bubbledeck- ec 2 (tính toán)

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Appendices

A. Appendix A Brochure UK

B. Appendix B Geometry for Standard Deck sizes

C. Appendix C Eurocodes 2 Practical Use

D. Appendix D Comments to Eurocodes 2

E. Appendix E Shear according to Eurocodes 2

F. Appendix F BubbleDeck Standard Details

G. Appendix G Examples

H. Appendix H Brochure UK Site Installation


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Appendix A Brochure UK


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CI/SfB(23) Eq4

Part 1 September 2008

The Original Voided Flat Slabswith BubbleDeck

B u b b l e D e c kS t r u c t u r e S o l u t i o n s

P r o d u c tI n t r o d u c t i o n

U N I T E D K I N G D O M

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W h a t

Reinforcing mesh, topRecycled plastic hollow Bubble void former

Reinforcing mesh, bottom cast into optionalconcrete filigree biscuit permanent formwork

i s t h e B u b b l e D e c k S y s t e m ?

Advantages

Design FreedoReduced

Dead WeightLonger Spans

Green andSustainable

FastConstruction

Want to know more?ubbleDeck Technical Manual

ubbleDeck Design Guide

nteractive CD ROM withubbleDeck slab calculator

re also availablepon request


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BubbleDeck is a revolutionary method of virtually eliminating concrete from the middle of a floor slab not performing any

structural function, thereby dramatically reducing structural dead weight. BubbleDeck is based on a new patented technique

- the direct way of linking air and steel. Void formers in the middle of a flat slab eliminates 35% of a slabs self-weight

removing constraints of high dead loads and short spans.

Incorporation of recycled plastic bubbles as void formers permits 50% longer spans between

columns. Combination of this with a flat slab construction approach spanning in twodirections the slab is connected directly to insitu concrete columns without any beams -

produces a wide range of cost and construction benefits including:-

Design Freedom flexible layout easily adapts to irregular & curved plan layouts. Reduced Dead Weight 35% removed allowing smaller foundation sizes. Longer spans between columns up to 50% further than traditional structures. Downstand Beams eliminated quicker & cheaper erection of walls and services. Load bearing walls eliminated facilitating MMC with lightweight building envelopes. Reduced concrete usage 1 kg recycled plastic replaces 100 kg of concrete. Environmentally Green and Sustainable reduced energy & carbon emissions.

The overall floor area is divided down into a series of planned individual elements, either 3 or2.4 metres wide dependant upon site access, which are manufactured off-site using MMC

techniques. These elements comprise the top and bottom reinforcement mesh, sized to suit

the specific project, joined together with vertical lattice girders with the bubble void formerstrapped between the top and bottom mesh reinforcement to fix their optimum position. This

is termed a bubble-reinforcement sandwich which is then cast into bottom layer of pre-cast

concrete, encasing the bottom mesh reinforcement, to provide permanent formwork

within part of the overall finished slab depth.

On site the individual elements are then stitched together with loose reinforcement simplylaid centrally across the joints between elements. Splice bars are inserted loose above the pre-cast concrete layer betweenthe bubbles and purpose made mesh sheets tied across the top reinforcement mesh to join the elements together. After the

site finishing concrete is poured and cured this technique provides structural continuity across the whole floor slab the

joints between elements are then redundant without any structural effect to create a seamless floor slab.

BubbleDeck has proved to be highly successful in Europe since its invention ten years ago. In Denmark and Holland over 1million square metres of floors have been constructed in the last seven years using the BubbleDeck system in all types of

multi-storey buildings.

Bubb leDeck i s a s imp le s o lu t ion tha t e l imina t e s non - w or kingdead load in f l oo r s w h i l e f u l l y r e t a in ing s t r eng th .

T h e e n g i n e e r i n g s o l u t i o n t h a t r a d i c a l l yi m p r o v e s b u i l d i n g d e s i g n a n d p e r f o r m a n c e

w h i l e r e d u c i n g t h e o v e r a l l c o s t .

BubbleDecksheight savingallowed 2floors to beaddedduringconstruction

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Simple s i t e i n s t a l l a t i o n(Type A - F i l i g r ee E l emen t s )

Temporary Support Propping on parallel beams at 1.8

to 2.4 metre spacing

Placing Elements Semi pre-cast elements mechanically

lifted into position

Joint Reinforcement Insert loose bottom splice bars

and tie top mesh across joints between elements

Shear Reinforcement Insert loose bars across columns

Edge reinforcement Insert edge bars and hairpins

around slab perimeter

Perimeter shuttering Fix shuttering to bottom pre-cast

concrete layer & tie to top mesh reinforcement

Soffite shuttering Prop plywood across tolerance joints

between element bays and between elements & columns Preparation Seal joints between elements, clean and

moisten bottom pre-cast concrete layer

Concreting Pour, vibrate and float 10mm max.

aggregate in-situ concrete

Temporary works Remove, typically after 3 5 days,

according to specific site advice

Finishing no further work required, the slab is complete

unless requirement for exposed soffite

BubbleDeck

is a two-wayspanning hollow

deck in whichrecycled plastic

bubbles serve thepurpose of eliminating

non-structural

concrete

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t y p e s

Type A Filigree Elements, where the bottom of the bubble-reinforcement sandwich includes a 70mm thick pre-cast concretelayer acting as permanent formwork within part of the finished slabdepth replacing the need for soffite shuttering. The elements are

placed on temporary propping, loose joint, shear & edgereinforcement added, perimeter and tolerance joints shuttered and then the remaining

slab depth concreted.

Most commonly specified being suitable for the majority of new-build projects. Requires fixed ormobile crane to lift into position due to weight of manufacturedelements as delivered to site.

Type B Reinforcement Modulescomprising pre-fabricated bubble-reinforcement sandwich elements.The modules are placed ontraditional site formwork, loose joint,shear & edge reinforcement added and thenconcreted in 2 stages to the full slab depth.Suitable for suspended ground floor slabs and alteration /refurbishment projects, particularly where site access isextremely restricted. Can be manually lifted into position.

Type C Finished Planks, delivered to the building site as completepre-cast factory made slab elements with the full concrete thickness. Thesespan in one direction only and require the inclusion of supporting beams or wallswithin the structure.

Version Slab Bubbles Span Cantilever Span Completed Site ConcreteThickness (Multiple bays) Maximum Length (Single bay rows) Slab Mass Quantitymm mm metres metres metres kN/m2 m3/m2

BD230 230 180 5 8.1 2.8 5 6.5 4.26 0.112BD280 280 225 7 10.1 3.3 6 7.8 5.11 0.146BD340 340 270 9 12.5 4.0 7 9.5 6.22 0.191BD390 390 315 11 14.4 4.7 9 10.9 6.92 0.219BD450 450 360 13 16.4 5.4 10 12.5 7.95 0.252BD510* 510 410 15 18.8 6.1 11 13.9 9.09 0.298BD600* 600 500 16 21.0 7.2 12 15.0 10.30 0.348

BubbleDeck can be supplied in 3 types ofmanufactured elements:

versionsB u b b l e d e c k s l a b

Element

The appropriate BubbleDeck slab version is bespoke engineered to suit building configuration, span length betweenapplied loadings and vertical alignment of supports. Indicative spans are given as a guide to what can be achieved. full calculation FE analysis these are based on 20mm concrete cover to bottom rebar (1 hour fire resistance); live lo2,dead load 1.5 kN/m2 and lightweight external envelope maximum 6 kN/m line load. Completed slab mass and Site ConQuantity based on 3 x 9 metre pre-cast elements with 35 kg/m2 total reinforcement.

* New 2006

BubbleDeck slab

configurations:

Agrment

certification

pending, outside

scope of KOMO

technical

certificate.

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Selected B u b b l e D e c k p r o j e c t sLe Coie HousingThe largest BubbleDeck structure so far erected in Great Britain wascompleted 6 weeks ahead of programme. The structure comprises 7,800m2of BubbleDeck floor slabs between 3 and 6 stories high supported on in-situreinforced concrete columns. Over 400,000 of savings were realised as adirect result of incorporating BubbleDeck into this project, amounting to a3% saving off the TOTAL project cost.

The Main Contractor subsequently found the BubbleDeck systembenefits continue throughout the whole construction process withfaster and cheaper erection of external & internal walls plus fastand easy installation of services below the flat soffites.

Chris Dunne, Project Architect, commented:- Our originalsolution for Le Coie was a steel frame with Bison floor planks &structural concrete topping in the 5 to 6 storey areas, with loadbearing blockwork supporting a composite metal deck in the lower sections.

The BubbleDeck technique not only saved a considerable sum but simplifiedthe buildings structure, removing my co-ordination headache of gettingservices around or through beams required with a traditional solution.Wewere also able to eliminate all load bearing walls down the middle of eachflat, required to support the short spans of composite metal decks, givingmore internal space and fantastic flexibility.

I will definitely consider BubbleDeck

for use on my future projects.

These are only a few of many projects withBubbleDeck floors.

For many others and new projects see ourWEB site: www. BubbleDeck-UK.com

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Media CityThis 32.000 m2 building wasconstructed with greattransparency, revealing a hugeopen atrium. This atrium is the fulcrum and heart of the

building. The spaces are formed in soft, organicshapes that allow light to spill onto every

single workplace in the building.To achieve these wide, open, internal

spaces a BubbleDeck structure of post tensioned 450mm deepfloor plates, achieving 16 metrespans between columns wasselected - dramatically reducingstructure dead weight and

enabling long spans. The flexibility

of BubbleDeck also facilitatedconstruction of the soft flowing,

organic shapes forming the floors aroundthe central atrium.

Millennium TowerOriginally designed with hollow core planks, late in thedesign stage it was determined that BubbleDeck wouldrealise considerable cost and time savings. Adopting

BubbleDeck also reduced the structural floor zonedepth due to omission of beams, lowering theoverall buildings height.Another consideration was the lack of storagespace on the building site which is located close tomajor arterial roads and streets. The floors were onaverage erected, cast and completed in half thetime - 4 days instead of 8 days it would havetaken to construct with hollow core planks. Half way through constructing the structure it wasdecided to add another 2 floors which was madepossible within the overall height of the original buildingdue to BubbleDeck reducing structural floor depth.

City Hall and OfficesBubbleDecks superior cantilevering abilityachieved 3.3 metre cantilevers from a280mm deep slab with 7.5 metre internalspans between columns. The buildingprovides a City Hall and financial centrefor Danske Bank containing 4,000 m2

floor area. The slender slab without anybeams secures maximum light from thefacades, which is enhanced by an internalatrium. This project won Building of theYear 2004 award for offices andcommercial buildings.

BubbleDeck

BubbleDeck ishe ONLY officiallycertified voided flatslab system havingbeen granted KiwaN.V. KOMO CertificateK22722, recognisedn the Building

Regulations asequivalent toan AgrmentCertificate.

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A BubbleDeck slab has the same applied load carrying capacity withonly 50% of the concrete required for a solid concrete slab, or withthe same slab thickness has twice the load carrying capacity using65% of the concrete required by a solid concrete slab.

Schematic design basic principleAs a general guide for project scoping purposes the maximum achievablespans for each BubbleDeck slab depth is usually determined by deflectionlimitations. This criteria is controlled by the ratio of span / effective depth(L/d) stipulated in BS8110 and modified by applying a factor of 1.5,permitted by BS8110 to take account of BubbleDecks dramatically lowerdead weight than traditional solid flat slabs.

L/d 30 for simply supported floors(single spans)L/d 39 for continuously supported floors(multiple spans)L/d 12.5 for cantilevers.

The effective depth of a BubbleDeck slab is the overall depth less standard20mm concrete cover (achieving 1 hour fire resistance) from the bottommesh reinforcement to underside of the slab. Where 90 minute fireresistance is required deduct 25mm off overall slab depth, or for 120minute fire resistance deduct 30mm off overall slab depth. In the case of spanning onto columns without beams use the longest dimensions

between columns, where the slab will span onto walls or beams use theshortest span dimension.

As an example for BD280 slab version, with 1 hour fireresistance, d is 260mm so 39xd indicates a maximum 10.14metre continuously supported (multiple bay) span; 30xdindicates a maximum 7.8 metre simply supported (single baspan, and 12.5xd indicates a maximum 3.25 metre cantilevpotentially feasible. This basic principle has been verified fodead loadings up to 4.5 Kn/m2 following full calculations onmany projects as a generally reliable indication.We can refithis approximate indication by full calculation and we woulpleased to give you advice on a specific project.

Post tensioningWhen mega spans are required(above 15 metres) we can providea PostTensioned (PT)BubbleDeck solution. The abovedeflection limits can beincreased by up to 30% withpost-tensioned BubbleDeckslabs.

Solid d e c k c o m p a r i s o n s

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By virtually eliminating concrete in the middle of a slab BubbleDeckmakes a significant contribution to reducing environmental impact.Guidance from the ODPM requires the direct environmental effects of buildingto be considered, including usage of natural resources and emissions resultingfrom construction. Not only is concrete usage reduced by up to 50% within abuildings structure but knock-on benefits can be realised through reducedfoundation sizes. BubbleDeck can make a big contribution towards achievingBREEAM targets.

Every 5,000 m2 of BubbleDeck floor slab can save:- 1,000 m3 site concrete. 166 ready mix lorry trips. 1,798 Tonnes of foundation loads or 19 less piles. 1,745 GJ energy used in concrete production & haulage. 278 Tonnes of CO2 green house gases emissions.

BubbleDeck structures are also Sustainable with the system allowing frame re-use for future

purposes. The envelope and all internal work can be removed from a BubbleDeck building

and the original frame simply refitted for a new purpose. The two way spanning nature of

BubbleDeck slabs allows any internal layout to be reconfigured to new uses within theoriginal design load parameters.

Data based on typical 4,500 m2

Office Building with 7.5 x 7.5 metre multiplespans between in-situ or precast concrete columns.

Assumptions:1) Lightweight external envelope (curtain walling or equal).

2) Typical office live load 2.5 kN/m2

+ 1.5 kN/m2

for lightweight partitions, computer floor, finishes & services.3) Overall stability braced by stair / lift core shear walls in both cases BubbleDeck transfers lateral loads to cores.4) Energy from materials transport cement 50 miles, aggregate 10 miles (to ready mix plant) and concrete 5

miles (to site).

Relative values in % of solid slabCarrying capacity 25 50 25Dead load 75 50 40Dead load / Carrying capacity3:1 1:1 1.5:1

Absolute values in % of solid slabCarrying capacity 100 200 100Slab dead load 100 65 50Utility value of 300 200concrete increasedA BubbleDeck has twice the capacity with 65% concrete and

the same capacity with 50% concrete compared toa solid slab.

arrying capacitylab Dead load

Solid slab BubbleDeck BubbleDecksame thickness same capacity

Green

Consider

c r e d e n t i a l s

t h e b e n e f i t s

Slab Site Concrete Site Concrete Total Slab Embodied CO 2Depth Volume Quantity Dead Load Energy Emissions(mm) m3 / m2 m3 (Tonnes) (Giga Joules) (Tonnes)

Solid Slab 310 0.31 1,395 3,376 3,278 522BubbleDeck 230 0.11 495 1,758 1,707 272BD SAVES 80 0.20 900 1,618 1,571 250

BubbleDeck

floors make asubstantialcontribution toreducing carbonemissions arisingfrom construction.

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Appendix B Geometry for Standard Deck sizes


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Appendix C Eurocodes 2 Practical Use


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The practical use of Eurocode 2

Rod Webster Concrete Innovation & Design Page 1

1 Introduction

When or before Eurocode 2 is introduced in early 2003, most engineers will need to beassured that it can be used as a practical concrete design tool, as well as producingeconomic results. If they are not assured of this, practices will continue to use BS 8110 in

preference to adopting the new code.

Necessary guidance in the form of explanatory literature, process flowcharts, spreadsheetsand other software etcetera is in preparation. This brief report will attempt to summarise the

principal design procedures required by EC2, compare them with their BS 8110counterparts, and demonstrate that the transition to EC2 need not be a difficult process.

2 Comparisons with BS 8110

2.1 Loading EC2 BS 8110

Loaded spans: Worst of G = 1.35, Q = 1.05and G = 1.15, Q = 1.5

G = 1.4, Q = 1.6

Unloaded spans: G = as above G = 1.0 Loading pattern: All + adjacent + alternate spans All spans + alternate spans

For the sake of simplicity, G = 1.35 and Q = 1. 5 may be used for loaded spans ( with G =1.35 on unloaded spans ), although this would be very conservative. Both G and Q are

marginally lower than in BS 8110, but for unloaded spans G is higher, reflecting a lower probability of variation in dead loads. For a typical member with Qk = 0.5 G k , maximumULS loading would be 13.6% lower than for BS 8110. The use of the same value for G throughout also reduces the effect of pattern loading, thus marginally reducing spanmoments.

The loading code, EN 1991-1-1, stipulates values of imposed loads that vary onlymarginally from current UK practice ( e.g. 3 kN/m 2 for offices ). This code stipulates weightsfor both construction materials and stored materials, and it should be noted that the densityof normal weight reinforced concrete should be taken as 25 kN/m 2.

2.2 Cover

Nominal covers required for durability and bond are fairly similar to BS 8110. However,nominal cover to EC2 is in two parts, C nom= C min+ c, where c is a design tolerancevarying from 0 to 10mm, depending upon quality assurance level. This can have the effectof increasing cover to slabs when larger diameter bars are used, as C min bar and c must

be added.

2.3 Materials EC2 BS 8110 Partial factor, concrete: c = 1.5 c = 1.5 Partial factor, steel: s = 1.15 s = 1.05


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Rod Webster Concrete Innovation & Design Page

At first inspection, the higher s factor in EC2 would appear disadvantageous. However, thisdifference is almost exactly neutralised by the introduction of reinforcing steel with f yk =500 N/mm 2.

