Bolt Pattern Force Distribution Calculator

This calculator works out how a total applied force splits between the bolts in a circular bolt pattern, giving you the load on each bolt based on its position and the direction of the force. You enter the number of bolts, the circle radius, the total force, and the angle of that force, and it returns the maximum bolt load and the load on each individual bolt. The result is the worst-case force that the most heavily loaded bolt must withstand, which is the value you need for sizing bolts or checking a joint.

Formula

The force on each bolt in a circular pattern is the sum of a direct shear component and a moment-induced component. For a force applied at the centroid of the bolt group, the direct shear on each bolt is simply the total force divided by the number of bolts:

F_direct = F / n

When the line of action of the force passes through the centroid, the moment is zero and all bolts share the load equally. But if the force is applied away from the centroid, or if the load is eccentric, a moment is created. For a pure moment applied to a circular bolt group, the force on each bolt is proportional to its distance from the centroid. For a circle, all bolts are at the same distance (the radius), so the moment-induced force on each bolt is:

F_moment_i = (M * r_i) / Σ(r_j²)

where M is the applied moment, r_i is the distance of bolt i from the centroid, and the sum is over all bolts. For a circular pattern, r_i = r for all bolts, so the sum becomes n * r². The total force on a bolt is the vector sum of the direct and moment components. The maximum occurs on the bolt closest to the direction of the applied force (or opposite, depending on the moment direction).

For a force F acting at a distance e from the centroid, the moment is M = F * e. In the common case where the force is applied at the centroid but at an angle, the direct component is F/n in the direction of the force, and the moment component is zero. However, when the force is not applied at the centroid, the moment creates additional loads. The calculator above assumes the force is applied at the centroid (no eccentricity), so the moment term is zero. To account for an eccentric load, you would need to input the eccentricity distance.

For the calculator above, we assume the force is applied at the centroid, so the maximum bolt load is simply F/n. But the calculator includes a placeholder for the moment term, which you can modify if you know the eccentricity. If you have an eccentric load, use the formula:

F_max = F/n + (F * e * r) / (n * r² / 2)

where e is the eccentricity (distance from centroid to line of action). For a circular pattern, the second moment of area about a diameter is n * r² / 2, which is why that term appears.

Worked Example

Using the default values: 8 bolts, radius 100 mm, force 10,000 N, angle 0°.

1. Direct shear per bolt: F/n = 10,000 / 8 = 1,250 N
2. Moment is zero (force at centroid), so moment component = 0 N
3. Maximum bolt load = 1,250 N
4. Average bolt load = 1,250 N

So each bolt carries 1,250 N. If the force were applied with an eccentricity of 50 mm, the moment component would be (10,000 * 50 * 100) / (8 * 100² / 2) = 50,000,000 / 40,000 = 1,250 N, making the maximum load 2,500 N on the most heavily loaded bolt.

When to Use This Calculator

This calculator is useful for mechanical design, such as bolted flange connections, wheel lug nuts, or any circular bolt pattern subject to a known force. It helps you determine whether a given bolt size and grade can handle the load, or to compare different bolt patterns. It is also used in structural engineering for base plates and anchor bolts.

You should use this when the force is applied through the centroid of the bolt group (no moment). If the load is eccentric, you need to modify the formula to include the moment term. The calculator gives you the worst-case bolt load, which you compare to the allowable shear or tensile stress for your bolt material.

How to Read the Results

The maximum bolt load is the force on the most heavily loaded bolt. This is the number to use for bolt sizing. The average load is the direct shear component. If the maximum is much higher than the average, the joint is inefficient – you might want to increase the radius or add more bolts to reduce the peak load.

For example, if your bolt has a shear capacity of 5,000 N and the calculator shows a maximum load of 4,800 N, the bolt is adequate but with little margin. If the maximum exceeds the capacity, you need a larger bolt or a different pattern.

Common Mistakes

• Forgetting the eccentricity: Many real joints have the force applied away from the centroid, creating a moment. Ignoring this underestimates the bolt load.
• Unit mix-ups: Ensure force is in newtons, radius in millimeters (or all in consistent units). The calculator uses N and mm, but you can convert: 1 inch = 25.4 mm, 1 lbf = 4.448 N.
• Assuming all bolts share equally: Only true when the force is perfectly centered and no moment exists.
• Rounding too early: Keep full precision in intermediate steps to avoid significant errors in the final result.

Limitations of the Formula

This calculator assumes the bolts are equally spaced on a perfect circle, the joint is rigid, and the load is static. It does not account for bolt preload, friction between plates, prying action, or dynamic loads. For fatigue or impact loads, a more detailed analysis is needed. Also, the formula gives the force on the bolt, not the stress – you must divide by the bolt’s cross-sectional area to get stress.

For a single bolt, the shear stress is F / A, where A is the area. For tensile loads, use the tensile stress area. Always check the bolt grade’s yield strength and apply a safety factor.

Frequently Asked Questions

Q: What is the difference between shear and tensile load on a bolt?
A: Shear load acts perpendicular to the bolt axis, trying to cut the bolt. Tensile load acts along the axis, pulling the bolt. This calculator assumes shear, but the same formula can be used for tensile if the force is axial.

Q: How do I convert the force to stress?
A: Divide the force by the bolt’s cross-sectional area. For shear, use the shank area; for tensile, use the tensile stress area (about 0.75 times the nominal area for standard threads). Compare to the material’s allowable stress.

Q: Can I use this for a non-circular pattern?
A: No, this formula is specific to circular patterns. For arbitrary patterns, you need a more general method using the centroid and polar moment of inertia.

Q: What if the force is not at the centroid?
A: Then you must include the eccentricity. The moment is F * e, and the additional bolt load is (M * r) / (Σr²). For a circle, Σr² = n * r², so the extra load is (F * e * r) / (n * r²).

Q: Why is the maximum load higher than the average?
A: Because the moment adds to the direct shear on one side and subtracts on the other. The bolt on the side opposite the force direction gets the highest load.

Q: How many bolts should I use?
A> More bolts reduce the average load, but also reduce the moment resistance if the radius stays the same. A common rule is to use at least 4 bolts, but the optimal number depends on space and cost. The calculator helps you see the trade-off.

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in n | Number of bolts | - | 8 | 3
in r | Bolt circle radius | mm | 100 | 1
in F | Total applied force | N | 10000 | 0
in a | Force angle | deg | 0 | 0
out max_load | Maximum bolt load | N | F / n + (F * r * cosd(a - 0)) / (n * r^2 / 2) | 1
out avg_load | Average bolt load | N | F / n | 1