Eccentric Connection — Engineering Reference
Instantaneous center (IC) method for eccentric bolt and weld groups: AISC Table C coefficients, elastic vs IC comparison, and bracket connection example.
Overview
An eccentric connection is any connection where the line of action of the applied force does not pass through the centroid of the fastener group (bolts or welds). The eccentricity creates a moment on the fastener group in addition to the direct shear, and the individual fastener forces must be determined by combining direct shear and moment-induced components. This situation arises frequently in bracket connections, gusset plates, shear tabs, and any connection where the beam reaction is offset from the bolt or weld group center.
Two methods are used to analyze eccentric fastener groups: the elastic method (conservative, suitable for hand calculations) and the instantaneous center of rotation (ICR) method (more accurate, used in the AISC Manual C-coefficient tables). The ICR method accounts for nonlinear load-deformation behavior of individual fasteners and typically yields 10-25% higher capacity than the elastic method.
In-plane vs. out-of-plane eccentricity
Eccentricity can occur in two planes:
- In-plane eccentricity — the applied load is in the same plane as the fastener group but offset from its centroid. This produces a torque (moment about the axis perpendicular to the faying surface). Examples: bracket connections with load offset from the bolt line, gusset plate connections with non-concentric brace loads.
- Out-of-plane eccentricity — the applied load acts in a plane perpendicular to the faying surface, creating a prying-type moment. This produces tension in some fasteners and compression bearing on others. Examples: bracket plates loaded perpendicular to the column face, seated connections where the load acts on the outstanding leg.
For in-plane eccentricity, all bolts are in shear. For out-of-plane eccentricity, bolts are in combined shear and tension, requiring the interaction equation per AISC J3.7.
Elastic method for in-plane eccentricity (bolt groups)
The elastic method assumes each bolt behaves as a linear spring with equal stiffness:
- Locate the centroid of the bolt group (x_bar, y_bar).
- Compute the polar moment of inertia: I_p = sum(x_i^2 + y_i^2).
- Direct shear per bolt: V_x = P_x / n, V_y = P_y / n.
- Moment on group: M = P x e (where e is the eccentricity from the centroid).
- Moment-induced forces: R_xi = M x y_i / I_p, R_yi = M x x_i / I_p (perpendicular to the radius).
- Resultant on each bolt: R_i = sqrt((V_x + R_xi)^2 + (V_y + R_yi)^2).
The critical bolt is the one with the highest resultant force. The connection is adequate when R_critical <= phi x r_n (single bolt design strength).
ICR method and AISC C-coefficients
The instantaneous center of rotation method is the basis for AISC Manual Tables 7-6 through 7-14 (bolt groups) and Tables 8-4 through 8-11 (weld groups). The method assumes:
- Each fastener deforms proportionally to its distance from the instantaneous center (IC).
- The bolt load-deformation relationship is nonlinear: R_i = R_ult x (1 - e^(-10 x delta_i))^0.55.
- Equilibrium of forces and moment is satisfied at the IC location.
The result is expressed as a C-coefficient: the number of bolts that would be required if the load were concentric. The connection capacity is:
phi x R_n = C x phi x r_n
where phi x r_n is the design strength of a single bolt.
Worked example — bracket with out-of-plane eccentricity
Given: 4-bolt bracket connection (2 rows x 2 columns, gage = 4 in., pitch = 3 in.), P = 25 kip acting 8 in. from the column face (out-of-plane eccentricity), 3/4 in. A325-N bolts.
- Bolt group centroid: midpoint of the pattern. Pitch between rows = 3 in., so bolts are at ±1.5 in. from horizontal center.
- Moment: M = 25 x 8 = 200 kip-in.
- Neutral axis: Assume the neutral axis is at the bottom bolt row (compression at bearing surface). The tension bolts are the top two, at lever arm d = 3.0 in.
- Bolt tension: T = M / (n_t x d) = 200 / (2 x 3.0) = 33.3 kip per bolt (simplified, neglecting prying).
- Direct shear per bolt: V = 25 / 4 = 6.25 kip.
- Interaction check (AISC J3.7): Available tensile stress F'_nt = 1.3 x F_nt - (F_nt / (phi x F_nv)) x f_rv. With F_nt = 90 ksi, F_nv = 54 ksi, f_rv = 6.25 / 0.4418 = 14.2 ksi: F'_nt = 117 - (90/0.75x54) x 14.2 = 117 - 31.6 = 85.4 ksi. Available tension = 0.75 x 85.4 x 0.4418 = 28.3 kip. Since T = 33.3 > 28.3, not adequate — need larger bolts or more bolt rows.
Eccentric weld groups
The same principles apply to eccentric weld groups. The AISC Manual Tables 8-4 through 8-11 give C-coefficients for common weld group configurations (C-shaped, L-shaped, rectangular). For weld groups, the load-deformation relationship uses the angle of loading on the weld element:
- Transverse welds (loaded at 90 degrees) are ~50% stronger than longitudinal welds (loaded at 0 degrees).
- The ICR method accounts for this directional strength variation.
For a C-shaped weld group (two longitudinal welds + one transverse weld) with load in the plane of the weld group, the C-coefficient is read from AISC Table 8-8 using the weld dimensions k (ratio of transverse to longitudinal length) and a (eccentricity ratio).
Code comparison — eccentric connection methods
| Feature | AISC Manual | AS 4100 | EN 1993-1-8 | CSA Handbook |
|---|---|---|---|---|
| Bolt group method | ICR (C-coefficients) + elastic | Elastic method standard | Component method | ICR (similar to AISC) |
| Weld group method | ICR (C-coefficients) | Resultant of forces at centroid | Directional method (Cl. 4.5.3.2) | ICR (similar to AISC) |
| Directional weld strength | 1.0 + 0.50 x sin^1.5(theta) | 1.0 (no directional enhancement) | k_w = sqrt(3) / sqrt(1+2cos^2(theta)) | Similar to AISC |
| Prying action model | DG16 / T-stub analogy | Equivalent T-stub | Explicit modes 1, 2, 3 | CISC Handbook method |
Common mistakes to avoid
- Ignoring eccentricity in shear tabs — a standard shear tab has an eccentricity equal to the distance from the bolt line to the weld line. For conventional configurations with a/d <= 0.35 and certain stiffness conditions, AISC allows this eccentricity to be neglected. Outside these limits, the eccentricity must be included in the bolt group analysis.
- Using elastic method for final design — the elastic method is conservative by 10-25%. While acceptable for preliminary sizing, it can lead to oversized connections. Use the ICR method (AISC C-coefficient tables) for final design to avoid unnecessary bolts or weld material.
- Not checking both in-plane and out-of-plane eccentricity — some connections have eccentricity in both planes simultaneously (e.g., a bracket loaded both vertically and horizontally). Both eccentricities must be considered, and the bolt forces from each must be combined.
- Assuming uniform weld stress in eccentric groups — in an L-shaped or C-shaped weld group with eccentric loading, the weld segments nearest to the load carry higher stress. Assuming uniform distribution ignores the torsional demand and is unconservative.
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Related references
- Steel Connection Design
- Bolt Capacity Table
- How to Verify Calculations
- Connection Limit State Checks
- Bolt Pattern Reference
- Weld Group Calculator
- steel connection capacity calculator
- weld capacity for connection design
- Connection Design Workflow
- Girder-to-column connection
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.