Rivet bearing (hole-bearing) stress

What does this quantity describe?

Bearing stress describes the contact pressure between the cylindrical rivet shank and the plate's hole wall. It is referenced not to the cylindrical surface but to the projected rectangular area d0·t: σl = F/(n·d0·tmin), where tmin is the smallest sum of plate thicknesses acting in the same direction.

This is similar to a chair leg on soft ground: what matters for ground pressure is not the actually curved contact surface but the projected area with which the leg presses down — for bearing stress, that is the side-view rectangular area of diameter times plate thickness.

Formula and variables

σl = F / (n · d0 · tmin)

• σl = F/(n·d0·tmin)
• F = σl·n·d0·tmin
• tmin = F/(σl·n·d0)

Choose the inputs correctly

Transverse load F, rivet hole diameter d0, number of load-carrying rivets n, and the governing, smallest involved plate thickness tmin set bearing stress.

How to use the calculator

Enter load, rivet diameter, rivet count and the thinnest involved plate thickness to check bearing stress. For multiple overlapping plates, the sum of the thinnest layers acting in the same direction always governs.

Worked example

20,000 N over 4 rivets with a 10 mm diameter and an 8 mm governing plate thickness give σl = 20,000 N / (4 · 10 mm · 8 mm) = 62.5 MPa.

Understand the result and units

A bearing stress of 62.5 MPa is well below typical allowable values of about 400 MPa for structural steel; in this example shear stress, not bearing, is the more critical loading — see the required-rivet-count calculator.

Force is given in N, diameter and plate thickness in mm, and the resulting pressure in MPa (N/mm²).

When bearing governs instead of shear

Because allowable bearing stress (σl,allow ≈ 1.5·Rm) is markedly higher than allowable shear stress (τa,allow ≈ 0.6·Rm) for the same material, shear is usually the governing failure mode for typical geometries. Bearing becomes critical mainly for very thin plates with a comparatively large rivet diameter, since the bearing area d0·t then becomes small relative to the rivet cross-section A0. Comparing both checks, as shown in the required-rivet-count calculator, reveals which failure mode actually governs in a specific case.

Typical applications

The calculation is used alongside the shear check to ensure the rivet hole does not elongate through local yielding of the plate material; especially thin plates with large rivet diameters are prone to this.

Assumptions, limits and common mistakes

The model assumes pressure evenly distributed over the projected area. In reality, pressure at the hole wall is unevenly distributed and highest at the load-facing edge, which can cause gradual hole elongation before the nominal limit is formally reached.

Common mistake: A common mistake is using the wrong plate thickness in multi-layer stacks instead of the thinnest layer acting in the same direction. It is also easy to skip the bearing check entirely, even though it can well govern for thin plates with large rivet diameters.