Steel Stack and Chimney Design Guide -- ASME STS-1

Self-supporting steel stacks are industrial landmarks -- from the 200-foot boiler stacks at power plants to the 60-foot process stacks at chemical facilities. Unlike building columns, stacks are governed by wind, not gravity. A stack's circular cross-section sees the same wind load regardless of direction and is susceptible to aeroelastic instability (vortex shedding) that can cause catastrophic fatigue failure within hours if not addressed. ASME STS-1 (Steel Stacks, 2021 Edition) is the primary US design standard, supplemented by CICIND (International Committee on Industrial Chimneys) for international practice and ASCE 7 for wind loads.

Wind Loading on Cylindrical Structures

Wind loading on a steel stack is fundamentally different from wind on a building. ASCE 7-22 Chapter 29 governs "Chimneys, Tanks, and Similar Structures" with separate provisions for along-wind (drag) and across-wind (vortex shedding) response.

Along-wind force: The design wind force F = q_z x G_f x C_f x A_f where q_z = velocity pressure at height z = 0.00256 x K_z x K_zt x K_d x V^2 (psf). G_f = gust effect factor (0.85 for rigid structures under 4-second natural period, otherwise calculated per ASCE 7 Section 26.11). C_f = force coefficient: 0.7 for a moderately smooth circular cylinder at a typical Reynolds number, but conservatively increased to 1.0 for stacks with external attachments (ladders, platforms, piping). A_f = projected area = D x h for each segment.

Worked example -- along-wind moment: 100-ft tall, 4-ft diameter steel stack. Exposure C (open terrain). V = 115 mph. K_z at z = 66 ft (2/3 height) = 2.01 x (66/1,200)^(2/9) = 1.10. q_z = 0.00256 x 1.10 x 1.0 x 1.0 x 115^2 = 37.2 psf. G_f = 0.85 (assumed rigid). C_f = 1.0. F = 37.2 x 0.85 x 1.0 x (4 x 100) = 37.2 x 0.85 x 400 = 12,648 lb = 12.6 kips. Overturning moment at base: M_OT = F x h/2 = 12.6 x 50 = 630 kip-ft. This moment governs the base plate and foundation design. The shear force at base: V_base = 12.6 kips. Self-weight of a 100-ft x 4-ft x 3/8-in stack: W = pi x D x t x h x 490 lb/ft^3 = 3.14 x 4 x 0.03125 x 100 x 490 = 19,240 lb = 19.2 kips. Eccentricity e = M/P = 630 kip-ft / 19.2 kips = 32.8 ft >> stack radius of 2 ft -- the base is in overturning and anchor bolts are definitely required.

Vortex Shedding and Aeroelastic Instability

Vortex shedding is the single most important design consideration for steel stacks. When wind flows past a cylinder, alternating vortices detach from opposite sides at a frequency f_s = S x V / D, where S (Strouhal number) = 0.18 for Reynolds numbers below 2 x 10^5 (typical for stacks 2-8 ft diameter at wind speeds 10-80 mph), and S = 0.22 for supercritical Reynolds numbers above 3.5 x 10^6 (rare for steel stacks, only in hurricane winds for large-diameter stacks).

Critical wind velocity: When the shedding frequency equals the stack's natural frequency (f_n), the stack enters lock-in -- it vibrates in the cross-wind direction at f_n with amplitudes proportional to the inverse of the Scruton number. V_crit = f_n x D / S. For a 100-ft x 4-ft diameter cantilever stack with t = 3/8 in: I = pi x D^3 x t / 8 = 3.14 x (48)^3 x 0.375 / 8 = 16,286 in^4. The fundamental natural frequency of a uniform cantilever: f_n = (0.56 / h^2) x sqrt(E x I / m). m = weight per unit length / g = (490 x 3.14 x 4 x 0.375/12 / 386.4) = 0.5 lb-sec^2/in/in. f_n = (0.56 / 1200^2) x sqrt(29 x 10^6 x 16,286 / 0.5) = (3.89 x 10^-7) x sqrt(945 x 10^9) = 3.89 x 10^-7 x 972,000 = 0.378 Hz. This is a very low natural frequency -- stacks are flexible structures. V_crit = 0.378 x 4 / 0.18 = 8.4 ft/s = 5.7 mph. Critical wind speeds this low occur daily, so vortex-induced vibration is virtually certain without mitigation.

Scruton number and damping: The Scruton number quantifies the stack's inherent resistance to vortex-induced vibration: Sc = (4 x pi x m x zeta) / (rho x D^2). m = mass per unit length (slugs/ft), zeta = structural damping ratio (0.002-0.005 for unlined steel stacks, 0.01-0.02 for refractory-lined stacks), rho = air density = 0.00238 slugs/ft^3. For the example stack with m = (19,200/100)/32.2 = 5.96 slugs/ft, zeta = 0.003: Sc = (4 x 3.14 x 5.96 x 0.003) / (0.00238 x 16) = 0.225 / 0.0381 = 5.9. Per ASME STS-1 Section 5.3, stacks with Sc < 10 for unlined stacks or Sc < 20 for lined stacks require vortex shedding analysis and likely mitigation.

Mitigation -- Helical Strakes: Three-start helical fins (strakes) wrapped around the upper one-third of the stack disrupt the organized vortex shedding and prevent lock-in. Strake geometry per ASME STS-1 and CICIND: strake height h_s = 0.10D, strake pitch p_s = 5D, strake width = 0.01D (minimum). For the 4-ft stack: h_s = 4.8 in, pitch = 20 ft. The strakes are typically 1/4- or 3/8-inch plate welded continuously to the shell. Strakes add approximately 2-3% to the total stack weight but effectively eliminate vortex-induced vibrations. Alternative: aerodynamic spoilers (tuned mass dampers are possible but expensive and less reliable).

Base Plate and Anchor Bolt Design

Stack base plates differ from building column base plates because the axial load (self-weight) is very small compared to the overturning moment. The design follows AISC Design Guide 1 (Base Plate and Anchor Rod Design) with one critical modification: the eccentricity e = M_u / P_u almost always exceeds the base plate half-width (large eccentricity case). The bearing stress distribution is triangular on one side, with the opposite side in uplift resisted by anchor bolts.

For a circular base plate (most common for stacks), the design method per DG1 for a circular plate with bolts on a bolt circle: Assume a rectangular compression stress block under the compression side, ignore concrete bearing on the tension side. The compression resultant acts at the centroid of the triangular stress block. Solve for the compression zone length Y and anchor bolt tension T by satisfying force and moment equilibrium: C = P_u + T, M_u = C x (D_bp/2 - Y/3) - P_u x (D_bp/2) (taking moments about the base plate center).

Base plate bending: The base plate is checked for bending at the face of the shell (cantilever bending under bearing pressure) and at the bolt circle (cantilever bending under bolt tension). Required plate thickness: t_p >= sqrt(4 x M_u_plate / (phi_d x Fy x 1.0)). For a base plate with 12 in overhang beyond the shell, with bearing pressure f_p = 1,500 psi (on 4,000 psi grout), the cantilever moment per inch: M = f_p x overhang^2 / 2 = 1,500 x 12^2 / 2 = 108,000 in-lb/in. t_p = sqrt(4 x 108,000 / (0.90 x 36,000 x 1.0)) = sqrt(432,000 / 32,400) = sqrt(13.33) = 3.65 in. Use 3-3/4 in thick base plate (ASTM A36 or A572 Gr. 50).

Anchor bolt design: Tension per bolt + shear from wind. Bolts must be checked per ACI 318-19 Chapter 17 (anchoring to concrete). Steel strength: N_sa = A_se x f_uta (A_se = tensile stress area). Concrete breakout: N_cb = (A_Nc / A_Nco) x psi x 16 x lambda x sqrt(f_c) x h_ef^(1.5). Prying action in the bolt chair plate must also be checked. Anchor bolts for stacks are fatigue-critical because wind direction changes thousands of times over the stack life -- for high-wind regions (V > 115 mph), a high-cycle fatigue check per ACI 318-19 Section 17.10 applies with the fatigue stress limit = (Delta_S)_max = 0.40 x f_uta for bolts with cut threads.

Thermal and Corrosion Considerations

Stacks operating at elevated temperatures (300-800 F for boiler stacks) require thermal expansion accommodation and corrosion protection for both interior flue gas and exterior weathering. Thermal expansion: Delta_L = alpha x L x Delta_T = 6.5 x 10^-6 x 1,200 in x (500 - 70) = 3.35 in. A sliding base with PTFE/stainless bearing pads, oversized bolt holes, and belleville washers accommodates this growth. Internal refractory lining (brick, gunite, or stainless steel liner) provides both thermal insulation and corrosion protection. A 1/16- to 1/8-inch corrosion allowance is added to the shell thickness for unlined stacks.

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Disclaimer

This page is for educational and reference use only. Stack design must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) for site-specific wind loads, seismic conditions, operating temperatures, and local building code requirements.