How to use this calculator
- Enter the bolt count. Enter the number of equally spaced bolts on the circle.
- Enter the bolt circle diameter. Enter the BCD; the radius R is half of it.
- Enter the moment and shear. Enter the torsional moment M about the centre and any in-plane direct shear V.
- Read the per-bolt forces. Read the worst-case F_max plus the tangential F_t and direct F_v components.
How it works
A bolt pattern that carries an in-plane torsional moment M plus a
direct shear V is solved by the elastic (bolt-group / eccentric
shear) method. The moment is resisted by a tangential force on each bolt,
proportional to its distance from the pattern centroid. On a single circle every
bolt sits the same distance R = BCD/2 from the centre, so each carries the same
tangential force:
F_t = M / (N · R)
The direct shear is shared equally between the bolts:
F_v = V / N. These are vectors; the most-loaded bolt is where they line
up, so the worst-case demand is their sum:
F_max = F_v + F_t
That is the shear demand per bolt — compare it to the bolt’s shear
capacity, not its tensile rating.
The same workflow is often searched as a bolt group force calculator, bolt pattern shear calculator, eccentric bolt group calculator or bolt circle load calculator. After finding the demand here, compare the result with the bolt shear strength calculator and the bolt bearing stress calculator. If the job starts from hole coordinates, use the bolt circle coordinate calculator first.
Worked example
Verified against the live calculator
Take 6 bolts on a 100 mm bolt circle (R = 0.05 m) carrying
a 300 N·m moment with no direct shear. The tangential force per bolt is
F_t = 300 / (6 × 0.05) = 1000 N, F_v = 0, so
F_max = 1000 N. Now add a 600 N direct shear:
F_v = 600 / 6 = 100 N, and the worst-case bolt sees
F_max = 100 + 1000 = 1100 N. The calculator returns these directly.
Frequently asked questions
How do you calculate the shear force per bolt in a bolt pattern?
For a circular pattern, split the load into two parts. The torsional moment gives a tangential force on each bolt F_t = M / (N · R), where N is the bolt count and R the bolt-circle radius. The direct shear is shared equally, F_v = V / N. The worst-case bolt adds them: F_max = F_v + F_t.
Is this a bolt group force calculator?
Yes. This is a bolt group force calculator for a single circular bolt pattern. It uses the elastic bolt-group shear method to estimate the worst-loaded bolt from direct shear plus an in-plane moment.
When should I search for bolt pattern shear instead of bolt shear strength?
Use bolt pattern shear when you need the demand on each bolt in a group. Use the bolt shear strength calculator after that to compare the worst bolt demand against capacity for the selected bolt size, grade and shear plane.
What is the elastic (bolt-group) method?
The elastic or "eccentric shear" method assumes rigid plates and shares an applied moment among the bolts in proportion to each bolt’s distance from the group centroid. On a single bolt circle every bolt is the same distance R from the centre, so they all carry the same tangential force F_t = M / (N · R).
Why add the direct and tangential forces directly?
They are vectors, so they truly add only where they point the same way. F_max = F_v + F_t is the worst case — it assumes the direct shear and the moment’s tangential force are collinear on the most-loaded bolt. It is conservative; a full vector sum at the true angle gives an equal or smaller value.
What radius do I use — and what are the units?
Use the bolt-circle radius R = BCD / 2 (half the bolt circle diameter). The math is unit-safe: with the moment in N·m, the radius is taken in metres, so F_t = M / (N · R) returns newtons. The calculator handles the conversion; you just enter BCD in mm or inches.
Is this the shear demand or the bolt capacity?
This is the demand — the shear each bolt must carry. Compare F_max against the bolt’s allowable shear capacity (from its grade, the shear plane, and whether the threads are in the shear plane). The joint is adequate when capacity exceeds F_max with your required factor of safety.
Does this work in metric and imperial?
Yes — enter the bolt circle diameter in mm or inches, the moment in N·m or lbf·ft, and the shear in N or lbf; the per-bolt forces are shown in N, kN, tonne and lbf. Toggle SI/Imperial in the header.
Method & assumptions
- Elastic (eccentric shear) bolt-group method: rigid plates, the moment shared in proportion to each bolt’s distance from the centroid.
- Equal-size bolts on a single concentric circle, all the same distance R from the centre — so each carries the same tangential force F_t = M/(N·R).
- F_max = F_v + F_t is the conservative collinear sum; the true vector sum at the actual angle is equal or smaller.
- For a general eccentric bolt group calculator with irregular bolt positions, use the same elastic method with each bolt's distance from the group centroid.
- In-plane shear and moment only — no prying, tension or out-of-plane load. The result is the demand; check it against the bolt’s shear capacity and factor of safety.