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V s
M
=
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α M
M s
L b
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ETAG 001 bending equation for stand-off
5.2.3.2 Steel failure
b ) Shear load with lever arm
V Rk , s
= α M M Rk , s [ N ] ( 5.5 ) l
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
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Shear load acting on anchors installed with standoff creates bending in the anchors . Other than for a grouted standoff , ACI 318 anchoring-to-concrete provisions do not consider anchor bending with respect to standoff conditions ; however , bending could be a controlling shear failure mode . Provisions for considering anchor bending are given in European publications such as a European Technical Approval Guideline ( ETAG ) published by the European Organization for Technical Approvals ( EOTA ). ETAG 001 Metal Anchors for Use in Concrete Annex C : Design Methods for Anchorages includes provisions for calculating a shear resistance ( strength ) that results from internal anchor bending . PROFIS Engineering uses the ETAG 001 Annex C provisions to consider bolt bending as a possible shear failure mode . These provisions can be summarized as follows : |
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where
α M
= see 4.2.2.4
l = lever arm according to Equation ( 4.2 )
M Rk , s
= M 0 Rk , s ( 1 - N sd / N Rd , s ) [ N m ] ( 5 . 5a )
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 load acts on an anchorage having standoff .
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If a standoff condition exists for an anchorage , an applied shear load can create bending in the anchors . An internal bending resistance ( M 0 ) can
Rk , s be calculated using the material properties of the anchor element . M 0 is Rk , s designated M 0 in PROFIS Engineering . s M0 can be reduced by a factor
Rk , s
( 1 – N sd / N Rd , s
) if tension load also acts on the anchors to give a design bending resistance ( M Rk , s
), which is designated M s in PROFIS Engineering . The parameter N1 corresponds to the highest “ design ” tension load acting on an individual anchor in the anchorage ( designated N ua in PROFIS Engineering ), and the parameter N Rd , s corresponds to the calculated steel resistance for a single anchor in tension ( designated ϕN sa in PROFIS Engineering ). The parameter
“ α M
” corresponds to the amount of rotational restraint the fixture is capable of undergoing ; and the parameter “ l ” ( L b in PROFIS Engineering ) corresponds to the “ lever arm ”, which ETAG 001 Annex C defines as the distance from where the shear load is assumed to act , to the “ point of fixity ” in the concrete where the internal bending moment is assumed to act .
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The design shear resistance ( V Rk , s ) can be calculated per Equation ( 5.5 ) using α M
, M Rk , s and l . PROFIS Engineering calculates a design shear strength using α M
, M s and L b
. This design strength ( designated ϕV sM
) is checked against the highest factored shear load acting on an individual anchor in the anchorage ( V ua
). Reference the figures to the left .
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PROFIS Engineering calculation . |
ϕV s
M
= ϕ
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α M
M s
L b
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Reference the Equations and Calculations section of the report for more information on the following PROFIS Engineering parameters . The corresponding ETAG 001 Annex C parameters are noted below in parenthesis .
M s
( M Rk , s ): Resultant flexural resistance of the anchor
L b
( l ): Internal lever arm adjusted for spalling of the surface concrete
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Reference the Variables section of the report for more information on the following PROFIS Engineering parameters : |
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α M
( α M
): Rotational restraint modification factor
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Reference the Results section of the report for more information on the following PROFIS Engineering parameters . The corresponding ETAG 001 Annex C parameter is noted below in parenthesis . |
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V s
M
: Nominal shear strength for bending
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ϕV s
M
( V Rk , s
): Design shear strength ( resistance ) for bending
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