Product Technical Guides : US-EN Post-Installed Rebar Guide - Page 35

Post-Installed Reinforcing Bar Guide
6.0 WHAT ’ S THE BACK STORY ?
The following formulation of the interface shear design method proposed by Palieraki [ 14 ] is a simplification based on conservative assumptions . It consists of the summation of friction and dowel action effects ( see Eq . ( 18 )) with modification terms that account for surface roughness , reinforcing quantity and grade , reinforcing embedment and bond strength , and loading type ( i . e ., static vs . cyclic ). As shown in Figure 53 , the approach proposed by Palieraki provides excellent agreement with an extensive database of test results .
V n
= A c ( β f
f
+ β d
d
) ( Eq . 18 )
Shear contribution from dowel action can be calculated using equation 20 :
d
2
1.3 ‧ n ‧ d b f l f c y
=
where
A c
( psi ) ( Eq . 20 ) d b
= diameter of interface dowel reinforcement ( in .) n = number of dowels crossing interface
A c
= area of interface transected by n dowels ( in 2 ) where
V n
= nominal interface shear strength ( lb .) f
d
β f
β d
= nominal interface shear contribution from friction ( psi )
= nominal interface shear contribution from dowel ( psi )
= contribution factor for friction = contribution factor for dowel action
A c
= surface area of interface ( in 2 )
The shear contribution from friction can be calculated using equation 19 :
f = 0 . 33 [ ( f ' c ) 2 ‧ ( f c , vf
+ f ext ) ] 1 / 3 where
f c , vf
f ext
f bu
= compression stress over interface due to action of dowel reinforcement , and is equal to the lesser value of the equations below .
f y
‧ A vf = ( psi )
5 ‧ f bu ‧ l e
‧ A vf
=
d b
‧ A c
( psi )
= uniform stress over interface due to externally applied normal force ( positive for compression , negative for tension ) ( psi )
= bond strength associated with the post-installed bar ( psi ) l e
= embedment length of the dowel ( in .)
A vf
= area of interface dowel reinforcement ( in 2 ) f y
= yield stress of interface dowel reinforcement ( psi ) f ' c
A c
( psi ) ( Eq . 19 )
= concrete uniaxial compressive strength ( psi )
The contribution factors have been experimentally established as follows :
Friction contribution factor , β f
, for non-cyclic shear loading across the interface :
Surface roughness shear keys , or where f ext
≥ + 0.1 f ' c
0.8 mechanically roughened ( 1 / 4-in . amplitude ) 0.6 not roughened 0.4 not roughened , steel formed surface ( very smooth ) 0.2
Friction contribution factor , β f
, for cyclic ( seismic ) shear loading across the interface = 0.4 . Dowel action contribution factor , β d for non-cyclic shear loading across the interface :
Dowel embedment
For cyclic shear , use l e ≥ 10d b and β d
= 0.75 .
Example : Shear dowels ( compare with examples provided in 2.6.1 and 6.5.1 )
Requirement : Determine the embedment requirement for post-installed reinforcing bars used to connect a new 8-inch thick shotcrete ( pneumatically-placed ) shear wall to an existing concrete wall ( Figure 9 ). Bars are # 5 at 12 in . x 16 in . over face of wall . Existing shear wall is 10 in . thick with 4 ksi normal weight concrete . Try dowels embedded the minimum of 12 diameters ( cyclic shear ).
v u
= 9 ksf = 63 psi
A c
= 12 ‧ 16 = 192 in 2 f bu β d l e
> 8d b
0.75
= 1090 lb . / in2 ( characteristic bond strength in cracked concrete per ACI 355.4 )
V n
= A c ( β f
‧ f + β d d ) β f
33 2021