load due to the concrete displacement of the void formers. The bending moments and column reactions are reduced consequently.
•
Reduced stiffness of the slab due to the presence of the void formers. The deflection of the slab is influenced consequently.
•
Reduced shear capacity of the slab due to the presence of the void formers. This requires the identification of slab areas with too high shear in which the void formers mustn’t be placed.
These three elements have to be taken into account in the structural design process and their application is discussed in this manual. The Cobiax slab is dimensioned with the methods used for traditional flat slabs and compatible with any concrete design code.
Cobiax area solid area
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 1/28
Engineering Manual This manual focuses on the in-situ application of the Cobiax technology and contains the following parts: •
Chapter 1: Introduction
•
Chapter 2: Specification of the different Cobiax void former types (page 3)
•
Chapter 3: Cross sectional configuration of slabs incorporating Cobiax cage modules (page 4)
•
Chapter 4: Design process of Cobiax slabs with a practical example and guidance for the application with Finite Element (FE) software (pages 5 to 11)
•
Chapter 5: Cobiax shop drawings and execution (pages 12 to 18)
•
Appendices containing the technical background on which the design guidelines are based: o Appendix A: Bending (page 19) o Appendix B: Stiffness (page 20) o Appendix C: Shear (pages 21 to 23) o Appendix D: Punching (page 24) o Appendix E: Fire protection (page 25) o Appendix F: Sound insulation (page 26) o Appendix G: Various technical issues (pages 27-28)
The Cobiax slab technology holds the «National Technical Approval», registration number Z-15.1-282, issued by the German Institute of Building Technology (DIBt)
The Cobiax technology and products are internationally patented
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 2/28
Engineering Manual 2.
PRODUCT SPECIFICATIONS
2.1 Product families Cobiax Slim-Line cage modules, designated CBCM-S-xxx (identified by a number [xxx] which is the respective void former’s height in mm).
Cobiax Eco-Line cage modules, designated CBCM-E-xxx (identified by a number [xxx] which is the respective void former’s height in mm).
For slab depths 200 mm to 340 cm
For slab depths 350 mm to 600+ mm
The Cobiax cage modules are made of hollow void formers placed in positioning cages of ~2.50 m length acting as wire chairs. 2.2 Product main parameter 550
600
Ð
Ð
Ð
CBCM-E-450
500
Ð
CBCM-E-405
450
Ð
CBCM-E-360
400
Ð
CBCM-E-315
350
Ð
CBCM-E-270
325
Ð
CBCM-S-220
300
Ð
CBCM-S-200
275
Ð
CBCM-S-180
[-]
250
Ð
CBCM-S-160
Cobiax cage module type
225
Ð
CBCM-S-140
Recommended
200
CBCM-S-120
[mm]
CBCM-S-100
Slab depth
Dead load reduction* per m2 [kN/m2] -1.40 -1.64 -1.88 -2.10 -2.32 -2.56 -2.80 -2.86 -3.34 -3.82 -4.29 -4.77 Stiffness correction factor
[-]
0.92 0.92 0.92 0.92 0.91 0.91 0.91 0.92 0.91 0.90 0.90 0.89
Shear reduction factor
[-]
0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.55 0.55 0.55 0.55 0.55
Cage module support height [mm]
110
130
150
170
190
210
230
275
320
366
411
457
Void former height
[mm]
100
120
140
160
180
200
220
270
315
360
405
450
Void former horizontal diameter
[mm]
315
315
315
315
315
315
315
270
315
360
405
450
Spacing between void formers
[mm]
35
35
35
35
35
35
35
30
35
40
45
50
Void former centre line spacing
[mm]
350
350
350
350
350
350
350
300
350
400
450
500
Number of void formers per m2
[-]
8.16
8.16
8.16
8.16
8.16
8.16
8.16
11.11
8.16
6.25
4.94
4.00
[m3/m2] 0.056
0.066
0.075
0.084
0.093
0.102
0.112
0.114
0.134
0.153
0.172
0.191
Concrete displacement per m2 Void formers per cage module**
[-]
7
7
7
7
7
7
7
8
7
6
5
5
Equivalent area per cage module
[m2]
0.86
0.86
0.86
0.86
0.86
0.86
0.86
0.72
0.86
0.96
1.01
1.25
*) assuming a concrete density of 25 kN/m2
**) made to fit the 2.50 m long cages
Table 1 – Main parameter of Cobiax cage modules
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Engineering Manual 3.
