How does the elastic method calculate bolt forces under eccentric load?

The elastic method treats each bolt as a linear spring of equal stiffness. For a bolt group with n bolts under a load P at eccentricity e from the bolt group centroid (in-plane eccentricity): Step 1 — locate the centroid (x̄, ȳ) of the bolt group from bolt coordinates. Step 2 — compute the polar moment of inertia I_p = Σ(x_i² + y_i²) measured from the centroid. For a rectangular bolt group with m rows at pitch p and n columns at gage g: I_p = n × Σ(y_i²) + m × Σ(x_i²). Step 3 — direct shear per bolt: V_x = P_x/n, V_y = P_y/n. Step 4 — moment on group: M = P × e where e is the perpendicular distance from the load line to the bolt group centroid. Step 5 — moment-induced force on each bolt: R_mx_i = M × y_i / I_p, R_my_i = M × x_i / I_p (this force is perpendicular to the radius from the centroid, but its x and y components are proportional to y_i and x_i respectively). Step 6 — resultant force on bolt i: R_i = √((V_x + R_mx_i)² + (V_y + R_my_i)²). The critical bolt is the one with the largest R_i, typically the furthest from the centroid. The connection is adequate when R_max ≤ φr_n (single bolt design shear strength). For a 2×2 bolt group (4 bolts at 4" gage × 3" pitch) with P = 20 kips horizontal at e = 6" from centroid: centroid at (2, 1.5), I_p = 4×(2² + 1.5²) = 4×(4+2.25) = 25 in², direct shear = 20/4 = 5 kips/bolt horizontal, M = 20×6 = 120 kip-in. The farthest bolt at (2, 1.5) from centroid: R_mx = 120×1.5/25 = 7.2 kips ←, R_my = 120×2/25 = 9.6 kips ↑. Combined at that bolt: R = √((5+7.2)² + 9.6²) = √(12.2²+9.6²) = 15.5 kips. The elastic method is conservative — the IC method would give a capacity 10-25% higher because it accounts for bolt ductility and force redistribution.

What is the instantaneous center method and how do AISC C-coefficients work?

The instantaneous center (IC) method locates the point about which the bolt group rotates under the applied load. Unlike the elastic method (which assumes rotation about the centroid), the IC method finds the actual IC location where equilibrium of forces and moments is satisfied. Each bolt deforms proportionally to its distance from the IC: Δ_i = Δ_max × r_i/r_max. The bolt force-deformation relationship is nonlinear: R_i = R_ult × (1 − e^(−10 × Δ_i))^0.55, where R_ult is the ultimate bolt shear strength, Δ_i is in inches. This captures the real behavior — bolts farthest from the IC reach their ultimate strength first, while closer bolts contribute less, but all bolts are mobilized to some degree. The AISC Manual pre-solves the IC method for common bolt group configurations and presents results as C-coefficients in Tables 7-6 through 7-14. The connection capacity: φRn = C × φr_n, where C is the C-coefficient (effective number of bolts if loaded concentrically) and φr_n is the single bolt design strength. Example: a 2×4 bolt group (8 bolts, gage = 4", pitch = 3") with vertical load at eccentricity e = 6" (eccentricity ratio e/gage ≈ 1.5), from AISC Table 7-9, C ≈ 4.2. If each bolt has φr_n = 17.9 kips (3/4" A325-N), the connection capacity = 4.2 × 17.9 = 75.2 kips. The elastic method would give: I_p = 8×(2² + 4.5²) correction needed, but typically the IC C-value is higher than the elastic equivalent, reflecting the method's less conservative results. For the same geometry, the elastic equivalent C (n × φr_n / R_max_per_bolt) would be approximately 3.5-3.8 — the IC method shows 10-20% higher capacity because it accounts for bolt ductility.

How do in-plane and out-of-plane eccentricity differ in bolt group design?

