Steel Bolt Group Analysis (ASD)

How it calculates

The Steel Bolt Group Analysis (ASD) calculator applies the elastic method from the AISC Steel Construction Manual to determine the maximum shear demand on any bolt in an arbitrarily arranged bolt group subjected to in-plane shear and moment loads.

Bolt group geometry

Bolt positions are defined by their X and Y coordinates. The centroid of the bolt group is calculated assuming all bolts have equal tributary area:

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

Bolt positions are then expressed relative to the centroid.

Moment of inertia

The polar moment of inertia I_z (in^2, treating each bolt as a unit area) is the sum of squared distances from all bolts to the centroid:

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

This is used to distribute the torsional component of applied moment to each bolt location.

Load distribution

For a bolt group loaded by a vertical shear V and an in-plane moment M (which may arise from an eccentrically applied load), the elastic method distributes forces as follows:

Direct shear (vertical, shared equally):

• V_p = V / n

Torsional shear due to moment (varies by position):

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

Total bolt forces (vector sum):

• V_t = V_p + V_e (total vertical shear)
• H_t = H_e (total horizontal shear)
• Resultant: R = sqrt(V_t^2 + H_t^2)

Critical bolt identification

The calculator evaluates R at every bolt in the group. The maximum resultant R governs the connection design.

Utilization = R / R_allowable ≤ 1.0

where R_allowable is the allowable shear strength per bolt (to be specified by the engineer based on bolt grade, diameter, and connection type per AISC Tables).

Multiple load cases

The ASD version supports multiple applied load combinations in a single run - each case is analysed against the bolt group geometry, and the governing (maximum) bolt demand is reported. This removes the need to manually process each combination separately.

Eccentricity

When the load is applied at an offset from the bolt group centroid, the eccentricity e is the horizontal distance from the load line to the centroid. The moment input M can be entered directly or derived from the product of shear force and eccentricity.