Bolt Group Calculator: Force on Each Bolt

The force on each bolt in a group loaded off-centre, and the most heavily loaded bolt.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

When a load acts away from the centre of a bolt group, it does two things: it pushes the group sideways, and it twists it. The elastic method shares the direct shear equally among the bolts, and resists the twisting moment with forces on each bolt proportional to its distance from the centroid, at right angles to that distance.

Enter the bolt positions, the load components and where the load acts. The calculator gives the force on every bolt and the largest one, which you compare with the bolt shear capacity from your standard or supplier.

Formulas used

  • M = (x_l - \bar x)F_y - (y_l - \bar y)F_x
  • J = \sum r_i^2
  • F_i = \sqrt{\left(\frac{F_x}{n} - \frac{M y_i}{J}\right)^2 + \left(\frac{F_y}{n} + \frac{M x_i}{J}\right)^2}

Worked example

With the default numbers in the calculator above:

  1. Centroid of the bolt group: (50, 75) mm
  2. Polar sum of the distances squared: 32500 mm²
  3. Moment about the centroid: 4000 kN mm
  4. Resultant force on each bolt (direct shear plus torsion): 4 bolts
  5. Most heavily loaded bolt: 14.48 kN

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Is this the elastic or the plastic method?

The elastic method. It is conservative compared with the instantaneous centre method.

Does it check the bolt?

No. It gives the force. Compare it with the bolt capacity, and check bearing on the plate and prying separately.

What origin do I use for the positions?

Any. Use the same origin for the bolt positions and the load position.

Related calculators

Further reading: Shigley, Mechanical Engineering Design (bolted and welded joints); steel connection design handbooks.

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