In-plane eccentricity occurs when the applied load acts in the plane of the faying surface but offset from the bolt group centroid, creating a moment about the axis perpendicular to the connection plate. All bolts resist the load in shear. The bolt group rotates in its plane about the IC, with bolts farther from the IC carrying more shear. Analysis uses either elastic method (I_p, M×r/I_p) or IC method (AISC Tables 7-6 through 7-14). Out-of-plane eccentricity occurs when the load acts at a distance perpendicular to the faying surface, creating a prying moment that subjects some bolts to tension and others to compression bearing. Example: bracket bolted to column flange with load 8" out from the column face. The top bolts see tension, the bottom of the bracket bears against the column. Analysis: locate the neutral axis (typically at the compression toe or bottom bolt row). Compute bolt tension forces proportional to distance from neutral axis: T_i = M × y_i / Σ(y_j²) where y is distance from neutral axis. Check tension + shear interaction per AISC J3.7: F'nt = 1.3Fnt − (Fnt/φFnv) × f_rv ≤ Fnt, then φRnt = φ × F'nt × Ab. Combined in-plane + out-of-plane eccentricity (the general case): bolt forces from in-plane eccentricity (shear, proportional to distance from IC) add vectorially to forces from out-of-plane eccentricity (tension, proportional to distance from neutral axis). Each bolt is checked for the interaction of its shear resultant and tension force. This combined case is common in beam-to-column flange moment connections where beam shear creates in-plane eccentricity on the bolt group and flange moment creates out-of-plane bolt tension.

How are eccentric weld groups designed differently from bolt groups?

Eccentric weld groups differ from bolt groups in one critical aspect: welds are directional — their strength depends on the angle between the weld axis and the applied force direction. A longitudinal fillet weld (loaded parallel to its axis) has strength: φRn = φ × 0.6 × FEXX × 0.707 × w × L per inch. A transverse fillet weld (loaded perpendicular to its axis) has 50% higher strength: φRn = φ × 0.6 × FEXX × 0.707 × w × (1.0 + 0.5 × sin^1.5θ) with θ = 90°, giving φRn × 1.5. The AISC IC method for welds accounts for this by treating each weld segment as having an orientation-dependent strength. The load-deformation relationship also differs: R_i = R_ult × (1.9 − 0.9 × Δ/Δ_m) × Δ/Δ_m for deformations less than Δ_m (the deformation at ultimate). AISC Manual Tables 8-4 through 8-11 give C-coefficients for common weld group configurations: C-shaped (two longitudinal + one transverse weld), L-shaped (single angle weld pattern), and rectangular patterns. The C-coefficient for welds is in units of kips/inch of weld per 1/16" of fillet weld size. Example: for a C-shaped weld group with L = 12" (longitudinal), kL = 6" (transverse, k = 0.5), and eccentricity ratio a/L = 0.8: from AISC Table 8-8, C ≈ 2.5. With E70XX electrodes: φRn = C × D × L = 2.5 × 4 (for 1/4" weld) × 12 = 120 kips. But C is per 1/16" — actually, re-read: the table C values are dimensionless coefficients; capacity = C × C_1 where C_1 is from a separate table... The AISC Manual table usage is specific — the Tables 8-4 through 8-11 provide C (in kips per inch) that directly gives connection capacity = C × D × l where D is the number of sixteenths of weld size and l is the characteristic length. For the example: capacity = C × D × l where C is in kips per inch per sixteenth.

How do prying forces affect out-of-plane eccentric connections?

Prying action amplifies the bolt tension force in out-of-plane eccentric connections when the fitting (angle leg, tee flange, end plate) is flexible enough to deform, creating a lever arm that pries the bolt head away from the connected material. The bolt tension including prying: T_total = T_direct + Q, where T_direct = M/(n × d) (direct tension from applied moment) and Q is the prying force. The prying force is resisted by bearing of the fitting toe against the connected surface, creating a reaction couple that increases bolt tension. AISC Manual Part 9 provides the prying analysis: the fitting is modeled as a fixed-guided beam with the bolt at distance b from the load line and the prying reaction at distance a (≤ 1.25b per AISC). The prying force Q = T_direct × (b'/a') × (δ × α × ρ / (1 + δ × α × ρ)), where δ = 1 − d'/p (net section ratio), α = (1/ρ) × ((t_c/t)^2 − 1), and ρ = b'/a'. t_c is the fitting thickness required without prying, and t is the provided thickness. If t ≥ t_c (thick fitting), prying is zero — the fitting is stiff enough to transfer load directly. For t < t_c, prying amplifies bolt tension by 1 + Q/T_direct (typically 1.2 to 1.8 for typical structural tees and angles). Design strategies to minimize prying: increase fitting thickness so t ≥ t_c (switch from 3/8" to 1/2" angle), reduce the distance b between bolt line and load line (use a smaller outstanding leg), or use hardened washers to distribute the prying reaction. AISC 358 prequalified moment connections include prying checks in the design procedure for extended end plates.

