EN 1993-1-8 Clause 3.6 — Bolt Resistance Overview

EN 1993-1-8 Clause 3.6 governs the design resistance of individual fasteners. Bolted connections are classified into five categories (A to E) based on the loading type (shear or tension) and whether the bolts are preloaded:

Category Loading Bolt Type Limit State Criteria
A Shear Non-preloaded Fv,Ed <= Fv,Rd AND Fv,Ed <= Fb,Rd (bearing type)
B Shear Preloaded Fv,Ed,ser <= Fs,Rd,ser at SLS; Fv,Ed <= Fv,Rd AND Fv,Ed <= Fb,Rd at ULS
C Shear Preloaded Fv,Ed <= Fs,Rd at ULS (slip-resistant at ultimate)
D Tension Non-preloaded Ft,Ed <= Ft,Rd AND Ft,Ed <= Bp,Rd (punching shear)
E Tension Preloaded Ft,Ed <= Ft,Rd AND Ft,Ed <= Bp,Rd

Categories A and D are the most common in building construction (bearing-type connections with snug-tight bolts). Categories B and C apply to connections where slip is unacceptable (fatigue loading, oversize holes, or where bolts also resist shear in a tension connection).

Bolt Shear Resistance — Fv,Rd (Table 3.4)

The design shear resistance per bolt and per shear plane:

Fv,Rd = alpha_v x f_ub x A / gamma_M2

Where:

A_s vs A — The Critical Distinction

The shear plane almost always passes through the threaded portion in typical bolted connections (grip length includes at least some thread). Therefore, always use the tensile stress area A_s, not the gross shank area A, unless the designer specifically details the connection so the shear plane is in the unthreaded shank. This is rarely practical for standard connections.

Bolt Size Gross Area A (mm^2) Stress Area A_s (mm^2) A_s / A Ratio
M12 113 84.3 0.746
M16 201 157 0.781
M20 314 245 0.780
M22 380 303 0.797
M24 452 353 0.781
M27 573 459 0.801
M30 707 561 0.794
M36 1018 817 0.803

The stress area A_s is approximately 75-80% of the gross area. Using A instead of A_s overestimates shear resistance by 25-34% — a dangerous error.

Quick Shear Capacity Table — Single Shear, Threads in Shear Plane

Bolt Grade f_ub (MPa) alpha_v gamma_M2 M12 Fv,Rd M16 Fv,Rd M20 Fv,Rd M24 Fv,Rd M30 Fv,Rd
4.6 400 0.6 1.25 16.2 kN 30.1 kN 47.0 kN 67.8 kN 107.7 kN
5.6 500 0.6 1.25 20.2 kN 37.7 kN 58.8 kN 84.7 kN 134.6 kN
8.8 800 0.6 1.25 32.4 kN 60.3 kN 94.1 kN 135.6 kN 215.4 kN
10.9 1000 0.5 1.25 33.7 kN 62.8 kN 98.0 kN 141.2 kN 224.4 kN

For double shear connections, multiply values by 2. For shear plane in unthreaded shank (alpha_v = 0.6 for 10.9), the 10.9 values increase by 20%.

Bolt Tension Resistance — Ft,Rd (Table 3.4)

The design tension resistance per bolt:

Ft,Rd = k2 x f_ub x A_s / gamma_M2

Where:

Quick Tension Capacity Table — k2 = 0.9 (Standard Bolts)

Bolt Grade f_ub (MPa) M12 Ft,Rd M16 Ft,Rd M20 Ft,Rd M24 Ft,Rd M30 Ft,Rd
4.6 400 24.3 kN 45.2 kN 70.6 kN 101.7 kN 161.6 kN
5.6 500 30.3 kN 56.5 kN 88.2 kN 127.1 kN 202.0 kN
8.8 800 48.6 kN 90.4 kN 141.1 kN 203.3 kN 323.1 kN
10.9 1000 60.7 kN 113.0 kN 176.4 kN 254.2 kN 403.9 kN

Tension failure can also occur by punching shear of the bolt head through the connected ply (Bp,Rd). For thin plates, this may govern.

Combined Shear and Tension — Table 3.4 Interaction

When bolts are subjected to combined shear Fv,Ed and tension Ft,Ed, EN 1993-1-8 Table 3.4 requires:

Fv,Ed / Fv,Rd  +  Ft,Ed / (1.4 x Ft,Rd)  <=  1.0

This linear interaction is simpler than the AISC elliptical interaction but slightly more conservative for moderate tension ratios. The 1.4 factor on Ft,Rd reflects test evidence that moderate tension does not severely degrade shear capacity, though the connection must still be checked for the full bearing and tension resistances independently.

