Beton- und Volume 107 ISSN 0005-9900 Stahlbetonbau A …parsmangroup.com/uploads/downloads/Design...

9Volume 107September 2012, p. 590-600ISSN 0005-9900A 1740

Reprint

Beton- undStahlbetonbau

Design and construction of two-way spanning reinforced concrete slabs with flattened rotationally symmetrical void formers

Dipl.-Ing. Christian AlbrechtProf. Dr.-Ing. Andrej AlbertDr.-Ing. Karsten PfefferProf. Dr.-Ing. Jürgen Schnell

2 © Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin. Concrete and Reinforced Concrete Construction 107 (2012), Issue 9

DOI: 10.1002/best.201200027

TOPICChristian Albrecht, Andrej Albert, Karsten Pfeffer, Jürgen Schnell

Design and construction of two-way spanning reinforcedconcrete slabs with flattened rotationally symmetricalvoid formers

1 Introduction

Voided flat plate slabs enable a type of construction thatcan be more cost-effective than customary solid slabs dueto the reduction in the amount of material used andtherefore of the dead load. Reduction of the dead load al-so means that lower loads have to be introduced into thesubsoil which goes is associated with a variety of staticadvantages.

While one-way spanning voided flat plate slabs with con-tinuous void chambers have already been part of the priorart for some time, in recent years there has also been in-creasing use of two-way spanning voided flat plate slabs.Due to the bi-axial load transfer, these systems can also bemanufactured by the cast-in-place method and as a resultcan also be used for flexible horizontal plan shapes. Void-ed flat plate slabs are not included in the current codesand standards. General Technical Approvals can be usedin Germany as proof of suitability. So far, the only two-way spanning voided flat plate slab system with approvalis the “Eco-Line” system with spheres as void formers [2].This system is suitable for slab depths of 30 to 60 cm andhas already been presented here [1]. The “Slime-Line” sys-tem has now been developed so that slabs with a depthabove 20 cm can also be used. The load bearing ability ofthe system has been determined within the framework ofa research project funded by the AiF (Allianz IndustrieForschung = Industrial Research Alliance). Installation

and design engineering rules have been specified in addi-tion to design.

2 Manufacture and installation of the void formers

The void formers described in this article (Slim-Line voidformers) for reinforced concrete slabs differ in shape fromspherical void formers (Eco-Line void formers). However,both versions similarly have linear void former modulesconsisting of retaining cages with integrated void formers(Fig. 1). The retaining cages are made of reinforcementsteel and the void formers of recycled plastic (polyethyl-ene high-density, PE-HD or polypropylene, PP). Thesemodules are installed between the upper and lower rebarlayer for displacing the concrete using the cast-in-placemethod.

Hollow body systems are increasingly used for the realizationof lightweight, two-way spanning concrete slabs, resulting ineconomic and resource-efficient constructions. The specialstructural behaviour of these systems must be considered inthe design and construction. Experimental investigations arerequired in order to establish a safe design model. Numericalinvestigations can be used to model the tests can be modelledand carry out parametric studies. Simplifications and designtools enable a simple design and construction similar to that ofconventional reinforced concrete slabs. The level of safety re-quired by the building authority is met by considering the de-sign and detailing rules of two-way spanning concrete slabswith flattened rotationally symmetrical void formers.

Bemessung und Konstruktion von zweiachsig gespanntenStahlbetondecken mit abgeflachten rotationssymmetrischenHohlkörpernZur Realisierung von leichten, zweiachsig gespannten Deckenwerden Hohlkörpersysteme vermehrt eingesetzt, was zu einerwirtschaftlichen und ressourcenschonenden Bauweise führt.Bei der Bemessung und Konstruktion muss das besondereTragverhalten dieser Systeme berücksichtigt werden. Es wer-den experimentelle Untersuchungen notwendig, um ein abgesi-chertes Bemessungsmodell aufstellen zu können. Mittels nu-merischer Untersuchungen können die Versuche nachgerech-net und Parameterstudien durchgeführt werden. Vereinfachun-gen und Bemessungshilfen ermöglichen den Tragwerksplanerneine einfache Bemessung und Konstruktion analog der massi-ven Flachdecke. Bei Berücksichtigung der Bemessungs- undKonstruktionsregeln können zweiachsig gespannte Stahlbeton-decken mit abgeflachten rotationssymmetrischen Hohlkörpernauf dem bauaufsichtlich geforderten Sicherheitsniveau herge-stellt werden.