CONFIGURATION OF THE SLAB CROSS SECTION
The Cobiax cage modules are directly installed on the bottom reinforcement. The top reinforcement is directly placed on the positioning cages replacing the wire chairs. 3.1 Slim-Line typical cross section
Rebars v2 and v3 must be placed in perpendicular direction to the cage modules 3.2 Eco-Line typical cross section
Rebar v2 and v3 must be placed in perpendicular direction to the cage modules 3.3 Slab depth parameter z: Void former height; y: Cage support height; x: Void former centre line spacing v1 & v2: Diameter of top longitudinal/transversal reinforcement v3 & v4: Diameter of bottom transversal/longitudinal reinforcement u1: Top concrete cover; u2: Bottom concrete cover Slab depth t = u1+ u2+ v1+ v2+ v3+ v4+ y + construction tolerance of 5–10 mm
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 4/28
Engineering Manual 4.
STRUCTURAL DESIGN PROCESS FOR COBIAX SLABS
4.1 Introduction Below six steps explain the generic design process for Cobiax flat slabs with the help of Finite Element (FE) software. The process is based on the common methods used for the structural design of concrete flat slabs and compatible with any code. The accompanying example is based on the “Axis VM 9” FEM software but the underlying principles are applicable to any FEM software allowing the design of flat slabs. 4.2 Design Step c – Assumptions, data input, and Cobiax parameter
Define the input data such as slab geometry, static system, loads, material values, concrete covers in the same way as you do for a solid slab. Enter and model the slab in your FEM software.
Assume an appropriate slab depth in the same way as you do for a solid slab.
Based on the chosen slab depth, identify the corresponding Cobiax cage module type from Table 1 in paragraph 2.2. as well as the corresponding dead load reduction and stiffness correction factor Example
FEM Model of a slab (3D view) containing some openings and supported on columns; the following assumptions are made: •
Modulus of elasticity of concrete E (Young modulus): E = 34’000 N/mm²
•
Concrete density: 25 kN/m3
•
Top and bottom rebar cover: 25 mm
•
Slab depth: 300 mm
•
Resulting Cobiax cage module: CBCM-S-180 with: o Dead Load reduction -2.32 kN/m2 o Stiffness correction factor 0.91 © Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 5/28
Engineering Manual 4.3 Design Step d – Additional dead load pattern
Based on experience, the net void former area in a slab is in a range of 70-80%. For pre-design purposes it is recommended to use a value of 70% as average voided area in a slab. Thus, the average dead load reduction is to be adapted.
Create an additional dead load pattern for your FE model which equals to 70% of the identified dead load reduction from Step c. Apply this additional dead load pattern to the gross slab area as a surface load acting in the opposite direction (upwards sense). Example
•
Dead load (DL) of solid slab: 0.3 m x 25 kN/m3 = 7.50 kN/m2 (slab self weight)
•
Additional dead load pattern with an oppositely oriented surface load of: 70% x -2.32 kN/m2 = -1.62 kN/m2
4.4 Design Step e – Stiffness modification and deflection calculation
Modify the modulus of elasticity E of concrete assumed in your calculation model by multiplying its value with the stiffness correction factor identified under Step c.
OR: If your FEM software allows, modify the global stiffness factor of the slab by multiplying its value with the stiffness correction factor identified under Step c.
Compute the resulting deflection incorporating the additional dead load pattern from Step d and the modified stiffness.
Check if the calculated deflection complies with your criteria. If yes, continue with Step f. If no, adjust the slab depth accordingly and restart at Step c. Example •
Modification of E: 0.91 x 34’000 N/mm² = 30’940 N/mm²
•
OR: changing of the global stiffness factor from 1 to 0.91
continued on next page… © Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 6/28
Engineering Manual Example (continued from step e)
Calculation of the slab deformation and verification of its compliance with the chosen deflection criterion. Depending on the FEM software used the deformation calculation is linear (State Ι, elastic) or non-linear and allows to calculate the long-term deflection (State ΙΙ, cracked). For the linear case the elastic deformation values obtained from the calculation are treated in the same way as for solid slabs for the evaluation of the long term deflection. 4.5 Design Step f – Shear criteria and solid area identification
Hand-calculate the maximum allowable shear force Vc (or design concrete shear stress [depending on the code you use]) for a solid slab with the same depth as assumed under Step c. Multiply this value with the corresponding Cobiax shear reduction factor from Table 1 in paragraph 2.2 to obtain the corresponding maximum allowable shear force (or design concrete shear stress) for the voided slab.