Numerical example: For M20 8.8 bolts with Fv,Ed = 60 kN and Ft,Ed = 40 kN:

Bearing Resistance — Fb,Rd (Clause 3.6.1)

The design bearing resistance per bolt:

Fb,Rd = k1 x alpha_b x f_u x d x t / gamma_M2

Where:

k1 Factor (Perpendicular to Load)

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

The maximum k1 = 2.5 applies when e2 >= 1.5 x d0 or p2 >= 3.0 x d0. For standard edge distances (e2 = 1.5 x d0), k1 = 2.5. For tight edge distances, k1 reduces significantly:

alpha_b Factor (In Direction of Load)

alpha_b = min(alpha_d, f_ub/f_u, 1.0), where:

The term f_ub/f_u accounts for bolt/plate strength ratio. For 8.8 bolts (f_ub = 800 MPa) in S355 plate (f_u = 470 MPa): f_ub/f_u = 800/470 = 1.70. For 8.8 bolts in S275 plate (f_u = 410 MPa): f_ub/f_u = 800/410 = 1.95. Since alpha_b <= 1.0, f_ub/f_u only governs when the bolt is weaker than the plate — typical for Grades 4.6 and 5.6 in S355 plate.

Typical alpha_b values for M20, d0 = 22 mm, inner bolts:

For end bolts with e1 = 1.2 x d0 = 26.4 mm: alpha_d = 26.4/(3 x 22) = 0.40 — end bolts often govern bearing resistance.

Slip-Resistant Connections — Categories B and C (Clause 3.9)

When slip must be prevented under service loads (Category B) or ultimate loads (Category C), preloaded bolts are required.

Slip Resistance per Bolt

Fs,Rd = k_s x n x mu x Fp,C / gamma_M3

Where:

Slip Factors — mu (Table 3.7)

Surface Preparation Class Typical Treatment mu
Class A — Blasted, no paint Grit/shot blast, loose rust removed 0.50
Class B — Blasted, alkali-zinc paint Blast + zinc silicate (50-80 um) 0.40
Class C — Wire brushed, no paint Power wire brush, loose rust removed 0.30
Class D — As-rolled, all surfaces Mill scale intact, no treatment 0.20

Class A surfaces (grit-blasted, unpainted) are the standard assumption for slip-resistant connections unless otherwise specified. Class B is the most common in practice as it allows painted faying surfaces with a qualified zinc silicate primer. The Chinese and Hong Kong Steel Codes specify mu = 0.45 for blast-cleaned surfaces with inorganic zinc silicate paint -- between Class A and B.

Category B (SLS) vs Category C (ULS)

Category B: Slip must not occur at serviceability limit state. At ultimate limit state, the connection may slip into bearing. Verification:

Category C: Slip must not occur at ultimate limit state. More onerous:

Category C is required for connections where slip would be catastrophic (e.g., columns splices in moment frames), connections with bolts in tension that rely on friction to transfer shear, and connections with oversize holes or long slotted holes.

Preload Forces — Table 3.6

Preload force per bolt Fp,C = 0.7 x f_ub x A_s:

Bolt Size M12 M16 M20 M22 M24 M27 M30 M36
8.8 47 kN 88 kN 137 kN 170 kN 198 kN 257 kN 314 kN 458 kN
10.9 59 kN 110 kN 172 kN 212 kN 247 kN 321 kN 393 kN 572 kN

Preload is achieved by controlled tightening: torque method (with calibrated wrench), combined method (torque + part-turn), or direct tension indicators (DTI washers). The torque method is most common but has +/- 25% accuracy. For slip-resistant connections, the combined method or DTI washers are recommended.

Torque Values for Achieving Preload (Typical, k = 0.18 Lubricated)

Bolt Size M16 M20 M22 M24 M27 M30 M36
8.8 Torque 250 Nm 490 Nm 670 Nm 850 Nm 1250 Nm 1690 Nm 2970 Nm
10.9 Torque 315 Nm 615 Nm 840 Nm 1065 Nm 1560 Nm 2120 Nm 3710 Nm

Values are approximate. Actual torque depends on k-factor (nut factor), which varies with lubrication, plating, and thread condition. Always verify with preload tests for critical connections.

Worked Example — M20 Grade 8.8, 4-Bolt Group, Shear 200 kN

Connection details:

Step 1 — Shear Resistance per Bolt

Fv,Rd = 0.6 x 800 x 245 / 1.25 = 94,080 N = 94.1 kN per shear plane

For a single-shear connection:

Total shear resistance = 4 x 94.1 = 376.4 kN
Shear utilisation = 200 / 376.4 = 0.531 — shear OK

Step 2 — Bearing Resistance per Bolt

Plate (end bolt) — alpha_d:

alpha_d = e1 / (3 x d0) = 40 / (3 x 22) = 40 / 66 = 0.606

f_ub/f_u = 800 / 470 = 1.70 (but alpha_b capped at 1.0) alpha_b = min(0.606, 1.70, 1.0) = 0.606

Edge bolts — k1 (perpendicular):

k1 = min(2.8 x 35/22 - 1.7, 2.5) = min(2.8 x 1.591 - 1.7, 2.5) = min(4.455 - 1.7, 2.5) = min(2.755, 2.5) = 2.5

Bearing resistance per bolt:

Fb,Rd = 2.5 x 0.606 x 470 x 20 x 12 / 1.25 = 2.5 x 0.606 x 470 x 240 / 1.25
       = 2.5 x 0.606 x 90,240 / 1.25
       = 2.5 x 54,685 / 1.25
       = 136,713 / 1.25
       = 109,370 N
       = 109.4 kN per bolt

For inner bolts (alpha_d uses p1 = 100 mm):

alpha_d = 100/(3 x 22) - 0.25 = 1.515 - 0.25 = 1.265 -> capped at 1.0
alpha_b = min(1.0, 1.70, 1.0) = 1.0
Fb,Rd,inner = 2.5 x 1.0 x 470 x 20 x 12 / 1.25 = 2.5 x 470 x 240 / 1.25 = 2.5 x 112,800 / 1.25 = 225,600 N = 225.6 kN

The end bolts govern bearing. Total bearing capacity = 4 x 109.4 = 437.6 kN.

Step 3 — Final Check

Limit State Capacity Demand Utilisation Status
Bolt shear (governs) 376.4 kN 200 kN 0.531 OK
Bearing (end bolt) 437.6 kN 200 kN 0.457 OK

The M20 8.8 bolt group is adequate for V_Ed = 200 kN. Shear governs at 53% utilisation. If the bolts were loaded eccentrically, the elastic vector or ICR method must be used, and the critical bolt utilisation will be higher.

gamma_M2 Values — Comparison Across National Annexes

The partial safety factor gamma_M2 applies to bolts, welds, and plates in bearing. EN 1993-1-8 recommends gamma_M2 = 1.25. However, National Annexes may specify different values:

Country / Region gamma_M2 Effect on Bolt Resistance vs. 1.25
EN Recommended 1.25 Baseline
UK NA 1.25 No difference
Germany NA (DIN) 1.25 No difference
France NA 1.25 No difference
Netherlands NA 1.25 Same as recommended
Italy NA 1.25 Same as recommended
Singapore NA (SS EN 1993) 1.25 Adopts recommended value

All major European National Annexes adopt the recommended gamma_M2 = 1.25 for bolts. This is in contrast to gamma_M0 and gamma_M1 where some National Annexes deviate (e.g., UK NA uses gamma_M1 = 1.00 instead of the recommended 1.00 — effectively identical). For practical design, gamma_M2 = 1.25 can be used across all European jurisdictions unless the project specification requires otherwise.

Note: The Chinese steel code GB 50017 uses a partial factor of 1.111 for high-strength bolt shear (effectively a resistance factor phi = 0.9). This results in approximately 11% higher design resistance compared to EN 1993-1-8 for the same bolt. Engineers working across jurisdictions should adjust capacity tables accordingly.

Staggered Bolt Patterns and Block Tearing

Block Tearing — Veff,Rd (Clause 3.10.2)

For bolt groups loaded in shear, block tearing (block shear) must be checked. This is a failure mode where a block of material tears out of the plate:

Veff,1,Rd = f_u x Ant / gamma_M2  +  (1/sqrt(3)) x f_y x Anv / gamma_M0   (concentric loading)
Veff,2,Rd = 0.5 x f_u x Ant / gamma_M2  +  (1/sqrt(3)) x f_y x Anv / gamma_M0   (eccentric loading)

Where:

Block tearing is often the governing limit state for end plates with small edge distances and closely spaced bolts. In the worked example above, with e2 = 35 mm and plate thickness 12 mm, block tearing should be verified if the end distance e1 is tight.

Design Checklist — Bolted Connections per EN 1993-1-8

  1. Bolt grade and size selection: Choose from M12-M36, Grades 4.6/5.6/8.8/10.9
  2. Hole clearance: Standard d0 = d + 2 mm for M12-M24; d + 3 mm for M27-M36
  3. Spacing and edge distances: Verify e1/e2 >= 1.2 x d0, p1 >= 2.2 x d0, p2 >= 2.4 x d0 (Table 3.3)
  4. Shear check: Fv,Ed <= Fv,Rd per bolt (use A_s for threads in shear plane)
  5. Bearing check: Fb,Rd using k1 and alpha_b from Clause 3.6.1 — note distinction between end and inner bolts
  6. Combined shear + tension: Table 3.4 interaction if bolts carry both
  7. Slip resistance: If Category B or C, verify preload and surface preparation class
  8. Block tearing: Clause 3.10.2 for the bolt group (concentric or eccentric loading)
  9. Long joints: If L_j > 15 x d, reduce Fv,Rd by beta_Lf = 1 - (L_j - 15d)/(200d) >= 0.75
  10. Packing plates: If t_p > d/3 through the grip, increase bolt length; if total packer thickness > 6 mm, check for reduced slip resistance

Frequently Asked Questions

Why must the tensile stress area A_s be used instead of the gross shank area A for shear resistance?

The shear plane almost always intersects the threaded portion of the bolt in standard connections. The thread root diameter is smaller than the nominal shank diameter — for M20, the stress diameter d_s = 17.65 mm vs nominal d = 20 mm. Using A (314 mm^2) instead of A_s (245 mm^2) overestimates shear capacity by 28%. This is a common error in hand calculations and can lead to unsafe designs. Only use A when the shear plane is specifically detailed to pass through the unthreaded shank, which requires careful control of grip length and is rarely practical.

What is the difference between slip-resistant Category B and Category C connections?

Category B requires slip resistance at serviceability limit state (SLS) only — the connection may slip into bearing at ultimate limit state (ULS). Category C requires slip resistance at ULS, meaning the connection must not slip even under factored loads. Category C uses gamma_M3 = 1.25 (ULS) while Category B slip check at SLS uses gamma_M3,ser = 1.10. Category C is more conservative and is required for connections where slip would be structurally detrimental: column splices in moment frames, connections with bolts in combined shear and tension, telerance-critical structures, and connections with oversize holes.

How does EN 1993-1-8 bolt design compare to AISC 360?

Both codes use fundamentally similar approaches but differ in details. EN 1993-1-8: Fv,Rd uses alpha_v x f_ub x A_s / gamma_M2 with alpha_v = 0.6 (8.8/10.9 with threads in shear plane). AISC 360: phi x F_n x A_b with phi = 0.75 and F_nv = 0.563 x F_ub for threads in shear plane (Group A). For M20 8.8: EN gives 94.1 kN vs AISC gives 0.75 x 0.563 x 830 x 245 = 85.6 kN (using AISC F_ub = 830 MPa for A325M equivalent). The EN resistance is approximately 10% higher due to the different alpha_v/phi and f_ub values. For bearing, EN uses the k1 x alpha_b formulation while AISC uses Lc x t x F_u with phi = 0.75. Critical difference: EN uses gamma_M2 on the resistance side while AISC uses phi on the nominal strength — the numerical effect is that gamma_M2 = 1.25 corresponds to a resistance factor of 0.80.

When should preloaded bolts be specified instead of snug-tight bolts?

Preloaded (HSFG) bolts per EN 1090-2 are required when: (1) slip resistance is needed at SLS or ULS (Categories B and C); (2) connections subject to vibration, impact, or load reversal (fatigue loading); (3) connections where bolts carry both tension and shear (the preload maintains contact and prevents prying amplification); (4) oversize or slotted holes are used; and (5) connections in tension where joint decompression must be prevented (Column splices in tall buildings, tension flange splices in crane girders). For typical shear-only gravity connections in building frames, Category A with snug-tight bolts is adequate and more economical.

What is the effect of grip length and packing plates on bolt shear capacity?

EN 1993-1-8 Clause 3.6.1(4): For connections with a total grip length t_grip (including packing plates) exceeding 5 x d, the shear resistance Fv,Rd must be reduced. This is because longer bolts are more flexible and less able to bear uniformly against the hole wall. For grip lengths between 3d and 5d: minor reduction, typically 5-10%. For grip lengths > 5d: use engineering judgment or test data. Packing plates with a total thickness > d/3 must be extended beyond the joint with additional bolts to transfer the packing plate force into the connected member.

Related Pages

Educational reference only. All bolt resistances are per EN 1993-1-8:2005 with gamma_M2 = 1.25. Verify against the applicable National Annex for your jurisdiction. Shear capacities assume threads in the shear plane (use A_s). Preload values are for Class A faying surfaces unless stated otherwise. Slip factors must be confirmed by surface preparation specification and testing per EN 1090-2. All designs must be independently verified by a licensed Professional Engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION without professional structural engineering review.

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