*To view the figures and tables associated with this article, please refer to the flipbook above.*

Anchoring-to-concrete provisions in the American Concrete Institute (ACI) standard titled *Building Code Requirements for Structural Concrete* (ACI 318) illustrate how to calculate shear concrete breakout strength for two rows of anchors having one anchor in each row. Many anchorages consist of more than two anchor rows, having multiple anchors in each row, requiring the engineer to extrapolate these provisions. This article discusses how one could extrapolate ACI 318-19(22) provisions to calculate shear concrete breakout strength for anchorages consisting of multiple anchor rows with multiple anchors in each row.

## Overview of ACI 318-19(22) Anchoring-to-Concrete Provisions for Shear Concrete Breakout

Shear concrete breakout occurs at a fixed edge when shear load acts towards that edge. ACI 318-19(22) Section 17.7.2.1 provides equations for calculating nominal concrete breakout strength in shear for a single anchor (** V_{cb}**) and an anchor group (

**). These equations are as follows:**

*V*_{cbg}Single anchor (Eq. 17.7.2.1a)

Anchor group (Eq. 17.7.2.1b)

The parameters in (Eq. 17.7.2.1a) and (Eq. 17.7.2.1b) are defined in Table 1.

The parameter ** c_{a1}** referenced in

*Table 1*corresponds to the distance in the direction of the applied shear load from the center of a single anchor or from a line through a row of anchors to a fixed concrete edge. When an anchorage consists of multiple anchor rows, the nominal concrete breakout strength in shear for the group of anchors,

**, can be calculated using a**

*V*_{cbg}**value from a specific row. ACI 318-19(22) considers three cases for determining the value of**

*c*_{a1}**. Each case considers the spacing between anchor rows in the direction of the applied shear load, which influences where potential concrete breakout failure surfaces can develop, and the magnitude of shear load assumed to act on a particular row. ACI 318-19(22)**

*c*_{a1}*Fig. R17.7.2.1b*(reproduced in Figure 1) illustrates these three cases for a simple anchor arrangement consisting of two anchor rows, with one anchor in each row.

*Figure 2* illustrates how the three ACI 318-19(22) cases for shear concrete breakout could be extrapolated for an anchorage consisting of three rows with three anchors in each row. Case 1 (*Figure 2a*) assumes the shear load (** V_{ua}**) is equally distributed between Rows 1, 2, and 3 if the row spacings,

**and**

*s*_{y,12}**, are greater than or equal to**

*s*_{y,23}**. For Rows 1, 2, and 3, if the anchor spacings**

*c*_{a1,row 1}**s**and

_{x,1}**perpendicular to the direction of**

*s*_{x,2}**are less than or equal to**

*V*_{ua}**, the anchors in each of these rows are considered to act as a group per ACI 318-19(22) 17.5.1.3.1. Since**

*3c*_{a1,row 1}**and**

*s*_{y,12}**are greater than or equal to**

*s*_{y,23}**the**

*c*_{a1,row 1,}**value used to calculate**

*c*_{a1}**can be taken as equal to**

*V*_{cbg}**, and**

*c*_{a1,row 1}**can be assumed to be equally distributed on each anchor row. For the example illustrated in Figure 2a, Case 1 is satisfied if the design concrete breakout strength (**

*V*_{ua}**) calculated with**

*zV*_{cbg}**is greater than or equal to (**

*c*_{a1,row 1}**).**

*V*_{ua}/3Case 2 (*Figure 2b*) is an alternative design assumption to Case 1 and assumes a full failure surface could develop from the anchor row farthest from the fixed edge (Row 3) if the spacing between rows in the direction of ** V_{ua} **is greater than or equal to

**for the row nearest the fixed edge (**

*c*_{a1}**). The total shear load is assumed to act on Row 3. If the anchor spacings**

*c*_{a1,row 1}**and**

*s*_{x,1}**perpendicular to the direction of**

*s*_{x,2}**are less than or equal to**

*V*_{ua}**, the anchors in each of these rows are considered to act as a group per ACI 318-19(22) 17.5.1.3.1. Case 2 is satisfied if**

*3c*_{a1,row 1}**calculated for the anchors in Row 3 using**

*zV*_{cbg}**is greater than or equal to the total shear load**

*c*_{a1,row 3}**.**

*V*_{ua}Case 3 (*Figure 2c*) assumes a full failure surface can only develop from the anchor row nearest to the fixed edge (Row 1) because the spacing between rows in the direction of ** V_{ua}** is less than

**for the row nearest the fixed edge (**

*c*_{a1}**). The total shear load is assumed to act on Row 1. If the anchor spacings**

