# Example of Concrete Anchor Bolt Design Calculation – Part-1: Determining Steel Strength of Anchor Bolt in Tension

Anchor bolts are used extensively as foundation bolts for rotating equipments like machines and structural members like towers. The American Concrete Institute (ACI) 318 Appendix D has extensive guidelines for designing concrete anchor bolts.

This series of eight articles will cover all the design guideline of the ACI code with the help of the following concrete anchor foundation bolt design calculation example:

Problem statement of the design example

Fig.1: Anchor Bolt design Example Plan View

Fig.2: Anchor Bolt design Example Elevation

See the above two figures (Fig.1 and Fig.2) and design the cast in place anchor bolts according to the arrangement shown. Consider the factored tensile load as 20000 lb, factored shear load as 2300 lb and compressive strength of the concrete as 3500 psi.  Also assume that the column is mounted at the corner of a large concrete slab.

Design solution

The aim of this whole exercise is to calculate the design tensile strength and design shear strength of the group of anchor for a selected anchor bolt diameter and check if the design strengths are higher than the applied loads. If they are then we will declare that the selected bolt size is safe or else we will go for next higher size of the anchor bolts.

We will start with the anchor diameter of 0.75 inch and do the design calculations through the following eight parts:

Part-1: Determining Steel Strength of Anchor in Tension (presently we are here)

Part-2: Determining Concrete Breakout Strengths of Anchor in Tension

Part-3: Determining Concrete Pullout Strength of Anchor in Tension

Part-4: Determining Side-face Blowout Strength of Anchor in Tension

Part-5: Determining Steel Strength of Anchor in Shear

Part-6: Determining Concrete Breakout Strength of Anchor in Shear

Part-7: Determining Concrete Pryout Strength of Anchor in Shear

Part-8: Interaction of Tensile and Shear Forces

The calculation of steel strength of anchor in tension according to the ACI code goes like below:

Steel strength in tension, φNsa = φnAse,Nfuta……………………..D-3

Where,

Φ – Strength reduction factor and its value for ductile anchor bolt in tension is 0.75

Nsa – Nominal material (steel) strength of the group of anchor in lb

n – Total number of anchors

Ase,N – Single anchor bolt’s effective cross section area (to be obtained from manufacturer’s catalog) in square inch

futa – Specified tensile strength for a single anchor (to be obtained from manufacturer’s catalog) in psi

The 0.75 inch anchor typically has the following cross section and tensile strength values:

Ase,N = 0.334 square inch

futa=75000 psi

So, by putting these values, we can get the nominal material strength for the group of anchors in tension from the equation D-3 as

Φ Nsa = 0.75*4*0.334*75000 = 75150 lb

In the next part (part-2) we will calculate concrete breakout strength.

Let me know if you have any suggestions.

I am a graduate engineer. I love blogging, and mechanical designing ... Most of the CAD and design related articles are contributed by me. Apart from that i love involving myself designing the website and android apps developments...

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8. ##### Johnny R

I’m interested in the end result of anchor bolt strength as to how proper installation of the bolts plays in the ultimate results of it’s strength. If you install the bolts in wet concrete by pushing it into the concrete, you get air gaps and bubbles, off set bolts, height variations and this plays into it’s strength calculations. If you do the calculations based on a perfect installation, it becomes invalid when considering the real time install.

What can one do to make correct calculations based on installation variables?

Big thanks!!

10. ##### jungle84

You should vibrate the concrete during construction to ensure that there are no voids. The formulas were developed based on empirical testing that resulted in a 95% probability that the actual strength will exceed the nominal strength (ACI 318, Appendix D). Furthermore, the resistance factor is applied to account for variability in material strength and workmanship. If you have reason to believe that the installation will be poor, then you should reduce the capacity factor accordingly.

11. ##### John

Of course vibrating the concrete mix will definitely help get rid of the bubbles surrounding a bolt, but many other factors such as temperature, speed of the setting process, and length of time to vibrate, all are factors that can change the results. The big issue is that many contractors will not vibrate the foundation and that is the question, really. If you assume no vibration and inserting an anchor bolt into the concrete as compared to having an anchor bolt suspension system in place with the bolt in place before the pour, there must be some data on that, all conditions being equal that can be measured and quantified as to the strength variation.

Also, do you have any calculations or data that shows how much pressure in p.s.i. is put on an anchor bolt that is being held by a suspension system when the concrete is flowing around the bolt when it is being poured into the foundation forms?