Problem Statement

Design a base plate for a 200UC46.2 column in a braced-frame commercial building (3 storeys). The column is an interior column from the earlier column buckling worked example (phi_Nc = 1,304 kN).

Design data:

Step 1 — Concrete Bearing Capacity (AS 3600:2018 Clause 12.6)

Concrete bearing strength under the base plate:

f_b = 0.85 x phi x f'c x sqrt(A2/A1) <= 2.0 x phi x f'c

Where:

Try base plate: 350 mm x 350 mm x 20 mm:

A1 = 350 x 350 = 122,500 mm^2 A2 = 500 x 500 = 250,000 mm^2

sqrt(A2/A1) = sqrt(250000 / 122500) = sqrt(2.041) = 1.428

f_b = 0.85 x 0.60 x 32 x 1.428 = 23.32 MPa (Check limit: 2.0 x 0.60 x 32 = 38.4 MPa, so 23.32 MPa governs)

Required plate area: A1_req = N* / f_b = 650,000 / 23.32 = 27,875 mm^2 (167 mm x 167 mm equivalent)

The 350 mm x 350 mm plate (122,500 mm^2) is more than adequate. The actual bearing pressure:

f_b_actual = N* / A1 = 650,000 / 122,500 = 5.31 MPa << 23.32 MPa. OK.

The generous plate size is dictated by plate bending, not bearing — see Step 2.

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

The plate extends beyond the column as a cantilever. Critical cantilever dimensions:

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

m = (350 - 0.95 x 203) / 2 = (350 - 192.9) / 2 = 78.6 mm n = (350 - 0.80 x 203) / 2 = (350 - 162.4) / 2 = 93.8 mm

n = 93.8 mm governs (the wider projection).

Required plate thickness (yield line theory, ASI Base Plate Design Guide):

t_min = n x sqrt(2 x f_b_actual / (phi x f_y_plate))

Where f_b_actual is the actual bearing pressure (MPa): t_min = 93.8 x sqrt(2 x 5.31 / (0.90 x 300)) = 93.8 x sqrt(10.62 / 270) = 93.8 x sqrt(0.0393) = 93.8 x 0.198 = 18.6 mm

Use 20 mm thick base plate. 20 mm > 18.6 mm — OK.

Alternatively, if the plate were reduced to 300 mm x 300 mm:

A 300 x 300 x 16 mm plate works, saving 60% plate weight and reducing pedestal size to 450 x 450 mm (sqrt(A2/A1) = sqrt(202500/90000) = 1.50, f_b = 0.85 x 0.60 x 32 x 1.50 = 24.5 MPa > 7.22 MPa).

Preferred design: 300 x 300 x 16 mm base plate. More economical, adequate capacity.

Step 3 — Anchor Bolt Design (AS 4100 Section 9.3)

For a braced-frame column with pure axial compression, anchor bolts are designed for shear transfer only.

Shear per bolt: V*_bolt = V* / 4 = 35 / 4 = 8.75 kN

M20 Grade 4.6 bolt capacity (AS 4100 Clause 9.3.2.1): Tensile stress area A_s = 245 mm^2 (M20, coarse pitch) f_uf = 400 MPa

Single shear, threads included (conservative — threads in shear plane at grout interface): phi_V_f = phi x 0.62 x f_uf x A_s = 0.80 x 0.62 x 400 x 245 / 1000 = 48.6 kN

48.6 kN >> 8.75 kN. OK (0.18 utilization).

Bearing on base plate (16 mm plate, f_u = 440 MPa): phi_V_b = phi x 3.2 x d_f x t_p x f_up = 0.80 x 3.2 x 20 x 16 x 440 / 1000 = 360.4 kN >> 8.75 kN. OK.

Minimum embedment (headed anchors per AS 3600 Clause 17): Tension capacity of M20 Grade 4.6 bolt (for uplift cases, though negligible here): phi_N_tf = 0.80 x 245 x 400 / 1000 = 78.4 kN

Minimum embedment with a 50 mm anchor plate: bearing capacity at the anchor plate = area x concrete bearing strength = 2500 x 23.32 / 1000 = 58.3 kN. For full tension capacity, a 60 mm anchor plate is needed: 3600 x 23.32 / 1000 = 84.0 kN.

Specify: 4 x M20 Grade 4.6, 300 mm min embedment, with 60 mm x 60 mm x 8 mm anchor plates.

Step 4 — Weld Design (Column to Base Plate)

The column is fillet welded all around to the base plate. Weld must transfer the axial load (650 kN) plus any erection moment.

Fillet size: Minimum for 11.0 mm flange (AS/NZS 1554.1 Table 5.1): 5 mm. Use 6 mm for corrosion allowance and robustness.

Weld capacity (6 mm fillet, E48XX, SP category, AS 4100 Clause 9.7.3.10): phi_v_w = 0.80 x 0.6 x 480 x (0.707 x 6) / 1000 = 0.98 kN/mm

Column perimeter (approximate): p = 2 x (203 + 203) = 812 mm (neglecting fillet radii — conservative)

Weld capacity: phi_V_weld = 0.98 x 812 = 796 kN >> 650 kN. OK (0.82 utilization).

Design note: The weld is primarily loaded in compression (bearing of column end on base plate). The weld serves to: (a) resist shear transfer from column base to plate, (b) provide erection stability, and (c) resist any incidental tension from eccentricity or erection loads. The computed capacity is more than adequate.

Step 5 — Shear Transfer Mechanism

The horizontal shear of 35 kN must be transferred from the column to the footing. Two mechanisms are available:

Friction (steel on grout): Coefficient of friction mu = 0.40 (steel on non-shrink grout, unbonded) Friction capacity = mu x N* = 0.40 x 650 = 260 kN >> 35 kN

If friction is insufficient (seismic tension cases): Shear capacity of 4 x M20 anchor bolts (threads included) = 4 x 48.6 = 194.4 kN. Additionally, the bolts can be cast into the footing within 75 mm PVC sleeves (grouted after column alignment) to provide positive shear transfer. However, the sleeve annulus must be fully grouted to engage the bolt in shear — an air gap would allow bolt bending before shear engagement.

Recommendation: For this static braced frame building with V*/mu_N* = 0.13, rely on friction for shear transfer. Grout the anchor bolt pockets solid. For seismic design categories D or E (AS 1170.4), provide positive shear transfer through anchor bolts or shear key.

Step 6 — Grout Pad Design

Standard grout pad specification for Australian base plates:

Summary

Item Specification Notes
Base plate 300 x 300 x 16 mm, Grade 300 AS/NZS 3679.1
Anchor bolts 4 x M20 Grade 4.6 60x60x8 anchor plates
Embedment 300 mm minimum Headed anchors
Grout 25 mm non-shrink, 42 MPa min 50 mm reveal
Weld 6 mm fillet all around E48XX (W50X), SP cat.
Pedestal 450 x 450 mm, 32 MPa Confinement sqrt(A2/A1) = 1.50

Frequently Asked Questions

When does shear friction govern base plate design over anchor bolts? Shear friction (V_f = mu x N*) governs when the axial compression is high relative to the shear. For typical braced frames (mu = 0.40), V*/N* <= 0.40 means friction alone is adequate. For moment frames in seismic regions, V*/N* may exceed 0.40 during uplift reversals, and anchor bolts must be designed for the full shear. Australian practice conservatively designs anchor bolts for 100% of the shear regardless, treating friction as an additional safety margin.

How do I design a base plate for a moment-resisting column? Moment base plates require: (a) larger plate dimensions to develop the tension-compression couple, (b) stiffer plates (typically 30-50 mm thick) with stiffeners between anchor bolts, (c) tension capacity check of anchor bolts under moment, (d) consideration of the T-stub behaviour of the plate in bending around the tension bolts. The ASI Design Guide 3: Base Plates provides comprehensive procedures.

What are Australian standard anchor bolt grades? Grade 4.6 (f_uf = 400 MPa) is standard for mild steel anchor bolts. Grade 8.8 (f_uf = 830 MPa) is used for high-capacity anchor bolts in heavy columns or moment frames. Metric coarse pitch (M20-M36) is standard. AS 4100 Table 9.3.1 provides full bolt capacities. Always specify the bolt grade and embedment type on structural drawings — anchor bolt failure is a brittle, non-ductile failure mode and must be prevented.

When are shear keys required under base plates? Shear keys (typically a welded 50-100 mm deep UB/UC stub or fabricated cruciform under the base plate, cast into the footing) are required when: (a) V* > 0.40 x N* (friction exceeded), (b) anchor bolts are insufficient for shear, (c) seismic design requires a positive shear transfer mechanism, or (d) the column is subject to significant load reversals. The shear key is designed as a cantilever beam in the footing, checked for concrete bearing and steel bending.

This page is for educational reference. Base plate design per AS 4100:2020, AS 3600:2018, and ASI Design Guide 3. Verify plate capacities against ASI base plate design tables. All structural designs must be independently verified by a licensed Professional Engineer or Structural Engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION.