What (static) bearing pressure is applicable in design?

In many construction calculation reports in offshore and maritime industry, for static pressure surfaces, a material bearing pressure value is used equal to or less than yield strength. What is a bearing stress and why are engineers using such a low value?

Note that no roller or sliding surfaces are considered here! What is considered are two surfaces pressed together without dynamic movement.

In aerospace where structures contain lots of joints with fasteners, the bearing strength is a hot issue. Sometimes values are used up to 2 * σ_ult. In offshore, engineers love to weld everything rather than join it by fasteners. In lots of structural verification reports bearing values lower than yield are used, even if deformation is allowed. Probably this is inherited by the 'old' WSD (or ASD) methodology where all stresses need to be kept below yield.

For static loaded contact surfaces by bearing pressures two situations need to be considered separately:

1. Bearing strength in bolt holes;
2. Bearing strength not in bolt holes like fillers, compression areas etc.

There can be big differences in bearing allowables dependent on these situations. In AISC 360-10 it is stated that for situation based on linear stresses:

1. See chapter J3-10; the maximum bearing stress depends on the consideration whether deformation at service load is allowed or not. But the minimum allowable is 1.2-1.5*σ_ult (WSD; UF=0.6) or 1.8-2.0*σ_ult (LRFD).
2. See chapter J7; the max bearing stress allowed finished surfaces for WSD is 0.9*σ_0.2 (unity factor=0.6) and for LRFD 1.35*σ_0.2. Note that for WSD that this value may be increased with 1.33 when a unity factor of 0.8 is applicable.

Two things stand out here:

• Apparently there are 2 situations with separate bearing allowables that may be considered.
• Allowables can exceed the ultimate stress of the material.

Why is that?

The above practice is applicable for a (linear) bearing stress, which is the result of F/A (Force / bearing area).

The reason is that in joints with fasteners, bearing failure does not automatically lead to total failure of the joint. This is important to realise.

Even for situation 2 this can be the case. The engineer needs to determine whether or not deformation due to bearing pressure is a problem for function and behaviour of the structure. If not, really high bearing pressures are allowed (even above ultimate strength of the material).

How to handle high bearing stresses in FEA results?

In linear FEA calculations it is not rare that bearing peak pressures are higher than ultimate strength of the material. This doesn't have to be a problem. It can be verified by running a non-linear model to verify that strain results are reasonable low. The reason for this is the ratio between deviatoric and hydrostatic stresses. High bearing stresses (or high principal stresses) can be generated due to the reason that the material can't go anywhere. These high bearing stresses are caused by the hydrostatic stresses only, which cause volume change without any shape change. Hydrostatic stresses don't generate any strains! Therefore, to judge bearing stresses it is a good indication to look at the non-linear calculation results of the Von Mises stresses and the (plastic equivalent) strains in the bearing plate. As long as these are acceptable (average below σ_yield or σ_ult, dependent on the load case), high bearing stresses are acceptable.

In general, bearing stresses due to ULS load cases may be higher than yield, while in SLS they need to be kept below yield. A tip would always be to run the FEA model with non-linear material properties with LRFD loads including the material factor. This way a direct comparison can be made with the material properties.

In the example below a pressure of 125MPa is applied to a spherical bearing area, The FEA is run non-linear with non linear isotropic material properties. The pressures are near σ_ult (400MPa), while the Von Mises stresses are max 310MPa. Strains are relatively low (<5%), which shows that this load case is acceptable.