Blog

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,NN_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.

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

Before going to the calculation please refer the plan view of the anchor arrangement as below:

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:

A_NC =Area of the square shown in dotted line

= (15+15)*(15+15) = 900 Square Inch

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.

Calculation of N_b

N_b= k_c λ h_ef^1.5 f_c’ …………………D-7

Where,

K_c – a factor which has value of 24 for cast in concrete.

λ – A factor related to the reduced mechanical properties of concrete, for normal weight concrete  λ=1

h_ef – Effective embedment depth of anchor (in our case it is 10 inch).

f_c’ – Specified compressive strength of the concrete, in our case f_c’=4000 psi (refer problem statement)

So, by putting the value in D-7 we get:

N_b =24*1*10^1.5*4000^0.5

= 48000 lb

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,NN_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. In the next part (Part-3) of the foundation anchor bolt design calculation example, we will discuss about calculating the concrete pull out force in tension.

Shibashis Ghosh

Hi, I am Shibashis, a blogger by passion and an engineer by profession. I have written most of the articles for mechGuru.com. For more than a decades i am closely associated with the engineering design/manufacturing simulation technologies. I am a self taught code hobbyist, presently in love with Python (Open CV / ML / Data Science /AWS -3000+ lines, 400+ hrs. )