2.0 SHEAR
2.1 Concrete Breakout Failure Mode
Calculations ψ ec , V
Calculations ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering
ψ ec , V
17.7.2.3.1 Modification factor for anchor groups loaded eccentrically in shear , ψ ec , V , shall be calculated by Eq . ( 17.7.2.3.1 ). ψ ec , V
=
1
1 + e ́V
1.5c a1
≤ 1.0 ( 17 . 7.2.3.1 )
17.7.2.3 . 2 If the loading on an anchor group is such that only some of the anchors in the group are in shear , only those anchors that are in shear in the same direction shall be considered for determining the eccentricity e ́V in Eq . ( 17.7.2.3.1 ) and for the calculation of V cbg according to Eq .
( 17.7.2.1b ). 17.7.2.1 Nominal concrete breakout strength in shear , V cb of a single anchor or V cbg of an anchor group satisfying 17.5.1.3.1 , shall be calculated in accordance with ( a ) through ( d ): ( a ) For shear force perpendicular to the edge on a single anchor
The text below explains how PROFIS Engineering would determine the shear eccentricity parameter ( e ́V ) that is used to calculate ψ ec , V for an example when a torsion moment acts on four anchors . Assume a fixed edge is present in the x + direction and that concrete breakout will occur at the x + edge .
The moment creates loads in the x direction as follows :
• V 2 , x (+) on anchor 2 and V 4 , x
(+) on anchor 4 .
• V 1 , x ( - ) on anchor 1 and V 3 , x
( - ) on anchor 3 .
The moment creates loads in the y direction as follows :
• V 3 , y (+) on anchor 3 and V 4 , y
(+) on anchor 4 .
• V 1 , y ( - ) on anchor 1 and V 2 , y
( - ) on anchor 2 .
A
V cb
= Vc ψed , V ψ c , V ψ h , V
V b
( 17.7.2.1a )
A Vc0
( b ) For shear force perpendicular to the edge on an anchor group
V cbg
= A Vc ψ ec , V ψ ed , V ψ c , V ψ h , V
V b
( 17.7.2.1b )
A Vc0
PROFIS Engineering calculates a resultant shear load ( V resultant
) from the loads acting on anchors 1-4 that influence the x + fixed edge . PROFIS Engineering would assume only loads V 2 , x and V 4 , x influence the fixed edge with respect to loads acting in the x direction . Likewise , PROFIS Engineering would assume only loads
V 3 , y and V 4 , y influence the fixed edge with respect to loads acting in the y direction .
V resultant can be calculated with these loads as shown below . Concrete breakout is assumed to occur from anchors 3 and 4 . V resultant is eccentric ( e ́V ) with respect to the centroid of these anchors . This shear eccentricity ( e ́V ) can be calculated knowing the angle θ and the spacing ( s ) between anchors 3 and 4 .
V resultant
= [( V 2 , x + V 4 , x
) 2 + ( V 3 , y + V 4 , y
) 2 ] 0 . 5
= [( V x ) 2 + ( V y
) 2 ] 0 . 5 tan -1 θ = ( V x / V y
)
e ́V = ( s / 2 ) ( sin θ )
Reference the Variables section of the PROFIS Engineering report for more information on the following parameters :
e ́V : parameter for shear eccentricity .
c a1
: parameter for edge distance in the direction of the applied shear load .
Reference the Equations section of the PROFIS Engineering report for more information on ψ ec , V
.
194 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions