Problem Statement

Design a base plate for a W250x73 column (CSA G40.21 350W) in a braced frame building. The column is the ground floor interior column from the column capacity example (Cr = 2,067 kN from earlier worked example).

Design data:

Step 1 — Concrete Bearing Capacity (CSA A23.3 / CSA S16 Clause 25)

The bearing capacity of concrete under the base plate is governed by the confined bearing strength:

f_b = 0.85 x phi_c x f'c x sqrt(A2/A1) <= 1.7 x phi_c x f'c

Where:

Try base plate dimensions: 400 mm x 400 mm:

A1 = 400 x 400 = 160,000 mm^2 A2 = 400 x 400 = 160,000 mm^2 (pedestal same size as plate)

sqrt(A2/A1) = 1.0 (no confinement benefit — plate reaches pedestal edge)

f_b = 0.85 x 0.65 x 25 x 1.0 = 13.81 MPa

Required plate area: A1_req = Cf / f_b = 1,200,000 / 13.81 = 86,894 mm^2 (295 mm x 295 mm equivalent)

The 400 mm x 400 mm plate provides 160,000 mm^2 >> 86,894 mm^2. Plate area is more than adequate.

Check with larger pedestal (600 mm x 600 mm): A2 = 600 x 600 = 360,000 mm^2 sqrt(A2/A1) = sqrt(360000 / 160000) = sqrt(2.25) = 1.50

f_b = 0.85 x 0.65 x 25 x 1.50 = 20.72 MPa (but limited to 1.7 x phi_c x f'c = 1.7 x 0.65 x 25 = 27.63 MPa, so 20.72 MPa governs).

Required area with confinement = 1,200,000 / 20.72 = 57,915 mm^2 — even more reserve.

Typically, standardizing the pedestal at 600 x 600 mm provides a substantial confinement benefit at minimal additional concrete cost.

Step 2 — Plate Thickness (Cantilever Bending, CISC Method)

The plate is modeled as a cantilever extending beyond the column face. The critical cantilever dimension is:

m = (N - 0.95d) / 2 (projection beyond depth) n = (B - 0.80b) / 2 (projection beyond width)

Using the CISC convention (0.95d and 0.80b account for the fillet radius reducing the effective bearing area):

m = (400 - 0.95 x 253) / 2 = (400 - 240.4) / 2 = 79.8 mm n = (400 - 0.80 x 254) / 2 = (400 - 203.2) / 2 = 98.4 mm

The larger cantilever governs: n = 98.4 mm.

Plate thickness per yield line theory:

t_req = n x sqrt(2 x f_b / (phi x Fy))

Where f_b is the actual bearing pressure under the plate: f_b = Cf / A1 = 1,200,000 / 160,000 = 7.50 MPa

t_req = 98.4 x sqrt(2 x 7.50 / (0.90 x 350)) = 98.4 x sqrt(15.0 / 315) = 98.4 x sqrt(0.04762) = 98.4 x 0.218 = 21.5 mm

Use 25 mm thick base plate. 25 mm > 21.5 mm — OK with some reserve.

Check with confinement benefit (larger pedestal assumed, f_b = 7.50 MPa same since plate size unchanged): same result. The plate thickness governs regardless of pedestal size because the bearing pressure under the plate is identical.

Step 3 — Anchor Rod Tension Check

For a braced frame column with pure compression, anchor rods carry zero tension under axial load. However, they must resist the factored shear.

Shear per anchor rod: Vf_rod = Vf / 4 = 45 / 4 = 11.25 kN

Anchor rod shear capacity (CSA S16 Clause 25.3.2, AISC DG1 equivalent): For a 20 mm dia. F1554 Grade 55 rod (Ab = 314 mm^2): Vr_rod = 0.60 x phi x Ab x Fu = 0.60 x 0.80 x 314 x 517 / 1000 = 77.9 kN (threads excluded from shear plane — rod body in shear).

With threads included (conservative, threads cast in concrete): Vr_rod_threads = 0.70 x 77.9 = 54.5 kN.

54.5 kN >> 11.25 kN. OK with substantial reserve.

Minimum anchor rod embedment (CSA A23.3 Annex D): For a 20 mm rod in 25 MPa concrete, the minimum embedment to develop the full tensile capacity:

Tr_rod = 0.75 x phi x Ab x Fu = 0.75 x 0.80 x 314 x 517 / 1000 = 97.4 kN

Required embedment (bond strength ~ 1.2 MPa for deformed bars in tension): L_embed = Tr / (pi x d x bond) = 97,400 / (pi x 20 x 1.2) = 1,291 mm — this is excessive for a base plate anchor. In practice, use a headed anchor rod or anchor plate to develop the force through bearing rather than bond.

With a 50 mm square anchor plate at the rod end: Bearing area = 2500 mm^2. Concrete bearing strength at depth = 20.72 MPa (confined). Bearing capacity = 2500 x 20.72 / 1000 = 51.8 kN — not adequate for full tension.

Standard practice: specify 4 x 20 mm dia. ASTM F1554 Grade 55 anchor rods with 75 mm x 75 mm x 10 mm anchor plates, minimum 300 mm embedment. The anchor plate provides mechanical anchorage at the rod tip. For pure compression columns, 300 mm is typically sufficient.

Step 4 — Weld Design (Column to Base Plate)

The column is fillet welded to the base plate all around. The weld transfers the column axial load into the plate in compression.

Weld size: Minimum fillet weld for 14.2 mm flange thickness per CSA W59 Table 5.1 = 6 mm. Use 8 mm fillet weld for robustness.

Weld capacity (8 mm fillet, E49XX, longitudinal shear on column perimeter): Perimeter = 2 x (253 + 254) = 1,014 mm (approx, neglecting fillet radii). Vr_weld per mm = 0.67 x 0.67 x (0.707 x 8) x 490 / 1000 = 1.24 kN/mm

Total weld capacity = 1.24 x 1014 = 1,257 kN >> 1,200 kN. OK.

Weld design for shear transfer: The 45 kN factored shear is transferred through the base plate to the anchor rods via friction between the plate and grout (coefficient of friction mu = 0.40 for steel on grout). Friction capacity = 0.40 x 1200 = 480 kN >> 45 kN. Anchor rods are only engaged if slip occurs — the shear check above is conservative.

Step 5 — Grout and Levelling

A 25 mm non-shrink grout pad is standard for Canadian base plates. The grout must have compressive strength >= the concrete strength (25 MPa + margin = 35 MPa min). Key grouting requirements:

Summary

Item Specification Notes
Base plate 400 x 400 x 25 mm, 350W CISC standard
Anchor rods 4 x 20 mm dia. F1554 Gr 55 75x75x10 anchor plates
Embedment 300 mm minimum Headed anchors
Grout 25 mm non-shrink, 35 MPa 50 mm reveal
Weld 8 mm fillet all around E49XX
Pedestal 600 x 600 mm, 25 MPa For confinement benefit

Frequently Asked Questions

When does the A2/A1 confinement factor apply? The confinement factor sqrt(A2/A1) applies when the concrete support area (A2) is larger than the loaded area (A1) AND the support is geometrically similar and concentric. For a base plate on a pedestal: if the pedestal is the same size as the plate, A2/A1 = 1.0 (no benefit). If the pedestal is larger (common: 100-200 mm wider each side), A2/A1 > 1.0. The maximum value is 2.0 (doubled capacity). For base plates near the edge of a footing, A2 is limited by the edge distance.

How thick should base plates be for typical Canadian columns? For interior columns in braced frames (compression only, no moment): 20-30 mm for W200-W310 columns supporting up to 3,000 kN. For moment frame columns: 30-50 mm, with stiffeners required if plate thickness exceeds approximately 50 mm. The CISC Handbook provides pre-calculated base plate sizes for standard column sections.

Should base plates be designed for erection loads? Yes. During erection, the column is cantilevered from the base before beams are connected. Check anchor rod tension for the overturning moment from wind on the bare column plus 0.5 kN eccentric load from the erector. If inadequate, specify temporary guys or a larger anchor rod pattern.

This page is for educational reference. Base plate design per CSA S16:24 and CISC Handbook Part 7. Verify plate sizes against current CISC base plate tables. All structural designs must be independently verified by a licensed Professional Engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION.