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(OP)
Does anyone know of a formula for how the load is divided among a line of fasteners (bolts or rivets) when two strips are overlapped and joined by numerous (>2) fastenters in a row, then subjected to tension? I've found qualitative information that the end fasteners carry the bulk of the load, but no quantitative formulas. This same situation would apply to riveted joints in plates where more than 2 rows of rivets are used.

(OP)
I have found the answer to my earlier post. The problem was analyzed and experimentally verified by NACA (precursor to NASA) in the 1947 technical paper "Analytical and Experimental Investigation of Bolted Joints, Technical Note No. 1458", by Samuel J. Rosenfeld. It is available (free) in its entirety at:

http://naca.larc.nasa.gov/reports/1947/naca-tn-1458/naca-tn-1458.pdf

There are many other interesting reports at the same web site.

The importance of fastener load distribution depends on the application of the joint. If the joint is to be statically loaded, then an ‘average’ load distribution is satisfactory. The maximum running load of a riveted or bolted lap joint being equal to the number of fasteners multiplied by the joint strength of the fastener multiplied by the number of rows, divided by the pitch. If, on the other hand, the joint is subjected to regular cyclic stress, load distribution becomes very important from a fatigue point of view. This is particularly important under loading conditions in which the fasteners behave as linear elastic members. In a standard lap joint fastening together two plates, the critically and heighest loaded fastener is the one on each end. In a fatigue environment the end fasteners will fail first, increasing the burden on their neighbour and significantly weakening the joint.

In order to determine the load distribution, a finite element based analysis can be used. The joint is broken down into a series of spring elements. The plates are divided into a number of springs lying between each fastener, which is its self, portrayed as a spring. The spring constant of the plate is a function of cross sectional area and E (Youngs modulous), the spring constant of the fastener (C) is calculated using the NACA document. Once the equations describing deformations of these springs has been derived they can be solved simply in Excel using simple martix inversion methods (which Excel does very well). You don’t need to spend vast sums of dollars and time with expensive FEA software to do this.

The whole point of this exercise is to determine what variation in the plate thickness (spring stiffness) will give an even load distribution. The results of this detailed design and analysis can be seen in joints that are tapered or stepped. Boeing has a manual titled Structural Design for Durability which contains guidance on critical end fastener loads and fatigue resistant joints.

The next stage in the joint analysis is the assessment of the severity factor. This accounts for the effects of the fastener type, method of installation, interference, hole preparation and so on.

Once the severity factor has been determined the fatigue life of the joint can be predicted. This is very important in new designs and also in repair and modification. Fatigue life of repairs and mods can be compared to the original structure, which forms a sound basis for assessing its suitability.

Fastener load distribution is important and can be calculated with relative ease. If anyone would like to know more about this or would like some assistance feel free to contact me.

Nigel Waterhouse
n_a_waterhouse@hotmail.com

A licensed aircraft mechanic and graduate engineer. Attended university in England and graduated in 1996. Currenty,living in British Columbia,Canada, working as a design engineer responsible for aircraft mods and STC's.

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