Display the design shear force distribution in the slab model (incorporating the additional dead load pattern from Step d). Identify the areas of the slab for which the shear force exceeds above hand-calculated value for the voided slab. These areas correspond to the zones of the slab in which no void formers must be placed. Example •
Assume for the present example that the hand-calculation for the 300 mm deep solid slab gives a maximum allowable shear force of Vc = 100 kN/m
•
Shear reduction factor for the Cobiax CBCM-S-180 cage module: 0.50
•
The maximum allowable shear force for the voided slab is: Vc,Cobiax = 0.50 x 100 kN/m = 50 kN/m
continued on next page…
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Engineering Manual Example (continued from Step f) The shear force distribution in the slab is computed by maintaining the additional dead load pattern created under Step d. The areas exceeding the maximum allowable shear force Vc,Cobiax for the voided slab are visualized. Depending on the functionalities of the FEM software this can be done: Either as shear plot (the red hatched areas are zones in which the shear force is ≥ 50 kN/m and thus are executed without void formers):
Or alternatively as an isometric line shear force contours equalling to the value of 50 kN/m and delimiting the areas within which no void former are to be placed:
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Engineering Manual 4.6 Optional Design Step g – Dead load pattern refinement
Only required if you whish to maximise the accuracy of your calculation for column and foundation design, not suitable for pre-design purposes
Use the contours of the solid areas identified under Step f to refine the additional dead load case introduced in Step d. Remove the dead load reduction within the identified solid areas and increase the dead load reduction to 100% of the value identified in Step c in the remaining areas. Example The shear force contours equalling to the value of 50 kN/m are exported into a CAD drawing and this CAD drawing is re-imported in the background of the FEM model:
The additional dead pattern from Step d is deleted and a new pattern with an upward acting surface load equalling to 100% of the dead load reduction (2.32 kN/m2) around the shear force contours is created:
Continued on next page…
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Engineering Manual Example (continued from Step g) This new additional dead load pattern is added to the slab’s DL (slab’s self weight):
4.7 Design Step h – Slab rebar design and detailing
Generate the design moment distribution in the slab as well as the reactions. Dimension the bending and punching reinforcement.
Check if the resulting cross section is geometrically feasible. The cross-section build-up (see chapter 3) should be at least equal or inferior to the slab depth chosen in Step c. If it is less, the difference can be bridged with additional spacers or by fine-tuning the choice of the rebar diameters. If the cross-section is bigger than the chosen slab depth, the rebar diameters have to be modified or the slab depth increased.
Detail the slab and execute the reinforcement shop drawings. Example
Generation of the design moment distribution and required rebar content Continued on next page… © Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 10/28
Engineering Manual Example (continued from Step h) Cross-section verification after choice of reinforcement: •
Top and bottom rebar cover: 25 mm
•
Bottom re-bar chosen: 14 mm (x and y directions)
•
Top rebar chosen: 12 mm (x and y directions)
•
Cobiax cage module support height according to Table 1 of paragraph 2.2: 190 mm
Æ Σ 25mm + 25mm + 14mm + 14mm + 12mm + 12mm + 190 mm = 292 mm Æ 292 mm ≤ 300 mm The cross-section is OK (including a construction tolerance of 8 mm)
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Engineering Manual 5.
EXECUTION OF COBIAX SLABS
5.1 Cobiax shop drawings The Cobiax shop drawings are necessary for the proper installation of the Cobiax cage modules on site. Together with the structural drawings of the slab (or formwork drawings) and rebar drawings they are used by the contractor to carry out the slab. The Cobiax shop drawings need to contain the following elements: •
Slab contour showing the areas of the Cobiax cage modules, their type, positioning and orientation within the slab n
•
Typical cross sections of the slab with incorporated Cobiax cage modules o
•
Required amount of Cobiax cage modules and concrete p
•
Installation and concreting guidelines q
p n q
o
Figure 1 – Typical Cobiax shop drawing for a slab
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 12/28
Engineering Manual The preparation of the Cobiax shop drawings is best done based on the structural drawings of the slab (or formwork drawings) which provide the complete slab geometry, openings and slab bearing elements. The borders of the solid areas are defined by importing and superimposing the contour plot of the solid areas (generated and in Step f of the design procedure). The Cobiax cage modules can be drawn around these solid areas. As an additional piece of information, the rebar detailing should be available in order to know the orientation of the rebar and to draw the typical cross sections (and at the same time check its consistency). The orientation of the Cobiax cage modules is defined by the upper top and the lower bottom reinforcement bar (v1 and v4, see paragraph 3). All three elements need to follow the same direction.
