shear and torsion in hollow core slabs
TRANSCRIPT
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!