2.0 SHEAR
2.5 Steel Failure with Lever Arm
Results ϕV s
M
Results ETAG 001 Annex C Provision Comments for PROFIS Engineering
ϕV s
M
5.2.3.2 Steel failure b ) Shear load with lever arm
The characteristic resistance of an anchor , V Rk , s , is given by Equation ( 5.5 ).
V Rk , s
= α M M Rk , s [ N ] ( 5.5 ) l where α M
= see 4.2.2.4 l = lever arm according to Equation ( 4.2 )
M Rk , s
= M 0 ( 1 - N / N ) [ Nm ] ( 5 . 5a )
Rk , s Sd Rd , s
N Rd , s
= N Rk , s / Y Ms
N Rk , s
, Y Ms to be taken from the relevant ETA M 0 = characteristic bending resistance of an individual anchor
Rk , s
The value of M 0 for anchors according to current experience is obtained from
Rk , s
Equation ( 5.5b ).
M 0 Rk , s = 1 . 2 W el ƒ uk
[ Nm ] ( 5 . 5b )
The figures below illustrate ETAG 001 design assumptions with respect to bolt bending . PROFIS Engineering nomenclature for ACI 318 calculations is used in the illustrations .
Shear and tension load act on an anchor having standoff .
PROFIS Engineering uses the provisions given in the European Technical Approval Guideline ( ETAG ) titled ETAG 001 Metal Anchors for Use in Concrete Annex C : Design Methods for Anchorages to consider bolt bending as a possible shear failure mode . When a standoff condition exists for an anchorage , an applied shear load can create bending in the anchors . An internal bending resistance , designated M 0 , can be calculated using the material properties
Rk , s of the anchor element . M 0 is designated “ Rk , s M0 ” in PROFIS Engineering , and is calculated per s Equation ( 5.5b ). If tension load also acts on the anchor , M 0 is reduced by a factor designated
Rk , s
( 1 – N sd / N Rd , s
) per Equation ( 5.5a ), and the resultant design bending resistance is designated “ M 0 ” in Equation ( 5 . 5 ). Rk , s M0 is designated “ M ” in PROFIS Engineering . The parameter “ α ”
Rk , s s M in Equation ( 5.5 ) corresponds to the amount of rotational restraint acting on the fixture , and the parameter “ ” ( designated L b in PROFIS Engineering ) corresponds to distance from where the shear resistance is assumed to act , to the “ point of fixity ” in the concrete where the internal bending resistance is assumed to act .
Reference the figures to the left . The parameter V Rk , s in Equation ( 5.5 ) corresponds to the design shear resistance . Per Equation ( 5.5 ), PROFIS Engineering calculates a design shear resistance ; however , the calculations are based on ACI 318-19 strength design provisions . Therefore , PROFIS Engineering calculates a “ design strength ” with respect to bending which it designates “ ϕV sM
” using values for the parameters α M , M s
, L b and a strength reduction factor ( ϕ steel
) for steel failure in shear .
ACI 318 anchoring-to-concrete provisions require calculation of a “ nominal strength ” which is then multiplied by a strength reduction factor ( s ) ( ϕ-factors ) to obtain a “ design strength ”. The parameter “ V sM
” in PROFIS Engineering corresponds to the nominal shear strength with respect to bending , and is calculated as follows :
V s
M
= ( α M
M s
)/ L b
The parameter “ ϕV sM
” in PROFIS Engineering corresponds to the design shear strength with respect to bending , and is calculated as follows :
ϕV s
M
= ϕ steel [ ( α M
M s
)/ L b ].
The PROFIS Engineering parameter “ ϕV sM ”, therefore , corresponds to the parameter “ V Rk , s
” in
Equation ( 5.5 ).
Per ACI 318 anchoring-to-concrete provisions , ϕV s
M is checked against the factored shear load
( V ua ) acting on the anchor .
PROFIS Engineering calculation . ϕV s
M
= ϕ α M
M s
L b
Reference the Equations and Calculations section of the report for more information on the following PROFIS Engineering parameters .
M s
: resultant flexural resistance of the anchor M 0 : characteristic flexural resistance of the anchor s
L b
: internal lever arm adjusted for spalling at the surface concrete .
Reference the Variables section of the report for more information on the following PROFIS Engineering parameters :
α M
: rotational restraint modification factor .
Reference the Results section of the report for more information on the following PROFIS Engineering parameters .
V sM
: nominal shear strength ( resistance ) for bending
ϕ steel
: strength reduction factor for steel failure in shear
V ua
: factored shear load acting on the anchor .
336 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions