Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ Part-1: Determining Steel Strength of Anchor Bolt in Tension Anchor bolts are used extensively as foundation bolts for rotating equipment’s 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.
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ 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. The calculation of steel strength of anchor in tension according to the ACI code goes like below: Steel strength in tension, φN sa = φ n A se,N futa ……………………..D-3 Where, Φ – Strength reduction factor and its value for ductile anchor bolt in tension is 0.75 N sa – Nominal material (steel) strength of the group of anchor in lb n – Total number of anchors A se,N – Single anchor bolt’s effective cross section area (to be obtained from manufacturer’s catalog) in square inch f uta – 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: A se,N = 0.334 square inch f uta =75000 psi So, by putting these values, we can get the nominal material strength for the group of anchors in tension from the equation Φ N sa = 0.75*4*0.334*75000 = 75150 lb Part-2: Determining Concrete Breakout Strength of Anchor in Tension We will discuss how to calculate the concrete breakout strength according to the ACI 318 code in this part of the concrete anchor foundation bolt design calculation example. Please refer part-1 of the calculation to understand the design problem statement and the calculations for the anchor bolt materials strength If you refer the Fig.1 and the Fig.2 of the problem statement then it will clear to you that the distance between two surrounding anchors (in our case it is 6 inch) is less than three times the effective embedment depth (in our case it is 10 inch). So, as per ACI codes, the anchor arrangement can be termed as group and the ACI formula for calculating the concrete breakout strength for the anchor group is: φN cbg = (A Nc /A Nco )ψ ec,N ψ ed,N ψ c,N ψ cp,N N b ……………………………..D-5 Where, Φ – Strength reduction factor for breakout strength and its value for non-reinforcement in tension is 0.70 A Nc –Total projected area for the group of anchors of the failure surface as approximated by a rectangle with edges bounded by 1.5h ef (1.5*10 = 15 inch in our case) and the free edges of the concrete from the centerline of the anchors. Confused? You will be clearer while calculating it little later. h ef – Effective embedment depth of anchor (in our case it is 10 inch). A Nco – Total projected failure area approximated by a square bounded by 1.5h ef (1.5*10 = 15 inch in our case) from the centerline of the anchors at all the sides. ψ ec,N – Modification factor for the anchor group loaded eccentrically in tension, in our case there is no eccentric loading , so ψ ec,N =1. ψ ed,N – Modification factor for edge effect for the anchor group in tension, we will calculate it later.
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ Ψ c,N – Modification factor based on the presence and absence of crack in the concrete, we will calculate it later. ψ cp,N – Modification factor for post weld types of anchor. For cast in place anchor ψ cp,N = 1 N b – Basic concrete break out strength for a single anchor in tension, we will calculate it later. Calculation of A Nc or Foundation Bolt Design Calculations with Example as per ACI 318 ...
Fig.2.1: Anchor Bolt Plan for calculating Anc A NC =Area of the square shown in dotted line = (15+6+5)*(15+6+5) = 676 Square Inch
Calculation of A Nco Before going to the calculation please refer the plan view of the anchor arrangement as below:
Fig.2.2: Anchor Bolt Plan for calculating Anco A Nco =Area of the square shown in dotted line = (15+15)*(15+15) = 900 Square Inch
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ Calculation of ψ ed,N If, C a,min (minimum distances between two anchors, 6 inch in our case) is less than 1.5 times the h ef (1.5*10=15 inch in our case) then ψ ed,N = 0.7+(0.3*C a,min )/(1.5*h ef ) = 0.7+(0.3*6)/(1.5*10) = 0.82 Calculation of ψ c,N According to the code the value of ψ c,N =1 where concrete crack is likely to occur.
Now, by putting all the values in D-5 we get the Concrete breakout strength for the anchor group φN cbg =(A Nc /A Nco )ψ ec,N ψ ed,N ψ c,N ψ cp,N N b = 0.70*(676/900)*1*0.82*1*1*48000 = 20694.6131 lb so, finally we got the concrete break out strength of the anchor group in tension as 20694.6131 lb. Part-3: Determining Pullout Strength of Anchor in Tension Please refer the problem statement and the part-1, part-2 of this cast in place concrete anchor bolt design calculation example so that you will be in phase with this part (part-3) of the calculation. Here we will calculate the pull out strength of the concrete anchor according to the ACI 318 Appendix D codes. What is Anchor Pullout Strength? As the name suggests, it is the force required to uproot a anchor out of the concrete. Calculation According to ACI codes, the pull out strength of the group of anchors is given by φN pn =8nψ c,P A brg f’ c …………………………………..D-14 Where, Φ – Strength reduction factor for pull out strength and its value for non-reinforcement in tension is 0.70 ψ c,P – Modification factor for pullout strength based on the presence of concrete cracks, for the concrete with cracks at service load level ψ c,P =1. n – Number of anchor bolts, in our case n=4.
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ A brg – Net bearing area of the head of anchor bolt in square inch, in our case A brg =0.654 Square inch. f’ c – The concrete’s specified compressive strength in psi, in our case f’ c =4000 psi. So, by putting all the values in D-14, we get the pullout strength of the anchor group as φN pn =0.7*8*4*1*0.654*4000 lb = 58598.4 lb In the next part (Part-4) of the foundation anchor bolt design calculation example, we will discuss about calculating the concrete blow out strength in tension. Part-4: Determining Side-face Blowout Strength of Anchor in Tension In this part we will calculate the side-face blowout strength of the concrete anchor according to the ACI 318 Appendix D codes and also consolidate the results of the different types of anchor strengths in tension we have calculated so far. Please refer the problem statement and the part-1, part-2, part-3 of this cast in place concrete anchor bolt design calculation example so that you will be in phase with this part (part-4) of the calculation. What is Side-face Blow Out Strength? In simple term, it is the failure of the concrete due to the closeness of an anchor bolt with the side surface of the concrete foundation. When the anchor bolt is too close to the side then the possibilities are there that before breaking out the top concrete surface, the side surface get broken. While calculating side-face blowout the depth of the anchor bolt and the distance of the anchor from the closest edge are considered. Calculation According to ACI codes, you need to calculate the side face blowout only for the anchors which has the distance from the edge lesser than 0.4 times the depth of the anchor, or C a1 < 0.4*h ef ……………………………………………4.1 Where C a1 – Minimum distance from the anchor to the foundation edge (in our case it is 5 inch) h ef – Effective embedment depth of anchor (in our case it is 10 inch). So, from equation 4.1, 0.4**h ef is 4 which is less than C a1 so we need to calculate side-face blowout strength for this example. Summary of Calculated Strength Values in Tension Through the part-1, Part-2, part-3, and this part we have come out with the following strength values: Nominal material strength for the anchors (Φ N sa ) = 75150 lb Concrete breakout strength for the anchor group (Φ N cbg ) = 20694.6131 lb Pullout strength of the anchor group (Φ N pn ) = 58598.4 lb Side-face blowout strength = NA Out of these three strength values the smallest one will be the design strength.
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ So, the design strength in tension = 20694.6131 lb If you refer the problem statement for this foundation anchor bolt design calculation example then you can observe that tensile load (20000 lb) applied is lower than the calculated design strength in tension (20694.6131 lb), so, the design is safe under tensile load. Part-5: Determining Steel Strength of Anchor Bolt in Shear In this part (part-5), we will see the concrete anchor bolt design calculation example for calculating anchor material (steel) strength in shear according to the ACI 318 appendix D codes. But before that, please go through the problem statement and part-1, part-2, part-3 and part-4 of this series Calculation The formula for determining the steel strength in shear given in the American Concrete Institute code is: Steel strength in shear, φN sa = φnA se,N f uta ……………………..D-19 Where, Φ – Strength reduction factor and its value for ductile anchor bolt in shear; the value of it is 0.65 N sa – Nominal shear strength of the group of anchor in lb n – Total anchor number in the group, in our case the value is 4 A se,N – Effective cross sectional area of a single anchor, the value of it for the 0.75 inch anchor bolt is 0.334 square inch f uta – Specified tensile strength for a single anchor (to be obtained from manufacturer’s catalog) in psi, in our case the value is 75000 psi. Now, by putting the values in the equation D-19 explained above, we can obtain the value of the steel strength for the group of anchor is: Φ N sa = 0.65*4*0.334*75000 = 65130 lb You might have already observed that only difference between calculating the cast in place anchor bolt material strength in shear and in tension is the strength reduction factor. For shear it is 0.65 and for tension 0.75. Also, please remember that in both the cases we used Specified tensile strength. Part-6: Determining Concrete Breakout Strength of Anchor in Shear Before diving into the concrete anchor bolt design calculation example for calculating anchor breakout strength in shear, please go through the problem statement and part-1, part-2, part-3, part-4 and part-5 of this series. The calculation exercise is carried out according to the ACI 318 appendix D codes. Calculation The code gives the following formula for finding out the break out strength in shear for a group of anchor bolts φV cbg = φ(A Vc /A Vco )ψ ec,V ψ ed,V ψ c,V ψ cp,V V b ……………………………..D-22 Where, Φ – Strength reduction factor for breakout strength and its value for non-reinforcement in tension is 0.70
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ Avc– projected concrete failure area of the group of anchors, for calculation of strength in shear (in inch 2 vc ) as approximated by a rectangle with edges bounded by 1.5*Ca1 (1.5*5 = 7.5 inch in our case) and the free edges of the concrete from the centerline of the anchors. We will calculate it little later. Ca1 – Distance from the center of an anchor shaft to the edge of concrete in one direction (in inch). Refer Fig.1 below. A vco – Total projected shear failure area approximated by a square bounded by 1.5*Ca1 (1.5*5 = 7.5 inch in our case) from the centerline of a anchor at all the sides. We will calculate it little later. ψ ec,V – Modification factor for the anchor group loaded eccentrically in shear, in our case there is no eccentric loading , so ψ ec,V =1. ψ ed,V – Modification factor for edge effect for the anchor group in shear, we will calculate it later. Ψ c,V – Modification factor based on the presence and absence of crack in the concrete, in our case value of it = 1.. ψ cp,V – Modification factor for post weld types of anchor. For cast in place anchor ψ cp,V = 1 V b – Basic concrete break out strength for a single anchor in shear, we will calculate it later. Calculation of A Vc or Foundation Bolt Design Calculations with Example According to A...
