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Eurocode 3 Table of design properties for metric hexagonal bolts M5 to M39 (stress area, shear strength, tensile strength, bearing strength)

Description:
Design aid - Table of design properties for individual metric hexagonal bolts including stress area, yield strength, ultimate strength, shear resistance, tensile resistance, interaction between shear and tension, bearing resistance, punching shear resistance
According to:
EN 1993-1-8:2005 Section 3.8
Supported National Annexes:
The value of γM2 must be provided manually when different than 1.25.
All Calculations
Input
Part of the bolt inside which the shear plane or planes pass through. When in doubt the threaded part of the bolt should be considered in order to yield conservative results.
Steel partial material safety factor for resistance of joints with bolt connections in accordance with EN1993-1-8 §2.2 Table 2.1 and the National Annex.
Tables
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Strength properties for bolt steel according to EN 1991-1-8 Table 3.1
Bolt class
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Design properties for metric hex bolts (Typical coarse pitch thread)
DimensionsHole diameter d0 [mm]AreasTensile resistance Ft,Rd [kN]Shear resistance per shear plane Fv,Rd [kN]Bearing resistance per mm of connected plate thickness Fv,Rd / t [kN/mm] (for e1≥3d0, e2≥1.5d0, p1≥3.75d0, p2≥3d0)Punching resistance per mm of plate thickness under bolt or nut Bp,Rd / tp [kN/mm]
column 0column 1column 2column 3column 4column 5column 6column 7column 8column 9column 10column 11column 12column 13column 14column 15column 16column 17column 18column 19column 20column 21column 22column 23column 24column 25column 26column 27column 28column 29column 30column 31
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Minimum end distance, edge distance, and spacing for bolt fasteners according to EN1993-1-8 Table 3.3 (rounded up to nearest mm)
Normal round holesOversize round holesSlotted holes
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Edge distances and spacing of bolt fasteners according to EN1993-1-1
Edge distances and spacing of bolt fasteners (reproduced from EN1993-1-1 Figure 3.1
Charts
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Notes
  1. The design resistance of a group of fasteners may be taken as the sum of the design bearing resistances Fb,Rd of the individual fasteners provided that the shear resistance Fv,Rd of each individual fastener is greater than or equal to the design bearing resistance Fb,Rd. Otherwise the design resistance of a group of fasteners should be taken as the number of fasteners multiplied by the smallest design resistance of any of the individual fasteners as specified in EN1993-1-8 § 3.7(1). For this case elastic linear distribution of internal forces should be used as specified in EN1993-1-8 §3.12.
  2. For preloaded bolted connections which are slip-resistant at the Serviceability Limit State or the Ultimate Limit State the corresponding shear load Fv,Ed should not exceed the design slip resistance as specified in EN1993-1-8 §3.9 and Table 3.2. Only bolt assemblies of classes 8.8 and 10.9 may be used as preloaded bolts.
  3. According to EN1993-1-8 § 3.6.1(4) the design shear resistance Fv,Rd should only be used where the bolts are used in holes with nominal clearances not exceeding those for normal holes as specified in EN 1090-2 'Requirements for the execution of steel structures'.
  4. Minimum and maximum spacing p1, p2 and edge distances e1, e2 for bolts are given in EN1993-1-8 Table 3.3. The minimum values are: e1 ≥ 1.2d0, e2 ≥ 1.2d0, p1 ≥ 2.2d0, p2 ≥ 2.4d0, where d0 is the diameter of the hole, e1, p1 are measured parallel to the load transfer direction and e2, p2 are measured perpendicular to the load transfer direction.
  5. According to EN1993-1-8 Table 3.4 the bearing resistance Fb,Rd of the bolt is not affected by the spacing p1, p2 and edge distances e1, e2 provided that the following limits are observed: e1 ≥ 3.0d0, e2 ≥ 1.5d0, p1 ≥ 3.75d0, p2 ≥ 3.0d0.
  6. According to EN1993-1-8 § 3.6.1(12) where bolts transmitting load in shear and bearing pass through packing plates of total thickness tp greater than d / 3 the design shear resistance Fv,Rd should be multiplied by the reduction factor βp specified in EN1993-1-8 equation 3.3.
  7. According to EN1993-1-8 § 3.8(1) for long joints where the distance between the centers of the end fasteners measured in the direction of load transfer is more than 15d the design shear resistance Fv,Rd of all the fasteners should be multiplied by the reduction factor βLf specified in EN1993-1-8 equation 3.5.
  8. According to EN1993-1-8 Table 3.4 the bearing resistance Fb,Rd for bolts in holes other than normal should be multiplied by the following reduction factors: Oversized holes = 0.8, slotted holes with longitudinal axis perpendicular to the load transfer direction = 0.6.
  9. According to EN1993-1-8 Table 3.4 for countersunk bolts the tension resistance Ft,Rd is evaluated by considering k2 = 0.63 instead of k2 = 0.9. Therefore for countersunk bolts the calculated tension resistance Ft,Rd should be reduced by a factor of 0.63 / 0.9 = 0.7. In addition for countersunk bolts the bearing resistance Fb,Rd should be based on a plate thickness t equal to the depth of the connected plate minus half the depth of the countersinking.
  10. For bolts with cut threads where the threads do not comply with EN 1090 the relevant resistances should be multiplied by a factor of 0.85 according to EN1993-1-8 § 3.6.1(3).
Details