*c*_{a1,row 1}**and**

*s*_{x,1}**perpendicular to the direction of**

*s*_{x,2}**are less than or equal to**

*V*_{ua}**, the anchors in each of these rows are considered to act as a group per ACI 318-19(22) 17.5.1.3.1. Since**

*3c*_{a1,row 1}**and**

*s*_{y,12}**are less than**

*s*_{y,23}**, Case 3 assumes a full concrete breakout surface cannot develop from either Row 2 or Row 3, so the**

*c*_{a1,row 1}**value used to calculate**

*c*_{a1}–**is taken equal to**

*V*_{cbg}**. Case 3 is satisfied if**

*c*_{a1,row 1}**calculated for the anchors in Row 1 using**

*zV*_{cbg}**is greater than or equal to the total shear load**

*c*_{a1,row 1}**.**

*V*_{ua}If anchors are not rigidly attached (e.g., not welded) to a fixture, shear load cannot necessarily be re-distributed between rows, potentially precluding the assumptions utilized in Case 2. Examples of anchors not rigidly attached to a fixture include post-installed anchors and ASTM (American Society for Testing and Materials) F1554 headed bolts. However, if anchors are rigidly attached (e.g., welded) to a fixture, Case 2 is the default assumption when calculating ** zV_{cbg} **because the shear load can be redistributed to the back row of anchors, thereby permitting the assumptions utilized in Case 2. Examples of anchors rigidly attached to a fixture include AWS (American Welding Society) D1.1 headed studs.

## How To Determine C_{a1}? – Things To Consider

As noted on page 1, the parameter ** c_{a1}** corresponds to the distance in the direction of the applied shear load from the center of a single anchor or from a line through the center of anchors in a row to the edge where shear concrete breakout is assumed to occur. Shear concrete breakout occurs when the applied shear load causes the attached fixture to bear on the anchors such that a failure surface develops from the anchors to a fixed concrete edge.

If anchors are not rigidly attached to a fixture, an annular space exists between each anchor and the fixture. The origin of a potential failure surface depends on which anchors are assumed to be in bearing with the fixture and the spacing between anchors in the direction of the shear load. For example, if all anchors are centered in the fixture holes, bearing could occur simultaneously on each anchor as the shear load is applied, and a failure surface could develop from one or more anchor rows. However, if any anchors are not centered in the fixture holes, the location of potential failure surfaces becomes more difficult to predict because the fixture may be bearing on some anchors but not all of them. Likewise, the spacing between anchors in the direction of the shear load influences whether a full or partial failure surface can develop from a given anchor or anchor row assumed to be in bearing with the fixture.

Assuming which anchors are in bearing with the fixture also influences how the shear load can be distributed on those anchors. ACI 318-19(22) design assumptions consider two anchor rows with one anchor in each row. For anchorages consisting of more than two anchor rows with multiple anchors in each row, these design assumptions must be extrapolated to consider which anchor rows are in bearing with the fixture, permitting the formation of a potential failure surface, and the shear load distribution among these rows.

## Load Distribution On Anchors In Shear – Things To Consider

When an anchorage consists of more than two rows resisting shear load, the engineer must decide how the load is distributed on each row. For example, the anchorage shown in *Figure 3* consists of five rows. Assume the anchors are not rigidly attached to the plate. Shear load (** V_{ua}**) acts towards the

**edge. Assuming shear lag, only Rows 1, 2, 3, and 4 will be considered in this example to resist shear load. The edge distance**

*-y***c**corresponds to the distance of the anchors in Row 1 to the

_{a1,row 1}**edge (4**

*-y**inches*). Anchor spacing in the

**direction (**

*x***) equals 8**

*s*_{x}*inches*, so the anchors in each row act as a group because

**is less than**

*s*_{x}**. Spacing in the**

*3c*_{a1,row 1}**direction between each anchor row equals 6**

*y**inches*, which is greater than

**, so both Case 1 and Case 2 can be considered when calculating the design concrete breakout strength in shear (**

*c*_{a1, row 1}**). The distribution of**

*zV*_{cbg}**among rows 1, 2, 3, and 4 must now be considered. Case 1 assumes equal load distribution per row. Case 2 assumes the total shear load is applied to Row 4; however, consideration could be given to the possibility that some fraction of**

