Concrete cone failure

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 {\displaystyle N_{0}} of a single anchor in uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors is given by:^[2]

N 0 = f c t A N [ N ] {\displaystyle N_{0}=f_{ct}{A_{N}}[N]}

Where:

f c t {\displaystyle f_{ct}} - tensile strength of concrete

A N {\displaystyle 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 {\displaystyle N_{0}} of a single anchor in uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors is given by:^[2]

N 0 = k f c c h e f 1.5 [ N ] {\displaystyle N_{0}=k{\sqrt {f_{cc}}}{h_{ef}}^{1.5}[N]} ,

Where:

k {\displaystyle k} - 13.5 for post-installed fasteners, 15.5 for cast-in-site fasteners

f c c {\displaystyle f_{cc}} - Concrete compressive strength measured on cubes [MPa]

h e f {\displaystyle {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 e f 1.5 {\displaystyle {h_{ef}}^{1.5}} which differentiates from h e f 2 {\displaystyle {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.^[3]

Current codes take into account a reduction of the theoretical concrete cone capacity N 0 {\displaystyle 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.^[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.