Fig. 1 Types of void formers Eco-Line (sphere) and Slim-Line (flat void former)Hohlkörpertypen Eco-Line (Kugel) und Slim-Line (flacher Hohlkörper)

reprint: Concrete and Reinforced Concrete Construction 107 (2012), Issue 9 3

Ch. Albrecht, A. Albert, K. Pfeffer, J. Schnell: Design and construction of two-way spanning reinforced concrete slabs with flattened rotationally symmetrical void formers

TOPIC

Installation of the void former modules is carried out ac-cording to an installation drawing to be prepared sepa-rately. The installation plan is prepared allowing for theformwork plans and the structural calculation. In addi-tion to details regarding the position of the void formersand the remaining solid zones, the laying plan also in-cludes installation instructions. The minimum permissi-ble distance between centres of the void former modulesmust be taken into account during installation.

This distance between centres is universally 35 cm for theSlim-Line type void formers. An appropriate installationaid must be used to ensure compliance with the minimumdistance between centres (Fig. 2). Attention must also bepaid to the specified void former grid. A staggered layoutof void formers is not permitted. A consistently orthogo-nal grid must rather be maintained. The void former mod-ules must be installed and fixed in such a way that it is notpossible for them to drift sideways and move during con-creting.

An imposed load or shifting stop on the formwork may beused as a countermeasure against the buoyancy effect ofthe void former modules during concreting. The normalprocedure, however, is to concrete the void former areasin two layers. Care must be taken, however, when pour-ing the first concrete layer to ensure that the lower longi-tudinal bars of the void former modules are covered withbetween 2 cm and 4 cm of concrete. It must be ensuredthat complete compaction is also achieved underneaththe void former by choosing an appropriate concrete con-sistency, a grading curve with a maximum grain of 16 mmand the number of compaction points. The first concretelayer fixes the void former modules in position after cur-ing in preparation for pouring of the second concrete lay-er. To guarantee the bond between the two concrete lay-ers in the construction joint, proof of a correspondingbond with reduced bond surface must be provided andarrangements must be made for joint reinforcement ifnecessary.

3 Special features of the design3.1 General

Until now, slabs in general structural engineering havebeen designed in Germany in accordance with DIN-1045-1 [7] and since July 2012 in accordance with EC2[9]. Neither of these standards include the design of slabswith rotationally symmetrical void formers. Although it ispossible to refer to the rules for ribbed slabs when design-ing voided flat plate slabs, this leads to less cost-effectiveresults. In addition, the distance between centres of thevoid formers has to be increased in order to ensure theminimum bridge widths to be maintained.

It is necessary when using the voided flat plate slabs toanalyse the various failure modes and set up the designconcepts. Table 1 shows an overview of the design’s spe-

Fig. 2 Template to assure axis-centre distanceAnwendung einer Einbauhilfe für die Sicherstellung des Achs-abstandes

Table 1 Overview of special features of the design of hollow core slabsÜbersicht der Besonderheiten bei der Bemessung von Hohlkörperdecken

Failure type Restriction Illustration

Bending Reduced flexural compression zone if required

Shear force Reduced load bearing ability

Global punching Solid zones required

Local punching Restriction of concentrated load

Shear force transfer in manufactured construction joint

Reduced bonding surface

4 reprint: Concrete and Reinforced Concrete Construction 107 (2012), Issue 9


cial features. The individual approaches and possible so-lutions for designing the individual failure modes are de-scribed below.

3.2 General considerations with regard to load bearingbehaviour

It may generally be assumed that the load transfer of void-ed flat plate slabs is comparable to that of customarystructural engineering slabs. Although the reduced loadbearing ability of specific percentage contact areas mustbe taken into account without exception, this does notpresent structural engineers with any great challenge ifmodified design equations are used. The shape of the ro-tationally symmetrical void formers described here givesrise to interstitial spaces which lead to a spatial loadtransfer. This can be seen in Fig. 3. In horizontal plan andsection, it can be seen why designing the void formers us-ing the equations for the ribbed slab is very conservative.When designing ribbed slabs, only the “bridge” betweenthe void formers is taken into account. In actual fact,however, the entire remaining cross-section contributesto the load transfer. The crack surface of a shear forcefailure indicates the slab type’s spatial load transfer.

3.3 Bending

Usually the customary design aids, such as the kd or ωmethod, can be applied for the rectangular section forbending dimensioning of the slabs. However, as with T-beam cross-sections, one must check whether the com-pression zone height in the ultimate limit state is higherthan the area free from void formers. If this is the case, itis cost-efficient to take the compression zone between thevoid formers into account.

3.4 Shear resistance

The complex shear load bearing behaviour of the floorslabs had to be investigated experimentally. The tests

were conducted at Kaiserslautern University of Technolo-gy and are described in Section 5.2. In this case, the re-taining cages were not installed. Although the retainingcages have a positive effect on the shear resistance, an-choring of the cages is not comparable to the secured an-choring forms in accordance with [7] and [9] which is whythis percentage contact area which is on the safe side isdisregarded. By means of the tests, it was possible to de-termine the ratio of the shear resistance of the voided flatplate slab to that of a solid slab so that the design can beeffected in accordance with EC2, equation 6.2a [9] allow-ing for a reduction factor.

3.5 Global punching

Solid zones must be formed both near to columns and also on the margins of the voided flat plate slabs. The dimensions of the solid zone must first be specified forthe punching calculation. The solid zone must be selectedlarge enough that it is possible to verify the reduced shearresistance of the adjacent void former areas. Specifiedminimum dimensions ensure that the size of the solidzone is no smaller than the punching critical area of a sol-id slab. The punching calculation of the solid zone is thenconducted in accordance with EC2, Section 6.4 [9] withor without punching reinforcement.

3.6 Local punching

Local punching of the reflected ceiling plan above thevoid formers represents a special feature of the voided flatplate slabs. Due to the geometry of these areas, thepunching calculation in accordance with EC2 [9] doesnot lead to any realistic design which is why tests werecarried out here too, cf. Section 5.3. Based on the tests, itis possible in the ultimate limit state (ULS) to demon-strate design loads up to FEd = 10 kN on a minimum con-tact area of 10 × 10 cm2 even with a minimum reflectedceiling plan height of 5 cm and a concrete of strengthC20/25. A design equation is currently being developedfor local punching of the voided flat plate slabs.

Fig. 3 Section, horizontal plan and crack surface of hollow core slabs (void formers high 220 mm)Schnitt, Grundriss und Rissfläche bei Hohlkörperdecken (Hohlkörperhöhe 220 mm)



TOPIC

3.7 Bond resistance

For demonstration of the concreting joint, it is recom-mended to use the equation in accordance with EC2, Sec-tion 6.2.5 [9] in which the bond area must be reduced. Sofar no meaningful tests have been carried out for thiswhich is why initially, as a conservative assumption, thecomplete base area of the void formers in the projectionmust be deducted. The retaining cage may be estimatedfor the bond resistance if demonstration of anchoring issuccessful in accordance with [9].

4 Design rules

The solid zones statically required are specified duringthe course of design (Section 3). Consideration must alsobe given to constructional requirements when designingand when preparing the layout plans for the void formermodules (Fig. 4). These requirements will be summarisedsubsequently. In general, consideration must be given tothe required distances between the void former modulesand other building elements and assembly parts duringdetailed design and implementation.

Void formers must not be arranged above the supports ofthe slab to be created. A constructive solid zone at leastas wide as the distance between centres of the void form-ers must additionally be provided to the side of the sup-port’s edge (Fig. 5). In the case of Slim-Line void formers,this corresponds to a constructive solid zone of 35 cm tothe side of the support’s front edge. A solid zone as wide

as slab thickness h must be accomplished in the case ofrecesses and free slab edges.

5 Experimental investigations regarding the shearforce and local punching shear behaviour

5.1. General

Tests were carried out regarding the shear resistance andlocal punching to determine the load bearing abilities.The minimum and maximum concrete strengths aimedfor were tested in both test series. Void formers with thelargest and smallest available void former height wereused for the tests.

Fig. 4 Solid zones and void former areas in drawing and on siteMassivbereiche und Hohlkörperbereiche im Plan und bei der Ausführung

Fig. 5 Accomplishment of a constructive solid zoneAusführung eines konstruktiven Randstreifens



5.2 Experimental determination of the shear resistance

The aim of the tests was to determine the shear resistanceof the voided flat plate slabs in the most unfavourable in-stallation situation. For this purpose, the void formers –as already described in Section 3.4 – were installed with-out the retaining cages which meant that the positive ef-fect of the retaining cages on the shear resistance lying onthe safe side was disregarded. The height of the upper re-flected ceiling plan in the tests was 45 mm which corre-sponds to the minimum thickness of the upper reflectedceiling plan aimed at of 50 mm minus an allowance of5 mm. Thus, the tests were carried out with the minimumachievable percentage shear force contact area of theconcrete pressure zone. In addition, the distance betweencentres of the void formers among themselves was also re-duced by an allowance of 5 mm although in practice thevoid formers are fixed in position by the retaining cages.The width of the specimens was chosen as b ≥ 4 h in or-der to test a slab.

