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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.

### RE: Load Distribution Among Fasteners

Hi butelja!

I guess there is no formula available for the loads taken by each bolts, because the complete set up has many unknowns and we have 3 basic plane static equations. Yes u are right in saying that end fastners carry more load than the intermediate bolts. In general civil engineering practice these rivets/fasteners are designed assuming that all the fasteners share the loads equally. Infact we consider the critical path of the failure and then compute the tensile capacity of the connection(the objective of the civil engineer ends here). I guess as a Mechanical Engineers u must be well aware of this fact.
Yeah one thing can be done - analyse the connection on Ansys or Cosmos by FEA. I will try to check the answer and see if anything turns up.

Bye and thank you for a good querry.

### RE: Load Distribution Among Fasteners

Interesting question. As a structural engineer, we assume the load is always equally distributed. However, it seems to make sense that the end connection could potentially see the most load.

I have found no provision in the 1997 UBC to support this and wonder if a cyclical loading intensifies this effect.

Do you suppose that welds also have stress concentrations near the ends?

### RE: Load Distribution Among Fasteners

(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.

### RE: Load Distribution Among Fasteners

3
I have devised a method based on the NACA document you found. It is an excel spread sheet that determines the load distribution through joints, if you are interested in it let me know.

Nigel Waterhouse
nigelw@flightcraf t.ca
Kelowna Flightcraft
A licensed aircraft mechanic and a proffessional engineer, who attended university in England and graduated in 1996. Currenty living in British Columbia,Canada and working for Kelowna Flightcraft as a design engineer responsible for aircraft mods and STC

### RE: Load Distribution Among Fasteners

While the NACA document may be technically "correct", for normal structural calculations this issue is really not as critical as you may think. The nominal stresses calculated for a plate differ from the actual stresses due to a large number of factors such as neglecting friction, neglecting the plate deformations, neglecting tensile stress concentrations at holes, shearing stress is assumed uniform over connector cross section, and neglecting bending in the connectors. Also, poor alignment in hole locations, unequal tightening of connectors, and eccentricity in loading may create stresses that the designer cannot anticipate. Fortunately, the excellent ductility in steel creates a condition where, prior to reaching the ultimate strength of the connection, the plates and connectors deform plastically an amount sufficient to re-distribute the forces throughout the bolt pattern. This creates a condition where, under ultimate conditions, the assumptions used to calculate the nominal stresses are reasonably correct. This is why you don't see this issue show up in the AISC Specifications, etc.

### RE: Load Distribution Among Fasteners

The comments about ductility of structural steel (and some other metals that have not been hardened) are quite correct when we consider the ultimate strength of a statically loaded typical civil engineering structure.
However, structures that have connection with mechanical equipment that produces cyclic loading (particularly higher frequencies with stress reversals) may not quickly reach the point where the whole joint becomes ductile in normal service. The unequal stress situation may remain 'locked-in'. In instances like this the unequal load distribution may be critical and produce premature failure of the more highly stresses fasteners if they are not equally stressed

### RE: Load Distribution Among Fasteners

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

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.

Nigel Waterhouse
nigelw@flightcraf t.ca
Kelowna Flightcraft
A licensed aircraft mechanic and a proffessional engineer, who attended university in England and graduated in 1996. Currenty living in British Columbia,Canada and working for Kelowna Flightcraft as a design engineer responsible for aircraft mods and STC

### RE: Load Distribution Among Fasteners

CFPeng The detail of joint dynamics is very interesting. As a civil structural the assumptions of joint failure mode are as previously mentioned.
The performance of bolted timber connections however are probably more critical in that ultimate yield does not really have a true plastic state . ( or does it ? )
The other question that pops up is related to joint performance under seismic conditions. I am not sure if this is a serious concern.

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