Fastener Load Distribution in Multi-Fastener Joints
In a joint with multiple fasteners, the load is not shared equally. The stiffness of the plates, the flexibility of the fasteners, the spacing, the edge distance and the load path all determine how much load each fastener carries. This article explains why loads concentrate at the end fasteners, how fastener flexibility and plate stiffness interact to shape the distribution, what happens when a fastener yields, and how the load distribution is extracted from a finite element model.
Why Loads Are Not Equal
In a multi-fastener joint, the load transferred by each fastener is different. The fundamental reason is that the load in the plate changes at each fastener station — load is transferred from one plate to the other at each fastener, and the remaining plate load is carried to the next fastener. The first fastener in the joint sees the full plate load arriving from one side; it transfers a portion of this load to the other plate, and the remaining load continues to the next fastener. The last fastener sees the remaining load and transfers it to the other plate — after this, the first plate has no load. The end fasteners therefore handle the largest change in plate load, and they typically transfer the largest fastener load. The interior fasteners handle smaller incremental changes and transfer less load. This is the basic shear-lag mechanism that makes the load distribution peaked at the ends.
The end fasteners carry the highest load because the full plate load must enter and exit the joint at these locations. The interior fasteners transfer smaller increments. This is the shear-lag mechanism — it occurs even when all fasteners are identical.
The Role of Joint Flexibility
The joint flexibility — the combination of fastener flexibility and plate stiffness — determines the shape of the load distribution. A flexible fastener allows the two plates to displace relative to each other at the fastener location; this displacement reduces the load that the fastener attracts. A stiff fastener resists the relative displacement and attracts more load. The plate stiffness determines how the remaining load is redistributed along the joint: a stiff plate carries the load efficiently to the next fastener (more peaked distribution), while a compliant plate allows the load to spread (flatter distribution). The interaction between fastener flexibility and plate stiffness is captured by the ratio of the two: a high flexibility-to-stiffness ratio gives a flat distribution; a low ratio gives a peaked distribution. This is why assuming rigid fasteners gives a dramatically wrong distribution — it is the extreme case of zero flexibility, which produces the most peaked possible distribution.
Fastener Flexibility and Plate Stiffness Interaction
The load distribution can be understood as a balance between the fastener flexibility (which tries to spread the load) and the plate stiffness (which tries to concentrate it). Consider a row of fasteners in a lap joint. The plate carries the full load into the first fastener. A flexible first fastener transfers only a small portion of this load — most of the load continues in the plate to the second fastener. A stiff first fastener transfers a large portion — little load continues. The same logic applies at each subsequent fastener. The result is that flexible fasteners produce a distribution that decays gradually from the ends — the end fasteners still carry the most, but the peak-to-mean ratio is lower. Stiff fasteners produce a distribution that is sharply peaked at the ends — the end fasteners carry most of the load, and the interior fasteners carry little.
| Parameter | Effect on Load Distribution | Peak-to-Mean Ratio |
|---|---|---|
| High fastener flexibility | Load spreads — end fasteners transfer less, interior more | Lower — more uniform |
| Low fastener flexibility (stiff) | Load concentrates at ends — end fasteners transfer most | Higher — more peaked |
| High plate stiffness | Load carried efficiently to next fastener — little spreading | Higher — more peaked |
| Low plate stiffness (compliant) | Load spreads along plate — more sharing | Lower — more uniform |
| Rigid fasteners (limit) | All load at end fasteners — interior carry nothing | Maximum — most peaked |
Local Compliance and Spacing Effects
The fastener spacing affects the load distribution through the plate stiffness between fasteners. Close spacing means the plate span between fasteners is short and stiff — the load does not spread much between fasteners, and the distribution is more peaked. Wide spacing means the plate span is longer and more compliant — the load spreads more, and the distribution is flatter. However, wide spacing also means the joint is longer and heavier, and the bypass stress at each hole is higher (more load remains in the plate at each station). The edge distance — the distance from the edge fastener to the free edge of the plate — affects the load at the end fastener: a short edge distance means less plate material to spread the load, and the end fastener carries more. The local compliance — the compliance of the plate immediately around the hole, which deforms in bearing — also contributes to the fastener flexibility and affects the distribution.
Edge Effects
The end fasteners are special because they see the full plate load on one side and zero on the other. This produces the largest change in plate load and the largest fastener load. The edge fastener also experiences an edge effect: the plate material beyond the fastener (between the fastener and the free edge) is less constrained than the material between fasteners, and the bearing deformation at the edge hole is different. The edge effect can increase or decrease the end-fastener load depending on the edge distance and the plate stiffness. In practice, the end fasteners are almost always the most critical — they carry the highest load and have the highest bearing stress and bypass stress. The engineer should pay particular attention to the end fasteners in the fatigue analysis: they are the most likely initiation sites.
