Bolted Connection Theory - EN 1993-1-8 (Eurocode 3)
The theory behind this bolt data tool: the bolt property classes and their strengths, how the shear, bearing and tension resistances of a bolt are calculated to Eurocode 3 (EN 1993-1-8), how combined shear and tension is checked, how preloaded slip-resistant bolts work, and the spacing and edge-distance rules that the data tables enforce.
Run this method in the free calculator and export the result to Excel (.xlsx) or PDF.
A bolted steel connection is designed to Eurocode 3, EN 1993-1-8. Each bolt is checked for the actions it carries - shear, bearing, tension, or a combination - and the connection geometry must satisfy the spacing and edge-distance rules. This page explains the resistances behind the bolt data tables.
Bolt property classes
Bolts are graded by a two-number class such as 8.8 or 10.9. The first number times 100 is the ultimate tensile strength fub in MPa; the product of the two numbers times 10 is the yield strength fyb. So a class 8.8 bolt has fub=800 MPa and fyb=640 MPa. Classes 8.8 and 10.9 dominate structural work; 4.6 is used for light or non-structural fixings.
Shear and bearing resistance
In a bearing-type (non-preloaded) connection the load is transferred by the bolt shank shearing and bearing against the plate. The shear resistance per shear plane is
Fv,Rd=γM2αvfubA
where
Fv,Rdshear resistance of one bolt, per shear plane (a bolt in double shear has two planes, so twice this value)αv0.6 for classes 4.6, 5.6 and 8.8; 0.5 for class 10.9 (and 4.8, 5.8, 6.8) when the shear plane passes through the threadsfubultimate tensile strength of the boltAgross shank area if the shear plane is in the unthreaded shank, or the tensile stress area As if it passes through the threadsγM2partial factor for bolt resistance (= 1.25)
The plate the bolt bears against must also resist crushing:
Fb,Rd=γM2k1αbfudt
where
k1edge factor from the perpendicular distances e2, p2 (capped at 2.5)αbend and spacing factor from e1, p1 and fub/fu (capped at 1.0); it falls as the end and edge distances reduce, which is exactly why the spacing rules matterfuultimate strength of the connected platedbolt diametertplate thicknessγM2as above (= 1.25)
The bolt's capacity in shear is the lesser of Fv,Rd and Fb,Rd.
Tension and punching
A bolt in tension is checked for failure of the threaded part, and the connected plate for punching shear of the bolt head or nut. The tension resistance is
Ft,Rd=γM2k2fubAs
where
Ft,Rdtension resistance of the boltk20.9, or 0.63 for countersunk boltsfubultimate tensile strength of the boltAstensile stress area - smaller than the shank area because it allows for the reduced section at the threadsγM2partial factor for bolt resistance (= 1.25)
and the punching shear resistance of the plate under the head or nut is
Bp,Rd=γM20.6πdmtpfu
where
dmmean of the across-flats and across-corners dimensions of the head or nuttpthickness of the plate under the head or nutfuultimate strength of that plate
Combined shear and tension
A bolt that carries shear and tension at once must satisfy the linear interaction of Table 3.4:
Fv,RdFv,Ed+1.4Ft,RdFt,Ed≤1.0
where
Fv,Eddesign shear applied to the boltFt,Eddesign tension applied to the boltFv,Rdshear resistance from aboveFt,Rdtension resistance from above
The 1.4 in the tension term reflects that a modest tension does not greatly reduce shear capacity. Each individual check (shear ≤Fv,Rd and tension ≤Ft,Rd) must still be satisfied as well.
Preloaded (slip-resistant) bolts
Class 8.8 and 10.9 bolts can be tightened to a controlled preload, clamping the plates so the load is carried by friction rather than bearing:
Fp,C=0.7fubAs,Fs,Rd=γM3ksnμFp,C
where
Fp,Cthe controlled design preloadFs,Rdslip resistance of one boltkshole factor (1.0 for normal clearance holes)nnumber of friction (faying) surfacesμslip factor - 0.5 for blasted steel, less for as-rolled surfacesγM3partial factor for slip resistance
Slip-resistant connections are used where movement is unacceptable - fatigue details, reversing loads, or where alignment must be preserved.
Spacing, edge and end distances
Bolt positions are bounded both ways. Minimum distances stop the plate tearing out and keep the bearing factor up; maximum distances prevent local buckling between bolts and keep the parts in contact. The minimum values (Table 3.3) are
minimum distances
d0hole diameter (the limits below are all multiples of it)e1≥1.2d0end distance, in the direction of load transfere2≥1.2d0edge distance, perpendicular to the loadp1≥2.2d0spacing of bolts along the load directionp2≥2.4d0spacing of bolt rows perpendicular to the load
The data tables in this tool list the hole sizes and the minimum and maximum distances for every bolt diameter.
The partial factors γM2=1.25 (resistance of bolts) and γM3 (slip) and the slip factor class are set by the National Annex; category A-E connections (bearing vs slip-resistant) determine which checks govern.
Frequently asked questions
A bolt class is two numbers. The first number multiplied by 100 gives the ultimate tensile strength f_ub in MPa, and the two numbers multiplied together times 10 give the yield strength f_yb. So an 8.8 bolt has f_ub = 800 MPa and f_yb = 0.8·800 = 640 MPa, and a 10.9 bolt has f_ub = 1000 MPa and f_yb = 900 MPa. Classes 8.8 and 10.9 are the usual structural grades; 4.6 (f_ub = 400 MPa) is for light or non-structural fixings.
The shear resistance per shear plane is F_v,Rd = α_v·f_ub·A / γM2, where α_v = 0.6 for grades 4.6, 5.6 and 8.8 (and 0.5 for 10.9 when the shear plane passes through the threads), A is the relevant area (the full shank area if the shear plane is in the unthreaded shank, or the tensile stress area A_s if it passes through the threads), and γM2 = 1.25. A bolt in double shear has two planes, so twice the resistance. The bearing resistance of the connected plate must also be checked, and the lower value governs.
In a bearing-type connection the bolts are snug-tight and the load is transferred by the bolt shank shearing and bearing against the hole; some slip into bearing is accepted. In a slip-resistant (preloaded) connection class 8.8 or 10.9 bolts are tightened to a controlled preload F_p,C = 0.7·f_ub·A_s, clamping the plates so the load is carried by friction between the faying surfaces. Slip-resistant connections (categories B and C) are used where movement is unacceptable - fatigue, reversing loads or where alignment must be kept.
When a bolt carries shear and tension simultaneously, EN 1993-1-8 Table 3.4 gives a linear interaction: F_v,Ed/F_v,Rd + F_t,Ed/(1.4·F_t,Rd) ≤ 1.0. The factor 1.4 in the tension term means a moderate tension only mildly reduces the available shear. Both individual checks (shear ≤ F_v,Rd and tension ≤ F_t,Rd) must still be satisfied as well as the interaction.
Minimum spacing and edge/end distances stop the plate tearing out around the bolt and keep the bearing resistance high - the bearing factors α_b and k_1 fall as the end distance e_1 and edge distance e_2 reduce. EN 1993-1-8 requires at least p_1 = 2.2·d_0 spacing and e_1 = 1.2·d_0 end distance (d_0 = hole diameter). Maximum spacings prevent local buckling between bolts and keep the plates in contact to resist corrosion. The data tables list the minimum and maximum values for each diameter.
The tensile stress area A_s is the effective cross-sectional area used to calculate a bolt's tension and (through-thread) shear resistance. It is smaller than the nominal shank area because it accounts for the reduced cross-section at the threads - based on the mean of the pitch and minor diameters. For example an M20 bolt has a shank area of 314 mm² but a tensile stress area of 245 mm². This tool lists A_s for every standard diameter.
Ready to size your connection? Look up bolt strengths, hole dimensions, spacing limits and resistances for any bolt grade and diameter.
