Bolted and Welded Joints

Bolt grades, preload and torque, joint stiffness, shear and tension in bolts, thread engagement, and weld strength.

Joint types and how they fail

Joints are where structures usually fail: a part of a machine seldom breaks in its plain section, but at a hole, a weld or a fastener. A joint has to carry the load from one part to another and, in a machine, often do so for millions of cycles. The common methods are compared below.

JointStrengthsWeaknessesTypical failure
Bolted (preloaded)Dismountable, strong, no heat distortionHoles weaken the parts; loosening, fatigueBolt fatigue, loosening, thread stripping, joint slipping
WeldedStrong, rigid, continuous, no extra partsHeat distortion, residual stress, low fatigue strength, not dismountableFatigue cracks at the weld toe or root, lack of fusion
RivetedNo heat, good for dissimilar and thin materialsHoles; strength depends on the installationShear of the rivet, bearing and tear-out of the plate
Adhesive (bonded)Spreads the load, joins any material, sealsNeeds surface preparation; low peel strength; temperature and agingPeel and cleavage failure, a poor surface
Press, shrink and keyedNo fasteners; high torque (see Press, Shrink and Expansion Fits)Precision, assembly effortSlip, fretting

Bolts: sizes, grades and stress area

A bolt is described by its thread (M10 × 1.5: 10 mm nominal diameter, 1.5 mm pitch, coarse), its property class and its length. The threaded part carries the load over the tensile stress area At, a little smaller than the shank, which is the area to use in strength calculations: At = π ÷ 4 (d − 0.9382 p)². The class (4.6, 8.8, 10.9, 12.9) encodes the strength: the first number × 100 is the tensile strength in MPa, and the second ÷ 10 is the yield ratio.

Property classProof strength Sp (MPa)Yield Sy (MPa)Tensile Su (MPa)Use
4.6225240400Light, general (low carbon steel)
5.8380420520General
8.8600660830The standard structural and machine bolt (medium carbon, quenched and tempered)
9.8650720900Small sizes (M16 and under)
10.98309401 040High strength, machinery
12.99701 1001 220Very high strength (socket cap screws); sensitive to hydrogen embrittlement and notch
A2-70, A4-80 (stainless)450 to 600450 to 600700 to 800Corrosion-resistant; galls when tightened dry (use anti-seize)
Thread (coarse)At (mm²)Preload Fi = 0.75 Sp At (kN, class 8.8)Torque T = 0.2 d Fi (N·m, dry)
M620.19.011
M836.616.526
M1058.026.152
M1284.337.991
M16157.070.7226
M20245.0110.3441
M24353.0158.9762

Preload and tightening torque

A bolt in a good joint is not a simple pin: it is a spring that is stretched during tightening and clamps the parts together with the preload Fi. The preload is what holds the joint, keeps the nut from loosening, and above all makes the bolt see only a small part of any external load (see below), which protects it against fatigue. A rule for a reusable joint is Fi = 0.75 × Sp × At (75 percent of the proof load; 90 percent for a permanent joint). The tightening torque that produces it is T = K d Fi, where the nut factor K is about 0.2 for plain dry steel, 0.15 for lightly oiled and 0.18 for zinc plated; about 90 percent of the torque goes into overcoming friction under the head and in the threads and only 10 percent into stretching the bolt, so the preload scatters ±25 to 30 percent with torque control.

Worked example: an M10 class 8.8 bolt

  • At = 58 mm² (M10 × 1.5), Sp = 600 MPa. The preload is Fi = 0.75 × 600 × 58 = 26.1 kN (75 percent of the proof load).
  • The torque with K = 0.2 is T = 0.2 × 10 × 26 100 ÷ 1 000 = 52 N·m; lightly oiled (K = 0.15) the same preload needs only 39 N·m: tightening an oiled bolt to the dry torque overloads it by about 33 percent, a common cause of broken bolts.
  • The Bolt Torque and Thread Engagement Tool gives the same results for other sizes and classes.
  • Other methods: torque-angle (snug, then a set angle past yield) and direct tension indicators or hydraulic tensioners are more accurate for critical joints.

