By: Javier Encinas | November 7, 2016

The design of anchor rods has become more complex with the development of the ACI 318 anchorage provisions. This is the second part of our post regarding the design of anchor rods. In the first part we covered the ACI provisions for the design of anchor rods in tension. Now we will cover the design of anchor rods in shear, as well as the tension-shear interaction. Our software ASDIP Steel will be used to support our discussion.

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.

effective-anchor-rods-in-shear

Design of anchor rods for shear.

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

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

Shear steel strength formula

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. The CCD Method predicts the strength of a group of anchors by using a basic equation for a single anchor Vb, and multiplied by factors that account for the number of anchors, edge distance, eccentricity, cracking, etc.

Shear breakout formula in anchor rods

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.

shear-anchor-rods-breakout-area

A further complication arises when the plate 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 and provides a graphic view, as shown below.

anchor-rods-shear-breakout-area-avc

Similar 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 Code 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.

Shear pryout formula

What is the φ-factor for shear anchors?

The ACI 318 anchorage provisions follow the Ultimate Strength Design, therefore the nominal strengths must be affected by a φ-factor 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 tensile and shear forces.

When the anchor rods are subjected to both tension and shear forces, the design needs to satisfy the requirements of the interaction diagram shown below.

anchor-rods-tension-shear-interaction

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.

Detailed information is available about this structural engineering software by visiting ASDIP STEEL. You are invited to download a Free 15-Day Software Trial or go ahead and Place Your Order.

Best regards,

Javier Encinas, PE
ASDIP Structural Software

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