Bolt Group Force Distribution Calculator

How is force shared in a bolt group?

When the load on a connection does not pass through the centroid of the bolt group, the bolts are loaded in two ways. The force itself is shared equally by all bolts, which is the direct shear. The moment of the force about the centroid tries to rotate the plate and puts on each bolt a force that grows with its distance from the centroid and acts at right angles to the radius, which is the torsional shear. The actual bolt force is the vector sum of the two.

Formula

Direct shear is F′ = F / n and torsional shear is F″ = M × r / Σr². Here n is the number of bolts, r the distance of a bolt from the centroid, Σr² the sum of the squared distances of all bolts and M the moment of the load about the centroid. The critical bolt is usually the one farthest from the centroid whose torsional part points the same way as the direct shear.

Example

In the textbook example by Shigley four bolts sit at (±75, ±60) mm and a vertical load of 16 kN acts 425 mm from the centroid. Direct shear is 16 / 4 = 4 kN. The moment is 16 × 0.425 = 6.8 kN·m, each bolt is √(75² + 60²) = 96.0 mm from the centroid and the torsional shear is 6800 / (4 × 0.096) = 17.7 kN. The two bolts nearer the load carry a resultant of 21.0 kN and the two farther ones 14.8 kN. The calculator opens with this example loaded.

How to use the tool

Type the bolt coordinates one by one or use the grid and circle generators. Enter the load by components or by magnitude and angle, and give a point on its line of action. The tool reports the centroid, Σr², the components on every bolt and the most loaded bolt. Enter an allowable shear force per bolt to get the utilisation as well.

Limits

This calculation gives the force distribution only. Bolt shear and bearing resistance, tearing of the plate, edge distances and spacing are checked separately. The elastic method is a conservative assumption and suits preliminary sizing. For out of plane moments that pull on the bolts, the tension distribution in the anchor group tool can be used.