PROFIS ENGINEERING REPORT TENSION LOAD
Bond Failure Mode
Variables λ a
Variables ACI 318-14 Chapter 17 Provision Comments for PROFIS Engineering
λ a
17.2.6 Modification factor λ a for lightweight concrete shall be taken as :
Cast-in and undercut anchor concrete failure ......................... 1.0 λ Expansion and adhesive anchor concrete failure ...................... 0.8 λ Adhesive anchor bond failure per Eq . ( 17.4.5.2 ) ......................... 0.6 λ
where λ is determined in accordance with 19.2.4 . It shall be permitted to use an alternative value of
λ a where tests have been performed and evaluated in accordance with ACI 355.2 or ACI 355.4 .
19.2.4 Lightweight concrete 19.2.4.1 To account for the properties of lightweight concrete , a modification factor λ is used as a multiplier of √f ́c in all applicable provisions of this Code . 19.2.4.2 The value of λ shall be based on the composition of the aggregate in the concrete mixture in accordance with Table 19.2.4.2 or as permitted in 19.2.4.3 .
Table 19.2.4.2 — Modification factor λ [ 1 ] [ 2 ] 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 C33 Fine : ASTM C33 Coarse : ASTM C33
0.75
0.75 to 0.85 { 1 ]
0.85
0.85 to 1 [ 2 ]
1 Linear interopolation of 0.75 to 0.85 is permitted based on the absolute volume of normal weight fine friction aggregate as a fraction of the total absolute volume of fine aggregate .
2 Linear interopolation of 0.85 to 1 is permitted based on the absolute volume of normal weight coarse friction aggregate as a fraction of the total absolute volume of coarse aggregate .
19.2.4.3 If the measured average splitting tensile strength of lightweight concrete , f ct
, is used to calculate λ , laboratory tests shall be conducted in accordance with ASTM C330 to establish the value of f ct and the corresponding value of f cm and λ shall be calculated by :
The concrete mixture tested in order to calculate λ shall be representative of that to be used in the work . f ct λ = 6.7 f cm
1.5
≤ 1.0 ( 19.2.4.3 )
17.4.2.2 The basic concrete breakout strength of a single anchor in tension in cracked concrete , N b , shall not exceed
N ba
= k c λ a f ́c h ef
1.5
( 17.4.2.2a )
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 318-14 Section 17.2.6 references how λ a is calculated for various anchoring-to-concrete 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 17.2.6 , λ a is also used to calculate the “ basic bond strength in tension ” ( N ba ) per Eq . ( 17.4.5.2 ), 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 17.2.6 , 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 shown compliance to 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-ESR for the anchor . These ICC-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 ICC-ESR is used to calculate N b
, and the λ a
-value ( or provisions ) for bond failure referenced in the adhesive anchor ICC-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 .
17.4.5.2 The basic bond strength of a single adhesive anchor in tension in cracked concrete , N ba , shall not exceed
N ba
= λ a т cr πd a h ef
( 17.4.5 . 2 )
28 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-14 Provisions