The specimens were designed in such a way that theshear force failure occurred in a previously defined zonedue to the distances between the supports and the loadtransfer. It was possible to carry out two tests with onespecimen which saved material and time when conduct-ing the tests (Fig. 6).

So that realistic quantities of longitudinal rebars could beinserted in the specimens, threaded bar anchor steelSt 900/1100 with rib rows and a diameter of 15 mm was

chosen. The slightly higher relative rib area of the steelbars was taken into account. The longitudinal rebar wasdimensioned in such a way that a ratio of Mflexural failure/Mshear force failure ≈ 1.2 was present in the reference tests.The tests with minimum and maximum concrete strengthwere carried out with the smallest and largest void form-ers respectively. Each combination was tested three timeswith void formers and once without void formers as a ref-erence test. This resulted in a total of twelve tests withvoid formers and four reference tests.

The tests showed that failure of the voided flat plate slabsis comparable to failure of the solid slabs. Fig. 7 shows anexample of the cracking pattern. Failure of the specimenswith void formers occurred less abruptly by comparisonwith the reference tests.

For designing the shear resistance of the voided flat plateslabs tested, a reduction factor f for the solid slab shouldbe determined in accordance with EC2, equation 6.2a [9](cf. equation (5.1)):

(5.1)

For comparison with the experimental ultimate loads, themean value of the shear resistance was calculated whereγc = 1.0 and the actual building element width bw. A pref-actor 0.2 (cf. [5], re 10.3.3) and the mean concrete com-pressive strength were also assumed. The mean shear re-

V C ·k· · f k · ·b ·dRd,c Rd,c l ck cp w(100· )13

1ρ σ= +⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

Fig. 6 Longitudinal and cross-section of the specimens using the example of the void formers 100 mm highLängs- und Querschnitt der Versuchskörper am Beispiel der 100 mm hohen Hohlkörper



TOPIC

sistance can therefore be calculated according to equa-tion (5.2), wherein the factor f for the reference tests is1.0:

(5.2)

The reduction in the shear force of each individual test isthen calculated according to equation (5.3):

(5.3)

As the concrete compressive strengths were tested on dry-stored cubes and the design equation for the shear forcedesign calculation is based on concrete compressive

V f · · k · · f · b · dRm,c,cobiax l cm w0,2 (100 · )13ρ=

fV

VV

· k · · f · b · d

u

Rm,c

u

l cm w0,2 (100 · )13ρ

= =

strengths in wet-stored cylinders, it was necessary to con-vert the concrete compressive strengths for evaluation ofthe limit loads – see equation (5.4):

(5.4)

Conversion from cube compressive strength to cylindercompressive strength was carried out by means of a lineartrend line according to the concrete strengths in EC2,Table 3.1 [9]. Conversion from dry to wet stored cylindercompressive strengths was carried out in accordance withDIN 1045-2, Section 5.5.1.2 [8] with a factor of 0.92.

The test results in Tables 2 and 3 clearly show a differencebetween the tests performed with small and large voidformers. The mean value of the factor f is 0.69 for thetests with 100 mm high void formers and 0.52 with the220 mm high void formers. All factors f are above 0.5 ex-cept for test V-Q-22-20-2. It was possible to attribute thelower shear resistance of this test to a concreting error. Itmay be assumed that all intermediate sizes will deliverbetter results than the tests with the large void formers(220 mm). The difference as regards reduction of theshear resistance can be accounted for by the fact that theconcrete pressure zone in the tests with the higher voidformers was reduced much more significantly than in thetests with the flattened void formers due to their position.

Based on the experimental investigations, the shear resist-ance of voided flat plate slabs can be calculated accordingto equation (5.5):

(5.5)

f · f · ff

cm cm,dry c,cube,dry

c,cube,dry

0,92 0,92 (0,7953 0,0003· )·

·

= = +

V f · C · k · · f · b · dRd,c,cobiax Rd,c l ck w(100 · )13ρ=

Fig. 7 Sheared off specimens in the “Bridge” and in hollow body axis afterthe failure (void formers high 220 mm)Aufgesägter Versuchskörper im „Steg“ und in Hohlkörperachse nachdem Versagen (Hohlkörperhöhe 220 mm)

Fig. 8 Floor plan of the specimens of series 1 with load introduction surfaces on top and bottom (left) and experimental setup of the series 2 (right)Grundriss der Versuchskörper der Serie 1 mit Lasteinleitungsflächen auf Ober- und Unterseite (links) und Versuchsaufbau der Serie 2 (rechts)



In this case systematic compressiveforces should be disregarded and sys-tematic tensile forces should be ruledout. At the same time, the prefactor fmay be specified as a function of thevoid former height or as a uniform fac-tor taking the most unfavourable testsinto account. Factor f can be takenfrom the General Technical Approvalafter it has been granted.