Figure 2 – Shear contour plot of a slab, output from design Step f in paragraph 4.5 (hatched area has to be carried out without void formers)
Figure 3 – Corresponding Cobiax shop drawing taking into account the solid areas without void formers
Practically, the shaping of the solid areas is best done as shown below:
Figures 4,5 & 6 – The roundish shape of the solid area is incorporated in a rectangle and visualized as such in the shop drawing to keep installation on site simple
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 13/28
Engineering Manual The following principles should be applied when preparing the shop drawings: •
Along slab edges and openings it is recommended to leave out at least one row of Cobiax cage modules even if the shear force is not exceeded in these areas. This will avoid interference with U-bars and fixings at the edges and ease the installation works (see n on below Figure 7).
•
Where necessary, the Cobiax cage modules have to be cut to length in order to fit into their designated areas. The layout drawing should indicate the lengths of the cages (see o on below Figure 7).
n
n o
Figure 7 – Extract of Cobiax shop drawing For the Cobiax cage modules geometric data (for proper visualisation) and the concrete reduction (calculation of the required amount of concrete per slab) refer to Table 1 of paragraph 2.2.
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 14/28
Engineering Manual 5.2 Technical services installation Thanks to the modular conception of the Cobiax cage modules, the combination with other technical installations in the slab is possible. Such elements can be plumbing pipes, electrical cable ducts or post-tensioning cables. This is done by locally removing individual void formers or entire or partial cage modules.
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 15/28
Engineering Manual The Cobiax shop drawings can include and visualize the technical services installations. Practically, this can be handled by superposing the available drawings (e.g. plumbing, air-conditioning, etc.) on the Cobiax shop drawings and deleting the void formers in the respective areas. Figure 8 below shows the integration of plumbing ducts (brown line n). Electrical ducts (shown as green lines o) have to be installed afterwards in between the Cobiax cage modules.
n
o
n o
Figure 8 – Shop drawing extract
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 16/28
Engineering Manual 5.3 Site installation The site installation of the Cobiax cage modules follows a similar procedure as traditional wire chairs. Typically, the cage modules are installed by the steel fixers. In a first step, the formwork and bottom reinforcement is installed followed by below outlined procedure:
Formwork and bottom rebar installation Slim-Line
Eco-Line
Placing of cage modules according to the Cobiax shop drawings. Tying of the modules to the bottom rebar (approx 2 – 3 tie points per cage):
n Placing of the top reinforcement directly on the cage modules which take over the function of wire chairs:
o
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 17/28
Engineering Manual Casting of the first layer of concrete in order to cover the bottom reinforcement and lower longitudinal bars of the positioning cages and thereby anchor the cage modules. Even if the void formers will be subject to buoyancy at concrete vibration occurring at q they will not lift off as they are anchored in the first concrete layer:
p After the first layer of concrete has start to set (normally after 2 – 3 hours) the second and final layer of concrete will be cast:
q
Site impression: placing of Cobiax cage modules
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Engineering Manual APPENDIX A – BENDING The bending strength of Cobiax slabs has been investigated with laboratory tests using various slab depths and void former sizes. The bending behaviour has been proved to be comparable with the one of solid flat slabs. In slabs with common design loads and deflection criteria the compression zone remains above the Cobiax void formers so there is no prejudice for the design. Neutral axis
Fc Fso
Fsu Figure a – Neutral axis position above void former (normal case) Thus, the ultimate resistance moment of a cross-section of a Cobiax flat slab may be determined by usual the methods prescribed by the concrete design codes. In cases with excessive loads the determination and verification of the neutral axis’ position may be appropriate. Nevertheless, in practice such case is basically nonexistent as the deflection and reinforcement amount limitations keep the position of the neutral axis in the zone above the void formers.
