Presentation from fib symposium Prague 2011. Keywords: shear, one-way slabs, effective widths

1. Shear in One-Way Slabs
Subjected to Concentrated Loads
Eva Lantsoght, Dr. Cor van der Veen, Prof. Joost Walraven
14-6-2011
Delft
University of
Technology
Challenge the future

2. Overview
• Background
• Design practice
• Previous research
• Experiments
• Results and discussion
• Shear span to depth ratio
• Comparison to EN 1992-1-1 and Regan’s method
• Conclusions
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3. Background
Design practice (1)
Beam shear, one-way shear Punching shear, two-way shear
• Design: shear capacity of slabs
• Flexural failure before shear failure
• Punching shear formulas
• Beam shear formulas over effective width
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4. Background
Design practice (2)
• One-way shear: beam shear
formulas
• Code formulas: empirical
• Most experiments:
• Beams
• Heavily reinforced
• Slender (a/d ≥ 2,5)
• Small size
• Concentrated load
amount of shear experiments done
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5. Background
Design practice (3)
45° load spreading 45° load spreading – French practice
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6. Background
Design practice (4)
• Effective width
• Assume uniform stress
• Maximum stress over effective
width
• Load spreading 45° for design
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7. Background
Design practice (5)
• Lower bound: 2d
• Loads closer to support:
• Smaller beff
• Smaller Vult
• In beams: direct load transfer
• Larger Vult
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8. Background
Previous research
• Limited amount of experimental data available
• Regan (1982):
• Tests at simple and continuous support
• Small slabs (1,6m x 1,2m x 0,1m): size effect?
• Conclusion:
• Increase in shear capacity with decrease in shear span
• More shear capacity at continuous support
• Small slabs: tests on larger scale needed
• Formula of Regan
• Subdivision of perimeter
• Different contributions to ultimate load
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9. Goals
• Assess shear capacity of slabs
under concentrated loads
• Determine effective width in
shear
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10. Experiments
Test setup
Size: 5m x 2,5m x 0,3m
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11. Experiments
Test setup
Continuous support, Line supports
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12. Experiments
Test setup
Load: vary a/d and position along width
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13. Results and discussion
Shear span to depth ratio (1)
• Decrease: smaller effective width
• Increase due to direct load transfer
• EC2: β = av/2d for 0,5d ≤ av ≤ 2d
• S3/S4 to S5/S6: capacity 2x
• β in MC 2010
Influence of the distance to the support
on the shear capacity of slabs?
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14. Results and discussion
Distance to support (2)
•Influence of distance to support on measured peak load
•Smaller increase than expected from EC2
•Different behavior for beams and slabs
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15. Results and discussion
Comparison to EC2 and Regan (1)
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16. Results and discussion
Comparison to EC2 and Regan (2)
• Eurocode: underestimates capacity slabs
• French national annex:
• Higher strength for slabs under point load (redistribution)
• Better estimate
• Systematically low predictions for high strength concrete
• Regan’s formula:
• Developed for shear in slabs under point load
• Based on punching shear perimeter
• Best prediction
Shear in slabs is not a fully one-way shear failure, a certain
amount of two-way shear distribution is possible
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17. Conclusions (1)
• Shear span to depth ratio
• Clear influence on capacity
• Smaller influence than for
beams
• Suggest different behavior
• French National Annex
• Better results
• Unsafe for high strength
concrete
• Regan: Best design tool S4T2 Dominant shear crack
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18. Conclusions (2)
• Recommendations:
• Moment distribution at support
• Higher minimum shear stress
for slabs
• Concentrated loads
• Transverse redistribution
• Direct load transfer
• Different behavior slabs vs.
beams
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19. Key message
Slabs under concentrated
loads behave differently in
shear than beams
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20. Contact:
Eva Lantsoght
E.O.L.Lantsoght@tudelft.nl
+31(0)152787449
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21. Experiments
Specimens
Slab fc’ fct ρl ρt a/d M/S Aload
(MPa) (MPa) (%) (%) (mm x mm)
S1 35,8 3,1 0,996 0,132 2,26 M 200 x 200
S2 34,5 2,9 0,996 0,132 2,26 M 300 x 300
S3 51,6 4,1 0,996 0,258 2,26 M 300 x 300
S4 51,7 4,2 0,996 0,182 2,26 S 300 x 300
S5 48,2 3,8 0,996 0,258 1,51 M 300 x 300
S6 50,6 3,9 0,996 0,258 1,51 S 300 x 300
S7 82,1 6,2 0,996 0,258 2,26 S 300 x 300
S8 77,0 6,0 0,996 0,258 2,26 M 300 x 300
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22. Experiments
Test results
Name SS/CS Pu (kN) Failure Mode
S5T1 CS 1804 Wide beam shear
S5T4 SS 1755 Wide beam shear
S6T1 CS 1446 Wide beam shear
S6T2 CS 1423 Wide beam shear
S6T4 SS 1366 Wide beam shear
S6T5 SS 1347 Wide beam shear
S7T1 SS 1121 Wide beam shear + Punching shear
S7T2 CS 1172 Wide beam shear + Punching shear
S7T3 CS 1136 Wide beam shear + Punching shear
S7T5 SS 1063 Wide beam shear + Punching shear
S8T1 SS 1481 Wide beam shear
S8T2 CS 1356 Wide beam shear
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23. Results and discussion
Comparison to EC2 and Regan
Test data Pu/VRdc Pu/VRdcmins Pu/PRegan
AVG STD COV AVG STD COV AVG STD COV
S1 – S8 1,941 0,210 0,108 1,018 0,141 0,138 1,128 0,122 0,108
S1 – S8, SS 1,933 0,193 0,100 1,014 0,131 0,129 1,178 0,115 0,098
S1 – S8, CS 1,952 0,240 0,123 1,024 0,161 0,157 1,067 0,105 0,098
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