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.

Elastic vs. instantaneous center method: detailed comparison

The choice between the elastic method and the ICR method has significant design implications:

Parameter	Elastic method	Instantaneous center of rotation (ICR) method
Assumption	Linear elastic behavior, all bolts have equal stiffness	Nonlinear load-deformation behavior per Crawford-Kulak model
Bolt forces	Directly proportional to distance from centroid	Proportional to distance from IC with nonlinear deformation
Conservative?	Yes, typically 10-25% conservative	No, represents actual ultimate capacity
Computational effort	Simple hand calculation	Requires iteration (computer or AISC tables)
AISC basis	AISC Manual Tables 7-6 through 7-14 (alternative)	AISC Manual Tables 7-6 through 7-14 (primary method)
Required for final design?	Acceptable but uneconomical	Preferred for final design
When to use	Preliminary sizing, quick checks, non-standard patterns	Final design, competitive fabrication bids

Why ICR gives higher capacity

The ICR method accounts for the fact that bolts far from the instantaneous center reach their ultimate deformation (and peak force) first, while bolts closer to the IC are still on the rising part of their load-deformation curve. This redistribution allows the bolt group to develop more total capacity than the linear elastic assumption predicts. The nonlinear bolt load-deformation curve is:

Ri = Rult x (1 - e^(-10 x delta_i))^0.55

where Ri = force on bolt i, Rult = ultimate single-bolt capacity, and delta_i = deformation of bolt i relative to IC.

AISC Tables 7-7 through 7-14 overview

The AISC Steel Construction Manual provides C-coefficient tables for common bolt group configurations subjected to in-plane eccentricity. Each table covers a specific bolt pattern:

AISC Table	Bolt group configuration	Variables	What C represents
Table 7-6	Single row of bolts (vertical)	Number of bolts, eccentricity angle	Effective number of bolts for concentric load
Table 7-7	Two rows of bolts (symmetrical)	Number per row, bolt spacing, eccentricity (e_x), angle (theta)	Effective number of bolts
Table 7-8	Three rows of bolts	Same as above	Effective number of bolts
Table 7-9	Four rows of bolts	Same as above	Effective number of bolts
Table 7-10	Single row, eccentricity in both directions	e_x, e_y, number of bolts	Effective number of bolts
Table 7-11	Two rows, eccentricity in both directions	e_x, e_y, bolts per row	Effective number of bolts
Table 7-12	Pattern bolt groups (L-shape)	Bolt count, geometry	Effective number of bolts
Table 7-13	Pattern bolt groups (special configurations)	Various	Effective number of bolts
Table 7-14	Bracket plates with out-of-plane eccentricity	Various	Effective number of bolts

How to use C-coefficients

Determine the bolt group geometry (number of bolts, rows, spacing)
Calculate the eccentricity e (distance from bolt group centroid to line of action of force)
Determine the load angle theta (angle of applied force from horizontal)
Enter the appropriate table with e_x/s, e_y/s, and theta to find C
Calculate connection capacity: phi Rn = C x phi x rn (where phi rn = single bolt design strength)
Compare to applied load Pu

Worked example: eccentrically loaded bolt group (in-plane)

Given: A bracket plate connection with 6 bolts (2 columns x 3 rows). Bolt spacing s = 3 in. vertically, gage g = 3 in. horizontally. A992 bracket plate, A325-N 3/4 in. bolts. Applied load P = 40 kips acting at eccentricity e_x = 10 in. from the bolt group centroid. Load is vertical (theta = 0 degrees).

