PART 3 TENSION LOAD
Pullout 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 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 )
The concrete mixture tested in order to calculate λ shall be representative of that to be used in the Work .
1 λ a is a modification factor for lightweight concrete . 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 post-installed 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 uses the λ-value that has been input , to calculate a λ a
-value for the anchor being modeled . 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 . No reduction for lightweight concrete is required when calculating nominal pullout strength in tension for cast-in anchors per Eq . ( 17.4.3.4 ), because no √f ́c parameter is present in the equation . If cast-in anchors are being modeled for lightweight concrete conditions in PROFIS Engineering , ( λ a
= 1.0 λ ) will be used in the concrete breakout , side-face blowout and pryout calculations . The λ a
-value will be calculated per Section 17.2.6 . No λ a
-value will be used in the pullout calculations . The Variables section for pullout in the report will show the parameter λ a equal to 1.0 .
If post-installed expansion anchors or HIT-Z / HIT-Z-R threaded rods with HIT HY 200 adhesive are being modeled for lightweight concrete conditions in PROFIS Engineering , the software calculates a λ a
-value per Section 17.2.6 . The λ-value that has been input is multiplied by a factor of 0.8 ( expansion anchors ) or by a factor of 0.6 ( HIT-Z / HIT-Z-R with HIT HY 200 ) to obtain a λ a
-value for pullout calculations . This functionality is summarized to the left .
Reference the Equations and Calculations sections of the PROFIS Engineering report for more information on the parameter N pn or N pn , f ́c when lightweight concrete conditions are being modeled for post-installed anchors .
When lightweight concrete conditions are being modeled , PROFIS Engineering applies the parameter λ a as follows : cast-in anchors
N pn
= ψ c , p
N p
( 17.4.3.1 )
N p
= 8A brg f ́c ( 17.4.3.4 ) λ a
= 1.0 for pullout calculations mechanical anchors
N pn , f ́c
= N p , 2500 λ a
( f ́c / 2500 ) n where λ a
= 0.8 λ HIT-Z / R threaded rods used with HIT-HY 200 adhesive
N pn
= N p λ a where λ a = 0.6 λ
86 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-14 Provisions