Bolt Pattern — Engineering Reference

Eccentric bolt group analysis: elastic C-method, ICR method, AISC Tables 8-1 to 8-3 C-coefficients, polar moment of inertia, and interactive calculator.

Overview

A bolt pattern (or bolt group) is the arrangement of fasteners in a connection that collectively resists applied forces. When the line of action of the applied load passes through the centroid of the bolt group, all bolts share the load equally. When the load is eccentric — offset from the centroid — the bolt group must resist both a direct shear and a moment. Analyzing eccentric bolt groups requires either the elastic method or the instantaneous center of rotation (ICR) method.

The AISC Steel Construction Manual provides pre-computed C-coefficients in Tables 7-6 through 7-14 for common eccentrically loaded bolt groups, making hand calculations practical. For non-standard bolt patterns, the ICR method is computed iteratively using the load-deformation relationship for individual bolts.

Elastic method for eccentric bolt groups

The elastic method treats each bolt as a linear spring. For a bolt group subjected to an eccentric load P at eccentricity e from the bolt group centroid:

Direct shear on each bolt: V_direct = P / n (where n = number of bolts)
Moment on bolt group: M = P x e
Polar moment of inertia: I_p = sum(x_i^2 + y_i^2) for all bolts, where x_i and y_i are distances from each bolt to the group centroid
Moment-induced force on each bolt: R_moment = M x r_i / I_p, acting perpendicular to the radius r_i from the centroid

The resultant force on the critical bolt (the one farthest from the centroid on the side of maximum combined force) is the vector sum of V_direct and R_moment.

Instantaneous center of rotation (ICR) method

The ICR method (AISC Manual Part 7) is more accurate than the elastic method because it accounts for the nonlinear load-deformation behavior of bolts. Each bolt's force-deformation relationship is:

R_i = R_ult x (1 - e^(-10 x delta_i))^0.55

where R_ult is the bolt ultimate shear strength and delta_i is the deformation of bolt i. The bolt group capacity is found iteratively by assuming a center of rotation, computing bolt deformations (proportional to distance from the IC), summing forces and moments, and adjusting the IC location until equilibrium is satisfied.

The ICR method typically gives 10-20% higher capacity than the elastic method because it allows bolt force redistribution — the most heavily loaded bolts deform and shed load to less-loaded bolts.

Worked example — 4-bolt vertical line, eccentric shear

Given: 4 bolts in a single vertical line, 3 in. spacing, 3/4 in. A325-N bolts. Applied load P = 40 kip at eccentricity e = 6 in. from the bolt line.

Elastic method:

Bolt positions from centroid: y = +4.5, +1.5, -1.5, -4.5 in. (all at x = 0)
I_p = 4 x 0^2 + (4.5^2 + 1.5^2 + 1.5^2 + 4.5^2) = 45.0 in^2
Direct shear per bolt: V = 40/4 = 10.0 kip (downward)
Moment: M = 40 x 6 = 240 kip-in
Moment force on extreme bolt: R_m = 240 x 4.5 / 45.0 = 24.0 kip (horizontal)
Resultant on critical bolt: R = sqrt(10.0^2 + 24.0^2) = 26.0 kip
Bolt capacity: phi x R_n = 0.75 x 54 x 0.4418 = 17.9 kip. 26.0 > 17.9 — not adequate.

Using AISC Table 7-7 (C-coefficient for 4 bolts, s = 3 in., e = 6 in.): C ≈ 1.79. Capacity = C x phi x r_n = 1.79 x 17.9 = 32.0 kip. Since P = 40 kip > 32.0 kip, still not adequate — need more bolts or reduce eccentricity.

Standard bolt patterns

Common bolt layouts and their applications:

Pattern	Layout	Typical Use
Single vertical line	n bolts at spacing s	Shear tabs, single angles, light connections
Double vertical line	2 columns of n bolts, gage g	Moment connections, heavy shear connections
Rectangular group	m rows x n columns	Flange splice plates, base plates
Circular pattern	n bolts on a bolt circle	Round base plates, pipe flanges
L-shaped group	Bolts along two perpendicular legs	Angle connections, bracket connections

Key design considerations

Bolt spacing — AISC J3.3 requires a minimum center-to-center spacing of 2-2/3 x d (typically rounded to 3d) and a preferred spacing of 3d. Maximum spacing is 24t or 12 in. (J3.5) for connected elements in compression.
Edge distance — minimum edge distances per AISC Table J3.4 range from 3/4 in. (for 1/2 in. bolts) to 2 in. (for 1-1/4 in. bolts) at sheared edges. Rolled or gas-cut edges allow smaller distances.
Gage dimensions — AISC Manual Table 1-7A gives standard gages for W shapes. For a W14 with b_f = 10 in., the standard flange gage is 5-1/2 in. Using non-standard gages requires checking clearances for bolt installation.
Bolt group centroid — for symmetric patterns, the centroid is at the geometric center. For asymmetric patterns (e.g., staggered bolts), compute the centroid as the average of all bolt coordinates. All eccentricities are measured from this centroid.

Common mistakes to avoid

Using the elastic method where ICR is needed — the elastic method is conservative by 10-20% for most configurations. For heavily loaded eccentric connections, using the elastic method wastes bolt capacity and may lead to oversized connections.
Forgetting to include direct shear in the vector sum — when computing the critical bolt force, the direct shear (P/n) and the moment-induced force must be added as vectors, not scalars. Simply adding magnitudes is overly conservative when the forces act in different directions.
Mislocating the bolt group centroid — for bolt groups with mixed bolt sizes or patterns, the centroid must be computed precisely. An error in centroid location changes the eccentricity and all moment-induced bolt forces.
Ignoring out-of-plane eccentricity — bracket connections and seated connections often have out-of-plane eccentricity (the load is offset from the faying surface). This creates bolt tension in addition to shear, requiring a combined shear-tension interaction check per AISC J3.7.

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Related references

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.