Bolted Joint

Which bolt holds your parts together, and how tight should it be? Choose a metric bolt and strength class, enter the loads, and get the preload, the tightening torque and checks against slipping, separating, yielding and fatigue — or let the calculator find the smallest bolt that works.

FastenersVDI 2230 (simplified)Torque

Inputs

Input examples

What to do

The bolt is tightened to 90% of its yield strength, as is usual practice. Loads are per bolt. The joint stiffness is estimated with the VDI 2230 substitute cone for wide plates; for critical joints, do a full VDI 2230 analysis or a test.

The bolt

Thread size — metric coarse, ISO 261

Strength class

Loads on one bolt

Axial load F_A — pulling the parts apart

Transverse load F_Q — trying to slide them

The load

The joint

Clamp length l_k — total thickness of the clamped parts

Clamped parts

Friction between the parts μ_T

Tightening

Thread and head friction

Tightening method

How Does a Bolted Joint Work?

Tightening a bolt stretches it like a very stiff spring, and that spring squeezes the parts together with the preload. As long as the parts stay pressed together, friction carries sideways loads and the bolt hardly notices loads that pull the parts apart: most of that load just reduces the clamping pressure.

Only a small share — the load factor Φ — reaches the bolt as extra tension. That is why a properly preloaded bolt survives loads that would quickly break a loose one. Most of the tightening torque (about 90%) is lost to friction in the thread and under the head, so lubrication changes the preload a lot.

8.8R_m 800, R_p 640 MPa

≈ 90%torque lost to friction

Φ ≈ 0.1load share of the bolt

F_KR > 0parts stay closed

Joint Diagram

force vs. deformation

bolt (stretches)

clamped parts (compress)

with the axial load

Result

Enter the values above

Metric Threads

max. preload and torque, 8.8, μ = 0.12

Size	Pitch	A_s	F_M	M_A

Worked Techniques

Maximum Preload

While tightening, the bolt carries tension and twisting at the same time. The preload is chosen so that both together reach ν = 90% of the yield strength.

Example:

Load Factor

The bolt (resilience δ_S) and the clamped parts (δ_P) share the axial load. Stiff parts and a long, slender bolt keep Φ small. The factor n = 0.5 assumes the load enters halfway into the parts.

Example: steel parts, l_k = 2d: Φ ≈ 0.1.

Tightening Scatter

Friction varies from bolt to bolt, so the same torque gives different preloads. With a torque wrench the weakest bolt may have only 1/1.6 of the maximum preload; the joint must still hold with that, after the surfaces have settled a little.

Example:

Sources & Verification

References

R. G. Budynas & J. K. Nisbett, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 — Ch. 8 (Screws, Fasteners, and the Design of Nonpermanent Joints).