Shear and Torsion in Hollow Core Slabs

Shear and Torsion in Hollow Core SlabsHolcotors

A European research project

• European Commission• International Prestressed Hollow Core

Association • Bundesverband Spannbeton-Hohlplatten

• Castelo• Consolis• Echo• A. Van Acker

Financiers and collaboration partners

• Strängbetong• VTT• Chalmers

Shear and Torsion in Hollow Core Slabs

Karin LundgrenAss. ProfessorChalmers

Helén BrooPh.D. StudentChalmers

Björn EngströmProfessorChalmers

Matti PajariD.Sc. (tech.)VTT

Project started January 1, 2002 and ended December 31, 2004

Aim of the project• To use the capacity of the hollow core slabs

better• To develop methods to design for combined

shear and torsion in hollow core slabs– Single units– Whole floors

Practical cases where torsion appears

Concentrated load

Large openings

Skew ends.

Support on three edges

Alternating position of columns at slab ends.

Trimmer beam

Shear Torsion

Web shear tension failure Torsion failure

Combined shear and torsion in a hollow core unit

Design method used today (EN 1168):• Cracking means failure• Only crack in web is considered• One critical point• Stresses are added linearly

Torsional moment T

Shear V

Shear Torsion Interaction?

=+

45° Kritisk punkt

h/2

h/2

z Critical point

Tests on hollow core units loaded in shear and torsion

Q

Q

l = 7.0 m

QBeam element

Strands

FE model of hollow core unit

Concrete in compression

εc

σc

Concrete in tension

σc

εc

Steel in tensionσs

εs

Bond-slip relationshipτ

δ

Comparison of results• Maximum load• Load versus deflection• Failure mode• Crack pattern

Maximum load in test [kN]

Maximum load in analysis [kN]

10 %

10 %

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

ST400ST200

Comparison of results

0

50

100

150

0.0 1.0 2.0 3.0 4.0 5.0Η [mm]

Q [kN]

FEA

Test b

Test

Q/2 Q/2

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Coordinates [m]

δ [mm]

FEA Q = 86.3 kN

Test Q = 100.0 kN

Test b Q = 98.1 kN

Tests and FEA Q = 50.0 kN

Q/2 Q/2

Comparison of results

0

50

100

150

200

0.0 1.0 2.0 3.0 4.0 5.0 [mm]

Q [kN]

Q/2 Q/2

Test E1M

FEA E1M Test E1

FEA E1

δ

0

50

100

150

200

250

300

0.0 2.0 4.0 6.0 8.0◊ [mm]

Q [kN]

Test E1M

Test E1

FEA E1

FEA E1M

Q

δ [mm]

Thin plastic sheet

Mortar bed

Neoprene

Effect of neoprene

1091870

1037 1093

Strand

Concrete

Neoprene

ST400E1 Web 5

0

50

100

150

200

250

0.00 0.10 0.20 0.30

Microstrain [-]

Load [kN]

El 870El 1037El 1091El 1093

ST400E1-Web 4

0

50

100

150

200

250

0.0 2.0 4.0 6.0Displacement [mm]

Load [kN]

Critical section for shear tension crackin 400 mm unit

Cracking starts here 45°

45°

Critical point

h/2

h/2

z

Analytical model FE-analysis, pure shear

Conclusions FE-analyses of HC-units• FE-analyses of tests are able to capture

the overall behaviour:– Failure mode– Maximum obtained load– Crack pattern– Vertical deflections (until first crack)

• Large difference in capacity due to support condition

FE analyses to establish interaction diagram

x

0 1 2 3 4

A’B’ C’

B

A

C

'

'

'

Cy

Cy

By

By

Ay

Ay

δδ

δδ

δδ

=

=

=

x

y z

V T

0

50

100

150

0 100 200 300 400

T [kNm]

V [kN]

0

50

100

150

0 100 200 300 400

T [kNm]

V [kN]

EN 1168

Interaction diagram for 400 mm unit

0

10

20

30

40

50

60

0 50 100 150 200

T [kNm]

V [kN]

Interaction diagram for 200 mm unit

EN 1168

FE model of hollow core floor

Tie beam modelled by tyings

Interface elements to model joints

Beam elements to model single hollow core units

Reduced torsional moment

Design of hollow core slabs

Structural analyses Resistance analyses

FE-model for hollow core unit

V-T capacity

Analytical method in EN1168

V-T capacity

FE-model for floor M, V and T

Distribution diagram (α-factors) in EN 1168 M, V and T

FE-model for floor integrated with FE-model for hollow core unit Load capacity

Trad

ition

al

desi

gnIm

prov

ed d

esig

n

IV

III

II

I

<

<

<

Test on hollow core floor

Tie beam

Reinforcement

EN 1168

FEA

Designing a floor – Design level III and II

0

50

100

150

200T [kNm]

0 100 200 300 400V [kN]

1000

6000Q = 357 kNQ = 449 kNQ = 521 kN

-200-100

0100200300

0 2 4 6

V [kN] T [kNm]

z [m]

V

T

Q/2 Q/2

Simulation of a floor test – Design level I

0

100

200

300

400

500

600

0 1 2 3 4

δ [mm]

Q [kN]

Test

X

Y

Z

FE: Qmax= 480 kN

Test: Qmax= 521 kN

Design level

Floor, design example

0

100200

300

400500

600Qmax [kN]

III II I

Experiment 521 kN

EN 1168T

V

FEA

T

V X

Y

Z

357 kN

449 kN 480 kN

Conclusions

• Modelling methods for hollow core slabs weredeveloped– Hollow core floor ⇒ Sectional forces M, V and T

• Reduced torsional moment• Arbitary geometries and loadings

– Hollow core unit ⇒ Shear-torsion capacity• Higher resistance

• The capacity of the hollw core units can be used better

Thanks!