CSA S16 Connection Design Worked Example — Beam-to-Column Double Angle

Complete worked example of a shear-only bolted double-angle connection per CSA S16:24 Clause 21 and the CISC Handbook of Steel Construction 11th Edition. This example covers bolt shear, bolt bearing, block shear, angle flexure, and weld checks for a typical beam-to-column flange connection.

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PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (P.Eng.) before use in any project.

Problem Statement

A W460x74 floor beam frames into the flange of a W310x60 column. The connection must transfer the factored end reaction Vf = 350 kN from the governing NBCC 2020 load combination ULS-2: 1.25D + 1.5L. Design a double-angle bolted shear connection with M20 A325M bolts in bearing-type connections (threads excluded from shear plane, AX condition).

Step 1 — Bolt Shear Resistance (Cl. 21.2.3)

For M20 A325M bolts with threads excluded (AX condition) in single shear:

Vr_per_bolt = 0.60 * phi_b * Ab * Fu
            = 0.60 * 0.80 * 314 * 830 / 1000 = 125.1 kN per shear plane

where Ab = 314 mm^2 (M20 gross body area per CSA S16 Table 2), phi_b = 0.80 for bearing-type connections.

For double shear (each bolt passes through the beam web and both angle legs), the shear plane count = 2:

Vr_per_bolt_DS = 2 * 125.1 = 250.2 kN (theoretical)

In practice, the beam-web side governs because the angle legs are shop-attached with their own set of bolts (single-shear on the angle-to-beam interface). The connection has two shear planes that must both be checked:

• Beam web bolts (field): bolts in double shear through beam web + both angles
• Column flange bolts (field): bolts in single shear through outstanding angle leg + column flange

Column flange side (single shear, 3 bolts):

Vr_3_bolts = 3 * 125.1 = 375.3 kN > 350 kN  ✓ (0.933 utilisation)

Beam web side (double shear, 3 bolts):

Vr_3_bolts_DS = 3 * 250.2 = 750.6 kN >> 350 kN  ✓

The column flange side (single shear, 3 bolts) is the governing interface. Three M20 A325M bolts per angle leg are adequate.

Step 2 — Bolt Bearing Resistance (Cl. 21.2.4)

Check bearing on the thinnest connected plate — the angle leg at 9.5 mm (assuming the beam web tw = 9.0 mm is the thinnest):

Bearing at the column flange (tf = 13.0 mm, standard 22 mm bolt holes):

For standard holes, bearing resistance per bolt:

Br = 3.0 * phi_br * t * d * Fu    where phi_br = 0.80

For angle leg (t = 9.5 mm, Fu = 450 MPa):
Br = 3.0 * 0.80 * 9.5 * 20 * 450 / 1000 = 205.2 kN per bolt

For beam web (t = 9.0 mm, Fu = 450 MPa):
Br = 3.0 * 0.80 * 9.0 * 20 * 450 / 1000 = 194.4 kN per bolt

Both exceed the bolt shear resistance of 125.1 kN per bolt — bolt shear governs over bearing, which is the preferred design outcome. The edge distance check (Cl. 21.3.2) requires:

• Minimum edge distance = 1.5 _ d_hole = 1.5 _ 22 = 33 mm
• Use 40 mm edge distance (standard angle leg, bolt line at 50 mm from heel)

Step 3 — Block Shear on Angle Leg (Cl. 13.11)

Check block shear on the outstanding leg of one L89x89x9.5 angle. With 3 bolts spaced at 70 mm centres and 40 mm edge distance:

Tr + Vr = phi_u * (Ut * Ant * Fu + 0.60 * Agv * (Fy + Fu) / 2)
        = 0.75 * (1.0 * 276 * 450 + 0.60 * 1,710 * (350 + 450) / 2) / 1000
        = 0.75 * (124,200 + 0.60 * 1,710 * 400) / 1000
        = 401.0 kN per angle

Total for 2 angles = 802.0 kN >> 350 kN ✓

Block shear is not critical for this connection. The controlling limit state is bolt shear at the column flange interface.

Step 4 — Connection Geometry

The standard double-angle detail for this connection:

Step 5 — Weld Check (Alternative: Shop-Welded / Field-Bolted)

As an alternative to the shop-bolted / field-bolted connection, the angles may be shop-welded to the beam web and field-bolted to the column flange. The weld between the angle heel and the beam web must transfer Vf = 350 kN over two angles.

Fillet weld resistance per CSA S16 Cl. 13.13.4:

For E48XX electrode (matching 350W base metal, XU = 480 MPa):

Vr_weld = 0.67 * phi_w * Aw * Xu * (1.00 + 0.50 * sin^1.5(theta))

For longitudinal loading (theta = 0°):  Vr = 0.67 * phi_w * Aw * Xu
For 6 mm fillet weld: Aw = 6 * L_weld / sqrt(2) mm^2 per mm of length

phi_w = 0.67 for fillet welds.

Required weld length per angle:

Vf_per_angle = 350 / 2 = 175 kN

Required throat area per mm: 175,000 / (0.67 * 0.67 * 480) = 175,000 / 215.5 = 812 mm
Required 6 mm weld length: L = 812 / (6 / sqrt(2)) = 812 / 4.24 = 191 mm
Use 240 mm of 6 mm fillet weld (full angle length) per angle  ✓

Step 6 — Beam Web Shear Check

Verify that the beam web itself does not fail in shear at the connection. The factored shear resistance of an unstiffened web per CSA S16 Cl. 13.4:

Vr_web = phi * 0.60 * Fy * d * tw
       = 0.90 * 0.60 * 350 * 457 * 9.0 / 1000
       = 777.4 kN >> 350 kN ✓

The beam web has ample shear capacity. For coped beams, check the reduced section separately using the net depth at the cope.

Step 7 — Final Connection Summary

Frequently Asked Questions

Can I use a single plate (shear tab) instead of double angles?

Yes. Single-plate shear connections (shear tabs) are governed by CSA S16 Cl. 21.7 and CISC Handbook Table 3-37. The single plate is shop-welded to the column and field-bolted to the beam web. Advantages: fewer pieces, no coping of the beam (no block shear reduction), one-sided bolting (easier erection). Disadvantages: eccentricity moment must be considered in the bolt group and plate design, and the single plate is approximately 60-75% as efficient as a double-angle connection for the same number of bolts. For Vf = 350 kN, a single plate of 10 mm thickness with 5-M20 bolts would be required (vs 3 bolts per side for double angles). The choice is typically driven by the fabricator's preference and the beam framing sequence.

What erection clearance is needed for beam-to-column connections?

For beams framing between column flanges, the beam cut length must be 8-12 mm shorter than the clear distance between the column flanges. This provides 4-6 mm gap at each end for erection tolerance. For the double-angle connection, the angles are detailed with 3 mm gap between the angle heel and the column face (the gap closes when the bolts are tightened). The beam setback to column is 10 mm. These clearances prevent binding during erection and allow the beam to be dropped in from above.

How do I specify the bolt hole type and size for Canadian connections?

CSA S16:24 Table 2 specifies hole sizes:

• Standard round: d + 2 mm for M16-M24, d + 3 mm for M27-M36
• Oversized: d + 5 mm for M20-M36 (requires slip-critical connection)
• Short-slotted: d x (d + 5 mm) or larger (requires slip-critical)
• Long-slotted: d x 2.5d or larger (requires slip-critical and additional checks)

For this connection, 22 mm standard round holes are specified (M20 + 2 mm). Standard holes are the default for bearing-type connections. Oversized or slotted holes are used only when adjustment is required and must be clearly noted on the structural drawings with the corresponding slip-critical bolt installation specification.

Related pages: CSA S16 Bolt Design Guide → | CSA S16 Beam Design → | Canadian Steel Sections → | NBCC Load Combinations → | Bolt Hole Sizes →