EngineerBenchCalculating loads in an in-plane bolt group
A force and an in-plane moment do not generally divide equally between bolts. This model adds an equal share of direct force to the moment-induced force at each bolt. The moment contribution depends on each bolt's position relative to the group's centroid and the distribution of the whole pattern.
Use one coordinate system
Enter every bolt's X and Y position in the same units and keep force and moment signs consistent. Translating the entire pattern does not change its relative geometry. Missing or misplaced bolts can change both the centroid and the highest-loaded location.
Compare the most heavily loaded bolt
The resultant at each position is a vector combination, not the sum of independent maximum components. The model assumes equal bolt stiffness and an elastic in-plane load distribution. It does not evaluate out-of-plane tension, prying, frictional slip resistance, or flexibility of the connected plates.
Combining force components at each bolt
A direct force contributes the same vector share at every bolt in the equal-stiffness model. A moment contributes a tangential force whose magnitude increases with distance from the group centroid. Adding the magnitudes of those two contributions is generally wrong because their directions vary around the pattern. Combine X components and Y components first, then calculate each resultant.
Bolts farther from the centroid can contribute more resistance to an in-plane moment, but changing a pattern also changes the group's summed squared radius. Recalculate the complete group when adding or moving a fastener instead of adjusting only the new bolt's row. Use a common coordinate origin and a consistent moment sign; translating every coordinate equally should not alter the relative load distribution. Check the largest resultant against an appropriate connection-capacity method. The model does not determine which holes contact first, how friction shares load before slip, or whether the plate is rigid enough to justify the assumed elastic distribution.
Formula
Fi = F/n + (M/Σr²)(−yi, xi). Resultants are evaluated bolt by bolt, preserving force direction.