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# 17.7.2 *Concrete breakout strength of anchors in shear*, **V**_{cb}

_{cb}

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Nominal concrete breakout strength in shear,

**of a single anchor or***V*_{cb}**of an anchor group satisfying 17.5.1.3.1, shall be calculated in accordance with (a) through (d):***V*_{cbg}(a) For shear perpendicular to the edge on a single anchor

(17.7.2.1a) |

(b) For shear perpendicular to the edge on an anchor group

(17.7.2.1b) |

(c) For shear parallel to an edge,

**or***V*_{cb}**shall be permitted to be twice the value of the shear calculated by Eq. (17.7.2.1a) or (17.7.2.1b), respectively, with the shear assumed to act perpendicular to the edge and ψ***V*_{cbg}_{ed,V}taken equal to 1.0.(d) For anchors located at a corner, the limiting nominal concrete breakout strength shall be calculated for each edge, and the lesser value shall be used.

**is the projected area of the failure surface on the side of the concrete member at its edge for a single anchor or an anchor group. It shall be permitted to evaluate**

*A*_{Vc}**as the base of a truncated half-pyramid projected on the side face of the member where the top of the half-pyramid is given by the axis of the anchor row selected as critical. The value of**

*A*_{Vc}**shall be taken as the distance from the edge to this axis.**

*c*_{a}_{1}**shall not exceed**

*A*_{Vc}**, where**

*nA*_{Vco}**is the number of anchors in the group.**

*n*If anchors are located in narrow sections of limited thickness such that both edge distances

**and thickness***c*_{a}_{2}**are less than***h*_{a}**1.5**, the value of*c*_{a}_{1}**used to calculate***c*_{a}_{1}**in accordance with 17.7.2.1.1 as well as for the equations in 17.7.2.1 through 17.7.2.6 shall not exceed the greatest of (a) through (c).***A*_{Vc}(b)

*h*/1.5_{a}(c)

**, where***s*/3**is the maximum spacing perpendicular to direction of shear, between anchors within a group***s***is the projected area for a single anchor in a deep member with a distance from edges of at least**

*A*_{Vco}**1.5**in the direction perpendicular to the shear. It shall be permitted to calculate

*c*_{a}_{1}**by Eq. (17.7.2.1.3), which gives the area of the base of a half-pyramid with a side length parallel to the edge of**

*A*_{Vco}**3**and a depth of

*c*_{a}_{1}**1.5**.

*c*_{a}_{1}A = 4.5(_{Vco}c_{a}_{1})^{2} |
(17.7.2.1.3) |

If anchors are located at varying distances from the edge and the anchors are welded to the attachment so as to distribute the force to all anchors, it shall be permitted to evaluate the strength based on the distance to the farthest row of anchors from the edge. In this case, it shall be permitted to base the value of

**on the distance from the edge to the axis of the farthest anchor row that is selected as critical, and all of the shear shall be assumed to be resisted by this critical anchor row alone.***c*_{a}_{1}Basic concrete breakout strength of a single anchor in shear in cracked concrete,

**, shall not exceed the lesser of (a) and (b):***V*_{b}(a) | (17.7.2.2.1a) |

**for anchors with a constant stiffness over the full length of embedded section, such as headed studs and post-installed anchors with one tubular shell over full length of the embedment depth;**

*ℓ*=_{e}*h*_{ef}**for torque-controlled expansion anchors with a distance sleeve separated from expansion sleeve;**

*ℓ*= 2_{e}*d*_{a}**in all cases.**

*ℓ*_{e}≤ 8*d*_{a}(b) | (17.7.2.2.1b) |

For cast-in headed studs, headed bolts, or hooked bolts that are continuously welded to steel attachments, basic concrete breakout strength of a single anchor in shear in cracked concrete,

**, shall be the lesser of Eq. (17.7.2.2.1b) and Eq. (17.7.2.2.2) provided that (a) through (d) are satisfied.***V*_{b}(17.7.2.2.2) |

where

**is defined in 17.7.2.2.1.***ℓ*_{e}(a) Steel attachment thickness is the greater of

**0.5**and 3/8 in.*d*_{a}(b) Anchor spacing

**is at least 2.5 in.***s*(c) Reinforcement is provided at the corners if

*c*_{a}_{2}≤ 1.5*h*_{ef}(d) For anchor groups, the strength is calculated based on the strength of the row of anchors farthest from the edge.

Modification factor for anchor groups loaded eccentrically in shear,

**ψ**, shall be calculated by Eq. (17.7.2.3.1)._{ec,V}(17.7.2.3.1) |

If the loading on an anchor group is such that only some of the anchors in the group are in shear, only those anchors that are in shear in the same direction shall be considered for determining the eccentricity

**in Eq. (17.7.2.3.1) and for the calculation of***e*'_{V}**according to Eq. (17.7.2.1b).***V*_{cbg}Modification factor for edge effects for single anchors or anchor groups loaded in shear,

**ψ**, shall be determined by (a) or (b) using the lesser value of_{ed,V}**.***c*_{a}_{2}(a) If c_{a}_{2} ≥ 1.5c_{a}_{1}, then ψ_{ed,V} = 1.0 | (17.7.2.4.1a) |

(b) If c_{a}_{2} < 1.5c_{a}_{1}, then | (17.7.2.4.1b) |

Modification factor for the influence of cracking in anchor regions at service load levels and presence or absence of supplementary reinforcement,

**ψ**, shall be determined as follows:_{c,V}(a) For anchors located in a region of a concrete member where analysis indicates no cracking at service load levels, ψ

_{c,V}shall be permitted to be 1.4.(b) For anchors located in a region of a concrete member where analysis indicates cracking at service load levels, ψ

_{c,V}shall be in accordance with Table 17.7.2.5.1.**Table 17.7.2.5.1—Modification factor where analysis indicates cracking at service load levels, ψ**

_{c,V}Condition | ψ_{c,V} |
---|---|

Anchors without supplementary reinforcement or with edge reinforcement smaller than a No. 4 bar | 1.0 |

Anchors with reinforcement of at least a No. 4 bar or greater between the anchor and the edge | 1.2 |

Anchors with reinforcement of at least a No. 4 bar or greater between the anchor and the edge, and with the reinforcement enclosed within stirrups spaced at not more than 4 in. | 1.4 |

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