The joint diagram: stiffness and external load

Bolted joint diagram: preload and external loadforce (kN)bolt stretch →← compression of membersbolt (stiffness kb)members (km, stiffer)Fi = 26.1 kN (preload)bolt force Fb = Fi + C P = 28.6 kNclamp force Fi − (1 − C) P = 18.6 kNHere kb : km = 1 : 3, so C = kb ÷ (kb + km) = 0.25: a 10 kN external load adds only 2.5 kN to the bolt.
The joint diagram: the bolt and the clamped members as two springs, with a preload F_i and an external load P.

The bolt stretches and the clamped members are compressed by the preload, so the bolt and the members are two springs with stiffnesses kb and km. When an external tensile load P pulls the joint apart, it relieves some of the compression of the members and adds only a part to the bolt: Fb = Fi + C P and Fm = Fi − (1 − C) P, with the joint constant C = kb ÷ (kb + km). Because the members are normally much stiffer than the bolt, C is small (0.1 to 0.3): most of the external load is taken by relief of the clamping force, not by the bolt. The joint separates only when P exceeds P0 = Fi ÷ (1 − C).

Worked example: an external load of 10 kN

  • The bolt stiffness is kb = At E ÷ Lgrip = 58 × 200 000 ÷ 30 ≈ 387 kN/mm for a 30 mm grip; the clamped steel members are about three times stiffer (typical), so C = 1 ÷ (1 + 3) = 0.25.
  • With Fi = 26.1 kN and P = 10 kN: the bolt force is Fb = 26.1 + 0.25 × 10 = 28.6 kN (only 2.5 kN extra) and the clamping force drops to 26.1 − 0.75 × 10 = 18.6 kN.
  • The joint would separate at P0 = 26.1 ÷ 0.75 = 34.8 kN.
  • The bolt stress is 28.6 kN ÷ 58 mm² = 493 MPa, below the proof strength of 600 MPa. The safety factor against yielding (proof) is np = (Sp At − Fi) ÷ (C P) = (34.8 − 26.1) ÷ (0.25 × 10) = 3.48, and against separation n0 = Fi ÷ (P (1 − C)) = 3.48.
  • Lesson: tighten the bolt to its proper preload and keep the joint stiff; a loose bolt carries the full external load and fails by fatigue.

Bolts in shear and tension

A bolt can carry a transverse load in two ways. In a bearing (shear) connection the bolt shank bears on the hole walls and is loaded in shear: the capacity per shear plane is about 0.6 Su A (A the area at the shear plane: the shank, or At if the threads cross it). In a friction-grip (slip-critical) connection the preload clamps the plates and friction carries the load: the slip load is μ n Fi (μ = 0.3 to 0.5 for clean steel, n friction surfaces). Both are checked together with the bearing stress on the plate and the tear-out of the plate edge (edge distance at least 1.5 to 2 d).

Worked example: the wall bracket

The bracket of the figure below carries 2 000 N at 150 mm: the moment 300 000 N·mm tends to pull the upper bolt out of the wall. With the bolts 110 mm apart and the pivot at the lower edge the tension in the upper bolt is about T = M ÷ s = 2 727 N and the shear is F ÷ 2 = 1 000 N per bolt. With M10 class 8.8 bolts at preload 26.1 kN the external tension adds only C T = 682 N to the bolt (stress +11.8 MPa), and the clamp force is still far above zero: the joint does not open. The shear (1 000 N) is carried by friction, μ Fi = 0.3 × 26.1 kN = 7.8 kN per bolt, nearly eight times the demand (the bolt’s own shear capacity is 0.6 × Su At = 28.9 kN). A smaller bolt (M6 or M8) would do for strength; the size is set by the stiffness and the wall material.

A wall bracket: load, moment and boltsF = 2 000 NL = 150 mm (to the load)s = 110 mmtension Tpivot (bottom edge)Moment on the joint:M = F × L = 2 000 × 150= 300 000 N·mmUpper bolt tension (about thelower edge, bolts s apart):T ≈ M ÷ s ≈ 2 700 NShear per bolt = F ÷ 2 = 1 000 N
A wall bracket: the load creates a moment that puts the upper bolt in tension.

