2.0 SHEAR
2.3 Steel 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 wc lb / ft 3 λ
1.0 λ 0.8 λ 0.6 λ
< 100 0.75 ( a ) 100 ≤ wc ≤ 135 0.0075wc ≤ 1.0 ( b )
> 135 1.0 ( c )
Table 19.2.4.1 ( b ) — Values of λ for lightweight concrete based on composition of aggregates Concrete Composition of Aggregates λ
All-lightweight Lightweight , fine blend
Sand-lightweight
Sand-lighweight , course blend
Normal weight
Fine : ASTM C330 Coarse : ASTM C330 Fine : Combination of ASTM C330 and 33 Coarse : ASTM C330 Fine : ASTM C33 Coarse : ASTM C330 Fine : ASTM C33 Coarse : Combination of ASTM C330 and 33 Fine : ASTM C33 Coarse : ASTM C33
0.75 0.75 to 0.85 { 1 ] 0.85 0.85 to 1 [ 2 ]
[ 1 ] Linear interpolation from 0.75 to 0.85 is permitted based on the absolute volume of normal weight a fine aggregate as a fraction of the total absolute volume of fine aggregate .
[ 2 ] Linear interpolation from 0.85 to 1 is permitted based on the absolute volume of normal weight course aggregate as a fraction of the total absolute volume of course aggregate .
1
When calculating nominal concrete pryout strength in shear ( V cp or V cpg
), λ a is a modification factor for lightweight concrete that is used to calculate the parameter “ N ba
” per Eq . ( 17.6.5.2.1 ). Generally speaking , ACI 318 applies a multiplier to the parameter √f ́c to “ account for the properties of lightweight concrete ”, and designates this parameter “ λ ”; however , λ is also used in the bond strength calculation for N ba
. 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 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 postinstalled adhesive anchors , PROFIS Engineering multiplies the λ-value that has been input by a factor of 0.6 ( adhesive anchor bond failure ), for the λ a
-value to calculate N ba
.
Reference the Equations and Calculations sections of the PROFIS Engineering report for more information on the parameter N ba
.
17.6.5 . 2.1 Basic bond strength of a single adhesive anchor in tension in cracked concrete , N ba , shall be calculated by Eq . ( 17.6.5.2.1 ).
N ba
= λ a т cr πd a h ef
( 17.6.5.2.1 )
264 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions