base-plate

name	base-plate
description	Column base plate design — AISC Design Guide 1, axially loaded, moment base plates, anchor rod design, grout, bearing on concrete, ACI 318 anchor provisions.
metadata	{"priority":5,"promptSignals":{"phrases":["base plate","column base","anchor rod","anchor bolt","column base plate","base plate design"],"minScore":4}}

Column Base Plate Design — Complete Skill (AISC Design Guide 1)

Axially Loaded Base Plates

Required Bearing Area

A₁_req = P_u / (φ_c × f'_c × A₂_factor)

If A₂ ≥ 4A₁ (large concrete area): φ√(A₂/A₁) term applies, max 2× A₂ = full concrete area supporting load Concrete bearing: φ_c × f'_c × (1 + √(A₂/A₁)) / 2... simplified:

AISC Design Guide 1 (concentric): Concrete bearing strength: f_p = 0.85f'c × √(A₂/A₁) ≤ 1.7f'c Required area: A₁ = P_u / (0.60 × f_p) [ASD] or A₁ = P_u / (0.65 × 0.85f'c) [LRFD, per ACI 318]

Plate Dimensions (N × B)

N = √A₁ + Δ (preferred square first) Δ = (0.95d - 0.80b_f)/2 (projection check from column) B = A₁/N

Round up to nearest ½" increment. Keep N,B ≥ column d + 4"

Plate Thickness (Axial Only)

Cantilever model for plate bending: Required thickness t_p from bending of plate cantilevering from column flanges: m = (N - 0.95d)/2 [cantilever dim from flange] n = (B - 0.80b_f)/2 [cantilever dim from web] λn' = λ√(d×b_f)/4 where λ = min(2×√(A₁_f)/A_plate, 1) [for weak axis between flanges]

Governing cantilever: l = max(m, n, λn') t_p ≥ l × √(2P_u / (0.9F_y × B×N))

Moment Base Plates (Eccentric Load)

Eccentric Axial + Moment

Resultant eccentricity: e = M_u/P_u Compare to kern: e_kern = N/6

Case 1 (e ≤ N/6): full bearing, no tension on anchor rods f_max = P_u/(BN) × (1 + 6e/N), f_min = P_u/(BN) × (1 - 6e/N) Design plate as cantilever under f_max

Case 2 (e > N/6): tension in anchor rods, partial bearing Solve for bearing zone Y: P_u × (e + N/2 - Y/2) = T × (f + N/2 - Y) (assuming bearing block at compression side) T = anchor rod tension, f = bolt gauge to compression edge Combine: Y = A + √(A² - B) where A,B from geometry

Bearing pressure: f_p = 2P_u/(3×q×Y) where q = B×0.85f'c (bearing capacity per unit length)

Iterate to find Y, then anchor force T.

Anchor Rod Design (ACI 318 Ch. 17 / AISC DG1)

Anchor Rod Types

• Cast-in (preferred): F1554 Gr 36, 55, 105 (F_y = 36/55/105 ksi)
• Post-installed (drilled): expansion, undercut, adhesive anchors

Capacity Checks (per anchor, LRFD)

Steel: φ_n = 0.75 × 0.75 × F_uta × A_se (tension) Steel shear: φ_vn = 0.65 × 0.6 × F_uta × A_se

Concrete breakout (tension): N_cb = A_Nc/A_Nco × ψ_ed × ψ_c × ψ_cp × N_b N_b = k_c × √f'c × h_ef^(1.5) [basic, k_c = 24 for cast-in] A_Nco = 9h_ef² (projected area, single anchor) h_ef = effective embedment depth

Concrete breakout (shear): V_cb = A_Vc/A_Vco × ψ_ed × ψ_c × V_b V_b = min(7(l_e/d_o)^0.2 √d_o × √f'c × c_a1^1.5, 9√f'c × c_a1^1.5)

Concrete pryout (shear): V_cp = k_cp × N_cp (k_cp = 1 or 2)

Pullout: N_pn = ψ_c × N_p, N_p = 8A_brg × f'c (headed anchor)

Interaction: (N_ua/φN_n)^(5/3) + (V_ua/φV_n)^(5/3) ≤ 1

Minimum Edge Distance and Spacing

c_min ≥ 1.5h_ef (for breakout) s_min ≥ 3d_o (spacing of anchors) h_ef ≥ 8d_a (embedment, cast-in) or per manufacturer (post-installed)

Grout

Non-shrink grout: 1"-2" (typical) between base plate and concrete Grout must be included in anchor length computation Leveling nuts during erection, then grout

Weld: Base Plate to Column

All-around fillet weld: size = min(t_flange, t_web) × appropriate coefficient Column axial transferred via fillet weld if not milled to bear Milled bearing: no weld required for compression (just hold-down for uplift)

Output

Provide: N×B [in], t_p [in], anchor rod size + grade + embedment, governing concrete breakout check, bearing pressure f_p [ksi].