Ingenieurbüro für Tragwerksplanungund Bauberatung

Load bearing behaviour of prestressed hollow core slabs on flexible supports

Technical Seminar in Aachen 26./27.10.2011

Dr.‐Ing. Thomas Roggendorf

2

slim-floor-constructionshollow core slab

integrated floorbeam (IFB)

head plate

column

3

flexible supports

section 1-1

middle slab edge slab

transversebending

shear deformation andtransverse bending

4

contents

• experimental investigations

• numerical investigations

• data base and design model

• experimental investigations

5

determination of the shear resistance on rigid supports

(DIN EN 1168, annex J)

reference tests

6

full-scale tests

edge slab

tie rods

ring beam

concrete grout

7

• reduced composite behaviour• surrounding ring beam

• modified slabs without outer hollow cores• filling of hollow cores after appr. 3 hrs

test parameters

• beam stiffness• bearing details

• filling of outer hollow cores• horizontal constraints in transverse direction

slab typesA: hsl = 265 mm; bw /bsl = 0,28B: hsl = 250 mm; bw /bsl = 0,40

1

2

3

4

5

6

7

8

8

test results (1)sh

earf

orce

vfl[

kN/m

]

deflection u [mm]

9

test results (2)

no. slab parametershear resistanceon rigid supp. vr

[kN/m]

shear resistanceon flex. supp. vfl

[kN/m]

vfl/vr

[-]

beam deflection u

[mm]

10

contents

• experimental investigations

• numerical investigations

• data base and design model

11

calibration of material parameters

reference tests

plane of symmetry

slab A

slab Bsh

earf

orce

vr[k

N/m

]

deflection u [mm]

tests slab Atests slab B

slab

slab

slab

12

full-scale tests

calibration of composite behaviour

shea

rfor

cevf

l[kN

/m]

deflection u [mm]

test 2

tests 3,4

load cyclesbeam

plane ofsymmetry

edge slablongitudinal joints

bearing surface

slab

slab

IFB

13

tensile damage dt [-]

normal stressσz [N/mm²]

-15,0

-6,0

3,0

0,01

0,3

1,0

load bearing behaviour (1)

+

+

-

-

y

z

(0 ≤ dt < 1,0)

• main impact transverse shear

14

• without friction in the bearing surface no transverse shear• remaining impact transverse bending (“vierendeel-effect“)

load bearing behaviour (2)

tensile damage dt [-]

normal stressσz [N/mm²]

-15,0

-6,0

3,0

0,01

0,3

1.0

y

z

(0 ≤ dt < 1,0)

15

influence of the beam stiffness

dt [-]

0,01

0,3

1,0

• considerable increase in beam stiffness necessary to increase the shear resistace

• effects of flexible supports also occur on apparently stiff beams

vfl/

vr

slab Aslab B

(slab A)

16

contents

• experimental investigations

• numerical investigations

• data base and design model

17

test data base• 31 tests (Finland und Germany)• slab thickness hsl: 150-500mm• beam span Lb: 3,6 -10,0m

vfl/

vr

18

test data base• 31 tests (Finland und Germany)• slab thickness hsl: 150-500mm• beam span Lb: 3,6 -10,0m

prestressed concretePC T-section with profiled webPCU T-section with plane web

reinforced concreteRC T-section with cast in-situ topping

pate

nted

com

posi

te

sect

ions

vfl/

vr

steelWQ cap-sectionIFB IFB-section

compositeDE DELTA-beamLB LB-beamLBL LBL-beamA A-beamSUP SUPER-beamMEK MEK-beam

19

design model

full composite action at low load levels(uncracked joints)

reduced composite action at the ultimate limit state (cracked joints)

20

impacts on flexible supports

transverse shear

transversebending

outermostweb

21

cross section idealised as framework (vierendeel-beam)

determination of inner forces

• analytical determination of inner forces due to tranverse shear c possible ⇒ τxz,c, τzy,c

• inner forces due to transverse bending depend on unknown bedding properties in thebearing surface