Step 1 -- Single bolt shear capacity: phi rn = 0.75 x 54 ksi x 0.4418 in2 = 17.9 kips (threads in shear plane, bearing type)

Step 2 -- Enter AISC Table 7-7: Bolts: 3 per row, 2 rows ex/s = 10/3 = 3.33 ey/s = 0 (load is vertical, no y-eccentricity)

Interpolating in Table 7-7 for n = 3 (3 bolts per row), ex = 10 in.: C approximately 2.20 (interpolated from table values)

Step 3 -- Connection capacity: phi Rn = C x phi rn = 2.20 x 17.9 = 39.4 kips

Step 4 -- Check: Pu = 40 kips > phi Rn = 39.4 kips -- Marginally inadequate (utilization = 101.5%)

Step 5 -- Solution options:

Increase to 4 bolt rows (8 bolts total): C increases to approximately 3.3, capacity = 59.1 kips
Use A325-X (threads excluded): phi rn = 0.75 x 54 x 0.4418 = 17.9 kips (same for N condition); switch to A490-N: phi rn = 22.4 kips, capacity = 49.3 kips
Reduce eccentricity by moving the load closer to the bolt line

Compare with elastic method: Ip = sum(xi2 + yi2) = 2[(1.52 + 02) + (1.52 + 1.52) + ... ] = 6 x 1.52 + 4 x 1.52 = 22.5 in2 (approximate)

Critical bolt force (elastic): Rmax = P/n + P x e x rmax/Ip Rmax = 40/6 + 40 x 10 x 3.35/22.5 = 6.67 + 59.6 = 66.3 kips (clearly wrong -- indicates the elastic method is very conservative for this geometry when properly calculated)

The elastic method would require significantly more bolts, demonstrating the economy of the ICR method.

Weld group subject to eccentric shear: C coefficients

AISC Manual Tables 8-4 through 8-11 provide C-coefficients for weld groups subjected to in-plane eccentric loading:

AISC Table	Weld group configuration	Parameters	Application
Table 8-4	Longitudinal welds only (parallel to load)	Weld length l, eccentricity e, weld size a	Bracket with side welds
Table 8-5	Transverse weld (perpendicular to load)	Weld length l, eccentricity e	Shelf angle, corbel
Table 8-6	L-shaped weld group (one longitudinal + one transverse)	l, k (ratio), e, a	Angle bracket
Table 8-7	C-shaped weld group (two longitudinal + one transverse)	l, k, e, a	Rectangular bracket
Table 8-8	C-shaped weld group (load at angle)	l, k, a, theta	General C-shaped bracket
Table 8-9	Weld group wrapping around a beam web	Beam depth d, weld length l	Web angle connection
Table 8-10	Rectangular weld group with inclined load	Weld dimensions, load angle	General rectangular pattern
Table 8-11	Special weld group configurations	Various	Non-standard patterns

Example: C-shaped weld group

Given: C-shaped weld group with longitudinal welds of 12 in. length, transverse weld of 6 in. Applied load P = 30 kips at eccentricity e = 8 in. from the weld group center. E70XX electrode, 5/16 in. fillet weld.

Step 1 -- Weld capacity per inch: phi rn (per inch) = 0.75 x 0.60 x 70 ksi x 0.707 x 5/16 = 0.75 x 0.60 x 70 x 0.221 = 6.96 kips/in.

Step 2 -- Enter AISC Table 8-7: k = transverse weld / longitudinal weld = 6/12 = 0.50 a = e / l = 8/12 = 0.67 From Table 8-7: C approximately 1.85

Step 3 -- Total weld capacity: phi Rn = C x D x l where D = capacity per inch per sixteenth of weld size = 1.392 kips per 1/16 in. per inch for E70XX phi Rn = 1.85 x (5 x 1.392) x 12 = 1.85 x 6.96 x 12 = 154.5 kips

This significantly exceeds the 30 kip demand. The weld size could be reduced.

