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.
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.
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.
- 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.