Thread engagement and tapped holes

The threads must be long enough that the bolt breaks before the threads strip. In a nut of matched strength about 0.8 d of engagement is enough (a standard nut is about 0.8 d high). In a tapped hole in a weaker material (aluminum, cast iron, plastic) the internal thread is the weak part and needs more length: roughly 1 d in steel, 1.5 d in cast iron and 2 d or more in aluminum.

Worked example: M10 into aluminum

The tensile (breaking) load of an M10 class 8.8 bolt is Su At = 830 × 58 = 48.1 kN. The shear area of an internal thread per mm of engagement is about π dp ÷ 2 = π × 9.03 ÷ 2 = 14.2 mm²/mm (with dp the pitch diameter). For 6061-T6 aluminum (shear strength 207 MPa) the engagement to strip at the same load is Le = 48 140 ÷ (207 × 14.2) = 16.4 mm (1.6 d). In steel the nut-height rule gives 8.0 mm. For a joint that is not tightened to the full strength the length can be shorter, but a thread insert (a steel helical coil) in the aluminum is the usual solution for repeated assembly.

  • Blind holes need a drilling depth beyond the thread length; a bolt too long can bottom out and not clamp. See the Tap Drill Size and Thread Pitch Lookup for the drill sizes.
  • Fine threads have a larger stress area and resist loosening a bit better but strip more easily in soft material.
  • Clearance holes are about 0.5 to 1 mm larger than the bolt (ISO 273 medium series): M10 → 11 mm; allow the thermal movement and the tolerance (see Fits and Tolerances).

Fatigue and loosening

A bolt under a pulsating load fails by fatigue at the first engaged thread, under the head, or at the thread run-out. The preload makes the bolt’s stress amplitude small: σa = C (Pmax − Pmin) ÷ (2 At). For the joint above with the load pulsing from 0 to 10 kN: σa = 0.25 × 10 000 ÷ (2 × 58) = 21.6 MPa, against an endurance limit of about 129 MPa for a rolled-thread class 8.8 bolt (Shigley): a large margin, as long as the preload is maintained (see Fatigue and Stress Concentration).

Cause of looseningPrevention
Embedment (settlement) of the surfaces, loss of preloadHard washers, fewer interfaces, a longer grip, retighten after the first load
Transverse vibration (slip of the head and thread)High preload, thread-locking adhesive, prevailing-torque nuts, wedge-locking washers (Nord-Lock), serrated flanges
Thermal cyclingDisc (Belleville) springs, long bolts, matching expansion coefficients
Gasket creepMetal-to-metal contact or stops, retighten
Vibration alone with no slipRarely loosens a well-preloaded bolt; check the preload and the joint design

Spring and split lock washers are almost useless against vibration; use proper locking methods, safety wire or a cotter pin for critical joints.

Welded joints

A butt weld with full penetration is as strong as the parent plate (if it is sound). A fillet weld is triangular, with a leg length s; the strength is calculated on the throat a = 0.707 s, the shortest section, in shear: the allowable shear stress is about 0.3 × the electrode tensile strength (AWS E70 electrodes: Su = 482 MPa, so τall ≈ 145 MPa). The load capacity per unit length is a × τall.

Worked example: two fillet welds

Two parallel fillet welds, leg 6 mm and length 100 mm each, join a plate in tension. Throat a = 0.707 × 6 = 4.24 mm. The allowable shear is 0.3 × 482 = 145 MPa. The strength is F = a × τ × Ltotal = 4.24 × 145 × 200 = 122 679 N (123 kN). The weld size is also limited by the thickness of the thinner part (minimum leg size 3 to 6 mm by the plate thickness) and a leg larger than the plate thickness is wasted.