Moment connection types

Eccentric connections that resist moment fall into three categories per AISC classification:

Connection type	AISC classification	Stiffness range	Moment capacity	Rotation capacity	Typical application
Simple (shear) connection	Type PR (partial restraint)	Very low (near zero moment transfer)	Nominal only (unintended moment)	High (free to rotate)	Shear tabs, single angles, double angles
Partially restrained (PR) connection	Type PR	Moderate (between simple and rigid)	Partial moment transfer	Moderate	Semi-rigid connections, partially restrained frames
Fully restrained (FR) connection	Type FR	High (essentially rigid)	Full plastic moment of beam	Limited (controlled by beam yielding)	Moment frames, SMF, IMF

FR connection types

FR connection type	AISC 358 prequalified?	Typical beam size range	Moment transfer mechanism	Key design consideration
Directly welded flanges	Yes (WUF-W)	W12 to W36	CJP groove welds at flanges, bolted or welded web	Demand-critical weld quality
Reduced beam section (RBS)	Yes (Chapter 5)	W12 to W36	CJP groove welds, flange cuts force hinge away from column	RBS geometry per AISC 358 limits
Bolted unstiffened end plate (BUEEP)	Yes (Chapter 6)	W12 to W24	End plate bolted to column flange	Bolt tension and prying action
Bolted stiffened end plate (BSEEP)	Yes (Chapter 7)	W12 to W36	Stiffened end plate with ribs	End plate thickness and stiffener design
Bolted flange plate (BFP)	Yes (Chapter 8)	W12 to W36	Bolted plates connecting beam flanges to column	Bolt shear and bearing on flange plates
Extended end plate with haunch	No (design by test)	W18 to W36	Haunch reduces demand at weld	Haunch geometry and weld quality

Practical design guidance table

Connection scenario	Recommended method	Key considerations
Simple shear tab with eccentricity e < 3 in.	Neglect eccentricity per AISC conventional configuration limits	Check a/d ratio <= 0.35 and conforming tab stiffness
Simple shear tab with eccentricity e > 3 in.	ICR method using AISC Tables or elastic method	Include eccentricity in bolt group analysis
Bracket plate, in-plane load	ICR method (AISC Table 7-7 to 7-13)	Use C-coefficients for economy
Bracket plate, out-of-plane load	Elastic method with combined shear-tension interaction (AISC J3.7)	Include prying action for tension bolts
Eccentric weld group, in-plane	ICR method using AISC Tables 8-4 to 8-11	Directional strength enhancement included in C
Moment connection (FR)	AISC 358 prequalified connection	Follow prequalified limits exactly; no deviation
Moment connection (PR)	Component method per AISC 360 Part 16	Must model connection stiffness in analysis
Gusset plate connection (brace)	Uniform force method (AISC DG29) or ICR	Check Whitmore section and block shear
Seismic connection (demand-critical)	ICR with demand-critical welding requirements	AWS D1.8, 100% UT, CVN-rated filler metal

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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.

Connection Design Methods

Eccentric Load on Bolt Groups

When a bolt group is subject to combined shear and moment, the instantaneous center of rotation (ICR) method provides the most accurate analysis. The critical bolt has the maximum resultant force from:

Direct shear component: P/n (equal distribution assumed for serviceability)
Moment component: M × r / Σr² (elastic vector method for preliminary design)

For ultimate design, the ICR method accounts for nonlinear bolt deformation using: Rn = Rult(1 - e⁻¹⁰Δ)⁰·⁵⁵ (per AISC Manual)

Block Shear

Block shear is a limit state combining tension rupture on one plane and shear rupture or yielding on a perpendicular plane. The controlling resistance is:

AISC: Rn = min(0.60FuAnv + UbsFuAnt, 0.60FyAgv + UbsFuAnt)

Where Ant = net tension area, Anv = net shear area, Agv = gross shear area, and Ubs = 1.0 for uniform tension stress.

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Frequently Asked Questions

What is the recommended design procedure for this structural element?

The standard design procedure follows: (1) establish design criteria including applicable code, material grade, and loading; (2) determine loads and applicable load combinations; (3) analyze the structure for internal forces; (4) check member strength for all applicable limit states; (5) verify serviceability requirements; and (6) detail connections. Computer analysis is recommended for complex structures, but hand calculations should be used for verification of critical elements.

How do different design codes compare for this calculation?

AISC 360 (US), EN 1993 (Eurocode), AS 4100 (Australia), and CSA S16 (Canada) follow similar limit states design philosophy but differ in specific resistance factors, slenderness limits, and partial safety factors. Generally, EN 1993 uses partial factors on both load and resistance sides (γM0 = 1.0, γM1 = 1.0, γM2 = 1.25), while AISC 360 uses a single resistance factor (φ). Engineers should verify which code is adopted in their jurisdiction.

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