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Engineering Manual APPENDIX B – STIFFNESS The void formers in the Cobiax slab reduce its stiffness compared to solid flat slabs. This stiffness reduction is expressed in factors. These stiffness factors are the ratios of the three-dimensional calculation of the second moment of area ΙCB for Cobiax slabs (taking into account the voids and assuming their vertically centred position) and ΙSolid for solid flat slabs. The calculation of the values is based on an un-cracked section. Below table provides the stiffness ratios of ΙCB / ΙSolid for the different void former types and possible slab depths: Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid Void former type Slab depth [cm] ΙCB / ΙSolid
CBCM-S-100 20 0.92
21 22 0.93 0.94
CBCM-S-120 22 0.91
23 24 0.92 0.93
CBCM-S-140 25 0.92
26 27 0.93 0.94
CBCM-S-160 27 0.91
28 29 0.92 0.93
CBCM-S-180 30 0.91
31 32 0.92 0.93
CBCM-S-200 32 0.90
33 34 0.91 0.92
CBCM-S-220 35 0.91
36 37 38 39 0.92 0.93 0.94 0.94
CBCM-E-270 40 0.92
41 42 43 44 0.93 0.93 0.94 0.94
CBCM-E-315 45 0.91
46 47 48 49 0.92 0.92 0.93 0.93
CBCM-E-360 50 0.91
51 52 53 54 0.91 0.92 0.92 0.92
CBCM-E-405 55 0.90
56 57 58 59 0.90 0.91 0.91 0.92
CBCM-E-450 60 0.89
61 62 63 64 65 66 67 68 69 70 0.90 0.90 0.91 0.91 0.92 0.92 0.92 0.93 0.93 0.93
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 20/28
Engineering Manual APPENDIX C – SHEAR Theoretical approach for shear strength According to the current standards, the calculation of the shear strength for traditional one-way spanning hollow core slabs is to be based on the smallest available web width of a the hollow cross section. With such a criterion used for twoway spanning voided slabs, the resulting shear strength for the Cobiax flat slab would only be about 10% of the shear strength of a solid flat slab of same thickness. However, for the Cobiax flat slab the smallest cross section width is only present at one singular point, i.e. directly between two void formers. Even at small distances away from this point in all three spatial directions, the available cross section width increases rapidly. Laboratory tests have revealed a much higher resistance to shear for Cobiax flat slabs than above mentioned value. Based on these test results, the below presented approach has been worked out for the determination of the maximum shear force capacity of the Cobiax flat slabs. This approach has been approved in the «National Technical Approval», registration number Z-15.1-282, issued by the German Institute of Building Technology (DIBt). Shear force resistance concept for Cobiax slabs Generally, the shear strength concept of solid concrete elements without shear reinforcement is based on the sum of several contributing bearing mechanisms: •
Shear resistance of the un-cracked compression zone Vc,comp
•
Aggregate interlocking along the shear crack Vc,cr
•
Shear resistance provided by the tension reinforcement Vc,D
In case of the Cobiax slab the aggregate interlocking contribution is reduced due to the presence of the void formers (see picture below). Thus, the shear resistance for a Cobiax flat slab is reduced and must be considered accordingly. The shear resistance contributions from the compression zones and the tension reinforcement remain uninfluenced.
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 21/28
Engineering Manual The percentage-wise shares of these three resistance contribution factors to the global shear resistance are unknown; research and literature propose various figures. To be on the safe side for the determination of the shear resistance concept of the Cobiax slab, a 100% share of the reduced aggregate interlocking Vc,cr is assumed. As a consequence of above assumption the effectively contributing concrete area in the relevant cross-section (see figures on the next page) will be considered instead of the smallest available web width in the tension zone of a given cross section. The relevant cross-section is not vertically positioned but at an inclination in the range of 30° to 45° which is the usual array of directions of the shear cracks. A geometric derivation (see figures on the next page) allows to conclude that the dimensioning value of the maximum admissible shear force for a Cobiax slab can assumed to be on the safe side 55% for the Eco-Line void formers and 50% for the Slim-Line void formers. With these reduction values, the maximum allowable shear force Vc (or design concrete shear stress depending on the code used) for the Cobiax slab can be calculated as follows: •
Eco-Line: Vc,Cobiax = 0.55 ⋅ Vc (where Vc is calculated according to the used code for a solid slab of same depth, reinforcement content and concrete grade)
•
Slim-Line: Vc,Cobiax = 0.50 ⋅ Vc (where Vc is calculated according to the used code for a solid slab of same depth, reinforcement content and concrete grade)
Therefore, areas in a Cobiax slab for which Vc,Cobiax is exceeded due to high shear concentration are to be executed without void formers and become solid slab areas. Above values have been empirically confirmed by a series of laboratory tests with a worst-case combination of input parameters. Up to a certain extent, the vertical cage bars of the positioning cages act as shear reinforcement which for the Eco-Line void former increases the shear resistance value up to 100% and for the Slim-Line void former up to 66%. However, this additional safety effect is not taken into account in above considerations and shear reduction factors as only the aggregate interlocking aspect is assumed to be contributing to the shear strength. Therefore, a considerable amount of additional safety is built into the shear resistance concept for Cobiax slabs.
