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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
Strength properties for bolt steel according to EN 1993-1-8 Table 3.1
Bolt class
Symbol Description 4.6 4.8 5.6 5.8 6.8 8.8 10.9
fyb (MPa) Yield strength 240 320 300 400 480 640 900
fub (MPa) Ultimate tensile strength 400 400 500 500 600 800 1000
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]Maximum bearing resistance per mm of connected plate thickness Fb,Rd / t [kN/mm]
(for adequate distances e1≥3d0, e2≥1.5d0, p1≥3.75d0, p2≥3d0)		Minimum bearing resistance per mm of connected plate thickness Fb,Rd / t [kN/mm]
(for minimum distances e1=1.2d0, e2=1.2d0, p1=2.2d0, p2=2.4d0)		Punching resistance per mm of plate thickness under bolt or nut Bp,Rd / tp [kN/mm]
Size Nominal diameter
d [mm]		 Nut width across flats
s [mm]		 Normal round hole Oversize round hole Short slotted hole Long slotted hole Gross area (unthreaded part)
Ag [mm2]		 Stress area (threaded part)
As [mm2]		 4.6 4.8 5.6 5.8 6.8 8.8 10.9 4.6 4.8 5.6 5.8 6.8 8.8 10.9 Interaction between shear and tension S235 / any S275 / 4.6, 4.8 S275 / ≥5.6 S355 / 4.6, 4.8 S355 / ≥5.6          S235                   S275                   S355                   S235                   S275                   S355         
M5 5 8 - - - - 19.6 14.2 4.09 4.09 5.11 5.11 6.13 8.18 10.2 2.73 2.27 3.41 2.84 3.41 5.45 5.68 see chart 3.60 4.00 4.30 4.00 4.90 0.96 1.14 1.30 4.68 5.59 6.37
M6 6 10 - - - - 28.3 20.1 5.79 5.79 7.24 7.24 8.68 11.6 14.5 3.86 3.22 4.82 4.02 4.82 7.72 8.04 see chart 4.32 4.80 5.16 4.80 5.88 1.15 1.37 1.56 5.85 6.99 7.96
M7 7 11 - - - - 38.5 28.9 8.32 8.32 10.4 10.4 12.5 16.6 20.8 5.55 4.62 6.94 5.78 6.94 11.1 11.6 see chart 5.04 5.60 6.02 5.60 6.86 1.34 1.60 1.82 6.43 7.68 8.76
M8 8 13 - - - - 50.3 36.6 10.5 10.5 13.2 13.2 15.8 21.1 26.4 7.03 5.86 8.78 7.32 8.78 14.1 14.6 see chart 5.76 6.40 6.88 6.40 7.84 1.53 1.83 2.08 7.60 9.08 10.35
M10 10 16 - - - - 78.5 58.0 16.7 16.7 20.9 20.9 25.1 33.4 41.8 11.1 9.28 13.9 11.6 13.9 22.3 23.2 see chart 7.20 8.00 8.60 8.00 9.80 1.91 2.28 2.60 9.36 11.18 12.74
M12 12 18 13 15 16×13 30.0×13 113 84.3 24.3 24.3 30.3 30.3 36.4 48.6 60.7 16.2 13.5 20.2 16.9 20.2 32.4 33.7 see chart 8.64 9.60 10.32 9.60 11.76 2.29 2.74 3.12 10.53 12.57 14.33
M14 14 21 15 17 18×15 35.0×15 154 115 33.1 33.1 41.4 41.4 49.7 66.2 82.8 22.1 18.4 27.6 23.0 27.6 44.2 46.0 see chart 10.08 11.20 12.04 11.20 13.72 2.68 3.20 3.64 12.28 14.67 16.72
M16 16 24 18 20 22×18 40.0×18 201 157 45.2 45.2 56.5 56.5 67.8 90.4 113.0 30.1 25.1 37.7 31.4 37.7 60.3 62.8 see chart 11.52 12.80 13.76 12.80 15.68 3.06 3.65 4.16 14.04 16.77 19.11
M18 18 27 20 22 24×20 45.0×20 254 192 55.3 55.3 69.1 69.1 82.9 110.6 138.2 36.9 30.7 46.1 38.4 46.1 73.7 76.8 see chart 12.96 14.40 15.48 14.40 17.64 3.44 4.11 4.69 15.79 18.86 21.49
M20 20 30 22 24 26×22 50.0×22 314 245 70.6 70.6 88.2 88.2 105.8 141.1 176.4 47.0 39.2 58.8 49.0 58.8 94.1 98.0 see chart 14.40 16.00 17.20 16.00 19.60 3.82 4.57 5.21 17.55 20.96 23.88
M22 22 34 24 26 28×24 55.0×24 380 303 87.3 87.3 109.1 109.1 130.9 174.5 218.2 58.2 48.5 72.7 60.6 72.7 116.4 121.2 see chart 15.84 17.60 18.92 17.60 21.56 4.21 5.03 5.73 19.89 23.75 27.07
M24 24 36 26 30 32×26 60.0×26 452 353 101.7 101.7 127.1 127.1 152.5 203.3 254.2 67.8 56.5 84.7 70.6 84.7 135.6 141.2 see chart 17.28 19.20 20.64 19.20 23.52 4.59 5.48 6.25 21.05 25.15 28.66
M27 27 41 30 35 37×30 67.5×30 573 459 132.2 132.2 165.2 165.2 198.3 264.4 330.5 88.1 73.4 110.2 91.8 110.2 176.3 183.6 see chart 19.44 21.60 23.22 21.60 26.46 5.16 6.17 7.03 23.98 28.64 32.64
M30 30 46 33 38 40×33 75.0×33 707 561 161.6 161.6 202.0 202.0 242.4 323.1 403.9 107.7 89.8 134.6 112.2 134.6 215.4 224.4 see chart 21.60 24.00 25.80 24.00 29.40 5.74 6.85 7.81 26.90 32.13 36.62