*V*_{ua}**acts on Rows 1, 2, and 3. Therefore, if Case 2 is considered,**

*V*_{ua}**could be calculated for each row using the**

*zV*_{cbg}**value for that row and checked against some fraction of**

*c*_{a1}–**assumed to be acting on that row.**

*V*_{ua}Case 1, shown in *Figure 3b*, assumes ** zV_{cbg}** is calculated using

**, and**

*c*_{a1,row 1}**is distributed equally among Rows 1, 2, 3, and 4.**

*V*_{ua}**is checked against (0.25**

*zV*_{cbg,row 1}**). Case 2, shown in**

*V*_{ua}*Figure 3c*, illustrates how the total shear load is assumed to act on Row 4, while some fraction of

**is assumed to act on Rows 1, 2, and 3.**

*V*_{ua}**is checked against**

*zV*_{cbg,row}_{n}**for each row.**

*V*_{ua,row n}The percent utilization for Case 1 (0.25** V_{ua}/zV_{cbg,row 1}**) must be checked against the highest percent utilization for Case 2 (

*V*_{ua,row n})/**).**

*zV*_{cbg,row n}The largest value controls the design.

For the anchorage shown in *Figure 4,* assume the anchors are not rigidly attached to the plate. Due to shear lag, only Rows 1, 2, 3, and 4 will be assumed to resist shear. The edge distance ** c_{a1,row 1}** equals 6

*inches*and the spacing in the

**direction between each anchor row equals 4**

*y**inches*. The spacing

**equals 8**

*s*_{x}*inches*, so the anchors in each row act as a group because

**is less than**

*s*_{x}**. Case 3 applies because the spacing in the**

*3c*_{a1,row 1}**direction between all anchor rows is less than**

*y***; therefore, a full failure surface can only develop from the anchors in Row 1 because the failure surfaces for the other anchor rows merge with each other. The total shear load (1.0**

*c*_{a1, row 1}**) is assumed to act on Row 1, and the design concrete breakout strength (**

*V*_{ua}**) calculated using**

*zV*_{cbg}**is checked against**

*c*_{a1,row 1}**.**

*V*_{ua}Now consider the anchorage shown in *Figure 5*. Assume five rows of anchors not rigidly attached to a plate are subjected to a shear load (** V_{ua}**) acting towards the

**edge. No shear lag is assumed, so all five rows can resist shear load. Assume**

*-y***equals 6**

*c*_{a1,row 1}*inches*. The spacing

**equals 8**

*s*_{x}*inches*, so the anchors in each row act as a group because

**is less than**

*s*_{x}**. The spacing**

*3c*_{a1,row 1}**between each row varies. Assuming which anchor rows resist shear load becomes more challenging, and it can be difficult to implement the load distribution assumptions of Cases 1, 2, and/or 3.**

*s*_{y}The spacings ** s_{y,12}**,

**and**

*s*_{y,34}**shown in**

*s*_{y,45}*Figure 5*are less than

**so Case 3 is relevant to calculating concrete breakout with respect to Rows 1 and 2, as well as Rows 3, 4, and 5. Case 3 assumes the failure surface from Row 2 merges into the failure surface for Row 1, and the failure surfaces from Rows 4 and 5 merge into the failure surface for Row 3. However,**

*c*_{a1,row 1}**shown in**

*s*_{y,23}*Figure 5*is equal to

**, so Case 2 is also relevant to calculating concrete breakout with respect to Rows 1 and 3. Therefore, the design must consider concrete breakout strength for failure surfaces originating from Row 3 (**

*c*_{a1,row 1}**) and Row 1 (**

*zV*_{cbg, row 3}**). If Case 3 is considered for these rows, then**

*zV*_{cbg, row 1}**could be assumed to act on either Row 3 or Row 1, and (**

*V*_{ua}**would be checked versus (**

*V*_{ua}/zV_{cbg, row 3})**). If Case 2 is considered for these rows, then some fraction of**

*V*_{ua}/zV_{cbg, row 1}**V**could be assumed to act on each row, and (

_{ua}**) would be checked versus (**

*V*_{ua, row 3}/zV_{cbg, row 3}**). Finally, the Case 2 results would need to be checked versus the Case 3 results, and the highest percent utilization (**

*V*_{ua, row 1}/zV_{cbg, row 1}**) would control the design. As can be seen, the complexity of the anchor configuration influences where potential failure surfaces can develop, as well as the shear load distribution on the anchors assumed to be resisting shear load.**

*V*_{ua,n }/zV_{cbg, n}## Summary

ACI 318-19(22) provides three design assumptions to calculate shear concrete breakout strength for anchors. Each assumption only considers two anchor rows having one anchor in each row. This article explained how these three design assumptions could be extrapolated to design anchorages consisting of multiple anchor rows with multiple anchors in each row. Consideration must be given to edge distances in the direction of the shear load, spacing between anchor rows in the direction of the shear load, and shear load distribution on anchor rows.■