PART 3 TENSION LOAD
Concrete Breakout 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 ...................... 0.8λ 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 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 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 : f ct λ = 6.7 f cm
1.5
≤ 1.0 ( 19.2.4.3 )
1 λ a is a modification factor for lightweight concrete that is used to calculate the “ basic concrete breakout strength in tension ” ( N b
) per Eq . ( 17.4.2.2a ) or Eq . ( 17.4.2.2b ). 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 ”. The parameter “ λ a
” is a modification of “ λ ” that specifically “ accounts for the properties of lightweight concrete ” with respect to anchoring-to-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 type of anchor being used , to obtain the parameter λ a
.
Post-installed mechanical anchors can be shown compliance 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 shown compliance 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 postinstalled anchor are derived from this testing and will be given in the ICC-ESR for the anchor . For post-installed anchor design , PROFIS Engineering uses a λ a
-value as referenced in the ICC-ESR provisions for the anchor . These ICC-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 N 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 ( expansion and adhesive anchor concrete failure ) or 0.6 ( adhesive anchor bond failure ), for the λ a
-value to calculate
N b
. Therefore , the PROFIS Engineering λ a -value for calculating N b
, when designing cast-in-place and undercut anchors , will equal the λ-value that has been input . Likewise , the PROFIS Engineering λ a
-value for calculating N b
, when designing expansion and adhesive anchors , will equal 0.8λ since the parameter N b is relevant to concrete failure .
Reference the Equations and Calculations sections of the PROFIS Engineering report for more information on the parameter N b
.
The concrete mixture tested in order to calculate λ shall be representative of that to be used in the Work .
17.4.2.2 The basic concrete breakout strength of a single anchor in tension in cracked concrete , N b , shall not exceed
N b
= λ a k c f ́c h ef
1.5
( 17.4.2.2a )
Alternatively , for cast-in headed studs and headed bolts with 11 in . < h ef
< 25 in ., N b , shall not exceed
N b
= 16λ a f ́c h ef
5 / 3
( 17.4.2.2b )
64 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-14 Provisions