5.3 Experimental determination of the local punching resistance

Point loads with small contact areasmay arise in both the as-constructedcondition, e.g. due to formwork sup-ports, and also during the useful life.The upper reflected ceiling plan abovethe void formers must be designed insuch a way that local punching is ruledout. Until now there have been no de-sign rules for local punching with thepresent geometry which is why 88small tests have been carried out forthis. The specimens were designed insuch a way that no reinforcement steellay inside the punching cones.

Two test series were carried out (Fig.8). Test series 1 with an upper reflectedceiling plan without nominal stressesand test series 2 with an upper reflect-ed ceiling plan under one-way span-ning tensile stresses in state II.

The following parameters were variedduring the test series:

– Concrete quality (C20/25 and C45/55)

– Reflected ceiling plan height abovevoid former (ccb = 2 to 12 cm)

– Load transfer area (Aload = 5 × 5 cm2

and 10 × 10 cm2)– Void former height (hHK = 100 mm

and 180 mm)

In test series 1, several tests were car-ried out on the top and bottom of aspecimen. The position and form ofthe load transfer was also varied at thesame time. In test series 2, a bendingmoment was applied by means of steeltongs prior to the vertical load whichled to rupturing of the upper reflectedceiling plan. The aimed-for tensilestress in the longitudinal rebar was300 N/mm².Ta

ble

2Ev

alua

tion

of th

e te

sts

with

100

mm

hig

h vo

id fo

rmer

sAu

swer

tung

der

Ver

such

e m

it 10

0 m

m h

ohen

Hoh

lkör

pern

S-1

00M

ean v

alue*

*

C20

/25

C45

/55

Info

rmat

ion

Des

ig.

Unit

V-Q

-10-

20-1

V-Q

-10-

20-2

V-Q

-10-

20-3

V-Q

-10-

20-4

V-Q

-10-

45-1

V-Q

-10-

45-2

V-Q

-10-

45-3

V-Q

-10-

45-4

Voi

d fo

rmer

––

S-1

00S

-100

S-1

00w

ith

out

S

-100

S-1

00S

-100

wit

h o

ut–

Sla

b w

idth

b[m

]1.

041.

041.

041.

041.

041.

041.

041.

04–

Sta

tic

hei

ght

d[m

]0.

160.

160.

160.

160.

160.

160.

160.

16–

Reb

ar p

erce

nta

geρ l

[–]

0.00

740.

0074

0.00

740.

0074

0.00

950.

0095

0.00

950.

0095

–

Sh

ear

forc

es fr

om c

ylin

der

and

load

str

uctu

reV

u1(V

u1,R

ef)

[kN

]13

1.86

120.

9512

5.93

189.

8815

9.69

150.

5215

4.48

247.

44–

Sh

earf

orce

from

dead

load

ΔV1

[kN

]–0

.30

–0.3

0–0

.83

0.22

–0.3

0–0

.30

–0.8

30.

22–

Sh

ear

forc

es in

co

llaps

ed s

tate

Vu

(Vu,

Ref

)[k

N]

131.

5612

0.65

125.

1019

0.09

159.

3915

0.22

153.

6524

7.65

–

Cyl

inde

r co

mpr

essi

ve

stre

ngt

h (

from

tes

t cu

be)

f cm

[N/m

m2 ]

21.7

121

.71

21.0

921

.09

49.5

949

.59

49.5

949

.59

–

Mea

n s

hea

r re

sist

ance

of

sol

id s

lab

VR

m,c

t[k

N]

169.

0616

9.06

167.

4216

7.42

242.

1124

2.11

242.

1124

2.11

–

Fact

or f

*f =

Vu/V

Rm

,c–

0.78

0.71

0.75

(1.1

4)0.

660.

620.

63(1

.02)

0.69

**F

acto

rs f

corr

espo

nd

to t

he

quot

ien

t of

max

imum

sh

ear

forc

e in

th

e te

sts

and

the

calc

ulat

ed m

ean

sh

ear

resi

stan

ce o

f a s

olid

sla

b**

Mea

n v

alue

of f

acto

rs f =

Vu/

VR

m,c

exce

pt fo

r th

e fa

ctor

s of

th

e re

fere

nce

tes

ts



TOPIC

Fig. 9 shows a punching cone and asawn-open specimen after the test. Itcan clearly be seen that the punchingcone runs tangentially along the voidformers starting at the outer edge ofthe load transfer. It becomes obviousin Fig. 10 how high the achievablepoint loads are. In most cases in prac-tice, it is sufficient to limit the designload in the ultimate limit state toFEd = 10 kN for a contact area of atleast 10 × 10 cm. In view of the test re-sults, this value is well on the safe side.For all other cases, a design conceptthat included the geometry and con-crete strength must be developed.

