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:
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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.
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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
