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§ 17

Bolt connection: number of bolts against shear

How many bolts are needed?

Answer: The competence objective says that you based on a sketch should be able to determine the number and dimension of bolts in a static connection. The calculator works out the shear-bearing capacity per bolt and per shear plane according to Eurocode 3 and how many bolts the design load requires. It only calculates shearing of the bolt itself. Edge bearing capacity, edge distances and hole distances and plate strength must be verified separately.

Formula

Fv,Rd = αv × fub × As ÷ γM2 pr. snitflade, når snittet går gennem gevindet (DS/EN 1993-1-8, tabel 3.4)

αv = 0,6 for klasse 4.6, 5.6 og 8.8, og αv = 0,5 for 10.9

Antal bolte = F_Ed ÷ (Fv,Rd × antal snitflader), rundet op

DK NA til DS/EN 1993-1-8: γM2 = 1,35 · γ0 · γ3 (γ0 = 1,0 i CC2, γ3 = 1,0 ved normal kontrolklasse). Den anbefalede EN-værdi uden nationalt anneks er 1,25.

Symbols and units in the formula
SymbolMeaningUnit
last_knDesign shear force on the joint F_Ed (incl. partial coefficients)kN
as_mm2Bolt dimension (stress area As, ISO 898-1)mm²
av_fubBolt class (αv × fub)MPa
snitCut surfaces per bolt—
gamma_m2Partial coefficient γM2 (DK NA at normal control class and CC2: 1.35)
=Required number of boltsbolte
=Shear load-bearing capacity per boltkN
=Utilisation at that number of bolts%

Validity and source

Source
DS/EN 1993-1-8, tabel 3.4: Fv,Rd = αv · fub · As ÷ γM2 · DK NA: γM2 = 1,35 · γ0 · γ3

Does not apply when

  • Sketch estimate and teaching. Long joints (over 15 × d) give reduction and hole edge capacity, edge distances, net cross-section and prestressed bolts are not included. Structural structures are designed and approved by the responsible designer.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Design shear force on the joint F_Ed (incl. partial coefficients)120 kN
  • Bolt dimension (stress area As, ISO 898-1)157 mm²
  • Bolt class (αv × fub)480 MPa
  • Cut surfaces per bolt1
  • Partial coefficient γM2 (DK NA at normal control class and CC2: 1.35)1.35

Giver

  • Required number of bolts3 bolte
  • Shear load-bearing capacity per bolt55.8 kN
  • Utilisation at that number of bolts72 %

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Sådan bruger du den

Når du ud fra en skitse skal dimensionere en boltet lask, et beslag eller en samling i et stålstativ, skal du vise hvor mange bolte der skal til. Beregneren regner boltenes overklipningsbæreevne efter DS/EN 1993-1-8 og det nødvendige antal. Hulrand, kantafstande og pladerne skal eftervises for sig.

Step by step

  1. Find den regningsmæssige forskydningskraft F_Ed fra lastberegningen (laster gange partialkoefficienter).
  2. Vælg boltdimension og -klasse. Spændingsarealet As står i ISO 898-1, fx 157 mm² for M16.
  3. Find antal snitflader: én ved to plader, to ved en dobbeltlask.
  4. Bæreevne pr. bolt = αv × fub × As ÷ γM2 × snitflader.
  5. Antal bolte = F_Ed ÷ bæreevne pr. bolt, rundet op. Tjek derefter hulrand og kantafstande.

Typical errors

  • At bruge den karakteristiske last. F_Ed skal være den regningsmæssige last med partialkoefficienterne.
  • At bruge skaftets areal, når snittet går gennem gevindet. Brug spændingsarealet As.
  • At glemme γM2 fra det danske nationale anneks (1,35) og bruge EN-værdien 1,25.
  • At stoppe ved boltene. Hulrandsbæreevnen og pladernes nettotværsnit er ofte mindre.

Examples from everyday life

Lask i et maskinstativ

En enkeltsnittet lask i et stativ skal overføre 120 kN regningsmæssig forskydning. Du vil bruge M16 i 8.8.

Design shear force on the joint F_Ed (incl. partial coefficients)
120 kN
Bolt dimension (stress area As, ISO 898-1)
M16 · As 157 mm²
Bolt class (αv × fub)
8.8 · αv 0,6 × fub 800
Cut surfaces per bolt
1 · single section (two plates)
Partial coefficient γM2 (DK NA at normal control class and CC2: 1.35)
1.35

It means: Hver bolt tager 55.8 kN, så der skal bruges 3 bolte. Udnyttelsen ved det antal er 72 %.

Dobbeltlask med M20

En samling i en kranbane-konsol har lasker på begge sider og skal tage 300 kN. Du prøver M20 i 8.8.

Design shear force on the joint F_Ed (incl. partial coefficients)
300 kN
Bolt dimension (stress area As, ISO 898-1)
M20 · As 245 mm²
Bolt class (αv × fub)
8.8 · αv 0,6 × fub 800
Cut surfaces per bolt
2 · double section (strap on both sides)
Partial coefficient γM2 (DK NA at normal control class and CC2: 1.35)
1.35

It means: Med to snitflader tager hver bolt 174.2 kN, og der skal bruges 2 bolte. Udnyttelsen bliver 86 %, så hulranden i laskerne bliver ofte det, der bestemmer.

Let beslag med 4.6-bolte

Et beslag til en gangbro skal tage 40 kN, og der bruges M12 i 4.6.

Design shear force on the joint F_Ed (incl. partial coefficients)
40 kN
Bolt dimension (stress area As, ISO 898-1)
M12 · As 84,3 mm²
Bolt class (αv × fub)
4.6 · αv 0,6 × fub 400
Cut surfaces per bolt
1 · single section (two plates)
Partial coefficient γM2 (DK NA at normal control class and CC2: 1.35)
1.35

It means: Hver bolt tager kun 15 kN, så der skal 3 bolte til, med en udnyttelse på 89 %. Med 8.8 kunne du nøjes med færre.

Rule of thumb

En M16 i 8.8 tager ca. 56 kN pr. snitflade med DK NA, en M20 ca. 87 kN.

How to check the answer

Antal bolte gange bæreevnen pr. bolt skal være mindst F_Ed. Få samlingen eftervist af den konstruktionsansvarlige.