6 Numerical investigationsregarding the shear load bearingbehaviour

6.1 General

Alongside the large-scale tests, physicalnon-linear FEM calculations on solidmodels were carried out at BochumUniversity using the DIANA software[6]. It was possible use the calculationsto realistically map the load bearingand deformation behaviour. The vol-ume elements employed, CHX 60 with20 nodes, and the laws of material be-haviour used corresponded essentiallyto the models described in [1] for theinvestigations regarding shear resist-ance. To reduce the computing effort,the calculations were performed onslab strips having a sixth of the actualspecimen width. The input variablesfor the selected fracture mechanicsmodels were determined based onlarge-scale test, in material tests and intheoretical considerations. The accura-cy of the calibrated computationalmodels rendered it possible to conducta parameter study on the influence ofinstallation variants which made itpossible to reduce the number of time-consuming and expensive large-scaletests.

Compared to the investigations on re-inforced concrete slabs with sphericalvoid formers described in [1], in thegrid generation of the “Slim-Line” typevoid formers, element shapes arise inwhich the included angles between theelement edges are sometimes very flat.Fig. 11 illustrates the FEM model of anembedded void former of the “Slim-Ta

ble

3Ev

alua

tion

of th

e te

sts

with

220

mm

hig

h vo

id fo

rmer

sAu

swer

tung

der

Ver

such

e m

it 22

0 m

m h

ohen

Hoh

lkör

pern

S-2

20M

ean v

alue*

*

C20

/25

C45

/55

Info

rmat

ion

Des

igU

nit

V-Q

-22-

20-1

V-Q

-22-

20-2

V-Q

-22-

20-3

V-Q

-22-

20-4

V-Q

-22-

45-1

V-Q

-22-

45-2

V-Q

-22-

45-3

V-Q

-22-

45-4

Voi

d fo

rmer

––

S-2

20S

-220

S-2

20w

ith

out

S-2

20S

-220

S-2

20w

ith

out

–

Sla

b w

idth

b[m

]1.

381.

381.

381.

381.

381.

381.

381.

38–

Sta

tic

hei

ght

d[m

]0.

310.

310.

310.

310.

310.

310.

310.

31–

Reb

ar p

erce

nta

geρ l

[–]

0.00

570.

0057

0.00

570.

0057

0.00

740.

0074

0.00

740.

0074

–

Sh

ear

forc

es fr

om c

ylin

der

and

load

str

uctu

reV

u1(V

u1,R

ef)

[kN

]19

8.92

171.

3919

4.34

383.

3727

0.52

249.

2625

3.27

498.

12–

Sh

earf

orce

from

dead

load

ΔV1

[kN

]2.

192.

190.

224.

272.

192.

190.

224.

27–

Sh

ear

forc

es in

co

llaps

ed s

tate

Vu

(Vu,

Ref

)[k

N]

201.

1117

3.59

194.

5638

7.63

272.

7125

1.45

253.

4850

2.39

–

Cyl

inde

r co

mpr

essi

ve

stre

ngt

h (

from

tes

t cu

be)

f cm

[N/m

m2 ]

22.7

622

.76

24.4

024

.40

42.7

542

.75

46.0

246

.02

–

Mea

n s

hea

r re

sist

ance

of

sol

id s

lab

VR

m,c

t[k

N]

365.

3236

5.32

373.

8837

3.88

490.

1449

0.14

502.

3150

2.31

–

Fact

or f

*f =

Vu/V

Rm

,c–

0.55

0.48

0.52

(1.0

4)0.

560.

510.

50(1

.00)

0.52

**F

acto

rs f

corr

espo

nd

to t

he

quot

ien

t of

max

imum

sh

ear

forc

e in

th

e te

sts

and

the

calc

ulat

ed m

ean

sh

ear

resi

stan

ce o

f a s

olid

sla

b**

Mea

n v

alue

of f

acto

rs f =

Vu/

VR

m,c

exce

pt fo

r th

e fa

ctor

s of

th

e re

fere

nce

tes

ts



Line” type without and with concealed edges. The influ-ence of the element’s shape on the numerical stability ofthe models and the influence of the number of elements,the iteration method, the convergence criteria and con-vergence accuracy, the number of iterative steps per loadstep and the load step width were investigated during anextensive convergence study. The result of this was that,compared to the calculations of the “Eco-Line” type vol-ume element models, a finer grid division is necessarywith a correspondingly increased number of iterativesteps per load step in order to achieve reliable calculationresults with the desired convergence accuracy even inhigh load steps.

