By: Javier Encinas | October 2, 2016

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

The anchor rods are usually subjected to a combination of tension and shear forces. The ACI treats separately tension and shear, and then it combines both effects in an interaction diagram. The Part 1 of this post will discuss the anchor rods in tension. Our software ASDIP Steel will be used to support our discussion.

Design of anchor rods for tension.

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 now 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, and basically they are provided to keep the base plate in place. 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.

tension-anchor-rods

The calculation of the tension in the anchor rods depends of the strain compatibility assumption for the base plate. For a discussion of the different theories please refer to our 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:

anchor-rods-tension-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 properties of the anchor material and the physical dimensions of the anchor. The nominal steel strength is:

Tension steel strength

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 Nb, and multiplied by factors that account for the number of anchors, edge distance, spacing, eccentricity, etc.

Tension breakout formula

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.

tension-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 Anc and the effective embedment depth hef and provides a graphic view, as shown below.

anchor-rods-tension-breakout-area-anc

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 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.

  • 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:

Tension pullout strength

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:

Side face blowout formula

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. 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 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.

The Part 2 of this post deals with the design of anchor rods for shear, as well as the tension-shear interaction. 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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