modified bond model for shear in slabs under concentrated loads
TRANSCRIPT
Challenge the future
DelftUniversity ofTechnology
Modified Bond Model for shearin slabs under concentrated loads
Eva Lantsoght, Cor van der Veen, Ane de Boer
2
One-way vs. two-way shear (1)
Beam shear, one-way shear Punching shear, two-way shear
• Punching shear over perimeter• Beam shear over (effective)
width
3
One-way vs. two-way shear (2)
• 3D representation of failure modes
4
Beam Shear Failure
• Since 1899 (Ritter)• 1955: collapse of
warehouse
• Most experiments:• Beams• Heavily reinforced• Small size• Slender (a/d ≥ 2,5)
• Basis for design codes
amount of shear experiments done
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Punching Shear Failure Categories of methods for punching shear
Shear stress Beam analogy
Strut and tie Plate theory / FEM
The nature of shear failure is still not fully understood!
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Slab bridge under live loads
7
Bond Model (1)
• Alexander and Simmonds, 1990
• For slabs with concentrated load in middle
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Bond Model (2)
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Modified Bond Model (1)
• Adapted for slabs with concentrated load close to support
• Geometry is governing as in experiments
• Determine factor that reduces capacity of “radial” strip
• Maximum load: based on sum capacity of 4 strips
10
Unequal loading of strips
• Static equilibrium• v2,x reaches max before
v1,x
'1, 0.1667x c
av f d
L a
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Loads close to free edge
Edge effect: when length of strip is too small to develop loaded length lw
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Comparison to experiments
Comparison between experimental results and (a) Modified Bond Model, (b) ACI 318-11 code, (c) NEN-EN 1992-1-1:2005.
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Comparison to experiments
AVG STD COV
Vexp/VACI 2,67 1,00 37%
Vexp,EC/VR,c 1,99 0,27 13%
Pexp/PMBM 1,33 0,14 11%
• Eurocode: increasing conservativism for higher capacities• MBM: follows 45º line better
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Summary & Conclusions
• Slabs under concentrated loads • Transition between one-way and
two-way shear
• Bond Model for concentric punching shear
• Modified Bond Model corresponds well to test results