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 22/28
Engineering Manual Geometric derivation of the shear reduction factor Graphically, the derivation of the 55% factor (example for Eco-Line shaped void former; the same concepts can be applied for the Slim-Line void formers to demonstrate the 50% value) can be done as shown below. The factor αbw,cobiax is the ratio of the remaining concrete section area and the total cross section area. The minimum value which is geometrically possible (and thus the relevant one) can be found at an inclination of 45° in cross-section 1 (note that for the calculation of the areas a concrete top and bottom cover of 2.5 cm has been subtracted from the vertical cross-section depth):
Cross section at 30° inclination:
Resulting cross-section 1
Resulting cross-section 2
Resulting cross-section 3
Resulting cross-section 2
Resulting cross-section 3
Cross section at 45° inclination:
Resulting cross-section 1
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Engineering Manual APPENDIX D – PUNCHING Punching around columns Due to shear force limitations the areas with high shear force concentration as for example around columns heads are to be executed without the Cobiax cage modules. The critical perimeters that are relevant for the punching shear design are located within these solid areas. The punching shear considerations in these areas are therefore as for solid flat slabs. It is recommended to explicitly verify that the determining perimeter for punching is located inside the solid zone as shown on below drawing. Should this not be the case, the solid zone has to be increased accordingly. The reduced dead weight of the Cobiax flat slab decreases the column reactions and allows to optimize the necessary amount of punching reinforcement.
Area without void formers
Local punching For heavy concentrated point loads it might be required to verify that these do not lead to local punching above the cavities created by the void formers. Test have been made to examine this issue. They show that for point loads of 50 x 50 mm size and a concrete cover of 50 mm above the tip of the Eco-Line void formers the ultimate load is about 200 kN (for a concrete compressive strength of 45 MPa). The tests have been done without top reinforcement and not taking into account the positioning cage’s top longitudinal bar. For very high point loads exceeding above critical value is recommended to leave out the void formers locally.
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Engineering Manual APPENDIX E – FIRE PROTECTION Irrespective of the construction code, the relevant parameter and dimensioning criteria driving the fire resistance classification of concrete building elements and in particular floors is: The concrete cover between the exposed surface of the building element and the first layer of the structural reinforcement Fire tests in specialised laboratories with Cobiax slab specimens have shown that above parameter and criterion can be applied with no limitation to the Cobiax flat slabs and that the Cobiax slabs can withstand fire in the same way as solid flat slabs. The current fire rating of Cobiax slabs stands for 180 minutes issued by the German Authorities (report P-SAC 02/III – 187 done by MFPA). The recorded heat propagation over time in the fire tests of the Cobiax slab specimens were found to be the same as for solid slabs. It was even found that the voids created in the concrete by the Cobiax cage modules have a slightly retarding effect on the instance of concrete spalling from the exposed concrete surface. In fact, in a first phase the voids absorb the internal steam pressure built-up (originating from concrete moisture) occurring in the concrete which otherwise would be directly pass into the concrete cover zone. However this beneficial effect is not quantifiable but nevertheless presents some extra safety margin. If exposed to open fire the void formers (made from HD-PE or PP) would decompose into H2O and CO2 which as such is not harmful.
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Engineering Manual APPENDIX F – SOUND INSULATION The two main relevant parameters for sound insulation rating of building elements are: •
Airborne sound insulation
•
Impact sound insulation
For both types of sound sources and depending on the construction codes used various prediction models, calculation and rating methods exist. The standards define tolerable sound levels for the different utilization of buildings. Building element dimensions are to be chosen such that they comply with these requirements. Sound insulation tests have been done on Cobiax slabs both with specimens in specialized laboratories as well as in completed buildings. The aim was to evaluate the sound insulation capacities of Cobiax slabs compared to solid flat slabs and to define an appropriate sound insulation rating method. The interpretation of these sound insulation measurements shows that for a Cobiax slab the same sound insulation evaluation methods can be used as for a solid flat slabs. For both, impact sound and airborne sound the main element for evaluating the sound isolation degree provided by concrete floors is the average mass per square meter of area of the considered building element. Usually, the codes provide charts showing the sound insulation of concrete floors in function of their depth, respective mass per unit area. The values obtained from these charts are then added up with the sound insulation values provided for the flooring build-up and the ceilings. The total sound insulation capability of a building element is thus the combination of the various materials used. Obviously, the average mass of a Cobiax slab is less than the one of a solid slab of same depth. Therefore, the sound insulation value for the Cobiax slab will be slightly different from a solid slab of same depth. The acoustic assessment of buildings incorporating Cobiax slabs can be based on the same methods as they are commonly used for traditional constructions based on the average surface mass of the Cobiax slabs. For a 20 cm deep slab fitted with CBCM-S-100 void formers (the thinnest possible Cobiax slab and thus the most critical one in terms of sound insulation) the following values have been measured on a “naked” (thus no additional flooring and ceiling) specimen in the laboratory: •
Airborne sound insulation: Rw,P = 56 dB
•
Impact sound level: Ln,eq,0,w,R = 76 dB
The average mass of this slab corresponds to an average concrete depth of 15 cm. © Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 26/28
Engineering Manual APPENDIX G – VARIOUS TECHNICAL ISSUES Earthquake and Dynamic Loading The dynamic properties of a building and its earthquake behaviour have to be assessed individually on a project by project base with the verification methods recommended by the respective codes. In case of an earthquake the reduced dead load of the Cobiax slab influences beneficially the horizontal forces acting on the bracing elements of the building structure (typically shear walls and lift cores). These forces – mainly driven by the horizontal member’s dead load – are reduced if the dead load of the slab is reduced. Up-to-date 3D dynamic modelling software will take into account the reduced dead load of the slabs and compute the deformation and moments accordingly. Compared to a solid slab of same thickness, the Cobiax slab has an improved vibration performance. Cobiax flat slabs have higher natural frequencies for common practice live loads compared to solid slabs due to their reduced dead load. Diaphragm action Despite the presence of the void formers the Cobiax slab still acts as a stiff plate and can transfer horizontal loads due to wind, building inclination, earthquake and temperature variations to the cores. Upon dimensioning, the upper and lower concrete cover to the void formers can be considered as a equivalent cross-section for simplification. It can be dimensioned as a rectangular cross-section for the internal axial forces. For very high forces exceeding the capacity of the equivalent cross-section the addition of solid strips without void formers acting as compression struts is recommended. qk
qk
H2 H1
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 27/28
Engineering Manual Cold joint When casting concrete for the Cobiax slabs a horizontal cold joint is created if the time gap between the two concreting stages is such that the first layer has dried out and hardened and thus the concreting of the second layer cannot be considered to be “wet-in-wet”. The impact of the cold joint can be controlled and compensated through the following factor: The vertical bars of the cages containing the void formers which are embedded in the first concreting layer act as shear dowels and provide sufficient interlocking between the two concrete layers.
CBCM-S-160
CBCM-S-180
CBCM-S-220
CBCM-E-270
CBCM-E-315
CBCM-E-360
CBCM-E-405
CBCM-E-450
CBCM-S-200
CBCM-S-140
CBCM-S-120
Cage rebar Ø [mm]
5
5
5
5
5
5
5
5
5
6
6
7
Rebar # per void*
4
4
4
4
4
4
4
4
4
4
4
4
Rebar area per void [mm2]
78.5
78.5
78.5
78.5
78.5
78.5
78.5
78.5
78.5
113
113
154
Voids per m2
8.16
8.16
8.16
8.16
8.16
8.16
8.16
11.11
8.16
6.25
4.94
4
Rebar Area per m2 [mm2/m2]
641
641
641
641
641
641
641
872
641
706
558
616
Cage module type
CBCM-S-100
Should a verification of the cold joint be required by taking into consideration the cross section area of the Cobiax cage module vertical rebar, the following figures can be applied:
*) vertical cage bars surrounding void former
© Cobiax Technologies AG • All rights reserved • Engineering Manual • Version 1.0-2010-EC • Page 28/28
