Bolted Connection Design — Bolt Group Calculator

Q: How is prying action calculated for tension connections?

Prying action occurs when a tension load in a bolt causes deformation of the connected plies, creating a lever arm that amplifies the bolt tension. Per AISC 360 J3-6 and EN 1993-1-8 6.2.4, the prying force Q = T × (b/a) × (1 - t/tc) where T is the applied tension, a and b are the distances from bolt centerline to the edge of the plate and to the applied load line, t is the plate thickness, and tc is the required plate thickness for no prying. The total bolt tension = applied tension + prying force. The prying action check is critical for tee-stub connections, end-plate connections, and splice connections where tension loads are transferred through relatively thin plates.

Q: What is the Instantaneous Center (IC) method for eccentric loads?

The Instantaneous Center (IC) method is the most accurate approach for analyzing eccentrically loaded bolt groups per AISC Manual Part 7. The IC is the point about which the bolt group rotates under load. Each bolt's deformation is proportional to its distance from the IC, and its resisting force is determined from the bolt stress-strain relationship. The method iteratively finds the IC location such that equilibrium is satisfied between the applied load and the sum of bolt forces. The IC method accounts for ductility of the bolt group and typically provides 20-40% higher capacity than the elastic (vector) method for concentric patterns.

Design and verify bolted steel connections with the free Bolted Connection calculator. Supports bolt group analysis under combined loading, prying action, bearing checks, and slip-critical connections.

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Core calculations run via WebAssembly in your browser with step-by-step derivations across AISC 360, AS 4100, EN 1993, and CSA S16 design codes. Results are preliminary and must be verified by a licensed engineer.

How the Bolted Connection Calculator Works

The bolted connection calculator performs comprehensive analysis of bolt groups under arbitrary loading conditions. Users begin by defining the bolt pattern — rectangular, circular, or custom coordinate-based layouts in 2D or 3D space. Each bolt is assigned a grade, diameter, and thread condition (included or excluded from shear plane). The applied loads — axial, shear, moment, and torsion — are entered as factored or service-level values depending on the design methodology.

The calculator then computes bolt forces using either the elastic (vector) method or the instantaneous center (IC) method. The elastic method assumes linear force distribution proportional to distance from the centroid, suitable for preliminary sizing and connections with limited rotational demand. The IC method iteratively locates the center of rotation that satisfies force equilibrium, providing a more accurate representation of the connection's ultimate capacity and typically yielding 10-30% higher capacity for eccentric load groups.

Code Provisions for Bolted Connections

Each supported design code approaches bolted connection design with specific provisions:

AISC 360 Chapter J — The AISC specification governs bolted connection design in the United States. Key provisions include: bolt shear strength per J3-6 (φRn = φ × Fnv × Ab), bearing strength at bolt holes per J3-6a (Rn = 1.2lc × t × Fu ≤ 2.4d × t × Fu), bolt tensile strength per J3-5 (Rn = Fnt × Ab), and combined shear and tension per J3-3a and J3-3b. Slip-critical connections are designed per J3-8 with slip resistance determined by Class A, B, or C surface conditions.

EN 1993-1-8 — Eurocode 3 Part 1-8 provides bolted connection provisions for European design. Categories A (bearing), B (slip-resistant at service), C (slip-resistant at ultimate), D (non-preloaded), and E (preloaded) are supported. Bolt shear resistance per Table 3.4: Fv,Rd = αv × fub × As / γM2. Bearing resistance: Fb,Rd = k1 × αb × fu × d × t / γM2. Tension resistance: Ft,Rd = k2 × fub × As / γM2.

AS 4100 Clause 9 — Australian standard provisions for bolted connections include: bolt shear capacity φVfn = φ × 0.62 × fuf × kr × krd × Ac × nn (threads included) or φ × 0.62 × fuf × kr × krd × Ac × nx (threads excluded). Bearing capacity φVb = φ × 3.2 × df × tp × fup. Tension capacity φNtf = φ × As × fuf.

CSA S16 Clause 13 — Canadian provisions follow similar limit states methodology with specific φ factors and resistance equations adapted for Canadian practice and material standards.

Design Inputs Explained

Bolt Pattern Geometry

The calculator supports up to 100 bolts per connection. Rectangular patterns are defined by number of rows, number of columns, pitch (vertical spacing), and gage (horizontal spacing). Circular patterns are defined by radius and number of bolts. Custom patterns accept individual X,Y coordinates for each bolt, allowing irregular layouts such as non-standard gages or offset bolts.

Bolt Properties

Each bolt requires: diameter (from 1/2 inch through 1-1/2 inch for imperial, M12 through M36 for metric), grade (A307, A325, A490, Grade 8.8, Grade 10.9, or SAE), thread condition (in or excluded from shear plane), and hole type (standard, oversized, short-slotted, or long-slotted). Slip-critical connections additionally require surface class selection (A, B, C, or galvanized).

Applied Loads

The calculator accepts: axial force (tension or compression), shear force (in-plane and out-of-plane), bending moments about both axes, and torsional moment. Loads can be entered as LRFD factored, ASD service, or unfactored values.

Connection Geometry

Plate thicknesses for each ply (connected material), material grades (Fy and Fu), and edge distances (top, bottom, side) must be specified. Weld details for welded-bolted hybrid connections are also supported.

Design Example — Eccentric Bolt Group

Consider a bracket connection with 8 bolts in a 4×2 pattern (4 rows at 3-inch pitch, 2 columns at 3-inch gage). The bolts are 7/8-inch diameter A325-N (threads included) in standard holes. The bracket is 10 inches tall with an eccentric load of 50 kips applied 8 inches from the bolt group centroid.

