Wind Girder Sizing: How Many Plates, and How Do I Check Local Buckling?

Wind Girder Purpose: Restraining Circumferential Buckling

A wind girder (also called a wind ring or wind brace) is a structural ring welded to the tank shell near the top. Its purpose is to restrain the shell from buckling outward under lateral wind pressure.

When wind pushes on the tank, it creates a pressure distribution that tries to deform the shell shape. Tall, slender tanks are vulnerable to circumferential buckling — the shell can snap inward (buckle) rather than simply flexing elastically. The wind girder provides a "stiff ring" at a strategic location (usually at the top, where deflection is greatest) to prevent this buckling mode.

Key insight: The wind girder doesn't eliminate wind stress; it limits the unsupported panel height of the shell and increases the buckling resistance. The calculation is similar to stiffening rings for external pressure — higher moment of inertia = higher resistance to buckling.

Section Modulus Requirement (Global Check)

API 650 Section 5.9.6 specifies the minimum section modulus (Zw) the wind girder must have:

Zw = (Pw × D² × H) / (2 × Sd × E × 1000)

Where:

• Pw = wind pressure (e.g., 0.89 × (V/190)² kPa)
• D = tank diameter
• H = tank height (or distance from base to girder, if not at top)
• Sd = allowable shell stress
• E = joint efficiency

The result is the minimum section modulus (in units of cm³ or in³ depending on metric/US). The girder must provide at least this Zw value.

Typical result: A 30m-diameter, 20m-tall tank in a 160 km/h wind zone might require Zw ≈ 10,000–15,000 cm³. A 300×50mm flat-bar section provides roughly 2,500 cm³. You'd need 4–6 plates (or build-up from smaller sections) to meet the requirement.

Local Plate Buckling: The Often-Missed Check

Once you've sized the girder to meet section modulus, you must check that the girder plates themselves don't buckle locally under compression stress.

What is local buckling? Imagine a wide, thin steel plate under compression. The plate can fail by the edges curling/buckling inward (plate buckling) before the material reaches yield stress. This is a geometric instability, like a ruler flexing when you push it.

Width/thickness ratios (b/t):** The susceptibility to local buckling is characterized by the plate's width-to-thickness ratio (b/t), where b = unsupported width of the plate edge, and t = plate thickness. Higher b/t = more vulnerable to local buckling.

Allowable b/t limits (per AISC or API rules):

• Flanges (wide parts) of girder plates: Typically b/t < 10–12 (depending on yield strength and stress condition)
• Web (tall parts) of girder plates: Typically b/t < 15–20

Example check: A 300mm-wide × 50mm-thick flat bar has b/t = 300/50 = 6, which is well within limits. A 500mm × 20mm plate has b/t = 25, which exceeds typical limits and requires intermediate stiffeners.

When Intermediate Stiffeners Are Required

If the girder's b/t ratios exceed allowable limits, you must add intermediate stiffeners (smaller ribs or bars welded perpendicular to the plate) to reduce the unsupported plate width.

Stiffener spacing: Stiffeners are placed at intervals (e.g., every 1–2 meters around the circumference) to reduce the unsupported plate span. Each stiffener acts as a "stopper" preventing local buckling of the plate between stiffeners.

Stiffener sizing: The stiffener itself must have sufficient moment of inertia to function effectively. Typical requirement: I_stiffener ≥ (b³ × t) / (12 × 10³), where b is the plate width and t is thickness. Small angles or flat bars work well.

Cost trade-off: Adding stiffeners increases fabrication complexity and cost. For large wind girders, stiffeners are common. For small girders (low b/t), they're unnecessary.

Diaphragm Plates and Connection Stiffness

The wind girder must be securely connected to the shell (typically with full-penetration welds). The connection must be stiff enough to transfer the girder's restraining force to the shell.

Diaphragm plates: In some designs, flat plates are welded radially between the girder and shell to stiffen the connection and distribute loads. These "diaphragms" increase the effective connection stiffness, preventing the girder from twisting or prying loose under wind loads.

When required: For very large tanks or very high winds, diaphragms are often specified. For smaller tanks, diaphragms may be optional — the girder-to-shell weld alone is sufficient.

Common Mistakes

Mistake 1: Calculating section modulus but ignoring local plate buckling.** The global check (Zw) is necessary but not sufficient. The girder plates must also pass local-buckling limits. A girder that meets Zw but has excessive b/t can still fail locally.

Mistake 2: Using very wide, thin plates to save material.** A 500mm × 15mm plate has good section modulus but terrible b/t ratio (33). Intermediate stiffeners become mandatory, negating the material savings. Better to use slightly thicker (25–30mm) plates with good b/t and no stiffeners.

Mistake 3: Mis-measuring plate width for b/t calculation.** The width (b) is the unsupported span — the distance between stiffening elements (girder edges, connection points, etc.). If you measure the total plate width and ignore intermediate support, your b/t calculation is wrong. Be precise about what's unsupported.

Mistake 4: Not accounting for stress concentration at stiffener connections.** Stiffeners create local stress concentrations where they're welded to the main girder plate. These concentrations can exceed average stress and trigger local buckling. Conservative sizing of stiffener spacing helps mitigate this.

Mistake 5: Forgetting that wind-girder moment varies with tank geometry and height.** If the girder is placed mid-height instead of at the top, the required Zw changes. Always calculate Zw for the actual girder location, not just assume "top of tank is standard."

Practical Tips

• Calculate section modulus (Zw) first; it determines the gross cross-sectional area you need. Then iterate on plate dimensions: how many plates, what width, what thickness?
• For each plate dimension, calculate b/t and check against allowable limits.** If b/t exceeds limits, either thicken plates or add stiffeners.
• Compare cost of thicker (fewer) plates vs. thinner (stiffened) plates. Sometimes thicker is cheaper due to lower fabrication complexity.
• Specify diaphragm plates for large tanks or high-wind zones.** They increase connection stiffness and are often worth the modest extra cost.
• Document the wind girder design (section modulus, plate dimensions, stiffener spacing, b/t checks) on the design drawing and in the design basis.** Future engineers need to understand the girder's load-carrying logic.
• Coordinate with the fabricator on girder construction options early.** Different fabricators have different plate availability, stiffener preferences, and cost structures. Get input before finalizing the design.

Related reading: Wind Load Design, Shell Support Rings, and Buckling Design.