The end fasteners are almost always the most critical. They carry the highest load, have the highest bearing stress and bypass stress, and are the most likely fatigue initiation sites. The fatigue analysis should focus on these locations.
Load Redistribution and Yielding
When a fastener reaches its yield load, its behaviour changes. In the elastic regime, the fastener stiffness is constant, and the load distribution is determined by the elastic stiffnesses. When a fastener yields, its effective stiffness decreases — it continues to carry load but at a lower rate (the tangent modulus in the plastic regime is lower than the elastic modulus). The reduced stiffness means the yielded fastener attracts less additional load — the load that would have gone to the yielded fastener is redistributed to the adjacent fasteners. This load redistribution can be beneficial: it spreads the load more evenly, and the peak fastener load is reduced. This is the principle behind limit-state design of fastener groups — allowing the end fasteners to yield and redistribute the load to the interior. However, the redistribution can also be detrimental: if the adjacent fasteners are already near their capacity, the additional load from the yielded fastener can cause them to yield as well — a progressive failure (unzipping) that can lead to joint failure. The engineer must assess whether the redistribution is stable (the load is safely shared) or unstable (progressive failure).
When a fastener yields, its effective stiffness decreases and load redistributes to adjacent fasteners. This can be beneficial (load spreading) or detrimental (progressive failure — unzipping). The engineer must assess whether the redistribution is stable or unstable.
Elastic Distribution and the Limit of Rigid Fasteners
In the fully elastic regime, the load distribution is determined entirely by the stiffness properties — fastener flexibility and plate stiffness. The distribution can be computed analytically for idealised joints (uniform spacing, identical fasteners, constant plate stiffness) using the shear-lag equation, or numerically using FEA with beam or spring fasteners. The limit of rigid fasteners — zero flexibility — gives the most peaked distribution: all the load is concentrated at the end fasteners, and the interior fasteners carry nothing. This is the distribution that a rigid-link FEA model produces, and it is the reason rigid links are not appropriate for final load-distribution analysis. The other limit — infinitely flexible fasteners — gives a uniform distribution where every fastener carries the same load. Real joints are between these limits, and the actual distribution depends on the stiffness ratio.
Extracting Load Distribution from FEA
In a finite element model, the fastener loads are extracted from the element forces. For beam fasteners, the axial force, shear forces and bending moments at each fastener are directly available from the beam element output. For spring or CBUSH elements, the element force is directly available. For connector elements, the connector force and failure margin are available. For solid bolts, the force must be integrated over a cross-section — typically by defining a free-body cut at the shear plane and summing the nodal forces. The extracted fastener loads should be checked for equilibrium: the sum of the fastener loads should equal the total transferred load, and the distribution should be physically reasonable (peaked at the ends, decaying inward). A load distribution that is not peaked at the ends, or that does not sum to the total load, indicates a modelling error — wrong fastener stiffness, wrong plate stiffness, or incorrect boundary conditions.
Verify the extracted load distribution: the sum of fastener loads must equal the total transferred load, and the distribution should be peaked at the ends. A distribution that is not peaked at the ends, or that does not sum correctly, indicates a modelling error.
Bearing and Bypass Interaction
At each fastener hole, the plate experiences two simultaneous stress conditions: the bearing stress from the fastener pressing against the hole wall, and the bypass stress from the load that passes through the plate without being transferred. The bearing stress is proportional to the fastener load; the bypass stress is proportional to the remaining plate load. The end fasteners have the highest bearing stress (highest fastener load) and the highest bypass stress (highest plate load on one side). The interaction between bearing and bypass stress determines the fatigue and static strength at each hole — this is the subject of Article 13 (Bearing and Bypass Loading). For the load distribution analysis, the key point is that the fastener load and the bypass load must both be known at each hole — the load distribution gives the fastener loads, and the plate load at each station gives the bypass loads. Together, they define the stress state at every hole in the joint.
Key takeaways
- Loads are not shared equally in a multi-fastener joint. The end fasteners carry the highest load because the full plate load must enter and exit the joint at these locations.
- Fastener flexibility spreads the load — flexible fasteners allow the plate to redistribute, reducing the peak load at the end fasteners. Stiff fasteners concentrate the load at the ends.
- Plate stiffness determines how quickly the load redistributes along the joint. Stiff plates redistribute slowly (peaked distribution); compliant plates redistribute quickly (flatter distribution).
- When a fastener yields, its effective flexibility increases and it carries less additional load — the load redistributes to adjacent fasteners. This can be beneficial (load sharing) or detrimental (progressive failure).