M33 33 50 36 41 43×36 82.5×36 855 694 199.9 199.9 249.8 249.8 299.8 399.7 499.7 133.2 111.0 166.6 138.8 166.6 266.5 277.6 see chart 23.76 26.40 28.38 26.40 32.34 6.31 7.54 8.59 29.24 34.93 39.80
M36 36 55 39 44 46×39 90.0×39 1020 817 235.3 235.3 294.1 294.1 352.9 470.6 588.2 156.9 130.7 196.1 163.4 196.1 313.7 326.8 see chart 25.92 28.80 30.96 28.80 35.28 6.88 8.22 9.37 32.17 38.42 43.78
M39 39 60 42 47 49×42 97.5×42 1190 976 281.1 281.1 351.4 351.4 421.6 562.2 702.7 187.4 156.2 234.2 195.2 234.2 374.8 390.4 see chart 28.08 31.20 33.54 31.20 38.22 7.46 8.91 10.15 35.09 41.91 47.76
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
Size Minimum end distance along load direction e1 [mm]
(e1 = 1.2d0)		 Minimum edge distance perpendicular to load direction e2 [mm]
(e2 = 1.2d0)		 Minimum center-to-center spacing along load direction p1 [mm]
(p1 = 2.2d0)		 Minimum center-to-center spacing perpendicular to load direction p2 [mm]
(p2 = 2.4d0)		 Minimum end distance along load direction e1 [mm]
(e1 = 1.2d0)		 Minimum edge distance perpendicular to load direction e2 [mm]
(e2 = 1.2d0)		 Minimum center-to-center spacing along load direction p1 [mm]
(p1 = 2.2d0)		 Minimum center-to-center spacing perpendicular to load direction p2 [mm]
(p2 = 2.4d0)		 Minimum edge distance e3 [mm]
(e3 = 1.5d0)		 Minimum edge distance e4 [mm]
(e4 = 1.5d0)
M12 16 16 29 32 18 18 33 36 20 20
M14 18 18 33 36 21 21 38 41 23 23
M16 22 22 40 44 24 24 44 48 27 27
M18 24 24 44 48 27 27 49 53 30 30
M20 27 27 49 53 29 29 53 58 33 33
M22 29 29 53 58 32 32 58 63 36 36
M24 32 32 58 63 36 36 66 72 39 39
M27 36 36 66 72 42 42 77 84 45 45
M30 40 40 73 80 46 46 84 92 50 50
M33 44 44 80 87 50 50 91 99 54 54
M36 47 47 86 94 53 53 97 106 59 59
M39 51 51 93 101 57 57 104 113 63 63
Adequate end distance, edge distance, and spacing for bolt fasteners in order to achieve maximum bearing resistance Fv,Rd according to EN1993-1-8 Table 3.4 (rounded up to nearest mm)
Normal round holesOversize round holesSlotted holes
Size End distance along load direction e1 [mm]
(e1 = 3.0d0)		 Edge distance perpendicular to load direction e2 [mm]
(e2 = 1.5d0)		 Center-to-center spacing along load direction p1 [mm]
(p1 = 3.75d0)		 Center-to-center spacing perpendicular to load direction p2 [mm]
(p2 = 3.0d0)		 End distance along load direction e1 [mm]
(e1 = 3.0d0)		 Edge distance perpendicular to load direction e2 [mm]
(e2 = 1.5d0)		 Center-to-center spacing along load direction p1 [mm]
(p1 = 3.75d0)		 Center-to-center spacing perpendicular to load direction p2 [mm]
(p2 = 3.0d0)		 Edge distance e3 [mm]
(e3 = 1.5d0)		 Edge distance e4 [mm]
(e4 = 3.0d0)
M12 39 20 49 39 45 23 57 45 20 39
M14 45 23 57 45 51 26 64 51 23 45
M16 54 27 68 54 60 30 75 60 27 54
M18 60 30 75 60 66 33 83 66 30 60
M20 66 33 83 66 72 36 90 72 33 66
M22 72 36 90 72 78 39 98 78 36 72
M24 78 39 98 78 90 45 113 90 39 78
M27 90 45 113 90 105 53 132 105 45 90
M30 99 50 124 99 114 57 143 114 50 99
M33 108 54 135 108 123 62 154 123 54 108
M36 117 59 147 117 132 66 165 132 59 117
M39 126 63 158 126 141 71 177 141 63 126
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:

  • Coarse pitch thread: For general applications coarse pitch thread bolts are used. They are designated by their nominal diameter d in mm prefixed by the letter 'M'. The standard coarse 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 coarse pitch thread bolts. The calculated strength properties for coarse 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 coarse 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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