Bearing Stress and Bolts
We have already learned in our discussion of bolt bearing type connections that bearing stress induced by the pressure contact between a bolt and a bolt hole is a failure mode that a designer must consider. This section of the website sheds some light on what is perhaps an often overlooked and poorly understood failure mode.
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References
 G. L. Kulak, J. W. Fisher, J. H, A. Struik – American Institute of Steel Construction (AISC) – Guide to Design Criteria for Bolted and Riveted Joints, Second Edition
 EN 199318:2005 – Eurocode 3 – Design of Steel Structures – Part 18 – Design of Joints
 EN 199311:????
1. Introduction
We learned in our discussion of bolt bearing type connections that after a major slip of the joint has occurred, one or more fasteners will have entered into contact against the edge of the bolt hole. A bearing stress is therefore developed in both the bolt and the material adjacent to the hole. This stress is initially concentrated at the point of contact; however, as the load increases, the bearing stress will exceed the yield stress of the weaker material, resulting in plastic deformation, thereby spreading the load over a larger area of contact. This distribution of load results in a more uniform stress field and conveniently enough, one which is easier to deal with analytically [1]. In general, bolts are stronger than the connected parts, therefore the distribution of stress is predicated by the partial embedment of the bolt in the connected part.
2. Bearing Capacity / Strength
There are varying approaches to determining the bearing capacity (strength) of an individual fastener depending on which code or standard you are using.
2.1 Simplified Approach
For any cylindrical member which is bearing against the inside surface of a round hole, such as a pin or bolt shank, the bearing stress can be approximated by assuming that the stress is distributed across an area equivalent to the rectangular projection of the cross section through the bolt, as illustrated in Figure 1. This bearing stress is therefore determined using the following formula:
(1)
Where:
=  the radial force (N), acting on the bolt section in bearing  
=  the diameter of the bolt (mm), which is equal to the major diameter, when the shank is in bearing, or the pitch diameter, when the threaded portion is in bearing  
=  the thickness of the part that is bearing against the bolt (mm), i.e. plate thickness 
Figure 1
Figure 1 – ????
This simplified approach will provide an engineer with a very quick and simple indication whether a particular joint design is likely to perform adequately in bearing. The engineer can then revisit the calculation later to perform more detailed calculations when refining the analysis.
2.1.1 A Word of Caution
The above calculation is clearly an approximation. The reader should note that when the clearance between the pin / bolt and the hole increases, the approximation becomes much less accurate and the engineer must take into account local bending stresses at the hole edge and across the net section. The effect is even more pronounced for a slotted hole. This is covered in detail in Clause XX of EN 199318:2005 [2].
3. Bearing Capacity – Eurocode 3 Method
Eurocode 3, EN 199318:2005 [2] provides some simple formulae for determining the bearing capacity (bearing strength) of a bolted joint. The design formulae have been generated with the intention of avoiding excessive deformation of the holes, rather than actual failure / rupture of the connection.
3.1 Single Lap Joints
Clause 3.6.1 (10) of Eurocode 3, EN 199318:2005 [2] provides a very simple calculation for determining the bearing capacity of a single lap joint with only one bolt row, assuming that the bolts are provided with washers under the nut and head:
(2)
Where:
=  the design bearing resistance (capacity) per bolt (N)  
=  the Ultimate Tensile Stress (UTS) of the connected plate, assuming it is lower than that of the bolt (N/mm²)  
=  the diameter of the bolt (mm)  
=  the minimum thickness of the two plates in the single lap joint (mm)  
=  partial safety factor related to the resistance of pins, bolts and rivets, as per EN 199311:???? [3] = 1.25 
3.1 ?????
In more complex situations, the formula is:
 P_{lim} = k_{1} × α × f_{u}/γ_{M2}
where
 k_{1} and α are factors that take into account other failure modes than the bearing pressure overload; k_{1} take into account the effects that are perpendicular to the tangent force, and α the effects along the force;
 k_{1} = min{2.8e_{2}/d_{0} ; 2.5} for end bolts,
k_{1} = min{1.4p_{2}/d_{0} ; 2.5} for inner bolts, e_{2}: edge distance from the centre of a fastener hole to the adjacent edge of the part, measured at right angles to the direction of load transfer,
 p_{2}: spacing measured perpendicular to the load transfer direction between adjacent lines of
fasteners,

 d_{0}: diameter of the passthrough hole;
 α = min{e_{1}/3d_{0} ; p_{1}/3d_{0} – 1/4 ; f_{ub}/f_{u} ; 1}, with
 e_{1}: end distance from the center of a fastener hole to the adjacent end of the part, measured in the direction of load transfer,
 p_{1}: spacing between centers of fasteners in the direction of load transfer,
 f_{ub}: specified ultimate tensile strength of the bolt.
In good design practice, the threaded part of the screw should be small and only the smooth part should be in contact with the plates;
Dependent on hole clearance, EN 199318 refers to the clearances of Table 11 of EN 10902 “normal round holes”. If this is followed then the eurocode method is OK.
Could also make a section on if clearance is loose, or a slotted hole is used (bending becomes an issue).