PROFIS Design Guide: US-EN Summer 2021 | Page 318

M _s

= M ⁰ s 1 –

N _au

ϕN _sa

ETAG 001 resultant flexural resistance of anchor

5.2.3.2 Steel failure

b ) Shear load with lever arm

M _{Rk , s}

= M ^{0 ( 1 ‒ N / N} ) [ Nm ] ( 5 . 5a )

Rk , s Sd Rd , s

The characteristic resistance of an anchor , V _{Rk , s} , is given by Equation ( 5.5 ).

where

V _{Rk , s}

= ^α M ^M Rk , s [ N ] ( 5.5 ) l

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} / γ _Ms

N _{Rk ,} s , γ _Ms to be taken from the relevant ETA

M ⁰ Rk , s ^{= 1 . 2 W} el ^f 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 anchorage with 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 .

The ETAG 001 parameter M ⁰ corresponds to a calculated internal

Rk , s

“ characteristic bending resistance ” for the anchor element . This parameter is designated M ^{0 in PROFIS Engineering . The ETAG 001 parameter M} s Rk , s corresponds to a calculated internal “ characteristic bending resistance ” that is modified to account for both tension and shear load acting on the anchor element . If only a shear load acts on the anchor , M _{Rk , s}

= M ⁰ . If both tension and shear

Rk , s load act on the anchor , ETAG 001 provisions require a reduction factor ( 1 – N _sd

/ N _{Rd , s}

) to be applied to M ^{0 to obtain M} . Therefore , if tension and

Rk , s Rk , s shear act on the anchor , M _{Rk , s}

= M ^{0 ( 1 – N / N} ) per ETAG 001 Equation ( 5 . 5a ).

Rk , s sd Rd , s

PROFIS Engineering designates the parameter corresponding to M _{Rk , s} as “ M _s

”.

The parameters “ N _sd ” and “ N _{Rd , s}

” in the ETAG 001 reduction factor ( 1 – N _sd / N _{Rd , s}

) correspond to the “ design steel tension force ” and the “ design resistance steel force ”, respectively . This reduction factor is designated ( 1 – N _ua

/ ϕN _sa ) in PROFIS

Engineering , where “ N _ua

” corresponds to the highest factored tension load acting on an individual anchor and “ ϕN _sa

” corresponds to the calculated steel design strength in tension for a single anchor . When both tension load and shear load act on an anchor with standoff , PROFIS Engineering calculates the internal bending resistance for the anchor as follows :

ϕM _s

= M ⁰ s ^{( 1 – N} ua ^{/ ϕN} sa ^).

The ETAG 001 parameter M ⁰ is defined by Equation ( 5 . 5b ) as shown to the left .

Rk , s

The parameter W _el corresponds to the “ elastic section modulus ” of the anchor element , and the parameter f _uk corresponds to the “ characteristic ultimate tensile strength ” of the anchor element .

PROFIS Engineering calculation .

ϕV _s

M

= ϕ

α _M

M _s

L _b

When performing bolt bending calculations , PROFIS Engineering designates the elastic section modulus for the anchor element “ S ” and the ultimate tensile strength for the anchor element “ f _{u , min}

”, where “ f _{u , min}

” corresponds to the “ minimum specified ultimate tensile strength ” of the anchor element . The PROFIS Engineering report defines the parameter “ M ⁰ ” using the following equation : s

M ⁰ s ^{= ( 1 . 2 ) ( S ) ( f} u , min ^).

Reference the Equations section of the report for more information on the following PROFIS Engineering parameters .

M ⁰ : Characteristic flexural resistance of the anchor s

( 1 – N _ua / ϕN _sa

): Reduction factor for tension load

Reference the Variables section of the report for more information on the following PROFIS Engineering parameters :

N _ua

: Factored tension load

ϕN _sa

: Design steel strength in tension

Reference the Calculations section of the report for more information on the following PROFIS Engineering parameters .

M ⁰ : Characteristic flexural resistance of the anchor s

( 1 – N _ua

/ ϕN _sa ): Reduction factor for tension load

M _s

: Resultant flexural resistance of the anchor