  • Weld groups in bending and torsion: treat the weld as a line with a second moment of area Iw about its centroid; the stress is then (M ÷ Iw) × distance combined with the direct shear.
  • Fatigue: welds have a much lower fatigue strength than the parent metal, because of the notch at the toe and root, residual stress and defects. The design codes (EN 1993-1-9, IIW, AWS D1.1) give detail categories; the endurance limit of a fillet weld is often only 20 to 40 percent of the plate’s.
  • Design for good welds: access for the welder, avoid weld stacking and sharp corners, balance the welds to limit distortion, specify the process, filler and inspection, and consider heat treatment for thick or alloyed parts.
  • Heat effects: the heat-affected zone of aluminum alloys loses much of its strength (6061-T6 drops to about 40 to 50 percent of its strength): design the weld in a low-stress region.
  • Quality: inspection (visual, dye penetrant, magnetic particle, ultrasonic, radiographic) for critical welds; follow the welding standard (ISO 5817 quality levels).

Rivets, adhesives and other joints

  • Rivets (solid, blind/pop, self-piercing) are loaded in shear and bearing, like bolts, and are quick for sheet; the strength comes from the rivet’s shear area and the plate’s bearing, and they have little preload so are poor against tension and vibration.
  • Adhesive joints carry shear well over a large overlap (a lap shear strength of 15 to 30 MPa for structural epoxies) but peel and cleavage poorly: design so that the bond is loaded in shear, with a large overlap, a clean prepared surface and the right cure. Combine with fasteners for safety.
  • Threaded inserts, rivet nuts and press-in nuts add strong threads in thin or soft parts.
  • Snap fits and clips in plastics are loaded by the elastic deflection of a beam (see Beam Bending and Deflection).
  • Clamps, hose clips and V-bands use friction and the capstan effect like belts.

Troubleshooting

SymptomLikely causeCheck
Bolts loosen in serviceLow preload, embedment, vibration slip, no lockingTorque and method; higher preload; a locking element; check the joint for slip
Bolt breaks below the head or at the first threadFatigue from low preload, too high a preload, a bending load or a misaligned facePreload (K factor), flatness of the seat, grip length, a loose joint
Threads stripShort engagement in soft material, over-tightening, a damaged threadEngagement length, thread inserts, the torque used
Joint opens or leaksPreload lost or the load above the separation loadPreload, gasket, stiffness; more bolts or a stiffer flange
Cracks at a weld toeFatigue, a notch, residual stressWeld detail; smooth the toe, post-weld treatment, a larger section
Stainless bolt seizes (galling)Dry tightening, high speed, fine threadsAnti-seize, lower speed, different materials
Adhesive joint peelsPeel loading, a poor surface, agingRedesign for shear; surface preparation

Related

FAQ

What is the right torque for a bolt?

It depends on the size, the class and the friction: T = K d Fi with Fi about 75 percent of the proof load and K 0.2 for dry steel, 0.15 oiled. Use the manufacturer’s or the engineering specification value for a critical joint, and the tool above for a first estimate.

Why does preload matter so much?

Because the clamped parts are stiffer than the bolt, a preloaded bolt takes only a small part of the external load, so its stress hardly changes and it does not fatigue. A bolt that is not preloaded sees the whole load and soon fails.

Can I reuse a bolt?

A bolt tightened within its elastic range (to 75 percent of the proof load) can be reused if the threads are undamaged. Torque-to-yield and high-strength structural bolts should be replaced.

Bolt or weld?

Bolts when the joint must be taken apart, or loaded in fatigue and the welding is hard; welds for continuous, rigid, leak-tight joints and where weight matters. Many structures use both.

References

  • Shigley, J. E. and Mischke, C. R., Mechanical Engineering Design, McGraw-Hill: screws, fasteners, welded and bonded joints.
  • ISO 898-1 (mechanical properties of fasteners), ISO 262 and ISO 724 (metric threads), VDI 2230 (systematic calculation of bolted joints).
  • AWS D1.1 (structural welding code), EN 1993-1-8 (design of joints), Bickford, J. H., An Introduction to the Design and Behavior of Bolted Joints.

Last reviewed: October 2026. Strengths and factors are typical; follow the applicable design code and test critical joints.