2.4 Stress block flexure

Eurocode 2

Section Strain Stress

neutral axis

As

As2

h d

x xd 2

s

sc F c F sc

F st

z

c f = f / cd cc ck c

f ck = characteristic concrete cylinder strength ( equivalent to 80% cube strength ).

For f ck 50 N/mm2, = 1, c = 0.0035, cc = 1.0 and = 0.8. As c is the same for both

codes, this results in concrete design strengths being 19.4% higher than in BS 8110 below.This difference gives advantage in terms of reinforcement areas because of the resultingincrease in the lever arm, z.

Section Strain Stress

neutral axis

As

As

h d

x 0.9xd

s

sc F c F sc

F st

z

c = 0.0035 f = 0.67 f / cd ck c

BS 8110

2.5 Stress block columns

In BS 8110, an identical stress block is used for both pure flexure and bending with axialload. In EC2 however, c the limiting concrete compressive strain, starts to reduce when theneutral axis x drops outside of the section height, h. This strain reaches a lower bound value(0.00175 for f ck 50 N/mm

2) when the section is in pure compression.

2


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The diagram below demonstrates this procedure. Effectively, the strain diagram has ahinge point, which falls at h/2 for normal strength concretes. This process is easilyautomated, but is not suited to hand calculation, so it is best accomplished by spreadsheet.

As few columns are very close to being in pure compression, this gradual reduction instrain, and hence compressive stress, has less effect than one might imagine.

General relationship When x > h Pure compression

h d

h/2 x

x s

0.00175 min 0.00175

0.001750.0035 max

hinge point

0.00175x /(x-h/2)

EC2 strain relationship at ULS (f ck 50 N/mm 2 )

2.6 Redistribution

EC2 BS 8110 Neutral axis limit: x/d - 0.4 x/d b - 0.4 Redistribution limit: 30% classes B & C 30% generally

20% for class A rebar 10% sway frames > 4 storeys 0% in columns 0% in columns

Limitations: Adjacent spans ratio 2

The EC2 x/d limit reduces for concrete with f ck > 50 N/mm2, otherwise both codes are very

similar.

2.7 Beam shear

A strut-and-tie model is used for shear reinforcement to EC2, which can have a varyingangle between the compressive struts and main tension chord. Cot is normally taken asthe maximum value of 2.5, but may be as low as 1.0 if required for high shear forces.

For UD loading, EC2 BS 8110 Shear resistance: = 0.7 f ck /200 0.5

k = 1 + (200/d) 2 vc = from Table 3.8 1 = A sl /bwd 0.02

At support face: V Rd,max = 0.9b wd.f cd /(cot + tan ) V max = 0.8 f cu 5 At d from support: V Rd,ct = 0.12k(100 1 f ck )

1/3 V c = v c.bvd If V Rd,ct V Ed nominal links If Vc ct V, nominal links

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Links: A sw /s = V Ed /(0.9d. . f cd cot ) A sv /sv =1.05 b v(v-vc ) /f yv Nominal links: A sw /s 0.5 . f cd bw /f ywd A sv /sv 0.42b v /f yv

Understandably, these approaches are somewhat different although both methods are simpleenough to apply. One can see from the above formulae that when more than nominal links

are required, EC2 ignores any contribution from the concrete. The strut-and-tie method produces an additional tension in the main steel where the compression strut meets thissteel. This effect is catered for by applying the shift rule when detailing ( see Section 3 ).

2.8 Punching shear

The calculation of punching shear is basically similar to BS 8110, except that the control perimeter is at 2d , rather than 1.5d from the column face, and follows a locus from thecolumn face, rather than being rectangular in shape.

2d

1.5d

EC2 BS 8110

Basic control perimeter: At 2d at 1.5d Control perimeter shape: Rounded corners Rectangular

Flat slab shear enhancement factors Internal: 1.15 1.15

Edges: 1.4 1.4 or 1.25Corners: 1.5 1.25

When links are required, EC2 allows a contribution of 75% of the concrete shear resistance(unlike beam shear ), and a radial distribution of links is assumed. An outer perimeter, atwhich no further links are required, is based upon the link arrangement rather than the basic

control perimeter.

The much higher enhancement factor of 1.5 for corner columns may prove critical in somecircumstances, when sizing flat slabs for shear. However, the method as a whole seems verylogical and may result in fewer links and be simpler to detail than the BS8110 method.

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2.9 Span to depth ratios

EC2 BS 8110

Basic L/d ratios: K factors from Table 7.4 used inequations 7.14a & b From Table 3.9

Tension steelmodifier: In equations From Table 3.10

Compression steelmodifier: In equations From Table 3.11

Flanged sections: 1 1 0.2b w /b f /3 0.8 Interpolated between Table

3.9 values

Long span modifier:Only used if there are brittle partitions

Flat slabs: 8.5 /L 1Otherwise: 7 /L 1

10 /L 1

Service stress

modifier:310 / s (steel service stress)

Formulae included in Table

3.10

These two methods are very similar, but in practice, Eurocode 2 effectively allowsmarginally shallower members than BS 8110. This is likely to be because the EC2 ratioshave made no allowance for early age overloading during construction, which can increasethe degree of cracking, particularly in slabs.

2.10 Maximum bar spacing

For normal internal exposure, EC2 recommends a maximum crack width of 0.4mmcompared to 0.3mm in BS 8110. However, the maximum bar spacings in Table 7.3 aresomewhat less than those now commonly used in the UK. This will tend towards the use ofslightly smaller diameter bars in slabs. The actual calculation of crack widths to clause 7.3.4allows more flexibility.

2.11 Beam flange widths

To both codes, effective flange widths may be calculated directly from the distances between points of contraflexure, but the default values below give an indication ofcomparative values.

EC2 BS 8110

Effective span, spans:Simple supports, L End span, 0.85L

Internal span, 0.7L

Simple supports, L End span, 0.85L

Internal span, 0.7L

Effective span, supports: Cantilever, L.Others, 0.15L either side of support. Not applicable

Effective b f , T-beam:

[b 1 /5+L eff /10] Leff /5

plus [b 2 /5+L eff /10] Leff /5 bw+b 1+b 2 bw+L eff /5 bw+b 1+ b2

Effective b f , L-beam: bw+{[b 1 /5+L eff /10] Leff /5} bw+b 1 bw+L eff /10 bw+b 1 b1 and b 2 are the actual flange outstands on either side of the web


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It should be noted that EC2 requires a portion of beam support steel to be spread across thewidth of flange. This is why a method is also provided for assessing the widths of tensionflanges.

2.12 Flat slabs

For flat slabs, the two codes are almost identical, the relevant EC2 clauses having beendrafted in Britain. Slightly more latitude is suggested however, for the apportioning ofmoments between column strips and middle strips.

M t,max , the limit on moment transfer into edge/corner columns, is approximately 10% lowerthan for BS 8110.

2.13 ColumnsSome of the terminology in Eurocode 2 relating to column design may be slightlyunfamiliar, with minimum eccentricities being described under imperfections and

buckling etcetera falling within second order effects. Alternative design methods aregiven, but the curvature method is similar in approach to current practice. As with BS8110, the column design process is quite tedious to perform manually, but is relatively easyto automate. The simplified method given for carrying out biaxial bending checks is morelogical than in BS 8110, and is simple to apply.

A comparison between the EC2 and BS column design processes is shown in the flowcharts below.

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3 Detailing

3.1 General

EC2detailing rules are slightly more complex than for BS 8110. It will no longer be possibleto make simple assumptions, such 35 or 40 diameters for an anchorage length, andtechnicians will need to learn the necessary skills, as there are differing anchorage rules fordifferent types of member. There are also many small changes to be learned, such as thedetailing of beam support steel within flanges, minimum reinforcement percentages, andnew rules regarding the staggering of laps.

3.2 The shift rule

This is the recommended method for working out curtailment points for beam

reinforcement, which at the same time ensures the provision of sufficient steel near tosupports, to accommodate the additional tensile forces generated by the strut-and-tie shearaction described in 2.7.

Basically, the bending moment envelope is shifted a distance between 0.45d and 1.125d and bars should have an anchorage length beyond their relevant shifted point of being nolonger required.

4 Unfamiliar processes 4.1 Strut-and-tie models

The strut-and-tie method should be used for the design of D-regions, which are described asdiscontinuities in geometry or action . Some such discontinuities are frame corners,corbels, or abrupt changes in section. It is also important to note that this method is impliedwithin the shear design process described in 2.7 and 2.8 above.

7

Typical node model for a corbel

a c

a H H Ed

H Ed

F Ed

F wd

F td

F Ed

z 0d hc

Rd,max

2

1


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Although widely used in other European countries, this approach, while not being

particularly complex, will be unfamiliar to many designers in the UK, so both engineers andtechnicians are likely to require guidance.

