Steel Bolt Group Analysis

How it calculates

The Steel Bolt Group Analysis (Free) calculator applies the elastic method from the AISC Steel Construction Manual to find the maximum shear demand on any bolt in an arbitrarily arranged bolt group under a single in-plane load case.

Bolt group centroid

Bolt positions are defined by their X and Y coordinates. The centroid of the group is computed assuming equal bolt areas:

• x_c = (sum of x_i) / n
• y_c = (sum of y_i) / n

All subsequent calculations use bolt coordinates measured from this centroid.

Polar moment of inertia

The polar moment of inertia I_z treats each bolt as a unit area:

I_z = I_x + I_y = sum(y_i^2) + sum(x_i^2)

I_z governs how the applied moment is distributed to individual bolts - the farther a bolt is from the centroid, the larger its torsional shear component.

Direct shear

The applied vertical shear V is shared equally among all n bolts:

V_p = V / n

Torsional shear from eccentricity

When the applied load acts at a horizontal distance e from the centroid, the resulting in-plane moment M = V × e is distributed to each bolt in proportion to its distance from the centroid:

• Vertical torsional component: V_e = M × x_i / I_z
• Horizontal torsional component: H_e = M × y_i / I_z

Resultant bolt force

The total vertical and horizontal forces on each bolt are summed and the resultant is found:

• V_t = V_p + V_e
• H_t = H_e
• R = sqrt(V_t^2 + H_t^2)

Utilization = R_max / R_allowable ≤ 1.0

The maximum R across all bolts in the group is the governing demand for connection sizing.

Using the output

The reported R_max is the raw elastic demand on the critical bolt. To complete the connection check, compare R_max against the allowable shear capacity for the chosen bolt diameter and grade from AISC Table 7-1 or Table J3-2. The elastic method is conservative relative to the instantaneous centre of rotation (IC) method for many common bolt configurations.