Fasteners installed near the end or edges of load-carrying members often carry more than just the applied load. They also carry a hidden load generated by bending moments in the load-carrying member. This additional load may outweigh the applied load by a great deal.

If the load–carrying member in the image below were infinitely rigid, the fastener would be required to resist only the applied 2P. But in most applications, a different loading condition develops. The flexibility of the load-carrying member typically demands that is edges or ends resist angular rotation caused by local loads.

For this analysis, bearing loads are assumed to be at a maximum at the edges, tapering to zero at the fastener centerline with a triangular load distribution. Under these conditions, fastener loads and stress are from:

*σ*_{max} = 24*sm*/(8*ws*^{3} – 4*R*^{3})

P_{1} = *σ*_{max}/6*s*(3*ws*^{2} – 4*R*^{3})

To use these equations, M, the resistive moment created by the bearing load, is conservatively set equal to the bending moment needs to maintain a fixed-end constraint of the load-carrying member. Then the first equation determines the maximum bearing stress and the second equation determines the resultant bearing load on the fastener.

Example: A 5-in wide bar is centrally loaded by a force of 10,000 lb and restrained at each end by a fastener passing through a hole with a radius of 0.5 in. The distance between the holes’ centerline is 36 in and the distance between the fastener centerline and the bar end is 2 in. What are the maximum bearing stress and maximum load on the fasteners?

From elementary strength of materials,

*M *= 2*PL*/8 = 10,000(36)/8 = 45,000 in-lb

Then maximum stress is found from the first equation as:

*σ*_{max} = 24(2)(45,000)/[8(5)(2)3 – 3*π*(0.5)4

= 6,800 psi

The bearing load, from the second equation, is then:

P_{1} = 6,800/6(2) [3(5)(2)2 – 4(0.5)3]

= 33,700 lb

The maximum load on the fastener is thus the bearing load plus half the applied load, or 38,700 lb.

Nomenclature:

*L* is the distance between fastener centerlines, in.

*M* is the resistive moment provided by the bearing load, in-lb.

*P* is half of the total load on the load bearing member, lb.

*P _{1}* is the resultant bearing load on the fastener, lb.

*R*is the radius of the fastener holes, in.

*s*is the distance from the fastener centerline to the end of the load carrying member, in.

*w*is the width of the load carrying member, in.

*σ*

_{max}is the maximum bearing stress, psi.

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