5 EC2 overview

5.1 General

The areas covered by this document are not exhaustive; only what are considered to be themore important and commonly used procedures have been discussed. Eurocode 2 is a verycomprehensive code and also includes rules for precast concrete, post-tensioned membersetcetera, but the focus here has been on everyday insitu reinforced concrete design.

5.2 Code philosophyThe general philosophy of EC2 is quite different from that found in BS 8110. The Eurocodeis less empirical and more logical in its approach. For example, variables such as partialfactors for materials are shown within formulae, rather than being built in as part of anobscure number. If one wishes to go into greater detail, there are appendices to the code thatgive derivation formulae for items such as creep coefficients and shrinkage strains, whichare most helpful when attempting to automate the design process.

EC2 makes no attempt to be a design guide; it is a code giving general rules. There are nosimplified tables of moment or shear factors for example, as one would be expected to lookfor these in separate design guides or standard textbooks.

In my view, EC2 has great potential of being accepted as a very good replacement for BS8110. Inevitably there will be those who wish to resist any change, but I am sure that, afteran initial learning period, the superiority and economic advantages of EC2 will universallyrecognised.

5.3 What is needed?

To smooth the transition to EC2, the following tools will be required; preferably to beavailable before the predicted formal release of the new code in early 2003.

General design guides Worked examples A Concise EC2 A full set of design spreadsheets Comparative and calibration studies An EC2 version of Economic Frame Elements

Hopefully, specialist software houses can also be encouraged to update their programs indue time. Of prime importance will be the availability of updated finite element software, asmoments generated by programs written to the ENV version of EC2 will not be correct.


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5.4 Factors of safety

There has been recent discussion regarding comparative factors of safety between BS8110 and EC2 ( also CP49! ), which shows a massive misunderstanding of the basic

principles of limit state design.

A true factor of safety can only be determined by comparing design loading with that at collapse. Partial factors for materials and loading are not safety factors; they only reflect degrees of

confidence. Any basic understanding of statistics proves that to simply multiply together sets of factors or

probabilities is completely meaningless.

The economic advantages of EC2 for flexural design are far greater than can be assessed bylooking at the partial factors for loading and materials alone.

For similar characteristic loading, ULS loading can be 10% to 15% less.

Rebar design stresses are almost identical, in spite of the differing factor. The difference in pattern loading may marginally increase support moments but reduce span

moments. For the same concrete mix, EC2 gives a concrete stress 19.4% higher than BS 8110, which in turn

increases the lever arm z. More generous span-to-depth ratios can lead to shallower members.

These economies would seem very significant. Shear and column design do not appear tohave been trimmed in the same way, but this must reflect our increasing understanding ofconcrete design. Slabs are by far the most economically critical elements, and here there isadvantage.

9


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BubbleDeck VoidedFlat Slab Solutions

Technical Paper

BubbleDeck Design andDetailing Notes guidance toengineers and detailers

October 2007


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BubbleDeck - guidance to engineering designers and detailers

Engineering design

Generally:

The engineering designer should be very familiar with the principals of slab designand particularly flat slabs as well as having a good grounding in general structuralengineering.

It is recommended, as a minimum, to have read a general text on flat slab designand the appropriate sections of Concrete Society Technical Report TR43 [i] andTR58 [ii] (Note TR43 is specifically for post tensioned slabs but there is useful andrelevant material there). Essential reading also is Eurocode 2 [iii] at least thesections on flexure and shear, with particular reference to punching shear.

CIRIA Report 89 [iv] and 110 [v] are also important background reading (although thelatter is somewhat obsolete, it contains useful material).

The engineer wishing to explore in greater depth should read Nielsen [vi]. This isespecially useful text as Nielsen was an influential member of the EC2 draftingcommittee and to a large degree, was responsible for bringing the code up to datewith recent advances in plastic theory instead of reliance on outdated empiricalpractices and over-reliance on elastic methods.

It is also helpful to read through the various reports of testing and studies done onBubbleDeck Slabs in Europe.

All design work should be checked or reviewed by a competent person. It is notrecommended to rely on Local Authority Building Control Checking as somechecking engineers lack the specialised knowledge and experience to properly checkadvanced RC designs.

The analysis and calculation of resistances for BubbleDeck is much the same as for ordinary slabs except for some additional criteria. It is essential that the engineeringdesigner has an understanding of analytical manual methods, particularly yield linetheory, and an understanding of the principals and application of finite elementanalysis. In the latter case an understanding of linear elastic and non-linear methodsis necessary.

Material properties:

Shear:

The shear resistance of BubbleDeck is a slightly conservative value, taken fromtests, which we use in design: 0.6 times the shear resistance of a solid slab of thesame thickness. If this is exceeded by the applied shear, at a column for example,we leave out the balls and use the full solid shear values. Test conducted inGermany, Denmark and Holland have shown the resistance to vary from about 65%

to 90% of a solid slab.


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Flexure:

Standard strength parameters and properties are used as for solid slabs.

Deflection:

Span depth ratio calculations for deflections are very approximate and are notappropriate in flat slabs of irregular layout except for the most simple or unimportantcases. FE modelling, including non-linear cracked section analysis is used tocalculate the deflection using normal structural concrete with a Youngs Modulus(secant) E cm , multiplied by 0.9 (see above) and a tensile strength, f ctm multiplied by0.8 (to reduce the crack moment as mentioned above this is mainly significant inthe computation of uncracked curvatures where the geometry of the concrete sectionis significant but is of increasingly negligible significance after cracking).

It is not presently possible to calculate for the difference in age related properties in

the filigree and in-situ concrete parts. This is not considered to be a significantweakness.

Design methods:

Generally:

For ULS, elastic or plastic methods may be used to determine the applied actions.The engineer should, however, be aware of the fundamental differences between thetwo theories.

For flexural design, plastic theory may lead, in practice, to more efficient use of reinforcement. This is usually applied, in the case of slabs, by the yield line theory the most celebrated exponent of this being K W Johansson. Johansson [vii] publisheda comprehensive work on the practical use of yield line theory as well as his originalwork on the theory itself. Kennedy and Goodchild [viii] have published a useful andvery readable introduction to the use of yield line theory also. Yield line theory is avery powerful tool by virtue of the relatively simple procedures involved leading toeconomic reinforcement quantities. It is not without need for caution, however, andcare needs to be excercised not to overlook SLS concerns.

The main reason for the economy of yield line design is that collapse mechanisms

are found (usually in an upper bound analysis) that involve the whole, or a very largepart, of a reinforcement zone in yielding since it can be shown that the whole mustfail before the structure can fail globally (bearing in mind there may be many upper bound mechanisms that need to be checked). This is in contrast to elastic design,which usually results in a fairly heterogeneous moment field for which the designer attempts to fit a practical arrangement of reinforcement. In fact, Nielsen vi states thatthe elastic theory can lead to an optimal arrangement of reinforcement and, inaddition, that there is no philosophical objection to the use of plastic theory indesigning the reinforcement for applied actions determined from the elastic theory. Itis evident from this that the use of elastic theory and, in this particular context elasticmoment results for slabs, it is only significantly uneconomic if the designer is too un-conservative about how the moment result field is covered by the reinforcement

provision and if there is no allowance for yielding and redistribution.


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For example, FE results for a slab may show a small but irregular area of high designmoment. The designer may apply rebar to this in a rationalised zone, probablyrectangular, which actually extends over areas where the design moments are verylow. It would be possible, with appropriate experience and judgment to adjustdownwards the quantity of reinforcement so that it actually yields at the intensemoments and redistributes moment to the less utilised areas. This might be checkedby utilising a work equation in the same way as yield line design is carried out. It isobviously important to ensure that the work done, the dissipation, in yielding areinforcement zone balances the work done by the external loads. In anapproximation, one could check that the dissipation of the applied reinforcementexceeds that of the required reinforcement from the elastic results.

Codes and published methods often give weight to concepts of column strips andmiddle strips but these are usually difficult to apply in irregular slabs. TR43 givesguidance on this, for example, and suggests that the column strip is determined as0.4 of the distance from the column centreline to the zero shear line. Some methodsfurther divide the column strip into an inner column strips and outer column strips. It

is recommended in most UK practice to concentrate most of the reinforcement, say2/3 of that in the column strip in to the inner column strip so that the reinforcementprovision will be greatest where the service moments, tending to the elastic end of the spectrum, are greatest and thus where most needed to resist cracking and limitrotation contributing to deflection. To prevent absurd concentration of rebar, one maytake the reinforcement for the average moments for the inner column strip andprovide this for the full width of that strip.

Another phenomenon tending to produce in economy from yield line design is that itutilises the technique of allowing support and span moments to yield according to thereinforcement chosen in such a way that the relative quantities in the top of the slabat supports and in the bottom at mid-span are optimised to what is available andpractical.

