2.0 SHEAR
2.1 Concrete Breakout Failure Mode
Variables λ a
Variables ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering
λ a
17.2.4.1 Modification factor λ a for lightweight concrete shall be in accordance with Table 17.2.4.1 . It shall be permitted to use an alternate value of λ a if tests are performed and evaluated in accordance with ACI 355.2 or ACI 355.4 . Table 17.2.4.1 — Modification factor λ a for lightweight concrete
Cast-in and undercut anchor concrete failure
Case λ a
[ 1 ]
Expansion , screw , and adhesive anchor concrete failure
Adhesive anchor bond failure per Eq . ( 17.6.5.2.1 ) [ 1 ] λ shall be in accordance with 19.2.4
19.2.4 Lightweight concrete
19.2.4.1 Except as required in Table 25.4.2.5 , the value of λ shall be determined using Table 19.2.4.1 ( a ) based on the equilibrium density , w c
, of the concrete mixture used in design , or Table 19.2.4.1 ( b ) based on the composition of the aggregate in the concrete mixture assumed in the design .
Table 19.2.4.1 ( a ) — Values of λ for lightweight concrete based on equilibrium density
w c lb / ft 3 ≤ 100 0.75 ( a )
100 ≤ w c ≤ 135 0.0075 w c
≤ 1.0 ( b ) > 135 1.0 ( c )
λ
Table 19.2.4.1 ( b ) — Values of λ for lightweight concrete based on composition of aggregates
1.0 λ 0.8 λ 0.6 λ
Concrete Composition of Aggregates λ All-lightweight
Lightweight , fine blend
Fine : ASTM C330 Course : ASTM C330
Fine : Combination of ASTM C330 and C33 Course : ASTM C330
0.75
0.75 to 0.85 [ 1 ] λ a is a modification factor for lightweight concrete that is used to calculate the “ basic concrete breakout strength in shear ” ( V b
) per Eq . ( 17.7.2.2.1a ), Eq . ( 17.7.2.2.1b ) or Eq . ( 17.7.2.2.2 ). ACI 318 applies a multiplier to the parameter
√f ́c to “ account for the properties of lightweight concrete ”, and designates this parameter “ λ ”. The parameter “ λ a
“ is a modification of “ λ ” that specifically “ accounts for the properties of lightweight concrete ” with respect to anchoringto-concrete calculations , hence the subscript “ a ” in “ λ a
”. Per Table 17.2.4.1 , the modification factor λ , determined per the provisions of Section 19.2.4 , is multiplied by an additional factor that is specific to the type of anchor being used , to obtain the parameter λ a
.
Post-installed mechanical anchors can be qualified for recognition under the International Building Code via testing per the ICC-ES acceptance criteria AC193 in conjunction with the ACI standard ACI 355.2 . Post-installed adhesive anchor systems can be qualified for recognition under the International Building Code via testing per the ICC-ES acceptance criteria AC308 in conjunction with the ACI standard ACI 355.4 . λ a
-provisions for a specific post-installed anchor are derived from this testing and will be given in the ICC-ES evaluation report ( ESR ) for the anchor . For post-installed anchor design , PROFIS Engineering uses a λ a
-value as referenced in the ESR provisions for the anchor . These ESR provisions typically correspond to the ACI 318 provisions for λ a
.
PROFIS Engineering users can input a λ-value based on the properties of the lightweight concrete being used in the application . Any λ-value between 0.75 and 1.0 can be input . Per ACI 318 provisions for determining λ a
, when designing castin-place anchors and post-installed undercut anchors , PROFIS Engineering uses the λ-value that has been input , for the λ a
-value to calculate V b
. When designing post-installed expansion and adhesive anchors , PROFIS Engineering multiplies the λ-value that has been input by a factor of 0.8 ( for concrete failure ) to calculate
V b
. Therefore , the PROFIS Engineering λ a -value for calculating V b
, when designing cast-in-place and undercut anchors , will equal the λ-value that has been input , and the PROFIS Engineering λ a
-value for calculating V b
, when designing expansion and adhesive anchors , will equal 0.8λ .
Reference the Equations and Calculations sections of the PROFIS Engineering report for more information on the parameter V b
.
Sand-lightweight
Sand-lightweight , course blend
Normal weight
Fine : ASTM C33 Course : ASTM C330
Fine : ASTM C33 Course : Combination of ASTM C330 and C33
Fine : ASTM C33 Course : ASTM C33
0.85
0.85 to 1 [ 2 ]
1
[ 1 ] Linear interpolation from 0.75 to 0.85 is permitted based on the absolute volume of normal weight fine aggregate as a fraction of the total absolute volume of fine aggregate .
[ 2 ] Linear interpolation from 0.85 to is permitted based on the absolute volume of normal weight course aggregate as a fraction of the total absolute volume of course aggregate .
185 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions