Concrete cone failure

{{Short description|Failure mode of anchors in concrete submitted to tensile force}}

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 $N_0$ of a single anchor in uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors is given by:{{Cite journal| issn = 0889-3241| volume = 109| issue = January| pages = 1–4| last1 = Fuchs| first1 = Werner| last2 = Eligehausen| first2 = Rolf| title = Concrete Capacity Design (CCD) Approach for Fastening to Concrete| journal = ACI Structural Journal| date = 1995}}

$N_0 = f_{ct} {A_{N}} [N]$

Where:

$f_{ct}$ - tensile strength of concrete

$A_{N}$ - 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 $N_0$ of a single anchor in uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors is given by:

$N_0 = k \sqrt{f_{cc}} {h_{ef}}^{1.5} [N]$ ,

Where:

$k$ - 13.5 for post-installed fasteners, 15.5 for cast-in-site fasteners

$f_{cc}$ - Concrete compressive strength measured on cubes [MPa]

${h_{ef}}$ - 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 ${h_{ef}}^{1.5}$ which differentiates from ${h_{ef}}^{2}$ 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.{{Cite journal| issn = 0376-9429| volume = 95| pages = 391–404| last1 = Ožbolt| first1 = Joško| last2 = Eligehausen| first2 = Rolf| last3 = Reinhardt| first3 = Hans-Wolf| title = Size effect on the concrete cone pull-out load| journal = International Journal of Fracture| date = 1999}}

File:Concrete Cone Group.png

Current codes take into account a reduction of the theoretical concrete cone capacity $N_0$ considering: (i) the presence of edges; (ii) the overlapping cones due to group effect; (iii) the presence of an eccentricity of the tension load.{{Cite journal| issue = Ccd| pages = 1–77| last = ACI| title = ACI 349.2 Guide to the Concrete Capacity Design ( CCD ) Method — Embedment Design Examples| journal = Concrete| date = 2004}}

=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). 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.

=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.{{Cite journal| doi = 10.1016/j.engfracmech.2006.01.019| issn = 0013-7944| volume = 74| issue = 1-2| pages = 168–178| last1 = Ožbolt| first1 = Joško| last2 = Eligehausen| first2 = Rolf| last3 = Periškić| first3 = G.| last4 = Mayer| first4 = U.| title = 3D FE analysis of anchor bolts with large embedment depths| journal = Engineering Fracture Mechanics| date = 2007}}{{Cite journal| doi = 10.14359/51689503| issn = 0889-3241| volume = 114| issue = 6| pages = 1519–1530| last1 = Nilforoush| first1 = R.| last2 = Nilsson| first2 = M.| last3 = Elfgren| first3 = L.| last4 = Ožbolt| first4 = J.| last5 = Hofmann| first5 = J.| last6 = Eligehausen| first6 = R.| title = Tensile capacity of anchor bolts in uncracked concrete: Influence of member thickness and anchor's head size| journal = ACI Structural Journal| date = 2017}}

=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.{{Cite book| publisher = Ernst&Shon|isbn=978-3433011430| last1 = Mallèe| first1 = Rainer| last2 = Eligehausen| first2 = Rolf| last3 = Silva| first3 = John F| title = Anchors In Concrete Structures| date = 2006}} The reduction is due to the impossibility to transfer both normal and tangential stresses at the crack plane.