6.2 Modelling of the shear resistance

A realistic simulation of the cracking pattern in the con-crete is particularly important for a numerical simulationof the shear load bearing behaviour. This is because it hasa significant effect on both the system’s overall stiffnessand also the shear force failure itself. The cracking pat-tern was recorded via the theoretical model of the“smeared” crack model. The cracks are not mapped dis-cretely in this model but rather as dilatation in the ele-ment. The fracture energy and the crack bandwidth arecrucial for a realistic description of the tension softeningof the concrete elements without reinforcement. The frac-ture energy is described via the descending branch of theσ-ε relationship after exceeding the dilatation at maxi-mum centric tensile strength in the element. In this case,the increasing dilatation in the element corresponds in re-ality to the increasing crack opening. The fracture energyis the energy required for complete crack opening and re-sults from the integral via the descending branch of the σ-ε relationship. It depends essentially on the granularstructure, the grain size and the concrete’s tensile strengthand is assumed according to the computation formula-tions in [4]. The crack bandwidth is a dimension from thecrack bandwidth theory according to [3] and describesthe area of strain softening of a cross-section duringcracking under tensile stress. It is necessary to establishthe crack bandwidth in order to prevent the tension soft-ening from being grid-dependent. It defines the damagedarea in the direction of the main tensile stresses in the el-ement. It is usually meaningful to determine the crackbandwidth as a function of the element volume. In thepresent case, however, manual determination of the crackbandwidth is more constructive due to the partly severedistortion of some elements.

It was possible to describe the tension resistance perpen-dicular to the crack with adequate accuracy using the ma-terial models explained. In reality, the shear stiffness re-maining due to aggregate interlock in the cracking orien-tation is determined by the crack opening and thereforealso by the size of the building element and the kinemat-ics of the cracked system. In the FEM simulation, this ef-fect is recorded by a reduction in the shear modulus (andtherefore also of the elastic shear stiffness defined as a

Fig. 9 Punching cone and sawed testing specimen after loading on top andbottomAusbruchkegel und aufgeschnittener Versuchskörper nach einer Belastung auf der Ober- und Unterseite

Fig. 10 Failure loads Fu as a function of the ceiling height mirrors ccb (series 1and 2)Bruchlasten Fu in Abhängigkeit von der Deckenspiegelhöhe ccb(Versuchsserien 1 und 2)

Fig. 11 FE-Model of the embedded void former of the „Slim-Line“ type used for the numerical simulation of the shear bearing behaviourFE-Modell eines eingebetteten Hohlkörpers vom Typ „Slim-Line“ für numerische Berechnungen zum Querkrafttragverhalten



TOPIC

product of the shear module and the cross-sectional area)using a shear retention factor. Due to the reduction in theshear stiffness of cracked elements, the stresses are redis-tributed leading both in the test and also in the numericalsimulation under increasing load and cracking to loadtransfer via a tied-arch model. The investigations carriedout showed that a reduction in the shear stiffness to anamount between 5–10 % of the shear stiffness arisingfrom state I as a function of the slab cross-section and ofthe void former geometry delivers appropriate results.Fig. 12 illustrates the excellent agreement between thestiffness curve and ultimate loads of test series V-Q-10-45and the results of the FEM calculation based on load-dis-placement curves. The results of the numerical simula-tions regarding the test program are summarised inTable 4.

7 Summary and outlook

Voided flat plate slabs cannot be designed without addi-tional considerations in accordance with Eurocode 2.The shear force in particular had to be determined exper-imentally. This article documents relevant tests conduct-ed at Kaiserslautern University of Technology to deter-mine the shear resistance of voided flat plate slabs of the“Slim-Line” type. The tests were successfully simulated atBochum University using the finite element method withthe result that it is now possible to examine other installa-tion configurations with the help of parameter studies.

Reduction factors which will enable a shear force designcalculation in accordance with the verification format ofEurocode 2 are being specified within the framework ofan ongoing approval procedure at the Deutsches Institutfür Bautechnik [German Institute of Structural Enginee-ring]. A General Technical Approval should then also in-

clude design rules which, similarly to the “Eco-Line” sys-tem, enable the slab system to be used safely in practice.

The punching resistance of the reflected ceiling planabove the void formers was also tested in an additionalseries of tests. These tests confirmed that the design loadsup to 10 kN usually occurring in structural engineeringcan easily be transferred with a minimum contact area of10 × 10 cm2.