Fig.1: Showing Ca1 for calculating Avc and Avco for Anchor Group
Fig.2: Anchor Bolt Elevation for calculating Avc Refer the above two figure (Fig.1 and Fig.2), it should be clear by now that A VC = 16.5*(5+6+16.5) = 453.75 inch 2
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ Calculation of A Vco
Fig.3: Anchor Bolt Elevation for calculating Avco By referring the above figure (Fig.3), we can calculate
Where, d a = Diameter of the anchor bolt in inch., in our case it is 0.75 inch. Remember we have started with the 0.75 inch anchor in the part-1 of this calculation. l e = Length of the anchor inserted inside the concrete in inch. In our case it is 10 inch. λ = A factor related to the reduced mechanical properties of concrete, for normal weight concrete λ=1. C a1 = we already know it from the Fig.1. Its value is 11 inch. f c ’ = Specified compressive strength of the concrete, in our case f c ’=4000 psi (refer problem statement of part-1). So, by putting all the values, the above equation (D-24) becomes
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/
Part-7: Determining Pryout Strength of Anchor in Tension In this part of the concrete anchor bolt design calculation example we will calculate the concrete pry out strength under shear force applied to the structural cast in place foundation anchor bolt of the column shown in the Figure-1 and 2 of the Part-1 of this design calculation series. What is Concrete Pryout Strength? This is something related to the coming out of the short and stiff anchors by breaking or chipping the concrete at the direction opposite to the applied shear force to the column. Design Calculation The code ACI 318 Appendix D gives the following equation: φV cpg =k cp N cbg ………………D-31 Where, Φ – Strength reduction factor for pryout strength and its value for non-reinforcement in tension is 0.70 V cpg – Pryout strength k cp – Factor, which has value =2 for the anchor longer than 2.5 inch. N cbg – Concrete breakout strength in tension (=20694.6131 lb, Refer Part-2) for the anchor group. Now, by putting all the values we get the pryout strength, Φ V cpg = 28972.45 lb Summary of Calculated Strength Values in Shear Through the part-5, Part-6, and this part we have come out with the following shear strength values: Nominal material strength in for the anchors (Φ V sa ) = 65130lb Concrete breakout strength for the anchor group (Φ V cbg ) =10821.297 lb Pryout strength of the anchor group (Φ V pn ) =28972.45 lb Out of these three strength values the smallest one will be the design strength.
Example of Concrete Anchor Bolt Design Calculation All credit of good work goes to http://blog.mechguru.com/machine-design/ So, the design strength in shear = 10821.297 lb From the problem statement (part-1), you can observe that applied factored shear force to the column = 2300 lb. Since, design strength in shear is much lower than the factored applied shear force, so, the anchor bolts are safe under shear Part-8: Interaction of Tensile and Shear Forces In this part of the concrete anchor bolt design calculation example we will see the interaction of tensile and shear forces for the structural cast in place foundation anchor bolt of the column. Please refer the Figure-1 and 2 of the Part-1 of this anchor design series. What the ACI 318 Codes says If, the factored shear load (2300 lb in our case, refer part-1) > 0.2* design strength in shear (10821.297 lb in our case, refer part-7) And, the factored tensile load (20000 lb in our case, refer part-1) > 0.2* design strength in tension (20694.6131 lb in our case, refer part-4) Then, (factored shear load / design strength in shear) + (factored tensile load /design strength in tension) <=1.2…………………..eq.8 For our case, the left hand side of the eq.8 becomes: (2300/10821.297) + (20000/20694.613) = 1.181, which is less than 1.2, so, we can conclude that the anchor bolt design is safe under the interaction of tensile and shear forces.
