The design of anchor rods has become complex and cumbersome with the development of the *ACI 318* anchoring provisions, originally in the *Appendix D* of the *ACI 318-11* and earlier, and in the *Chapter 17* of the *ACI 318-14* and later. This document covers the required steps in the process of the design of cast-in anchor rods normally encountered in column base plates.

Anchor rods are usually subjected to a combination of tension and shear forces. The *ACI 318* treats separately tension and shear, and then it combines both effects in an interaction diagram. Our software *ASDIP STEEL* will be used to support this discussion.

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## Tension anchor bolt design

Let's assume a typical column base plate with anchor rods at the corners. For compression columns with no moments, the bearing diagram is uniform, as shown in the left picture below. If we add a small moment, the bearing diagram varies but the full base plate is still under compression, as shown in the center picture below. In these two cases there’s no tension in the anchor rods. As the applied moment increases, only a portion of the plate is under compression and the anchor rods provide the required tension to maintain the static equilibrium, as shown in the right picture below.

The calculation of the tension in the anchor rods depends on the strain compatibility assumption for the base plate. For a discussion of the different theories please refer to the blog post* Base Plate and Anchor Rod Design*.

Once the tension force has been calculated, the anchor rods should be checked for the following failure modes:

**Steel failure**- This is a measure of the capacity of the anchor material, regardless of the anchoring conditions. The calculations are based on the material properties and the physical dimensions of the anchor. The nominal steel strength is:

where *Ase* is the effective cross sectional area of the anchor. *ASDIP STEEL* uses an internal database with the properties of different anchor sizes and materials.

**Concrete breakout**- It assumes a failure forming a concrete cone based on a prism angle of 35 degrees. This predicts the strength of a group of anchors by using a basic equation for a single anchor*Nb*, and multiplied by factors that account for the number of anchors, edge distance, spacing, eccentricity, etc. It should be noted that the eccentricity factor was developed for rigid plates, so the strain compatibility analysis should be used with the*ACI 318*anchorage provisions.

The denominator is the breakout area of a single anchor, and the numerator is the group breakout area. The former can be easily calculated, but the latter may be quite difficult, since it depends on the geometric conditions of the support, as shown below.

A further complication arises when the anchor is located less than *1.5 hef* from three or more edges, in which case the effective depth *hef* needs to be recalculated. *ASDIP STEEL* accurately calculates, for any support conditions, the breakout area *Anc* and the effective embedment depth *hef.* It generates a graphic view as shown below.

The calculation of the breakout failure mode is particularly important since a concrete failure would be non-ductile, and therefore it should be avoided. To prevent this kind of failure, the *ACI* allows the use of reinforcing steel across the failure surface. This anchor reinforcement, however, must be designed and detailed carefully so that the strength of the rebars can be developed at both sides of the failure surface.

**Pullout strength**- It's the load at which crushing of the concrete occurs due to bearing of the anchor head. The nominal tension pullout strength is:

The factor *ψcp = 1.4* for anchors located in a region of a concrete member where analysis indicates no cracking at service load levels, otherwise its value is 1.0. *Abrg* is the net bearing area of the anchor head.

**Concrete side-face blowout**- It assumes splitting of the concrete at anchors loaded in tension that are close to an edge (*hef > 2.5 Ca1*). The nominal side blowout strength is:

where "*s"* is the distance between the outer anchors along the edge.

## What is the *φ-*factor for tension anchors?

The *ACI 318* anchorage provisions follow the *Ultimate Strength Design*, therefore the nominal strengths will be affected by a *φ* factor in order to be compared to the factored tension force for anchor bolt design. The *φ-*factor is affected by the ductility of the anchorage. If the controlling failure mode is either the steel strength or the anchor reinforcement strength, then the failure will be ductile. Any concrete failure, either breakout, pullout or side blowout, will be a brittle failure.

The *ACI 318* penalizes brittle failures with a lower *φ-*factor of 0.70, unless a supplementary reinforcing is provided, in which case *φ *is 0.75*, *except for pullout. For ductile failures, the *φ-*factor is 0.75. Unlike the anchor reinforcement, the supplementary reinforcement does not need to be designed and detailed to take the full tension load.

## How do you calculate the shear in anchor rods?

The lateral forces acting on a structure will produce a horizontal reaction at the foundation level. For steel frames supported on base plates, a small horizontal force can be resisted by the friction between the plate and the underlying concrete. However, as the reaction increases, the friction may not be high enough to counteract the sliding force.

In this case, the base plate will tend to slide until the shear force is transferred to the anchor rods bearing laterally against the base plate. Base plates are usually fabricated with oversize holes to account for small misalignments of the anchor rods at the field, which would be expensive to fix. As a result, it's very unlikely that all rods will bear against the base plate as in a perfect watch mechanism. The *ACI* recognizes this by allowing only the front rods to be effective for shear resistance purposes, unless all washers on the rods are welded to the base plate, in which case all rods would be effective, as shown in the picture below.

## Shear anchor bolt design.

Once the shear force has been calculated, the anchor rods should be checked for the following failure modes:

**Steel failure**– This is a measure of the capacity of the anchor material. It shall be evaluated by calculations based on the material properties and the physical dimensions of the anchor. The nominal steel strength is:

where *Ase* is the effective cross sectional area of the anchor. *ASDIP STEEL* uses an internal database with the properties of different anchor sizes and materials.

**Concrete breakout**– It assumes a failure forming a concrete cone based on a prism angle of 35 degrees. This predicts the strength of a group of anchors by using a basic equation for a single anchor V*b*, and multiplied by factors that account for the number of anchors, edge distance, eccentricity, cracking, etc.

The first factor has to do with the group of anchors producing the failure cone. The denominator is the breakout area of a single anchor, and the numerator is the group breakout area. The former can be easily calculated, but the latter may be quite difficult, since it depends on the geometric conditions of the support, as shown below.

A further complication arises when the anchor is located less than *1.5 hef* from three or more edges, in which case the effective depth *hef* needs to be recalculated. *ASDIP STEEL* accurately calculates, for any support conditions, the breakout area *Avc* and the effective embedment depth *hef.* It* *generates a graphic view as shown below.

Similarly to the anchor rods in tension, the calculation of the breakout failure mode in shear is particularly important since a concrete failure would be non-ductile, and therefore it should be avoided. To prevent this kind of failure, the *ACI *allows the use of reinforcing steel across the failure surface. This anchor reinforcement, however, must be designed and detailed carefully so that the strength of the rebars can be developed at both sides of the failure surface.

**Concrete pryout**– The nominal pryout shear resistance can be approximated as one to two times the anchor tensile breakout resistance, with the lower value appropriate for*hef*less than 2.5 in. For base plates the applicable factor is 2.0.

## What is the *φ-*factor for shear anchors?

The *φ-*factor affects the nominal strength in order to be compared to the factored shear force in the anchors. The *ACI* establishes a *φ-*factor of 0.65 for ductile steel failures and 0.70 for concrete failures, unless a supplementary reinforcing is provided, in which case *φ *is 0.75.

The smaller *φ-*factors for shear than for tension do not reflect basic material differences but rather account for the possibility of a non-uniform distribution of shear in connections with multiple anchors. Unlike the anchor reinforcement, the supplementary reinforcement does not need to be designed and detailed to take the full shear load.

## Interaction of tension and shear forces.

We have discussed the anchor bolt design for tension and shear separately. When the anchor rods are subjected to both tension and shear forces simultaneously, the design needs to satisfy the requirements of the interaction diagram shown below.

## Are there any additional dimensional requirements?

The *ACI 318* establishes that the minimum center-to-center spacing of anchors shall be *4da* for cast-in anchors that will not be torqued, and *6da* for torqued cast-in anchors, where* da* is the anchor diameter. There is not a clear definition of "torqued anchor" in the code. The author's interpretation is that any anchor torqued beyond the snug tight should be considered as "torqued anchor". Most of the anchor rods utilized in base plates of building frames will not be torqued beyond the snug tight limit.

In addition, the minimum edge distances for cast-in anchors that will not be torqued shall be based on the specified cover requirements for reinforcement, which basically sets the concrete cover to a maximum of 3". However, it may be advantageous to use a larger anchor cover to increase the side-face blowout strength. For cast-in anchors that will be torqued, the minimum edge distances shall be *6da*.

## Takeaway

The design of anchor rods subject to tension and shear forces may be cumbersome and time-consuming. The current *ACI* anchorage provisions are complex, and a number of limit states must be checked. *ASDIP STEEL* includes the base plate and anchor bolt design, with multiple options to optimize the design in minutes.

Detailed information is available about this structural engineering software by visiting ASDIP STEEL. For seismic design of anchor rods see the blog post Anchor Bolt Design: Overview of the ACI Seismic Provisions. For our collection of blog posts about base plate and anchorage design please visit Anchor Rods Design.

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Best regards,

Javier Encinas, PE

ASDIP Structural Software

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