2.0 SHEAR
2.3 Steel Failure Mode
Calculations A Na
Calculations ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering
A Na
17.7.3.1 Nominal pryout strength , V cp for a single anchor or V cpg of an anchor group satisfying
17.5.1.3.1 , shall not exceed ( a ) or ( b ), respectively . ( a ) For a single anchor
( b ) For an anchor group
k cp
= 1.0 for h ef < 2.5 in . k cp
= 2.0 for h ef ≥ 2.5 in .
V cp
= k cp
N cp
( 17.7.3.1a )
V cpg
= k cp
N cpg
( 17.7.3.1b )
17.7.3.1.1 For cast-in anchors and post-installed expansion , screw , and undercut anchors , N cp shall be taken as N cb calculated by Eq . ( 17.6.2.1a ), and for adhesive anchors , N cp shall be the lesser of N a calculated by Eq . ( 17.6.5.1a ) and N cb calculated by Eq . ( 17.6.2.1a ).
17.7.3.1.2 For cast-in anchors and post-installed expansion , screw , and undercut anchors , N cpg shall be taken as N cbg calculated by Eq . ( 17.6.2.1b ), and 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 a of a single adhesive anchor or N ag of an adhesive anchor group satisfying 17.5.1.3.1 , shall be calculated by ( a ) or ( b ), respectively .
When calculating the nominal concrete pryout strength in shear ( V cp or V cpg
), the parameter A Na is a modification factor that accounts for the area of influence assumed to develop in concrete when a shear load applied to a single anchor or a group of anchors creates a prying ( i . e . tension ) action on the anchor ( s ). A Na is calculated with the edge conditions and anchor spacing that have been input into the PROFIS Engineering model . The geometry for A Na is defined by projected distances from the anchors that are in shear . The maximum projected distance from an anchor that is considered when calculating A Na is limited to “ c Na ”, where c Na corresponds to the edge distance parameter calculated per Eq . ( 17.6.5.1.2b ). Therefore , the maximum edge distance parameter used to calculate A Na equals c Na and the maximum spacing parameter used to calculate A Na equals 2.0c Na
. Per section 17.6.5.1.1 , using these limits for edge distance and spacing , and defining the parameter A Na0 per Eq . ( 17.6.5.1.2a ); the value for A Na will never be greater than nA Na0
, where n corresponds to the number of anchors in shear . This limit is described below .
The figure below illustrates how A Na is calculated for pryout when a shear load acts on a group of four anchors with fixed edge distances equal to c a1 and c a2 , and spacing parameters equal to s 1 and s 2
. Note that the maximum edge distance parameter used to calculate A Na equals c Na
. Anchors spaced greater than 2.0c Na from one another would not be considered to act as a group with respect to that spacing .
( a ) For a single adhesive anchor
|
N a
=
A
|
Na ψ ed , Na ψ cp , Na
N ba
|
( 17.6.5.1a ) |
|
A Na0
|
|
( 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
17.6.5.1.1 A Na is the projected influence area of a single adhesive anchor or an adhesive anchor group that is approximated as a rectilinear area that projects outward a distance c Na from the centerline of the adhesive anchor , or in the case of an adhesive anchor group , from a line through a row of adjacent adhesive anchors . A Na shall not exceed nA Na0
, where n is the number of adhesive anchors in the group that resist tension . 17.6.5.1.2 A Na0 is the projected influence area of a single adhesive anchor with an edge distance of at least c Na .
A Na0
= ( 2c Na ) 2 ( 17.6.5.1.2a )
A Na
= ( c a1 + s 1
+ c Na ) ( c a2
+ s 2 + c Na
) where : c a1 and c a2 are ≤ c Na s 1 and s 2 are ≤ 2.0 cNa
For the example above , if c a1 = c a2
= c Na and s 1
= s 2 = 2.0c Na
, then A Na would equal
( c Na + 2.0c Na
+ c Na )( c Na
+ 2.0c Na + c Na
) = 16c Na2 . The parameter A Nc
/ A Nc0 would equal 16c Na2 / 4c Na
2
= 4 . Therefore , since the maximum edge distance parameter
( c Na ) and maximum spacing parameter ( 2.0c Na
) have been assumed , A Na equals nA Na0
, where n = 4 corresponds to the number of anchors in the group that resist shear . where c Na
= 10d a т uncr ( 17 . 6 . 5 . 1 . 2b ) 1100
It is important to understand that “ A Na ” calculated for bond failure in tension is not necessarily the same as “ A Na
” calculated for concrete pryout failure in shear since the number of anchors in tension may not be the same as the number of anchors in shear .
Reference the Equations section of the PROFIS Engineering report for more information on A Na
. and c Na
.
268 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions