AISC 360-22 HSS Column Design — HSS6x6x1/2 Full Worked Example

Complete step-by-step HSS column design following AISC 360-22 LRFD provisions. This worked example covers an HSS6x6x1/2 column in ASTM A500 Grade C: compression capacity per Chapter E (flexural buckling), local buckling check per Table B4.1a, combined axial and flexural interaction per Chapter H (Section H1.1), and connection considerations per Chapter K. Every calculation step is shown with actual values and code clause references.

Problem Statement

PRELIMINARY — NOT FOR CONSTRUCTION. All results presented here are for educational and reference use only. Values must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any design or construction.

An HSS6x6x1/2 column supports a gravity load in a braced frame. The column is 14 ft long, pinned at both ends (K = 1.0) about both axes. In addition to the axial compression, the column carries a small bending moment from a beam framing into the face of the HSS, producing strong-axis bending about the x-axis. The column is ASTM A500 Grade C, the standard HSS grade for structural applications.

Design parameters:

• Section: HSS6x6x1/2, ASTM A500 Grade C (Fy = 50 ksi, Fu = 62 ksi)
• Length: 14 ft, pinned-pinned (K = 1.0)
• Factored axial load: Pu = 160 kips
• Factored strong-axis moment: Mux = 15 kip-ft
• Weak-axis moment: Muy = 0 (no applied moment about y-axis)

Section Properties (HSS6x6x1/2)

Obtained from AISC Steel Construction Manual Table 1-12 for square HSS sections. The HSS6x6x1/2 is a 1/2 in. wall thickness square HSS, commonly used for lightly to moderately loaded columns in braced frames and truss chords.

Step 1: Section Classification (AISC Table B4.1a)

Before computing compressive strength, classify the section for local buckling. For rectangular HSS in uniform compression, the width-to-thickness ratio is critical.

Case 12 — Rectangular HSS, flanges in uniform compression:

lambda_f = b / t = (b_flat) / t_des

The flat width of the HSS wall is the outside dimension minus three times the wall thickness (approximate centerline):

b_flat = 6.00 - 3 × 0.465 = 6.00 - 1.395 = 4.605 in.
lambda_f = 4.605 / 0.465 = 9.90

Case 13 — Rectangular HSS, webs in uniform compression: Same ratio applies for square HSS.

lambda_w = lambda_f = 9.90

Compactness limits for stiffened elements in uniform compression (Table B4.1a):

lambda_p = 1.12 × sqrt(E/Fy) = 1.12 × sqrt(29,000/50) = 1.12 × 24.08 = 27.0
lambda_r = 1.40 × sqrt(E/Fy) = 1.40 × 24.08 = 33.7

Classification: lambda_f = 9.90 < lambda_p = 27.0. Section is COMPACT.

Since the section is compact, no reduction for local buckling is required, and the full plastic capacity can be developed. The design compressive strength follows Section E3 (flexural buckling of members without slender elements).

Step 2: Flexural Buckling Capacity (AISC 360-22 Section E3)

Step 2a: Slenderness parameter

The column is pinned-pinned about both axes (Kx = Ky = 1.0). Effective lengths:

Lcx = Kx × L = 1.0 × 14 ft = 14 ft = 168 in.
Lcy = Ky × L = 1.0 × 14 ft = 14 ft = 168 in.

Slenderness ratios:

KLx/rx = 168 / 2.22 = 75.7
KLy/ry = 168 / 2.22 = 75.7

Both axes are identical for square HSS. The elastic buckling stress Fe is computed per AISC E3-4:

Fe = pi^2 × E / (KL/r)^2
   = pi^2 × 29,000 / (75.7)^2
   = 9.8696 × 29,000 / 5,728
   = 286,218 / 5,728
   = 49.97 ksi

Step 2b: Critical stress Fcr (AISC E3-2 or E3-3)

First confirm whether elastic or inelastic buckling governs. The transition slenderness:

Limit = 4.71 × sqrt(E/Fy) = 4.71 × sqrt(29,000/50) = 4.71 × 24.08 = 113.4

Or using Fe/Fy check: Fe = 49.97 ksi, Fy = 50 ksi
Fe/Fy = 49.97/50 = 0.999 ≈ 1.0

Since KL/r = 75.7 ≤ 113.4 and Fe/Fy ≈ 1.0 ≥ 0.44(Fy), inelastic buckling governs.

Use AISC Equation E3-2 for inelastic buckling:

Fcr = [0.658^(Fy/Fe)] × Fy
    = [0.658^(50/49.97)] × 50
    = [0.658^1.0006] × 50
    = 0.658 × 50
    = 32.90 ksi

Step 2c: Design compressive strength (phi_c = 0.90):

Pn = Fcr × Ag = 32.90 × 9.74 = 320.3 kips

phi_c × Pn = 0.90 × 320.3 = 288.3 kips

Check: Pu = 160 kips < phi_c*Pn = 288.3 kips. Compression OK. Utilization = 160/288.3 = 0.555.

Step 3: Flexural Capacity (AISC 360-22 Section F7)

HSS flexural strength per Section F7. For square HSS with compact flanges and webs (lambda ≤ lambda_p):

Nominal flexural strength — Plastic moment (F7-1):

Mn_x = Mp_x = Fy × Zx = 50 × 19.9 = 995 kip-in. = 82.9 kip-ft

Design flexural strength (phi_b = 0.90):

phi_b × Mn_x = 0.90 × 82.9 = 74.6 kip-ft

Check: Mux = 15 kip-ft < 74.6 kip-ft. Flexure OK but must be considered in interaction.

Step 4: Combined Axial and Flexure Interaction (AISC 360-22 Section H1.1)

For doubly symmetric members subject to flexure and compression, the interaction check per AISC H1.1a applies when Pu/phi_c*Pn ≥ 0.2:

Check the threshold:

Pu / phi_c*Pn = 160 / 288.3 = 0.555 ≥ 0.20

Since Pu/phi_c*Pn ≥ 0.2, use AISC Equation H1-1a:

Pu/(phi_c × Pn) + (8/9) × [Mux/(phi_b × Mnx) + Muy/(phi_b × Mny)] ≤ 1.0

160/288.3 + (8/9) × [15/74.6 + 0/74.6]
= 0.555 + (8/9) × [0.201 + 0]
= 0.555 + 0.889 × 0.201
= 0.555 + 0.179
= 0.734 ≤ 1.0

Check: Interaction ratio = 0.734 < 1.0. Combined loading OK.

Step 5: Connection Considerations (AISC 360-22 Chapter K)

HSS connections require special consideration because the closed section limits access to the interior for bolting. Typical HSS column connections include:

Directly Welded Connections (most common for HSS columns): The HSS column can be directly welded to base plates and cap plates. For the HSS6x6x1/2, the wall thickness of 0.465 in. provides adequate welding surface. A fillet weld of 1/4 in. size along the full perimeter provides a weld throat of 0.177 in. which, with E70XX electrodes, provides 1.392 kips per inch per sixteenth of weld. For a 1/4 in. fillet weld: capacity = 4 sixteenths × 1.392 = 5.57 kips/in. of length.

Weld perimeter = 4 × 6.00 = 24 in. Weld capacity = 5.57 × 24 ≈ 134 kips. For compression, the base plate bears directly, and the weld is primarily for erection stability and nominal tension, so this is adequate.

Through-Bolt Connections: For connecting beams to HSS columns, through-bolts can be used where access to both sides is available. Alternatively, blind bolts or single-sided fasteners (e.g., Lindapter Hollo-Bolts) can be used. AISC Design Guide 24 provides detailed guidance on HSS connection design.

HSS Wall Local Yielding: Under concentrated loads from beam connections, check HSS wall plastification per AISC K1 and K2. For a beam reaction transferred through a shear tab welded to the face of the HSS:

Per AISC K1-3 for transverse plate-to-HSS T-connections (limit state of HSS wall plastification):

Rn = Fy × t^2 / (1 - tp/B) × [2 × N/B + 4 × sqrt(1 - tp/B)]

where tp = plate thickness, B = HSS width, N = bearing length. This check must be performed for all HSS connections transferring concentrated loads.

Step 6: Summary of Design Checks

All checks pass. The HSS6x6x1/2 provides adequate capacity for the applied axial and flexural demands. A lighter section (HSS5x5x1/2 or HSS6x6x3/8) could be considered if additional checks confirm adequacy, though the 1/2 in. wall provides a robust welding platform that thinner walls may not offer.

AISC 360-22 HSS Column Design Overview

The design of HSS columns under AISC 360-22 follows several key provisions:

• Section E3 — Flexural Buckling: For doubly symmetric members without slender elements, the compressive strength is based on the column curve with the effective length KL and radius of gyration r.
• Section E4 — Torsional and Flexural-Torsional Buckling: For singly symmetric or unsymmetric shapes, or when torsional buckling governs. Closed HSS sections have high torsional stiffness (large J), making torsional buckling unlikely to govern unless the member is very slender.
• Section E7 — Members with Slender Elements: When b/t exceeds lambda_r, the effective area is reduced using the effective width concept per Section E7.2.
• Section H1 — Combined Flexure and Compression: The interaction equations in H1.1a and H1.1b provide a conservative check for beam-columns.
• Chapter K — HSS Connections: Special provisions for welded and bolted connections to HSS members, including limit states for chord wall plastification, punching shear, and sidewall yielding.

Design Optimization for HSS Columns

• Strength-to-Weight Ratio: HSS sections provide the highest compressive strength per unit weight of any steel shape due to their efficient closed cross-section and absence of local buckling-prone elements (when properly proportioned).
• Architectural Preference: Square and round HSS columns are preferred for architecturally exposed steel because of their clean, uniform appearance from all viewing angles.
• Connection Complexity: HSS connections are more complex than W-shape connections. Through-plate, end-plate, or proprietary blind-fastener systems add cost. Budget 10-15% premium for HSS column connections compared to equivalent W-shape connections.
• Fire Protection: HSS columns have a smaller surface area-to-volume ratio than W-shapes, which can reduce the required fire protection thickness. However, the closed shape makes internal fireproofing impossible, and intumescent coatings are often used.
• Concrete Filling: Concrete-filled HSS columns (CFT) per AISC Chapter I provide 20-40% additional compressive capacity without increasing the external dimension. The concrete fill delays local buckling of the steel tube and provides inherent fire resistance.

Frequently Asked Questions

What is the difference between HSS column design and W-shape column design under AISC 360?

HSS sections differ from W-shapes in three key ways for column design: HSS sections have no weak-axis buckling distinction (rx = ry for square HSS), local buckling is checked per Table B4.1a using the width-to-thickness ratio b/t (not bf/2tf and h/tw), and the torsional buckling limit state may govern for slender HSS sections. Additionally, HSS sections in Chapter E3 use the same column curve as W-shapes but with different effective length considerations for truss and frame applications.

When does local buckling govern HSS column design?

Per AISC Table B4.1a, HSS sections are classified as compact, noncompact, or slender based on the width-to-thickness ratio lambda = b/t. For rectangular HSS in uniform compression, the compact limit is lambda_p = 1.12 × sqrt(E/Fy) and the slender limit is lambda_r = 1.40 × sqrt(E/Fy). If lambda exceeds lambda_r, the section is slender, and local buckling reduces the effective area per Section E7. For HSS6x6x1/2 in A500 Grade C (Fy = 50 ksi), b/t = 11.0, which is well within the compact range.

Why are HSS columns preferred for architecturally exposed steel?

HSS columns offer clean, closed profiles without exposed flanges or bolt heads, making them the preferred choice for architecturally exposed structural steel (AESS). Square HSS eliminates the weak-axis buckling distinction (equal rx and ry), providing biaxial symmetry and efficient resistance to wind and seismic loads from any direction. Round HSS offers the added benefit of reduced wind drag and the most efficient cross-section for pure axial compression per unit weight.

How do you connect beams to an HSS column without through-bolts?

Several options exist: Welded shear tabs or end plates directly to the HSS face (check HSS wall plastification per Chapter K); single-sided blind bolts (e.g., Lindapter Hollo-Bolt, Huck Blind BOBTAIL); and through-plate connections where a vertical plate passes through slots cut in the HSS column and is welded on both sides. For moment connections to HSS columns, external diaphragm plates or internal stiffening elements may be required per AISC Design Guide 24.

Does concrete filling improve HSS column performance?

Yes. Concrete-filled HSS tubes (CFT) per AISC 360-22 Chapter I2 increase compressive capacity by 20-40% and provide inherent fire resistance. The concrete core delays local buckling of the steel tube and carries load after the steel yields. CFT columns achieve higher fire ratings without external protection than bare steel columns. The cost premium for concrete filling is typically 5-10% of the steel cost.

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Related References

• AISC Column Design Example — W12x65
• Column Buckling Equations Reference
• Effective Length K Factors
• HSS Connection Design Reference
• AISC Steel Construction Tables
• How to Verify Calculations
• Combined Loading Reference
• Steel Seismic Design Reference

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.