Definition of standard metric bolts

The standarized properties of metric bolts are specified in the international standard ISO 898-1:2009 'Mechanical properties of fasteners made of carbon steel and alloy steel - Part 1: Bolts, screws and studs with specified property classes - Coarse thread and fine pitch thread'. According to ISO 898-1 the bolts are characterized depending on their pitch thread:

  • Course pitch thread: For general applications course pitch thread bolts are used. They are designated by their nominal diameter d in mm prefixed by the letter 'M'. The standard course pitch thread metric bolt sizes are: M3, M3.5, M4, M5, M6, M7, M8, M10, M12, M14, M16, M18, M20, M22, M24, M27, M30, M33, M36, M39.
  • Fine pitch thread: For special applications fine pitch thread bolts may be used. They are designated as above also including the pitch of thread in mm e.g. M8 × 1, M14 × 1.5, M27 × 2 etc. In general the stress area of fine pitch thread bolts passing through the threaded part is larger as compared to the course pitch thread bolts. The calculated strength properties for course pitch thread bolts may be used conservatively for fine pitch thread bolts.

Geometric properties of metric bolts

Nominal diameter

The nominal diameter d is specified in mm as part of the bolt designation, e.g. 8 mm for M8 bolt. The standard metric bolt diameters are specified in the standard ISO 898-1 Tables 4 and 5. For typical coarse pitch thread bolts the standard sizes are: M3, M3.5, M4, M5, M6, M7, M8, M10, M12, M14, M16, M18, M20, M22, M24, M27, M30, M33, M36, M39.

Width of nut across flats

The width of the hexagon nuts across flats s is specified in ISO 898-2 Table A.1 for bolt sizes M5 to M39.

Hole diameter

The design shear resistance of bolts Fv,Rd as given in EN1993-1-8 Table 3.4 is only valid when the bolt is used in holes with nominal clearance not exceeding the values given in the standard EN 1090-2 'Requirements for the execution of steel structures', as specified in EN1993-1-8 §3.6.1(4). The resulting hole diameter d0 for each type of hole (normal, oversize, short slotted, long slotted) is determined by adding the nominal clearance given in EN 1090-2 Table 11 to the nominal diameter d of the bolt.

Nominal gross area

The nominal gross area Ag corresponds to the cross-sectional area of the unthreaded part of the bolt:

Ag = π⋅d2 / 4

Tensile stress area

The tensile stress area As corresponds to the reduced cross-sectional area inside the threaded part of the bolt. The tensile stress area depends on the thread and it can be calculated according to ISO 898-1 Section 9.1.6.1. For standard course pitch thread and fine pitch thread bolts the nominal stress area As is provided in ISO 898-1 Tables 4 to 7.

In general the tensile stress area and the shear stress area are different. According to EN1993-1-8 Table 3.4 the shear strength of the bolt may be based on the tensile stress area.

Definition of bolt classes 4.6, 4.8 etc.

The yield strength fyb and the ultimate tensile strength fub for bolt classes 4.6, 4.8, 5.6, 5.8, 6.8, 8.8, and 10.9 are given in EN1993-1-8 Table 3.1. The first number of the bolt class corresponds to the ultimate strength e.g. 400 MPa for classes 4.x, 500 MPa for classes 5.x, 600 MPa for classes 6.x, 800 MPa for classes 8.x, and 1000 MPa for classes 10.x. The second number corresponds to the ratio of yield strength to ultimate strength e.g. 60% for class 4.6 leading to a yield strength of 0.60 × 400 MPa = 240 MPa.

Tensile strength of bolts

The tension resistance of the bolt Ft,Rd is provided in EN1993-1-8 Table 3.4:

Ft,Rd = k2 ⋅ fub ⋅ As / γM2

where:

  • k2 is a coefficient that takes values k2 = 0.63 for countersunk bolts or k2 = 0.9 otherwise.
  • fub is the ultimate tensile strength of the bolt depending on the bolt class (see table above).
  • As is the nominal tensile stress area of the bolt.
  • γM2 is the partial safety factor for the resistance of bolts in accordance with EN1993-1-8 §2.2(2) Table 2.1 and the National Annex. The recommended value in EN1993-1-8 is γM2 = 1.25.