There is, however, an important feature of yield line design that must not beoverlooked: It design for ULS only and assumes that a collapse mechanism can existwhich mobilises all the concrete and steel used. This implies that the slab issufficiently ductile in all respects and requires that steel can reach the strainsrequired without exceeding the ultimate strain and that the concrete does not crushor crack excessively. Furthermore, it does not check the conditions at SLS and if over-reliance is placed on ductility it can sometimes lead to excessive cracking if large rotations occur at SLS which cannot be accommodated by the rebar suppliedwithout large tensile strains in the concrete.

There may also be an important point to observe if excessive yielding occurs whereone relies on shear resistance punching shear at columns for example. Accordingto modified compression field theory, it can be shown that shear softening may besignificant.

This is where the advantage of FE analysis and design are most significant; even if linear elastic models are used (there are non-linear plastic FE methods in existencebut they are not widely used). Modern software is available which simulates non-linear behaviour, including the effects of cracking in an iterative process on theelastic stiffness method and these have been shown to give good results. Using

these tools, checks on the SLS behaviour, including cracking and deflection can becarried out as well as a ULS design indicating where yield limits may occur.


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The FE methods also have the advantage of combining all the static analyses andchecking into one process that can be efficiently managed.

Shear:

The shear resistance of BubbleDeck is taken as 0.6 times the shear resistance of asolid slab of the same thickness. If this is exceeded by the applied shear, at a columnfor example, we leave out the balls and use the full solid shear values. UsingEurocode 2 iii (or any other code for that matter, with slight differences) one maycalculate the applied shear at 2d and subsequent perimeters from the column faceas per the code requirements, as well as at the column face itself. This would then becompared to the calculated resistance.

. If the applied shear is less than the un-reinforced hollow slab resistance, no further check is required.

. If the applied shear is greater than the hollow slab resistance we omit balls andmake it solid then check the solid part.

. If the resistance is still greater than the solid slab resistance and less than themaximum allowed, we provide shear reinforcement.

All is exactly as solid flat slab design. Additionally one places bottom bars as per CIRIA report R89 iv, designed to protect against progressive collapse these barsmay be checked using Rasmussens dowel calculation so that they can sustain, say75% of the accidental limit state shear force.

Punching shear, in difficult or complex cases, may also be checked using methodsdescribed in Nielsen vi. Indeed it is always a good idea to check using more than onemethod or theory as this can expose anomalies or mistakes that must be checked.

In calculating the shear resistance care and judgment should be exercised inemploying formulae which include a scale factor. The scale factor in shear is real but,according to Regan iv, there is evidence that it is diminished if the aggregate is alsoscaled. It must be remembered that aggregates are often smaller for the smaller BubbleDeck slabs and thus it is prudent to set the scale factor to the value it wouldhave for a slab of 450mm thickness in EC2 this amounts to setting k = 1.7.

At edge and corner columns, as well as at eccentric loaded columns and transfer loads, torsion and moment capacity should be checked. Nielsen gives methods for this. The designer should be aware that the resistance of the slab at edge and corner columns may be governed by torsion and flexure as well as punching shear. In fact it

is possible that flexural/tensional resistance at edges and corners will make punchingshear calculations at these positions irrelevant.

If shear reinforcement is required, a conservative assumption is to design thereinforcement to sustain the entire shear without the concrete contribution. This willassist in avoiding complications with strain softening in intense shear situations at theexpense of slightly more shear steel.

The valid detail for the joint at columns or walls is to arrange the filigree to embedinto the columns or walls so that shear over the full section can be mobilised.Sometimes there will be requests for a joint around the column where the filigree

does not reach the face of the support usually by a distance of 40mm to 50mm this is highly undesirable and complicates the shear design and there is no validatedmethod of design. If the detail is unavoidable one may, with care, be able to design


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the section assuming the filigree to be ineffective near the column or wall but this willproduce a greatly reduced shear resistance. At some distance from the column, if theshear reinforcement elements are properly anchored in the filigree and in-situ parts(that is anchored outside the main reinforcement planes), it may be argued that thesection can be re-combined and the full section used for these outer perimeters. Thisleaves some scope for engineering judgment.

Punching shear reinforcement may take the form of purpose made rebar, studs or Lenton Steel Fortress, according to practical constraints. It is important to applythese properly and to pay attention to the anchorage requirements of any system.Shear heads may also be design for extreme situations and may be structural steelor rebar beams. ACI318-05 [ix] gives recommendations for the design of these.

Longitudinal shear is only critical at high rates of change of applied moments (whichis of course gives the maximum transverse shear). Within the span, the rate of change of moment tends to be less than close to the supports. The areas close tosupports are usually solid however, and the filigree is in compression, so the intensityof longitudinal shear near the supports is mitigated. If a check is necessary, EC2gives values for shear between concrete cast at different times as well as the methodfor calculating the applied shear (the change in moment divided by the distancebetween the section considered and the point of zero moment, on average). Thegirder webs may be taken into account in reinforcing the interface but only onediagonal in every pair unless otherwise can be justified due to the web angle.

Flexure:

A standard method may be used provided that the depth of concrete in compressiondoes not overlap the ball zone by more than 20%. This is almost always the case in

all but extremely heavily stressed slabs.

The maximum moments are usually over the columns or supports. This means thecompression is in the slab bottom here, and this is usually in a solid zone, so therestriction on the depth of compression need not necessarily apply at columns andsupports.

A rectangular stress distribution or other appropriate distribution may be used in theconcrete. EC2 contains a useful and simple method but other plastic methods maybe used.

Steel should be ductility class B, especially if plastic design is used, unless specialcalculations prove class A to be satisfactory. This should ensure that the yield strainlimit is not reached prematurely in the reinforcement.

The engineer should exercise a degree of judgment when interpreting the results of FE analysis, especially if it is a linear elastic analysis. There are many mathematicalanomalies that can occur which can distort the results one way or another.Singularities, for example, can occur at concave corners and point loads andsupports these lead to absurdly high design moments. Some software uses peaksmoothing algorithms and, if these are not available, manual averaging or takingmoment at the support face may be an expedient choice.

Even with cracked section iterative analysis, high concentrations of moment and/or


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torsion can occur in corners and, although this is a reflection of reality, they can leadto very high reinforcement requirements. In manual analysis, and indeed in yield linemethods, these peaks are averaged out by implied yielding. This is legitimateprovided always that the structure, or any substructure, is globally elastic at SLS andprovided that the rotations implied by the yielding do not lead to excessive cracking(and consequent increase in deflection), particularly at the top of the slab at columns.Excessive cracking here may also indicate that shear strength is compromised. For these reasons, it is recommended that the top tension steel is bunched toward thecentre of such supports such practice is mentioned in several codes and literature.

Deflection:

Span depth ratio methods are not recommended, except in checking andapproximate or relatively unimportant cases. FE analysis is recommended for allslabs as there is no practical manual method that can be used with confidence. Evenunidirectional spans can be very tedious in the computation of deflections.

Where accurate deflections are required, the software runs iteratively, calculatingmodified and cracked element properties at each stage of the iteration, using theapplied reinforcement, until convergence is reached. The deflection using thismethod has been shown to have good agreement with tests conducted at the ECBPat Cardington (see Concrete Society Technical Report TR 58 ii).

Short term loadings cases are usually patterned, subject to engineering judgment,(chequerboard or parallel strips depending on the characteristics of the project) usingthe Frequent Combination set out in Eurocode 0 and using combination factors y1as appropriate. For long term loading, the Quasi-permanent combination is usedwith combination factors y2 as well as creep coefficient and shrinkage curvature

parameters if necessary. Shrinkage curvature is generally of low order compared toextrinsic effects L/1500 has been quoted as an order of magnitude of the defectioncomponent due to this.

The combination factors now available in EC0 represent a statistical method of estimating which part of the imposed load is variable and which is invariable.

For simplicity, and where it can be justified, the engineer may estimate long termloadings using the total permanent load and 50% of the imposed load without greatloss of accuracy. This is likely to be good enough for most ordinary building projects.

Non-linear, iterative analysis can take a long time on complex or large slab modelsso it is not generally efficient to run such an exacting analysis on every slab andevery load case. Partial models can be constructed to model limited parts of slabsand reasonably good results can be obtained with the exercise of some prudence. Itis recommended to calibrate such partial models by comparing them to the full modelunder comparable conditions so that the approximation represented by the partialmodel can be validated. In a similar way, elastic results may be used as a broadapproximation provided they use a modified elasticity and that this is calibratedagainst a more rigorous analysis.

Creep and shrinkage have been shown by tests to be only marginally higher than a

solid slab of similar dimension. Due to the precision of serviceability calculations thissmall difference is usually ignored.


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Vibration:

RC slab structures are generally less susceptible to vibration problems compared tosteel framed and light weight skeletal structures, especially using thin slabs.

However, BubbleDeck is light and is not immune from vibration in all cases so thismust be checked just as it should be in appropriate solid slab applications.

Where deflections are large, as indicated by the static design, it is often an indicationthat the structure is sensitive to vibration SLS issues.

