theory . For the development of these Tables , the strengths corresponding to the applicable limit states for single bars in tension for non-seismic applications ( i . e ., SDC A and B ) in ACI 318 Chapter 17 are taken as follows :
N steel
= A b ( 1.25 ƒ y
)
N breakout
= ф c k c , uncr ƒ ' c h ef , breakout
1.5
N bond
= ф b τ k , cr / uncr πd b h ef , bond
( E ) Wall
( N ) drilled-in dowels
( N ) shotcrete wall
Roughened surface , 1 / 4-in . amplitude
Section through a shotcrete onlay wall with post-installed dowels designed using anchor provisions whereby the concrete breakout and bond strengths with reduction factors applied are each set equal to the assumed bar yield strength . In CSA calculations , R for breakout and bond calculations is conservatively assumed to equal 1.0 . The resulting expressions are solved for h ef as follows : As governed by single-bar concrete breakout strength :
A b
1.25 ƒ y = ф c k c , uncr
( ) h ef , breakout
= A b ( 1 . 25 ƒ y ) 2 / 3 ф c k c , uncr ƒ ' c
ƒ ' c h ef , breakout
1.5 yields with minimum c a and s intended to preclude edge and spacing effects . As governed by single-bar bond strength :
A se , N
1.25 ƒ y = ф b τ k , uncr πd b h ef , bond yields h ef , bond
=
A b
( 1.25 ƒ y ) ф b τ k , uncr πd a with minimum c a and s intended to preclude edge and spacing effects . The controlling embedment ( in this case , the larger value of
h ef , breakout and h ef , bond
), is reported in the table together with the accompanying edge distances and spacing values .
Note : ACI 318 17.3.2.3 states : “ For adhesive anchors with embedment depths 4d a
≤ h ef ≤ 20d a the bond strength requirements shall be considered satisfied by the design procedure of 17.4.5 .” In accordance with 17.3.2.3 , ESR-3814 and ESR-4868 limit anchorage embedment depths to this range of values . These requirements recognize the limits of the uniform bond model adopted by ACI . Anchorage embedments published in the Hilti North American Product Technical Guide are based on assumptions that are intended to achieve development of the nominal yield stress in reinforcing bars . In some cases , the recommended bar embedment exceeds , by an acceptable margin , the 20 bar diameter limit established in ACI 318 Chapter 17 for the applicability of the uniform bond model . It is Hilti ' s view that the conservatism of the underlying assumptions , taken in aggregate , is sufficient to offset any reduction in the effective bond stress associated with these bond lengths . The designer may elect to employ alternate design assumptions for bar development based on the specific conditions for a given design .
Spacing : To account for the influence of nearby bars on the concrete resistance ( breakout / bond failure ), minimum spacing is calculated as the greater of 20d b
( τ k , uncr
/ 1100 psi ) 0 . 5 and 3h ef , breakout
Edge distance : To account for the effect of edge distance on the concrete resistance , minimum edge distance is calculated as the greater of 10d b
( τ k , uncr / 1100 psi ) 0 . 5 and 1.5h ef , breakout
.
In addition , for uncracked concrete , the minimum edge distance may be governed by the value of c ac
, the critical edge distance for splitting failure where the design assumes uncracked concrete and where there is no reinforcing to control splitting cracks .
In this case , the value of c ac is taken as :
( )
τ 0. 4 k , uncr c ac
= h ef
3.1 - 0.7 h 1160 h ef
where h ≤ 2.4 and h ef τ k , uncr is the characteristic bond strength stated in the Evaluation Service Report and cannot be taken as larger than :
k c , uncr h ef f ' c τ k , uncr
= —————— π∙d
The application of c ac to post-installed reinforcing bars in uncracked concrete is advisable where the EOR determines that splitting will be critical for the behavior of the connection at ultimate loads . The figure below represents two possible extremes for the calculation of edge distance . Condition I illustrates a bar anchored in a relatively thin and lightly reinforced slab . In this case , splitting is likely to be critical and the application of c ac as calculated in the equation above is advisable . At the other extreme , Condition II is represented by bars embedded in a heavily reinforced foundation where the ratio of h to h ef is large as judged by the EOR . In Condition II , splitting is unlikely to control the behavior and the c ac term may be neglected . In all cases , proper judgment based on the loading and geometry of the connection should be applied .
Anchor Fastening Technical Guide Edition 22 | 3.0 ANCHORING SYSTEMS | 3.1 ANCHOR PRINCIPLES AND DESIGN Hilti , Inc . 1-800-879-8000 | en español 1-800-879-5000 | www . hilti . com | Hilti ( Canada ) Corporation | www . hilti . ca | 1-800-363-4458
27