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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,VV_b……………………………..D-22

Where,

Φ – Strength reduction factor for breakout strength and its value for non-reinforcement in tension is 0.70

A_vc –  projected concrete failure area of the group of anchors, for calculation of strength in shear (in inch²) 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

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 inch²

Calculation of A_Vco

By referring the above figure (Fig.3), we can calculate

A_vco= 16.5*(16.5+16.5) = 544.5 inch²

Calculation of ψ_ed,V

For C_a2 <1.5 Ca1

ψ_ed,V = 0.7+(0.3*C_a2)/(1.5*C_a1) = 0.7+ (0.3*5)/(1.5*11) = 0.79

Where,

C_a2 – Minimum concrete edge distance from anchor perpendicular to C_a1.

Calculation of V_b

V_b=(7*√d_a*[l_e/d_a]^0.2 )*λ*√f’_c*(C_a1)^1.5 ………………………..D-24

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

V_b = (7*√0.75*[10/0.75]^0.2)*1*(√4000)*11^1.5

= 23482.02 lb

Now, from the equation D-22, after putting all the values at right hand side,

φV_cbg = φ(A_Vc/A_Vco)ψ_ec,V ψ_ed,V ψ_c,V ψ_cp,VV_b

= 0.7*(453.75/544.5)*1*0.79*1*1*23482.02 lb

= 10821.297 lb

The concrete break out strength in shear for the anchor bolt group according to the ACI codes is calculated as 10821.297 lb. The next part (Part-7) will talk about Concrete Pullout Strength in Shear.

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. )