Shear strength of bolts

The shear resistance of the bolt per shear plane Fv,Rd is provided in EN1993-1-8 Table 3.4:

Fv,Rd = αv ⋅ fub ⋅ A / γM2

where:

  • αv is a coefficient that takes values αv = 0.6 for bolt classes 4.6, 5.6, 8.8 or αv = 0.5 for bolt classes 4.8, 5.8, 6.8 and 10.9. When the shear plane passes through the unthreaded part of the bolt αv = 0.6.
  • fub is the ultimate tensile strength of the bolt depending on the bolt class (see table above)
  • A is the appropriate area for shear resistance. When the shear plane passes through the threaded part of the bolt A is equal to the tensile stress area of the bolt As. When the shear plane passes through the unthreaded part of the bolt A is equal to the gross cross-sectional area of the bolt Ag.
  • γM2 is the partial safety factor for the resistance of bolts in accordance with EN1993-1-8 §2.2(2) Table 2.1 and the National Annex. The recommended value in EN1993-1-8 is γM2 = 1.25.

Combined shear and tension

The interaction between shear and tension is expressed in EN1993-1-8 Table 3.4 according to the following linear relation:

Fv,Ed / Fv,Rd + (Ft,Ed / Ft,Rd) / 1.4 ≤ 1.0

where:

  • Fv,Ed is the applied shear load and Fv,Rd is the shear resistance of the bolt.
  • Ft,Ed is the applied tensile load and Ft,Rd is the tension resistance of the bolt.

Bearing strength of bolts

The bearing resistance of the bolt Fb,Rd should be verified against the applied shear load Fv,Ed in accordance with EN1993-1-8 Table 3.4:

Fb,Rd = k1 ⋅ αb ⋅ fu ⋅ d ⋅ t / γM2

where:

  • fu is the ultimate tensile strength of the connected plate
  • d is the nominal diameter of the bolt.
  • t is the thickness of the connected plate.
  • γM2 is the partial safety factor for the resistance of bolts in accordance with EN1993-1-8 §2.2(2) Table 2.1 and the National Annex. The recommended value in EN1993-1-8 is γM2 = 1.25.

The coefficient k1 is:

for edge bolts: k1 = min( 2.8⋅e2/d0 - 1.7, 1.4⋅p2/d0 - 1.7, 2.5 )
for inner bolts: k1 = min( 1.4⋅p2/d0 - 1.7, 2.5 )

where e2 is the distance between the center of the edge bolt and the end of the plate measured perpendicular to the load transfer direction, p2 is the distance between the centers of neighboring bolts measured perpendicular to the load transfer direction, and d0 is the diameter of the bolt hole.

The coefficient αb is:

αb = min( αd, fub/fu, 1.0 )

for end bolts: αd = e1/(3⋅d0)
for inner bolts: αd = p1/(3⋅d0) - 1/4

where e1 is the distance between the center of the end bolt and the end of the plate measured parallel to the load direction, p1 is the distance between the centers of neighboring bolts measured parallel to the load direction, and d0 is the diameter of the bolt hole.

Therefore, based on the equations above, the bearing resistance of the bolt Fb,Rd is not affected by the distances e1, p1, e2, p2 when the following conditions are satisfied:

for edge bolts: e1 ≥ 3.0⋅d0 and e2 ≥ 1.5⋅d0
for inner bolts: p1 ≥ 3.75⋅d0 and p2 ≥ 3.0⋅d0

Punching strength of bolts

The punching resistance of the bolt Bp,Rd should be verified against the applied tensile load Ft,Ed in accordance with EN1993-1-8 Table 3.4:

Bp,Rd = 0.6⋅π ⋅ dm ⋅ tp ⋅ fu / γM2

where:

  • dm is the mean of the across points and across flats dimensions of the bolt head or the nut, whichever is smaller.
  • tp is the plate thickness under the bolt or nut.
  • fu is the ultimate tensile strength of the steel plate.
  • γM2 is the partial safety factor for the resistance of bolts in accordance with EN1993-1-8 §2.2(2) Table 2.1 and the National Annex. The recommended value in EN1993-1-8 is γM2 = 1.25.

The value of the mean diameter dm is estimated as follows. The distance across flats s of the nut is given in the standard ISO 898-2. By approximately ignoring the corner rounding for a perfect hexagon the relation of the distance across points s' and the distance across flats s is s' = s / cos(30°) = 1.1547⋅s. Therefore the mean diameter dm is approximately:

dm = (s + 1.1547⋅ s) / 2 = 1.07735⋅s

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