The recommended allowable loads for an anchor or a group of anchors are obtained as follows :
Tension : Shear :
where :
N rec
N allow
V rec
V allow
ƒ A
N rec
= N allow
⋅ ƒ RN
⋅ ƒ A
V rec
= V allow
⋅ ƒ RV
⋅ ƒ A
= recommended tension load
= allowable load ( based on the mean value from laboratory testing to failure and a global safety factor )
= recommended shear load = allowable shear load = adjustment factor for anchor spacing ƒ RN
= adjustment factor for edge distance , tension loading ƒ RV1
ƒ RV2
ƒ RV3
= adjustment factor for edge distance , shear loading perpendicular and toward free edge
= adjustment factor for edge distance , shear loading parallel to free edge
= adjustment factor for edge distance , shear loading perpendicular and away from free edge
Adjustment factors are multiplicative and are applied for all edge and spacing conditions that are less than c cr and s cr
, respectively .
For example , the recommended tension load corresponding to anchor “ a ” in the figure below is evaluated as follows :
F rec , a
= F allow , a
⋅ ƒ Rx ⋅ ƒ Ry
⋅ ƒ Ax
⋅ ƒ Ay
Note that no reduction factor for the diagonally located adjacent anchor is required .
Similarly , for near-edge anchors , the edge distance adjustment factor ( s ) are applicable for cases where the anchor edge distance is such that :
where :
c min
c cr c min
≤ c < c cr
= minimum edge distance ; and
= critical edge distance ( anchor edge distance equal to or greater than the one requiring a reduction factor )
INTERACTION — ASD
Where anchors are loaded simultaneously in tension and shear , interaction must be considered . The usual form of the interaction equation for anchors is as follows :
N α d
V α d
V rec
=
[ ] —— + N [ ] —— rec
V rec where :
≤ 1 . 0
N d
= design tension load ( ASD );
V d
= design shear load ( ASD ); and α = exponent , 1 ≤ α ≤ 2
The value used for α corresponds to the type of interaction equation being considered . A value of α = 1.0 corresponds to a straight line interaction equation , while a value of α = 5 / 3 corresponds to a parabolic interaction equation .
SHEAR LOAD WITH LEVER ARM ( BOLT BENDING ) — ASD
When shear load is applied to a stand-off connection , the anchor bolt is subjected to combined shear and bending , and a separate assessment of the standoff condition is appropriate . In the absence of other guidance , the recommended shear load associated with bolt bending for anchors subjected to shear loads applied at a standoff distance z may be evaluated as follows : α M
⋅ M uM , 5 %
V rec
= ————— 1.7 ⋅ l where :
CRITICAL AND MINIMUM SPACING AND EDGE DISTANCE
Spacing adjustment factors are applicable for cases where the anchor spacing is such that :
s min
≤ s < s cr where :
s min
s cr
= minimum spacing between loaded anchors ; and
= critical spacing between loaded anchors ( anchor spacing equal to or greater than the one requiring a reduction factor ) α M
V rec
M uM , 5 %
f uta
= adjustment of bending moment associated with rotational restraint , where 1 ≤ α M
≤ 2
= recommended shear load corresponding to bending
= characteristic flexural resistance of a single anchor corresponding to approximately 1 / 2 degree rotation
= 1.2 * S * f u , min (
1 - —— N d
N rec
)
= minimum ultimate tensile strength of anchor
22 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