The lighter weight of BubbleDeck may be exploited if it can usefully alter the modalfrequencies of a slab generally raising them compared to a solid slab. The mosteffective weapons against vibration, particularly resonant vibration, are stiffness anddamping. If we consider damping to be similar to solid slabs, and concentrate onstiffness, we may observe that a BubbleDeck slab can provided over 2_ times the

stiffness obtained from a solid slab for the same quantity of concrete used. This canbe exploited in vibration sensitive applications.

At the present time, the static modification to the flexural stiffness is applied.However, future work may show that the static stiffness is not the same as theflexural stiffness in BubbleDeck slabs but the difference is thought to be minor compared to the effects of inaccuracies in modelling vibration problems.

TR43 i should be used for the procedures for determining vibration sensitivity andmodal superposition may used to determine the response for given excitation.

Fire resistance:

The fire resistance of the slab is a complex matter but is chiefly dependent on theability of the steel to retain sufficient strength during a fire when it will be heated andlose significant strength as the temperature rises. The temperature of the steel iscontrolled by the fire and the insulation of the steel from the fire. The degree to whichweakening of the steel is significant is related to the service stress at FLS.

The design then reduces to a determination of the combination of the amount of steeland amount of concrete cover to attain a balance of steel temperature and stress thatallows the structure to remain stable at FLS.

Advance or more complex design and analysis may include the determination of temperature profiles in the time domain, of cooling and the even effects of quenchingby fire fighting water.

A basic design may make use of the data tabulated in the BD technical manual for cover required for various fire resistance periods and steel stress. An analysis maybe carried out for FLS loading (roughly 0.7 of the ULS loading but this should becalculated according to EC2-1-2) and the applied moments obtained. This will allowthe designer to check various sections, using calculated moment curvaturerelationships, to determine the steel stress corresponding to the FLS moments.When these steel stresses are known they may be interpolated in the tabulated dataand cover or fire resistance thus estimated.


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A question that frequently arises concerns the pressure in the bubbles dur ingheating. Calculations have been carried out by Jrgen Breuning to show that this isnot a serious issue. In any case, all concrete is cracked and, in a fire, it is likely thatthe air would escape and the pressure dissipated.

If the standard bubble material is used (HDPE), the products of combustion arerelatively benign, certainly compared to other materials that would also be burning inthe vicinity. In an intense, prolonged fire, the ball would melt and eventually char without significant or detectable effect.

Seismic design:

This is a specialist area outside the scope of this brief technical note. However, theconcerns in Seismic design are largely similar to any flat slab structure.

Punching shear under seismic conditions is the most critical issue and damage at the

slab-column junction during sway reversals should be properly considered as well asamplification of the punching shear due to the vertical component of groundacceleration.

In computing the buildings response, the seismic designer should be closelyengaged with determination of the mass and the effect of this on modal spectrum.Using BubbleDeck a significant reduction of mass in the floor plate may be realisedtogether with an increase in modal frequency and reduction in the sway forces due tolateral acceleration.

Detailing:

BubbleDeck demands more from the detailer than normal flat slab design of thisthere is no doubt. The geometrical discipline required to coordinate the layering andspacing of factory fixed and site fixed rebar as well as the bubble module is far moredemanding and requires an attention to detail greater than ordinary detailing.

The BubbleDeck geometry is founded on the module size which, until recently,comprised 200mm, 250mm, 300mm, 350mm, and 400mm. Larger sizes have beenadded but the rules applying to the geometry still apply.

. The ball diameter is always 0.9 of the module. . The effective depth, except with heavy reinforcement may be approximated as

equal to the module. . The cover to the bubbles should be at least one ninth of the ball diameter.The cover to the bubbles and to the reinforcement may vary, of course, and this mayrequire adjustments to be made. Slightly more concrete that standard may be pouredto achieve a range of sizes intermediate to those imposed by the fixed module sizes.

The filigree or biscuit standard thickness is 60mm or 70mm depending on size of bottom steel. The bottom edges have a 6mm x 6mm bevel. At least two edges of every unit must have 25mm x 25mm bevel on the top to ensure that the splice bar has a filet of site concrete to seal it against attack by fire.

At a very early stage, the detailer should draft the sections to be used in a projectand verify the reinforcement geometry and especially the mesh spacing and girder


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size required.

Although the edge distance of the balls to the edge of the units, at internal edges thatwill be concreted, may follow the natural module; the cover to the bubble may beinsufficient at the outside of the slab so it may be necessary to leave out a row of

balls or otherwise plan the spacing with this in mind. Fixings are frequently made toedges of slabs so a slightly wider solid edge zone is often no bad thing.

Mesh will generally need to be custom mesh and it should be noted that machinemade meshes usually have one or more of the following restrictions:

. Max. bar size 16mm . Longitudinal bar spacing increments of 50mm c/c (eg 50mm / 100mm / 150mm /

200mm, etc.) . Min. distance from last bar to end 25mm . Cross wire spacing sometimes in 25mm increments but may be unrestricted

according to machine type.Girders are supplied in height increments of 10mm but some suppliers may supplyany size. The diagonals should be 63 approximately and must be welded securelyto the longitudinal bars (See CUR86 for a useful specification).

The standard girder spacing, as outlined in CUR86 is two balls maximum. Greater spacing than this is possible but the unit may be too flexible and crack more easilyduring transit or handling. The longitudinal girder bar should be 10mm minimum for the 200 and 250 modules and at least 12mm for 300 modules and above. The girder web bar may usually be 7mm or 8mm and 8mm is preferred except in lightapplications.

The section should be drafted so that the correct ball spacing is produced and so thatthe bubbles are restrained against movement laterally or vertically by at least twobars at the bottom and two bars at the top. It is usually sufficient to have two longbars in the bottom mesh controlling the position and two transverse bars at the top. Itis imperative that the ball cannot rise up more than a few millimetres when placed inthe casting bed. The top mesh should be low enough in the section to permit the topsite steel to be placed allowing for some tolerance.

The detailer should note that the ball will float up, during casting in the factory, until itis in contact with the closest top mesh bars. This means that the top mesh willusually control the height of the ball.

The top mesh does not usually fulfil an important function in the permanent state,except for an crack purposes, and is more significant in the temporary state (liftingand when spanning between props) when it has the important purpose of stabilisingthe top of the girder against lateral buckling. Clearly it also traps the bubbles in place.

Loose bars, not welded in the mesh, may be detailed to fit between the mesh bars,secured by tying wire, to achieve localised increases in steel area.

Splice bars are placed on top of the filigree and should be detailed so that they haveadequate clearance, spacing and anchorage. It will generally be more efficient to

provide more of smaller bars than few of larger ones. Anti-progressive-collapse barswill also pass through columns in two directions and lay directly on the filigree.


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Top site steel is detailed and placed in the normal way as for solid slabs. A heavyzone of steel will usually occur over columns with lighter steel on the column linesbetween these zones. In curtailing the top steel, it is advantageous to do so in a waythat does not result in the bars ending very close to a unit joint and thus complicatingplacement of splice mesh.

Where the top main site steel does not already form a top splice to the top mesh,narrow sheets of top mesh are used to lay over the joints to complete a continuoustop reinforcement.

All edges of the slab must be fitted with U-bars, whether they are support edges or not. This provides for the tensional resistance required at slab edges and thesatisfaction of the correct conditions for the development of the Kirchhoff boundaryforces. This is especially important near supports, like columns, and corners.

Shear reinforcement should be long enough to achieve correct cover top and bottombut must be anchored in the top and bottom steel zones. The lateral spacing shouldbe as close to 0.75 times the effective depth as practicable, but not greater. For radial arrangements of shear reinforcement, the circumferential spacing should besimilar in the case of the first element perimeter, which should be placed at amaximum of approximately 0.375 times the effective depth from the face of support.There will almost inevitably be conflict with the mesh and site steel and the spacingshould be varied by as small an amount as possible to clear this. In cases wherethere is doubt about the suitability of a position, and extra element may be placedadjacent.

To close the edge of the mesh and to provide transverse reinforcement to preventseparation of the filigree at the joints, the edges of the units should have 8mm hook

bars, along the edge, hooked around the bottom mesh and top mesh edge bars.

The mesh should be welded to the top and bottom of the girders and the weldsshould be sufficiently close together to resist pull-out from the filigree during liftingand should provide sufficiently close spacing to the top girder bar so that it does notbuckle when in compression. Triangular or three bar girders have better resistancebut are more difficult to install with sufficient space for the bubbles and other steel.

It is suggested that the welds between the mesh and the girders should be at amaximum spacing of 600mm spacing. The welds should not be too far apart as theymay allow the girder to pull out to easily from the filigree during lifting. They may also

provide insufficient restrain to the girder top bar which must be prevented frombuckling, especially when it is spanning across the props on site and supporting theconcrete pouring operation.

If fixings are to be made to the top of the slab when it is exposed to the weather, ahole should be drilled right through to enable trapped water to drain out.

References

[i] Technical Report 43, Post Tensioned Concrete Floors Design Handbook, TheConcrete Society.

[ii] Technical Report 58, Deflections in Concrete Beams and Slabs, The Concrete


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Society.

[iii] Eurocode 2 Eurocode 2: Design of concrete structures - Part 1-1: General rulesand rules for buildings, British Standards Institution.

[iv] CIRIA Report 89, Behaviour of Reinforced Concrete Flat Slabs, P E Regan,CIRIA, 1981.

[v] CIRIA Report 110, Design of Reinforced Concrete Flat Slabs to BS8110, CIRIA,Revised Edition 1994.

[vi] Limit Analysis and Concrete Plasticity, M P Nielsen, CRC Press, 2 nd Edition 1998.

[vii] Yield Line Formulae for Slabs, K W Johansson, Concrete Society

[viii] Practical Yield Line Design, Gerrard Kennedy and Charles Goodchild, BritishCement Association 1 st Edition 2003

[ix] ACI318-05, Building Code Requirements for Structural Concrete (ACI 318-05)and Commentary (ACI 318R-05)

BubbleDeck UK White Lodge,Wellington Road,St. Saviour,JERSEY, C.I.JE2 7TE

T: +44 (0)1534 725402F: +44 (0)1534 739115E: info@BubbleDeck- UK .comW: www.BubbleDeck-UK.com


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Appendix D Comments to Eurocodes 2


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Draft BD Annex to EC2

Bending:

Flexural or bending behaviour is elementary. Use the EC2 recommended procedures.

To avoid the situation that would exist if the depth of concrete in compression overlaps the ball zone, thedepth in compression must be limited so that the depth does not overlap by more than 20% of thecompression zone depth.

Deflection:

Methods:

Deflection is calculated from integration of curvatures or by software. If the latter is used, the engineer mustensure that the procedure either uses an appropriate procedure for cracked section analysis or useappropriate corrections to the modulus of elasticity.

The EC2 method for manual design closely resembles, and incorporates procedures for including the effectsof cracking and tension stiffening, methods developed by Branson and also Nielsen. It is proposed thatNielsens method and notation may be used as it is reasonably clear and concise.

In the case of two-way spans, the spans in each direction must be evaluated separately and then the resultscombined in a rational way.

Each span is divided into sections, usually equal lengths, and the curvatures computed for each from theexpression = M/EI. The curvature should be modified using Nielsens procedure, taking into account theratio of the cracking moment to the applied moment at the section. The curvatures at each section must thenbe integrated twice on the span to produce the deflected profile. A classic procedure for this is due toTimoshenko and the conjugate beam analogy may be used.

In the case of irregular plan forms and irregular spans, it is unlikely that hand methods will produce anythingbetter than an approximate estimate and computerised FE modelling will be necessary. FE Modelling using

non-linear and cracked section analysis has been shown to produce good results. Analysis using the grosssection properties must be avoided unless careful correlation of the equivalent elastic modulus is used. Anysoftware used must possess well documented explanations of the procedures used, must also have someform of validation and be obtained from a reputable company with appropriate quality assurance procedures.

Loading:

Slabs should be checked for long term and short term loading. Long term loading will normally be modelledby the application of a creep coefficient, and may include shrinkage curvature deflections, although the latteris usually of secondary magnitude. The creep coefficient should be determined with reference to the age artwhich the deflection is required but is will usually be of the order of 2.

The appropriate combination of loading in EC2, which refers to EC0 and EC1, for long term loading, is theQuasi-permanent combination. This requires the application of the full permanent load plus a proportion ofthe imposed load. Combination factors for the invariable part of the imposed load are given and these dependon the structures use they range generally from 0.3 to 0.7. However, since deflection calculations arenecessarily approximate, a combination factor of 0.5 may be applied to imposed loads without meaningfulloss of accuracy.

For short term loading, the Frequent combination is usually appropriate. Again combination factors aregiven to represent the variable parts of imposed loads and they again depend on the use of the structure.These may be applied to obtain an estimate of immediate deflection using short term material properties andloading on adjacent spans may be investigated if appropriate. It is important to note that the deflection due toimposed load only may not be obtained directly due to the non-linear effects of cracking so an analysis mustbe carried out for permanent and imposed load as well as permanence load only and the imposed loaddeflection obtained by subtracting one from the other.Deflection limits should be obtained wherever possible from the client or building user. However, theguidance on appropriate limits given in EC0 and EC2 may also be used.

Pre-camber may be specified to mitigate the effects of deflection. As a guide, such pre-camber should notnormally exceed Span/250 approximately.

It should be noted that large deflections, especially due to the permanent load alone, may indicate potentialvibration sensitivity that should be subject to a specialist investigation.


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References:

1. Enochsson, Ola & Dufvenberg, Peter - Concrete Slabs Designed With Finite Element Methods - LuleaUniversity of Technology.

2. Ferenc, Nmeth - Calculation of Reinforced Concrete Plates with non-orthogonal

reinforcement - Budapest, September, 1999

3. Eurocodes 0, 1 and 2.

4. Whittle RT - Design of reinforced concrete flat slabs to BS8110 - CIRIA Report 110 (2nd Ed. 1994)

5. Regan PE - Behaviour of reinforced concrete flat slabs - CIRIA Report 89.

10. Technical Report 43 - Concrete Society.

11. Technical Report 58 - Concrete Society.


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Appendix E Shear according to Eurocodes 2


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BubbleDeck International


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BubbleDeck International BubbleDeck International


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Appendix F BubbleDeck Standard Details


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Shear reinforcement Shear reinforcement

Princip Detail 08

Example of Intense Shear reinforcement above columnborn in element units


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Appendix G Examples


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Calculation Examples

1. Test 8 x 8

2. Millennium Tower

3. Shear

4. Project Ar up in Spain

5. Test 9 x 12

6. Parking

7. Steel

8. Moment Curves, India

9. Project Herstedlund in Denmark

10. Professor Kiss, Romania

11. Keops Project City Hall, Denmark

12. Deflection


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Example 1

Calculations

Dead load g = 4.50 kN/m2

Live load q = 20.0 -

----------------------

p = 24.5 kN/m2

Calculations are made with p = 1 kN/m2

x is measured from support

Model 1 max negative moment

per m width m,x = p (L x) 2 / 6

x = 0.0 m max m = 1 (4.2 0) 2 / 6 = 2.94 kNm/m

see figure 2 eff. B = 8.20 m

full B = 11.4 -with p = 24.5 kN/m2

we have eff. md = 2.94 * 24.5 * 11.4/8.2 = 100 kNm/m

Y10/125 m = 60 -

+ Y14/125 above col. see figure 2

area 2.4 x 2.4 m m = 120 * 2 * 2.4 / 8.2 = 70 -

ok, total m = 60 + 70 = 130 -

more than eff. md = 100 -

Max deflection

m is written at the form m,x = p L 2(1 x/L) 2/ 6

to be used in excel program for deflexion

moment- and deflexion are calculated in excel form

4 dead load

5 dead load plus imposed load

the calculation is executed with Y20 above columns regarding the deflections


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Example 1

2

Model 2

cantilever L = 2,0 m

per m width m,x = p (L x) 2 / 2

x = 0.0 m max m = 1 (2.0 0) 2 / 2 = 2.00 kNm/m

with p = 24.5 kN/m2

we have eff. md = 2.0 * 24.5 = 50 kNm/m

Y10/125 m = 60 -

+ Y14/125 above col. see figure 2

2 x 2.4 m m = 120 * 2 * 2.4 / 8.0 = 70 -

ok, total m = 60 + 70 = 130 -

more than eff. md = 50 -

Model 3Aas we here have only an example and it is obvious there will be no perceptible deviation

it is sufficient to regard only the simple part A (triangle) point forces at edge yielding is not

regarded

moment balance

simple moment m,0 * 6.4 = 24.5 * 6.4 * 4.7 2 / 6 = 577 kNm/m

m,0 = 90 -m = 24.5 * 2.0 2 / 2 = 50 -

max m = 90 50 = 40 -

Y10/125 m = 60 -


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Example 1

3

Model 4

It is directly seen:

The positive moment is obviously less than negative moment in model 1

The simple moment between columns is less than the real moment of the triangle figure

why regarding a 1.0 m strip between columns is sufficient

max m,0 = 24.5 * 5.0 2 / 8 = 76 kNm/m

less than the moment in model 3

Model 5

simple moment m,0 = 24.5 * 5.1 2 / 8 = 80 kNm/m

m1 = 24.5 * 2.0 2 / 2 = 50 -

m2 = 24.5 * 1.0 2 / 2 = 10 -

m = 80 (50 + 10) 0.5 = 50 -

Y10/125 m = 60 -


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Example 1

Model 6

the full yield line moment is less the individual yield line moments

At columns

Column 250 mm

load area max A = 4.1 * 4.1 0.5 * 4.0 (2.4 + 1.6) = 24.8 m2

load max P = 24.8 * 24.5 / 1000 = 0.61 MN

shear max = 0.61 / (0.25 + 0.28) 0.28 = 1.30 MPamore than

,d = 0.12 * * f,cd v = 2 / f,ck = 0.37 ,d = 0.12 * 0.37 * 20 = 0.84 ,d = 0.12 * 0.48 * 20 = 1,15 ?reinforcement necessary

shear strength

x = 0.25 + 0.28 P,u = 0.08 * 0.77 * 20 * (0.25 + 0.28) 0.28 E-3= 0.57 MN

0.08 * 4.22 = 0.34 = (gl)4.22 * 0.18 = 0.76 = (ny)0.76 * 0,08 = 0.06 = eff => 0.06 * 20 = 1.20 = > f,ct

facade and house end m = p a + p a 2 /2

corner m * 2a 2 = 2 * 2 p a * a 2 /2 + 2 p a 2 * a 2 /3

m = p a + p a 2 /3

less than m,fac.