22

transverse bending

Platte A

Platte B

vfl/

vr

slabslabslabslab

slabslabslabslab

23

wsl

slcompc,xzfc,xz bI

SVmk μβτ =

sl

eff,slc,xz b

hk

21

=

xw

compc,zyfc,zy lb

Vmk μβτ23

=

)2(23

31

33

33

fl,sleff,slj,wsl

fl,sleff,slj,wslc,zy hhnbbn

hhnbbk

+

+=

3

31

sl

q,sl

b

bfv b

EIEILk β+=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅−⎟⎟

⎠

⎞⎜⎜⎝

⎛−−⋅−

+⋅

= cppc,zyvct

xctxct

c,xzfcompsl

wslbw,R k

fff

mkSbIV a τατσσ

μβ

22 1

)1(

transverse shear (analytically)

transverse bending

equations

compVc μ=

24

calibration

• recalculation of 21 tests until (vfl /vr)cal = (vfl /vr)exp ⇒ μ

• composite action after cracking of the joints important

• except for beam types PC and SUP uniform μ - values

PC

contact surfaces under pressure

slab thickness hsl [mm]

mod

el p

aram

eter

µ[-]

25

design example (1)slab 1

Loads

• self weight of slabs: g = 4.9 kN/m²• additionional dead load: Δg = 0.5 kN/m²• service load: q = 2.8 kN/m²

beam: HEA 400 section (fyk = 355 N/mm²)

Lsl = 12 mVRd,ct = 122.4 kN/m² (according constr. approval)

Lb = 6.2 mE = 210000 N/mm²I = 45070 cm4

=> vEd,slab = 12/2 x (1,35 x [4.9 + 0.5] + 1.5 x 2.8) = 68.9 kN/m

=> Med,beam = 2 x 68.9 x 6.2² / 8 = 662 kNm

σs = 662 / 45070 x 200 x 10² = 294 < 355/1.15 = 309 N/mm²

u = 5/384 x 2 x 12/2 x (4.9 + 0.5 + 2.8) x 6.2 4 / EI = 2 cm

(corresponding to ≈ L/300)

vRd,ct,fl = 70.6 kN/m (58 %)(≈ vEd)

26

design example (2)main parameters of the shear resistance vRd,ct,fl

• cross section of the slab (especially hsl and EIsl,q/bsl3)

• share of Δg and q on the total load(e.g. Lsl = 8.0 m => vRd,ct,fl = 60.4 (49 %) < 70.6 (58 %) (vEd,Δg+q,max = 33.9 ≈/> 30.9)

• beam stiffness / beam span (EIb/Lb3)

(e.g. Lb = 5.1 m => vRd,ct,fl = 78.6 (64 %) > 70.6 (58 %) (Lb/u ≈ 500)

• beam type(„rough“ surface => vRd,ct,fl = 57.6 (47 %) < 70.6 (58 %)

27

parametric study

slab 1

slab 2

0,0

0,2

0,4

0,6

0,8

1,0

0 250 500 750 1000 1250

V Rd,c

t,fl/V

Rd,ct

[-]

beam span / deflection Lb/u [-]

βf = 1,0

0,0

0,2

0,4

0,6

0,8

1,0

0 250 500 750 1000 1250

V Rd,c

t,fl/V

Rd,ct

[-]

beam span / deflection Lb/u [-]

slab 1, = 5mslab 1, = 7,5mslab 2, = 8mslab 2, = 12m

βf = 0,7

Lsl

Lsl

Lsl

Lsl

28

experimental investigations

• shear resistance ratios vfl /vr between 0,52 - 0,78 (shear tension failure)• shear resistance determined by shear deformations of the edge slabs• no clear influence of the beam deflection in the range from Lb /100 - Lb /200

summary

numerical investigations

• premature failure attributable to transverse shear and transverse bending• significant increase in beam stiffness necessary to enhance the shear resistance• effects of flexible supports also occur on apparently stiff beams

data base and design model

• 31 tests from Finland and Germany available • design model based on the load bearing at the ULS (cracked joints)• transverse shear considered analytically and transverse bending empirically