Step 1: Compute bolt group properties. The centroid is at the geometric center. Polar moment of inertia J = Σ(xi² + yi²) = 4 × (1.5² + 4.5² + 1.5² + 1.5² + ...) = 162 in⁴.

Step 2: Elastic analysis. The applied moment M = 50 × 8 = 400 kip-in. The most stressed bolt (outermost at corner) has coordinates (1.5, 4.5) from centroid. Direct shear per bolt: Pv = 50/8 = 6.25 kips. Torsional shear: Pmt = M × r / J = 400 × √(1.5² + 4.5²) / 162 = 400 × 4.74 / 162 = 11.70 kips. The vector sum gives the resultant shear on the critical bolt.

Step 3: Check bolt shear capacity. For 7/8-inch A325-N: Fnv = 54 ksi (AISC 360 Table J3.2). Ab = 0.601 in². φRn = 0.75 × 54 × 0.601 = 24.3 kips per bolt. The critical bolt demand of approximately 17.0 kips is within capacity (DCR = 0.70).

Step 4: Check bearing. Plate material A36 (Fu = 58 ksi), edge distance 1.5 inches. lc = 1.5 - 0.9375/2 = 1.03 inches. Rn = 1.2 × 1.03 × 0.5 × 58 = 35.8 kips (governs) vs 2.4 × 0.875 × 0.5 × 58 = 60.9 kips. Bearing DCR = 17.0/35.8 = 0.47. OK.

Prying Action and Tension Connections

When bolts are loaded in tension, prying action develops as the connected plies deform, amplifying the tensile force in the bolts. Per AISC 360, the prying ratio q = (t/tc)² where t is the flange thickness and tc is the required thickness for no prying. Per EN 1993-1-8 6.2.4, prying is accounted for using the T-stub model, with effective flange length determined by yield line theory. The calculator computes the amplified bolt tension considering: flange thickness, bolt gage, edge distance, and flange yield strength. Thicker flanges reduce prying effects, with a minimum practical thickness of 1/2 the bolt diameter to limit prying magnification.

Slip-Critical vs Bearing-Type Connections

Slip-critical connections are specified in structures subject to fatigue, connections with oversized or slotted holes, and connections subject to load reversal or vibration. Faying surface preparation is critical: Class A surfaces (clean mill scale) provide μ = 0.30, Class B surfaces (blast-cleaned) provide μ = 0.50, and Class C surfaces (hot-dip galvanized with roughened surface) provide μ = 0.35. The slip resistance per bolt is Rn = μ × Du × hf × Tb × Ns, where Du = 1.13 (mean ratio of actual to specified pretension), hf = 1.0 for standard holes, Tb is the minimum bolt pretension, and Ns is the number of slip planes.

Bearing-type connections transfer load through bolt shank bearing and are more economical for non-cyclic loading. They require shorter bolt lengths and no surface preparation. However, they permit slip at service loads, which may not be acceptable in certain applications.

Bolt Pretension and Installation

Per AISC Table J3.1, minimum bolt pretensions for A325 bolts range from 12 kips (1/2-inch) to 64 kips (1-1/2-inch). For A490 bolts, the range is 15 kips to 102 kips. Pretension is achieved through: turn-of-nut method (most common), calibrated wrench method, direct tension indicators, or twist-off bolts. The calculator uses code-minimum pretensions but allows user-specified values for field-verified installations. Installation torque is computed as T = K × D × P, where K is the nut factor (typically 0.20 for as-received conditions), D is bolt diameter, and P is the required pretension.

Frequently Asked Questions

What bolt patterns are supported? The bolted connection calculator supports 2D and 3D bolt groups in rectangular, circular, and custom patterns. You can define arbitrary bolt coordinates for irregular bolt layouts. Both elastic (vector) and IC (instantaneous center) analysis methods are available.

What is the difference between slip-critical and bearing-type connections? Slip-critical connections transfer load through friction between faying surfaces and are required for connections with fatigue, oversized holes, or reversal of load. Bearing-type connections transfer load through bolt shank bearing against the connected plies. Per AISC 360 Chapter J, slip-critical connections use a lower design stress to ensure slip does not occur at service loads.

Which bolt grades are supported? The calculator supports ASTM A307 (low-carbon), A325 (F3125 Grade A325), A490 (F3125 Grade A490), A449, Grade 8.8, Grade 10.9, and SAE grades. Pretension loads are computed per code tables: AISC Table J3.1 for ASTM bolts and EN 1993-1-8 Table 3.4 for metric grades.

How is prying action calculated for tension connections? Prying action amplifies bolt tension when connected plies flex under load. The calculator uses the T-stub model per EN 1993-1-8 6.2.4 and the AISC method based on flange thickness ratio. The prying factor q ranges from 1.0 (no prying, thick flange) to 2.0+ (significant prying, thin flange). Flange thickness should be at least 0.5 × bolt diameter to control prying.

What is the Instantaneous Center (IC) method for eccentric loads? The IC method iteratively finds the center of rotation of a bolt group under eccentric loading, accounting for nonlinear bolt force-deformation behavior. Per AISC Manual Part 7, bolt deformation capacity is taken as Δmax = 0.34 inches for standard holes. The IC method yields higher capacity than elastic analysis for eccentrically loaded groups — typically 10-30% higher depending on geometry. It is recommended for final design of critical connections.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All results must be independently verified by a licensed Professional Engineer.