4


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Vietnam / test A1 encl 5 corner

Moment & deflexion - 4,2 m cantilever - short term - working load

Moment is given by m,x = - P * 0,7 * L * (1-x/L) - p*L*L * (1-x/L) (1-x/L) / 6Curvature is estimated as m,x / EI,c if m,x < m,w

m,w / EI,c + 1,3 ((m,x-m,w) / EI,w) if < m,x / EI,w and if m,x > m,w

m,0 = 0,0 kNm EI,w = 0,0 Span L = 4,2 m Steel b.s. xxx mm2 xxxP = 0,0 kN/m EI,w = 17,0 MNm Height h = 280 mm Steel t.s. xxx0 mm2 xxx +

p = 25,4 kN/m2 EI,w = 17,0 MNm Colum 250 mm Steel t.s. 000 mm2 ( 00)m,w = 45,3 kNm EI,c = 41,0 MNm2 Concrete 30 MPa

section load mom. crack. mom. curvature increase inclination defl. increase deflection deflection correct

x / L (-) m,g+q/2 m,w (-) m/EI dv = dL* m/EI v (= Q,k) du=v*dL u =u,x+du u.korr.

kNm/m kNm/m 1/m E-3 E-3 E-3 mm mm mm

1 0.00 100.1 45.3 5.30 0.56 -0.56 -0.12 0.0 0.0

2 0.05 90.4 45.3 4.55 0.96 -1.51 -0.32 -0.1 -0.1

3 0.10 81.1 45.3 3.84 0.81 -2.32 -0.49 -0.4 -0.44 0.15 72.4 45.3 3.17 0.67 -2.99 -0.63 -0.9 -0.9

5 0.20 64.1 45.3 2.54 0.53 -3.52 -0.74 -1.5 -1.5

6 0.25 56.3 45.3 1.95 0.41 -3.93 -0.83 -2.3 -2.3

7 0.30 49.1 45.3 1.39 0.29 -4.22 -0.89 -3.1 -3.1

8 0.35 42.3 45.3 1.03 0.22 -4.44 -0.93 -4.0 -4.0

9 0.40 36.1 45.3 0.88 0.18 -4.62 -0.97 -4.9 -4.9

10 0.45 30.3 45.3 0.74 0.16 -4.78 -1.00 -5.9 -5.9

11 0.50 25.0 45.3 0.61 0.13 -4.91 -1.03 -6.9 -6.9

12 0.55 20.3 45.3 0.49 0.10 -5.01 -1.05 -7.9 -7.9

13 0.60 16.0 45.3 0.39 0.08 -5.09 -1.07 -9.0 -9.0

14 0.65 12.3 45.3 0.30 0.06 -5.15 -1.08 -10.1 -10.1

15 0.70 9.0 45.3 0.22 0.05 -5.20 -1.09 -11.1 -11.1

16 0.75 6.3 45.3 0.15 0.03 -5.23 -1.10 -12.2 -12.2

17 0.80 4.0 45.3 0.10 0.02 -5.25 -1.10 -13.3 -13.3

18 0.85 2.3 45.3 0.05 0.01 -5.26 -1.11 -14.4 -14.4

19 0.90 1.0 45.3 0.02 0.01 -5.27 -1.11 -15.5 -15.5 20 0.95 0.3 45.3 0.01 0.00 -5.27 -1.11 -16.6 -16.6

21 1.00 0.0 45.3 0.00 0.00 -5.27 -1.11 -17.8 -17.8

sum

0.0

20.0

40.0

60.0

80.0

100.0

120.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

load mom. (-) m,g+q/2 kNm/mcrack. mom. m,w kNm/m

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

curvature (-) m/EI 1/m E-3deflection u.korr. mm


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Example 2 Millennium Tower


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Example 4 Project Arup in Spain


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Note 1 10-5-2009

Spain Arup structural options

rough investigation of mutual proportions between deflexions between different columnsassumed same EI over all

model 2A length diagonal 1 diagonal 2 cross m2/m1 (L2/L1) 4

ca moment *) L 2 / 16 L 2 / 13 L 2 / 10 L 2 / 8

ca. deflection **) L 4 / 160 L 4 / 130 L 4 / 100 L 4 / 80

distance in m 16.2 20.1 14.3 11.8 17%

ratios m 430 1250 420 240 34%

in relation to cross 1.8 5.2 1.8 1.0

model 2C length diagonal 1 diagonal 2 cross

ca moment *) L 2 / 16 L 2 / 13 L 2 / 10 L 2 / 8

ca. deflection **) L 4 / 160 L 4 / 130 L 4 / 100 L 4 / 80

distance in m 16.2 22.0 16.9 14.8 35%

ratios m 430 1800 815 600 45%

in relation to cross 0.7 3.0 1.4 1.0

*) used likely moment ratios (only to adjust the pure L 4 ratios) but the conclusion is clear,the capacity of the deck is improved more than 100%.

**) based on mL 2 / 10


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Example 5 Test 9 x 12


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1

Example 5

TEST MODEL 340 mm BubbleDeck slab 9.0 x 12.0 m

Materials

Concrete f,ck = 35 MPa , f,cd = 35/1,5 = 23 MPaSteel f,yk = 500-550 MPa , f,yd = 500/1,2 = 420 -

Load

BubbleDeck 340 mm g 5.4 kN/m2uniform test load - up to q 10.0 -

--------------ultimate load p 15.4 kN/m2

Rough calculationBased on p as variable

Model A 9.0 x 12.0 m slabsupported on 4 columnsX direction = element direction

in Y-direction slab span L,y = 2.4 7.2 2.4 m

cantilever L = 2.5 mm = p * 2.4 2 / 2 = 2.9 p kNm/m

with p = 15.4 ultimate m = 15.4 * 2.9 = 45 kNm/mcovered by 2*3m Y12/150 m = 90 * 2 * 3.0 / 9.0 = 60 -regular top mesh is ignored

inner bay L = 7.2 mm,0 = p * 7.2 2 / 8 = 6.5 p kNm/m

m = 2.9 p -

m = 6.5 2.9 = 3.6 p -


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2

with p = 15.4 ultimate m = 15.4 * 3.6 = 55 kNm/m covered by Y12/150 m = 90 -

in X-direction slab span L,x = 1.8 5.4 1.8 m

cantilever L = 1.8 mm = p * 1.8 2 / 2 = 1.6 p kNm/m

with p = 15.4 ultimate m = 15.4 * 1.6 = 25 -covered by 2*3m Y12/150 m = 90 * 2 * 3.0 / 12.0 = 45 -

inner bay L = 5.4 mm,0 = p * 5.4 2 / 8 = 3.6 p kNm/m

m = 1.6 p -m = 3.6 1.6 = 2.0 p -

with p = 15.4 ultimate m = 15.4 * 2.0 = 30 kNm/m

covered by Y10/150 m = 60 -

Shear

column D = 300 mmload Q = 15.4 * 12.0 * 9.0 / 4 = 410 kNmassive = 0.41 / (0.3 + 0.34) * 0.34 = 0.60 MPahollow = 0.60 / 0.6 = 1.00 MPa

in distance 0.9m hollow

= 0.41 /

(0.3 + 0.6) 0.34 *0.6 = 0.70 MPa


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Example 6 Parking


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1 7

, 0

5 . 0

5 . 0

5 , 0

7 , 0

C o

l u m n s

i n g r i

d 1 2

. 0 x

1 2 . 0

m

M o

d e

l A

1 2 . 0

1 : 1

0 0

/

3 4 0 m m

d e c

k

B u

b b l e D e c

k I n t e r n a

t i o n a

l

J .

B r e u n

i n g

* C o n s u

l t

R s e v a n g e n

8

D K -

3 5 2 0 F a r u m

P h / f a x

+ 4 5 4 4 9 5 5 9 5 9


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Juni 2001

Parking Model A

390 mm BubbleDeck slab

J. BREUNINGConsulting EngineerRsevangen 8DK-3520 FarumTlf. + 45 42 95 59 59


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bubbledeck- ec 2 (tính toán)

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