Bolt Group Calculator
This bolt group calculator analyzes an eccentrically loaded fastener pattern and returns the bolt group coefficient C, the design capacity of the group, and the demand-to-capacity utilization. It builds a rectangular bolt layout from your rows, columns, and spacings, then resolves the direct shear and the moment-induced shear on the most heavily loaded bolt. Capacities use AISC nominal shear stresses for A325 and A490 bolts with the 0.75 resistance factor for shear.
Formula
φRn = 0.75 · Fnv · Ab ; Group capacity = C · n · φRn ; C = 1 / max bolt force (unit load)
- C
- Bolt group coefficient from the elastic vector analysis (load divided by the controlling bolt force)
- Fnv
- Nominal bolt shear stress: 54 ksi for A325, 68 ksi for A490 (threads excluded)
- Ab
- Nominal bolt cross-sectional area = π·(d/2)² in²
- n
- Total number of bolts in the group
- φ
- Resistance factor for bolt shear, 0.75
How it works
- Define the pattern with the number of rows and columns and the row and column spacing (inches). The tool centers the pattern on its own centroid before analysis.
- Enter the eccentricity (horizontal offset of the load line from the centroid, in inches), the applied load magnitude in kips, and the load angle from vertical.
- Pick the bolt diameter and grade (A325 at Fnv = 54 ksi or A490 at Fnv = 68 ksi). The calculator reports the coefficient C, single-bolt capacity, group capacity C·n·φRn, and whether utilization stays at or below 1.0.
Worked example
A vertical line of three 3/4-inch A325 bolts at 3-inch spacing carries a 50-kip load applied 6 inches off the centroid.
- Bolt area Ab = π·(0.75/2)² = 0.4418 in²; single-bolt capacity φRn = 0.75 × 54 × 0.4418 = 17.89 kips.
- Polar moment Ip = 3² + 0² + 3² = 18 in²; direct shear = 1/3 per unit load, moment shear on the end bolt = 6 × 3 / 18 = 1.0.
- Controlling bolt resultant = sqrt(1.0² + 0.333²) = 1.054, so C = 1 / 1.054 = 0.95.
- Group capacity = 0.95 × 3 × 17.89 = 50.99 kips; utilization = 50 / 50.99 = 0.981.
C ≈ 0.95, group capacity ≈ 50.99 kips, utilization ≈ 0.981 — the connection is adequate (just under 1.0).
Frequently asked questions
- What does the bolt group coefficient C represent?
- C is the ratio of the total applied load to the force on the most heavily loaded bolt under a unit load. Multiplying C by the number of bolts and the single-bolt design shear gives the eccentric capacity of the whole group.
- Does this use threads-included or threads-excluded shear values?
- The built-in grades use the threads-excluded (X) nominal shear stresses from AISC: 54 ksi for A325 and 68 ksi for A490. If threads fall in the shear plane, the bolt capacity is lower and the group capacity should be reduced accordingly.
- How does eccentricity affect the result?
- A larger eccentricity increases the moment on the group, which raises the force on the outermost bolt and lowers the coefficient C. As eccentricity drops toward zero the load becomes nearly concentric and C approaches 1.0.
- Is this an elastic or ultimate-strength analysis?
- The coefficient here is computed with the elastic vector method, summing the direct shear and the moment-induced shear on each bolt. It is a conservative companion to the AISC instantaneous-center-of-rotation tables, which typically give slightly higher capacities.