Acknowledgement

The authors would like to thank the Federal Ministry ofEconomics and Technology (BMWi) for sponsoring theproject via the funding module for cooperation projectswithin the framework of the research programme “KeyInnovation Programme for Medium-sized Companies”.

Fig. 12 Load-displacement diagram of test series V-Q-10-45 and according diagram obtained from the FE-simulationLast-Verformungskurven der Versuchsreihe V-Q-10-45 zur Querkraft-tragfähigkeit im Vergleich zur numerischen Berechnung

Table 4 Results from experimental tests and FE-simulations – Investigation of the shear force capacityVersuchs- und Berechnungsergebnisse – Untersuchungen der Querkrafttragfähigkeit

Shear force [kN] Deflection under load transfer [mm]

Test Test FE calculation Test/FE** Test FE calculation Test/FE**

V-Q-10-20-1 132 9.2V-Q-10-20-2 121 130 0.97 8.8 9.3 0.94V-Q-10-20-3 126 8.3

V-Q-10-45-1 160 7.8V-Q-10-45-2 151 149 1.04 8.8 7.9 1.11V-Q-10-45-2 154 9.8

V-Q-22-20-1 199 6.8V-Q-22-20-2 171* 204 0.96 6 8.3 0.79V-Q-22-20-3 194 6.8

V-Q-22-45-1 271 8.5V-Q-22-45-2 249 248 1.04 6.5 6.5 1.15V-Q-22-45-3 253 7.5

** Due to a concreting error – not taken into account for quotient of test and FE** Quotient of the mean value of the test results and the result of the FE calculation


References

[1] ABRAMSKI, M.; ALBERT, A.; PFEFFER, K.; SCHNELL, J.: Expe-rimentelle und numerische Untersuchungen zum Tragver-halten von Stahlbetondecken mit kugelförmigen Hohlkör-pern. Beton- und Stahlbetonbau 105 (2010), Heft 6, S. 349–361.

[2] Allgemeine bauaufsichtliche Zulassung Z-15.1-282: Hohl-körperdecke System „COBIAX“, DIBt, Berlin, 2010.

[3] BAŽANT, Z. P.; OH, B. H.: Crack band theory for fracture ofconcrete. Materials and Structures, RILEM, 93 (16), S. 155–177, 1983.

[4] Comite Euro-International du Beton: CEB-FIP Model Code1990. London: Thomas Telford Services Ltd., 1993.

[5] DAfStb Heft 525: Erläuterungen zu DIN 1045-1. Beuth-Ver-lag, Berlin, 2. überarbeitete Auflage 2010.

[6] DIANA User’s Manual, TNO DIANA, Delft, Release 9.4.42012.

[7] DIN 1045-1-1:2008-08: Tragwerke aus Beton, Stahlbetonund Spannbeton Teil 1: Bemessung und Konstruktion.Beuth-Verlag, Berlin, 2008.

[8] DIN 1045-2:2008-08: Tragwerke aus Beton, Stahlbeton undSpannbeton – Teil 2: Beton – Festlegungen, Eigenschaften,Herstellung und Konformität – Anwendungsregeln zu DINEN 206-1. Beuth Verlag GmbH, Berlin, 2011.

[9] DIN EN 1992-1-1:2011-01: Eurocode 2: Bemessung undKonstruktion von Stahlbeton- und Spannbetontragwerken– Teil 1-1: Allgemeine Bemessungsregeln und Regeln fürden Hochbau. Deutsche Fassung EN 1992-1-1:2004 +AC:2010, Beuth Verlag GmbH, Berlin, 2011.

Autoren

Dipl.-Ing. (FH) Christian AlbrechtTechnische Universität KaiserslauternFachgebiet Massivbau und BaukonstruktionPaul-Ehrlich-Straße67663 [email protected]

Prof. Dr.-Ing. Andrej AlbertIfBF – Institut für Beton- und Fertigteilbau GmbH & Co. KGAn-Institut der Hochschule BochumLennershofstraße 14044801 [email protected]

Dr.-Ing. Karsten PfefferCobiax Technologies GmbHOtto-von-Guericke-Ring 1065205 [email protected]

Prof. Dr.-Ing. Jürgen SchnellTechnische Universität KaiserslauternFachgebiet Massivbau und BaukonstruktionPaul-Ehrlich-Straße67633 [email protected]

Beton- und Volume 107 ISSN 0005-9900 Stahlbetonbau A …parsmangroup.com/uploads/downloads/Design...

Documents

Transcript of Beton- und Volume 107 ISSN 0005-9900 Stahlbetonbau A …parsmangroup.com/uploads/downloads/Design...