LOAD DISTRIBUTION
As per ACI 318 Section 17.2 , load distribution should be determined on the basis of elastic analysis unless it can be shown that the nominal anchor strength is controlled by ductile steel elements . Where plastic analysis ( assumption of fully yielded anchors ) is used , compatibility of deformations must be checked .
BOLT BENDING — STRENGTH DESIGN
ACI 318 does not consider the possibility of bolt bending in detail as part of the design criteria . When stand-off is not grouted , it is recommended to consider bolt bending as a possible failure mode in shear because it could be a controlling shear failure mode . Per the ETAG 001 Annex C Part 4.2.2.4 , an additional check for shear load resulting from stand-off conditions can be performed when calculating nominal shear strengths .
V s
M
= whereby : α M
⋅ M s l
α M
|
= |
adjustment of bending moment associated |
|
|
with rotational restraint , where 1 ≤ α M ≤ 2 |
M S
= resultant flexural resistance of single anchor N
( ua
))
|
= |
0
M s (
1-
ФN sa
|
|
0
M s
|
= |
characteristic flexural resistance of single |
|
|
anchor |
Example of incompatibility of deformations ( displacements )
In most cases , elastic analysis yields satisfactory results and is recommended . It should be noted , however , that the assumption of anchor load linearly proportional to the magnitude of the applied load and the distance from the neutral axis of the group is valid only if the attachment ( e . g . baseplate ) is sufficiently stiff in comparison to the axial stiffness of the anchors . For additional information on elastic load distribution in typical column baseplate assemblies , the reader is referred to Blodgett , O ., Design of Welded Structures , The James F . Lincoln Arc Welding Foundation , Cleveland , Ohio .
Note : Assuming a rigid base plate condition , Hilti ’ s PROFIS Anchor analysis and design software performs a simplified finite element analysis to establish anchor load distribution on an elastic basis .
= 1.2 · S · f u , min
f u , min
|
= |
minimum nominal ultimate tensile strength |
|
|
of anchor element |
S |
= |
elastic section modulus of anchor bolt |
|
|
at concrete surface ( a uniform cross section |
|
|
is assumed ) |
= ( л * d 3 ) / 32
l |
= |
internal lever arm adjusted for spalling of the |
|
|
concrete surface as follows : |
= z + ( n ⋅ d o )
z |
= |
distance from center of base plate to |
|
|
surface of concrete ( standoff distance ) |
d o
= anchor outside diameter at concrete surface
n |
= |
0 , for loading with clamping at the concrete |
|
|
surface as provided by a nut and washer |
|
|
assembly ( required for mechanical anchors ) |
= 0.5 , for loading without clamping at the concrete surface , e . g ., adhesive anchor without nut and washer at concrete surface
Note that stand-off installations of post-installed mechanical anchors require a nut and bearing washer at the concrete
Example of elastic load distribution in a beam-wall connection surface as shown below for proper anchor function and to properly resist compression loads .
16 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