2.0 SHEAR
2.3 Steel Failure Mode
Calculations ψ ec2 , Na
Calculations ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering
ψ ec2 , Na
17.7.3.1 Nominal pryout strength , ………………… V1 of an anchor group ……….. shall not exceed …..( b )………..
( b ) For an anchor group
V cpg
= k cp
N cpg
( 17.7.3.1b )
17.7.3.1.2 ………………. for adhesive anchors , N cpg shall be the lesser of N ag calculated by Eq . ( 17.6.5.1b ) and N cbg calculated by Eq . ( 17.6.2.1b ).
17.6.5.1 Nominal bond strength in tension ………… N ag of an adhesive anchor group ……………. shall be calculated by ……( b )………….
( b ) For an adhesive anchor group :
N ag
= A Na ψ ec , Na ψ ed , Na ψ cp , Na
N ba
( 17.6.5.1b )
A Na0
17.6.5.3.1 Modification factor for adhesive anchor groups loaded eccentrically in tension , ψ ec , Na shall be calculated by Eq . ( 17.6.5.3.1 ).
Concrete pryout strength for a group of anchors in shear ( V cpg ) is calculated per Eq . ( 17.7.3.1b ).
With respect to bond failure , the parameter “ N cpg ” in this equation corresponds to the nominal bond strength ( N ag ), calculated per Eq . ( 17.6.5.1b ). The parameter “ ψ ec , Na
” in Eq . ( 17.6.5.1b ) is a modification factor that accounts for a resultant shear load that is eccentric with respect to the centroid of the anchors that are loaded in shear . ψ ec , Na is only considered for an anchor group loaded in shear when calculating V cpg
.
When shear load acting on a group of anchors is eccentric with respect to the y direction , PROFIS Engineering calculates “ ψ ec , Na
” per Eq . ( 17.6.5.1b ) and designates this parameter “ ψ ec2 , Na ”. PROFIS
Engineering designates the eccentricity parameter e ́N in Eq . ( 17.6.5.3.1 ) “ e c2 , N
” to likewise indicate that the software is considering eccentricity with respect to the y direction . If the resultant shear load acting on the anchorage is eccentric with respect to both the x and y directions ; PROFIS Engineering calculates “ ψ ec , Na
” for both directions .
The illustration below shows how PROFIS Engineering considers shear eccentricity when calculating V cpg
. The resultant shear load ( V res
) is eccentric in both the x direction and y direction with respect to the centroid of the anchors that are in shear . PROFIS Engineering defines the eccentricity of the shear load in the x-direction as the parameter “ e c1 , N
” and eccentricity in the y-direction as the parameter “ e c2 , N ”. ψ ec , Na
=
1
1 + e ́N c Na
( 17.6.5.3.1 )
17.6.5.3.2 If the loading on an adhesive anchor group is such that only some of the adhesive anchors are in tension , only those adhesive anchors that are in tension shall be considered for determining the eccentricity e ́N in Eq . ( 17.6.5.3.1 ) and for the calculation of N ag according to Eq . ( 17.6.5.1b ). 17.6.5.3.3 If a load is eccentric about two orthogonal axes , ψ ec , Na shall be calculated for each axis individually , and the product of these factors shall be used as ψ ec , Na in Eq . ( 17.6.5.1b ).
PROFIS Engineering calculates “ ψ ec , Na ” for both directions . ψ ec1 , Na
=
1
1 + e c1 , N c Na ψ ec2 , Na
=
1
1 + e c2 , N c Na
For this example , the value for “ ψ ec , Na ” used in Eq . ( 17.6.5.1b ) equals the product of ψ ec1 , Na and ψ ec2 , Na
: ψ ec , Na = ( ψ ec1 , Na
)( ψ ec2 , Na
). Reference the Equations section of the PROFIS Engineering report for more information on :
ψ ec , Na
: modification factor for shear eccentricity
Reference the Variables section of the PROFIS Engineering report for more information on the following parameters :
e c1 , N
: parameter for shear eccentricity with respect to the x direction
e c2 , N
: parameter for shear eccentricity with respect to the y direction . Reference the Calculations section of the PROFIS Engineering report for more information on :
c Na
: edge distance parameter for adhesive anchors
ψ ec2 , Na
: modification factor for shear eccentricity with respect to the y direction .
274 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions