Metric Bolt Group Calculator: How to Use It

A metric bolt group calculator works out the shear and tensile loads on each bolt in a pattern, plus the group’s resultant load and utilization, when you enter the bolt circle diameter, number of bolts, and applied force. You get the per-bolt load in newtons or kilonewtons and a check of whether the group is safely sized. This page explains the standard assumption behind the math, walks through a real example, and covers the common mistakes that lead to undersized or oversized bolted joints.

Formula

The calculator uses the standard elastic analysis for a bolt group under a direct shear force and an eccentric moment. It assumes all bolts are the same size, share the load equally for direct shear, and that the moment is resisted by bolt forces proportional to their distance from the centroid of the group.

For a circular bolt pattern with n bolts on a bolt circle diameter d, under a direct force F applied at an eccentricity e from the centroid:

• Direct shear per bolt: P_shear = F / n
• Moment on the group: M = F × e
• Shear from moment (maximum, at the bolt farthest from the centroid): P_moment = (M × r) / Σr², where r = d/2 for a circular pattern. For a symmetric circular group, this simplifies to P_moment = (M / r) / (n/2) = (2M) / (n × r) = (4M) / (n × d).
• Total maximum bolt shear: P_total = P_shear + P_moment (when the direct shear and moment act in the same direction on the critical bolt).

All forces are in kilonewtons (kN), dimensions in millimeters (mm). The result is the maximum shear load on the most heavily loaded bolt, which you then compare to the allowable shear capacity of the bolt (from a standard like ISO 898 or ASME B18.2.4.1M).

Worked Example

Using the default values: bolt circle diameter d = 200 mm, n = 8 bolts, applied force F = 50 kN, eccentricity e = 0 mm (centered load).

1. Direct shear per bolt: P_shear = 50 / 8 = 6.25 kN
2. Moment on group: M = 50 × 0 = 0 kN·mm
3. Shear from moment: P_moment = (50 × 0) / (200/2) / (8/2) = 0 kN
4. Total max bolt shear: P_total = 6.25 + 0 = 6.25 kN

The calculator shows 6.25 kN per bolt, which is exactly the direct shear. With no eccentricity, the moment term is zero.

When to Use a Bolt Group Calculator

Use this calculator when you are designing or checking a bolted joint where multiple bolts share a load. Typical situations include:

• Flange connections on pressure vessels or pipework
• Base plates for columns or equipment supports
• Bracket connections in steel structures
• Wheel hubs or coupling flanges in machinery
• Any circular pattern of bolts resisting a shear force and a moment

The calculator is especially useful in the early design stage to get a quick estimate of bolt size before doing a full finite element analysis or a detailed hand calculation per standards like Eurocode 3 or AISC.

How to Read the Results

The key output is the maximum bolt shear (P_total). This is the load that the most heavily loaded bolt must resist. Compare it to the allowable shear capacity of your bolt. For example, a property class 8.8 M12 bolt has a nominal shear strength of about 0.6 × 800 MPa × area, which is roughly 32 kN (but always use the exact value from the standard you are designing to).

If P_total is less than the allowable capacity, the bolt group is adequate. If it is higher, you need a larger bolt, more bolts, a bigger bolt circle, or a lower applied load. The utilization ratio is simply P_total / allowable, and you want that to be less than 1.0 (often less than 0.8 for safety).

Common Mistakes and Misconceptions

• Ignoring eccentricity: A load applied off-center creates a moment that dramatically increases the load on the farthest bolts. Even a small offset can double the load on a critical bolt.
• Mixing units: Always keep force in kN and length in mm. If you enter force in N and length in m, the moment will be off by a factor of 1000.
• Assuming equal load distribution: The elastic method assumes all bolts share direct shear equally, but in reality, bolt preload and joint stiffness affect distribution. The method is conservative for most cases.
• Forgetting the moment term: When e = 0, the moment is zero, but any real joint has at least a small eccentricity. Always include the actual offset.
• Using the wrong bolt count: The formula for moment shear uses n/2 because only the bolts on one side of the centroid resist the moment in the elastic analysis. If you use n, you will underestimate the load.

Limitations of the Simple Method

The elastic method (also called the “vector method”) is a simplification. It assumes bolts are elastic and that the joint rotates about the centroid. In reality, bolted joints can behave plastically, and the true load distribution depends on bolt spacing, plate thickness, and preload. For critical applications, use a more refined analysis:

• Instantaneous center of rotation method (more accurate for eccentric loads)
• Finite element analysis with contact and bolt pretension
• Design codes like AISC Manual or Eurocode 3 Part 1-8, which give specific procedures for bolt groups

Also, this calculator only covers shear. If your joint also experiences tension (prying forces, axial loads), you must check the combined stress using an interaction equation from the relevant standard.

How to Choose Bolt Size and Pattern

Once you have the maximum bolt shear, follow these steps to select a bolt:

1. Determine the required bolt area from the allowable shear stress: A = P_total / τ_allow.
2. Select a bolt diameter that provides at least that area (use the tensile stress area, not the nominal area).
3. Check the bearing stress on the plate (bolt hole) to avoid crushing.
4. Ensure the bolt circle diameter is large enough to fit the bolts and wrenches.
5. Verify edge distances and spacing per the standard you are using.

For example, if P_total = 6.25 kN and you use a property class 8.8 bolt with allowable shear stress of 400 MPa (0.6 × 800 MPa), you need an area of 6250 N / 400 MPa = 15.6 mm². A M6 bolt has a stress area of about 20.1 mm², so it would work, but you would likely choose a larger bolt for practical reasons.

Frequently Asked Questions

What is a bolt circle diameter? The bolt circle diameter is the diameter of the circle that passes through the centers of all bolt holes in a circular pattern. It is a key dimension for flange and coupling designs.

How do I account for multiple load cases? Run the calculator for each load case (e.g., dead load, live load, wind) and take the maximum P_total from any case. For combined cases, use the worst-case combination from your design code.

Can I use this for a rectangular bolt pattern? No, this calculator is specific to circular patterns. For rectangular patterns, the moment resistance is different; use a general bolt group analysis.

What is the difference between shear and tension in bolts? Shear is a force parallel to the bolt axis (actually perpendicular to the bolt shank), while tension is a force along the bolt axis. This calculator only handles shear; tension requires a separate check.

Why does the calculator not include a safety factor? The calculator outputs the raw load. You must apply your own safety factor based on the application and the governing code. Typical factors are 1.5 to 2.0 for static loads, higher for dynamic loads.

What if my force is in pounds or inches? Convert to SI units before using the calculator. 1 kN = 224.8 lbf, 1 mm = 0.03937 in. The calculator expects kN and mm.

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in d | Bolt circle diameter | mm | 200 | 0
in n | Number of bolts | - | 8 | 1
in F | Applied force | kN | 50 | 0
in e | Eccentricity (offset) | mm | 0 | 0
out P_shear | Shear per bolt | kN | F / n | 2
out M | Moment on group | kN·mm | F * e | 0
out P_moment | Shear from moment | kN | (F * e) / (d / 2) / (n / 2) | 2
out P_total | Max bolt shear | kN | P_shear + P_moment | 2