1.0 TENSION
1.6 Sustained Load 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
Sand-lightweight
Sand-lightweight , course blend
Normal weight
Fine : ASTM C330 Course : ASTM C330
Fine : Combination of ASTM C330 and C33 Course : ASTM C330
Fine : ASTM C33 Course : ASTM C330
Fine : ASTM C33 Course : Combination of ASTM C330 and C33
Fine : ASTM C33 Course : 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 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 .
17.5.2.2 Design of adhesive anchors to resist sustained tension shall satisfy Eq . ( 17.5.2.2 ) 0.55 ϕN ba
≥ N ua , s ( 17 . 5 . 2 . 2 ) where N ba is the basic bond strength in tension of a single adhesive anchor and is N ua , s the factored sustained tensile load .
17.6.5.2.1 Basic bond strength of a single adhesive anchor in tension in cracked concrete , Nba , shall be calculated by Eq . ( 17.6.5.2.1 ).
N ba
= λ a т cr π da h ef
( 17.6.5.2.1 )
1
ACI 318 anchoring-to-concrete provisions consider the following tension failure modes with respect to adhesive anchor systems :
• steel failure in tension .
• concrete breakout failure in tension .
• bond failure in tension .
λ a is a modification factor for lightweight concrete that is used to calculate various parameters for design with ACI 318 anchoring-to-concrete provisions . ACI 318- 19 Section 17.2.4.1 references how λ a is calculated for various anchoring-toconcrete failure modes . When considering concrete breakout failure in tension for an adhesive anchor application , the λ a
-value that is calculated equals 0.8λ .
This λ a -value would be used to calculate the basic concrete breakout in tension
( N b ) for the adhesive anchor being designed . Per Section 17.2.4.1 , λ a is also used to calculate the “ basic bond strength in tension ” ( N ba ) per Eq . ( 17.6.5.2.1 ), and the λ a
-value calculated for bond failure equals 0.6λ .
Generally speaking , with respect to concrete failure modes , ACI 318 applies a multiplier designated “ λ ” to the parameter √f ́c to “ account for the properties of lightweight concrete ”. 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 Section 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 anchor failure mode being considered , to obtain the parameter λ a
. Therefore , when designing adhesive anchors with ACI 318 anchoring-to-concrete provisions , a lightweight concrete multiplier ( λ a
= 0.8λ ) is applied to the parameter √f ́c when considering concrete breakout failure , and a lightweight concrete multiplier ( λ a
= 0.6λ ) is applied to the parameter “ т ” corresponding to the characteristic bond stress ( т cr for cracked concrete or т uncr for uncracked concrete ) when considering bond failure .
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 adhesive anchor system are derived from this testing and will be given in the ICC-ES evaluation report ( ESR ) for the anchor . These ESR provisions typically correspond to the ACI 318 provisions for λ a
. When modeling an adhesive anchor application in PROFIS Engineering , the λ a
-value ( or provisions ) for concrete breakout failure referenced in the adhesive anchor ESR is used to calculate N b
, and the λ a
-value ( or provisions ) for bond failure referenced in the adhesive anchor ESR is used to calculate N ba
.
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 adhesive anchors , PROFIS Engineering multiplies the λ-value that has been input by a factor of 0.8 to obtain the λ a
-value used to calculate N b . Per ACI
318 provisions for determining λ a
, when designing adhesive anchors , PROFIS Engineering multiplies the λ-value that has been input by a factor of 0.6 to obtain the λ a
-value used to calculate N ba
.
Reference the Equations and Calculations sections of the PROFIS Engineering report for more information on the parameters N b and N ba
.
154 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions