Engineering:Concrete cone failure
Concrete cone is one of the failure modes of anchors in concrete, loaded by a tensile force. The failure is governed by crack growth in concrete, which forms a typical cone shape having the anchor's axis as revolution axis.
Mechanical models
ACI 349-85
Under tension loading, the concrete cone failure surface has 45° inclination. A constant distribution of tensile stresses is then assumed. The concrete cone failure load [math]\displaystyle{ N_0 }[/math] of a single anchor in uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors is given by:[2]
[math]\displaystyle{ N_0 = f_{ct} {A_{N}} [N] }[/math]
Where:
[math]\displaystyle{ f_{ct} }[/math] - tensile strength of concrete
[math]\displaystyle{ A_{N} }[/math] - Cone's projected area
Concrete capacity design (CCD) approach for fastening to concrete
Under tension loading, the concrete capacity of a single anchor is calculated assuming an inclination between the failure surface and surface of the concrete member of about 35°. The concrete cone failure load [math]\displaystyle{ N_0 }[/math] of a single anchor in uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors is given by:[2]
[math]\displaystyle{ N_0 = k \sqrt{f_{cc}} {h_{ef}}^{1.5} [N] }[/math],
Where:
[math]\displaystyle{ k }[/math] - 13.5 for post-installed fasteners, 15.5 for cast-in-site fasteners
[math]\displaystyle{ f_{cc} }[/math] - Concrete compressive strength measured on cubes [MPa]
[math]\displaystyle{ {h_{ef}} }[/math] - Embedment depth of the anchor [mm]
The model is based on fracture mechanics theory and takes into account the size effect, particularly for the factor [math]\displaystyle{ {h_{ef}}^{1.5} }[/math] which differentiates from [math]\displaystyle{ {h_{ef}}^{2} }[/math] expected from the first model. In the case of concrete tensile failure with increasing member size, the failure load increases less than the available failure surface; that means the nominal stress at failure (peak load divided by failure area) decreases. [3]
Current codes take into account a reduction of the theoretical concrete cone capacity [math]\displaystyle{ N_0 }[/math] considering: (i) the presence of edges; (ii) the overlapping cones due to group effect; (iii) the presence of an eccentricity of the tension load. [4]
Difference between models
The tension failure loads predicted by the CCD method fits experimental results over a wide range of embedment depth (e.g. 100 - 600 mm).[2] Anchor load bearing capacity provided by ACI 349 does not consider size effect , thus an underestimated value for the load-carrying capacity is obtained for large embedment depths.[2]
Influence of the head size
For large head size, the bearing pressure in the bearing zone diminishes. An increase of the anchor's load-carrying capacity is observed . Different modification factors were proposed in technical literature.[5][6]
Un-cracked and cracked concrete
Anchors, experimentally show a lower load-bearing capacity when installed in a cracked concrete member. The reduction is up to 40% with respect to the un-cracked condition, depending on the crack width.[7] The reduction is due to the impossibility to transfer both normal and tangential stresses at the crack plane.
References
- ↑ 1.0 1.1 Cook, Ronald; Doerr, G T; Klingner, R.E. (2010). "Design Guide For Steel To Concrete Connections". University Of Texas Austin.
- ↑ 2.0 2.1 2.2 2.3 Fuchs, Werner; Eligehausen, Rolf (1995). "Concrete Capacity Design (CCD) Approach for Fastening to Concrete". ACI Structural Journal 109 (January): 1–4. ISSN 0889-3241.
- ↑ Ožbolt, Joško; Eligehausen, Rolf; Reinhardt, Hans-Wolf (1999). "Size effect on the concrete cone pull-out load". International Journal of Fracture 95: 391–404. ISSN 03769429.
- ↑ ACI (2004). "ACI 349.2 Guide to the Concrete Capacity Design ( CCD ) Method — Embedment Design Examples". Concrete (Ccd): 1–77.
- ↑ Ožbolt, Joško; Eligehausen, Rolf; Periškić, G.; Mayer, U. (2007). "3D FE analysis of anchor bolts with large embedment depths". Engineering Fracture Mechanics 74 (1-2): 168–178. doi:10.1016/j.engfracmech.2006.01.019. ISSN 00137944.
- ↑ Nilforoush, R.; Nilsson, M.; Elfgren, L.; Ožbolt, J.; Hofmann, J.; Eligehausen, R. (2017). "Tensile capacity of anchor bolts in uncracked concrete: Influence of member thickness and anchor's head size". ACI Structural Journal 114 (6): 1519–1530. doi:10.14359/51689503. ISSN 08893241.
- ↑ Mallèe, Rainer; Eligehausen, Rolf; Silva, John F (2006). Anchors In Concrete Structures. Ernst&Shon. ISBN 978-3433011430.
See also
- Fracture mechanics
- Concrete fracture analysis
- Size effect
- Anchor Cone
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