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Free Steel Shear Wall Calculator -- SPSW Design

Q: What is the difference between steel plate shear walls and conventional braced frames?

SPSW provides higher ductility and more uniform stiffness over the building height. The infill plate yields across the entire panel, distributing energy dissipation. Braced frames concentrate inelastic action at specific braces.

Q: What is the minimum infill plate thickness for SPSW?

AISC 341 limits infill plate slenderness to h/tw less than 2000 divided by sqrt(Fy). Practically, plates are 3/16 to 3/8 inch for low-rise and up to 1/2 inch for mid-rise. Plates under 3/16 inch are difficult to weld without distortion.

Q: How are HBEs and VBEs designed for SPSW?

HBEs (horizontal boundary elements) and VBEs (vertical boundary elements) use capacity design per AISC 341 Section F5.5. They must remain elastic under forces from the fully yielded and strain-hardened infill plate, designed for 1.2 times expected infill plate strength.

Design steel plate shear walls (SPSW) for seismic lateral resistance in low-rise, mid-rise, and high-rise steel buildings. The calculator determines infill plate thickness, horizontal boundary element (HBE) and vertical boundary element (VBE) sizes, tension field angle, and capacity-based design checks per AISC 341-22 Section F5, AISC 360-22, CSA S16 Section 27, EN 1993-1-5 and EN 1998-1, and AS 4100 Section 8.

A steel plate shear wall consists of a thin steel infill plate surrounded by a moment-resisting boundary frame of HBEs (beams) and VBEs (columns). Under lateral load, the infill plate develops a diagonal tension field after buckling elastically in shear. The tension field anchors to the boundary elements, providing strength, stiffness, and ductile energy dissipation through plate yielding. This mechanism is fundamentally different from reinforced concrete shear walls, which resist lateral load through shear-friction and diagonal compression struts, and offers advantages in constructability, architectural flexibility, and post-earthquake repairability.

SPSW configurations covered: unstiffened SPSW (thin plate, tension field governed), stiffened SPSW (intermediate stiffeners divide the panel into sub-panels with higher shear buckling capacity), coupled SPSW (two walls connected by coupling beams at floor levels), and composite SPSW (concrete encasement on one or both sides of the steel plate for additional stiffness and fire protection). Unstiffened SPSW is the most common configuration in North American practice and is the primary focus of AISC 341-22 Section F5.

What this calculator does not cover: concrete-filled composite plate shear walls (CF-CPSW, per AISC N690), coupled wall link beam rotation demands beyond elastic range, out-of-plane buckling interaction with gravity columns, and connection design for the VBE-to-base anchorage (use the column base design calculator for base connections).

How to Use This Calculator

Step 1 -- Define wall geometry. Enter the overall wall height from base to roof, the wall width (horizontal distance between VBE centerlines), and the number of stories. The calculator distributes the wall height into equal story heights unless individual story heights are entered explicitly. The aspect ratio (height/width) is computed; SPSW with aspect ratios between 0.5 and 2.5 are typical, with taller narrower walls requiring larger boundary elements due to higher overturning demands.

Step 2 -- Select infill plate. Enter the infill plate thickness (typ. 3/16 in, 1/4 in, 5/16 in, 3/8 in, or 1/2 in), yield strength (A36 at Fy = 36 ksi or A572 Gr 50 at Fy = 50 ksi), and stiffener configuration (unstiffened or stiffened with spacing ratio a/h). For unstiffened walls, AISC 341-22 Section F5.4 limits plate slenderness to h/tw ≤ 2000/√Fy (equivalent to h/tw ≤ 333 for 36 ksi steel, h/tw ≤ 283 for 50 ksi steel). The calculator automatically adjusts infill thickness if the slenderness limit is exceeded.

Step 3 -- Design boundary elements. Select trial HBE and VBE sections (W-shapes with Fy = 50 ksi, built-up sections for large demands). HBEs are designed as beams spanning between VBEs, resisting axial force plus flexure from the infill plate tension field anchorage. VBEs are designed as beam-columns resisting axial force from overturning moment plus flexure from tension field anchorage. The calculator checks AISC 360 Chapter H interaction equations.

Step 4 -- Enter seismic demands. Input the story shear at each level (from Equivalent Lateral Force, Response Spectrum, or Nonlinear Response History Analysis), the overturning moment at the base, and the seismic design category (SDC B through F per ASCE 7-22). For SDC D, E, or F, the capacity-based design provisions of AISC 341 F5.5 apply.

Step 5 -- Review infill plate capacity. The calculator determines the tension field angle alpha using the iterative procedure per AISC 341 Commentary Eq C-F5-1 and computes the nominal shear strength from the plate tension field. Drift is checked against the 0.025 hsx limit for SDC D-F (AISC 341 Table C1.5.2a).

Step 6 -- Verify capacity design. HBEs and VBEs are checked for the forces generated by the fully yielded and strain-hardened infill plate. The expected plate strength is calculated using Ry (1.3 for A36, 1.1 for A572 Gr 50) and the boundary elements must remain elastic under these amplified forces. HBE splices and VBE column splices are checked for 1.1 Ry Fy Ag per AISC 341 F5.6.

Engineering Theory -- SPSW Behavior

Infill Plate Tension Field Action

The thin infill plate buckles elastically in shear at very low load levels. For a 1/4-inch plate in a 12-ft story, the elastic shear buckling stress is approximately 2-5 ksi, corresponding to a buckling load of 10-25 kips -- far below the design seismic shear. After buckling, the plate develops a diagonal tension field oriented at angle alpha to the vertical, analogous to the tension field in a plate girder web (AISC 360 G3) but with the tension field spanning the full panel rather than being divided by intermediate stiffeners.

The nominal shear strength of the infill plate per AISC 341-22 Eq F5-1 is:

Vn = 0.42 * Fy * tp * Lcf * sin(2*alpha)

where Lcf is the clear distance between HBE flanges (wall width minus the VBE flange thickness on each side), tp is the infill plate thickness, and alpha is the tension field angle measured from the vertical. The factor 0.42 accounts for the von Mises yield criterion interaction between shear stress and the normal stress in the tension field.

The tension field angle alpha is determined from the relative stiffness of the boundary elements. When the VBEs are very stiff relative to the HBEs, alpha approaches 45 degrees and the tension field develops diagonally across the panel. When HBEs are much stiffer than VBEs, alpha deviates from 45 degrees. The angle is computed iteratively from:

tan(2*alpha) = (1 + tp * Lcf / (2 * A_vbe)) / (1 + tp * h / (2 * A_hbe))

where A_vbe and A_hbe are the cross-sectional areas of the VBE and HBE respectively, and h is the story height.

Capacity-Based Design of Boundary Elements

The boundary elements (HBEs and VBEs) are designed using capacity design principles per AISC 341-22 Section F5.5. The fundamental requirement is that the boundary elements must remain elastic under the forces from the fully yielded and strain-hardened infill plate. This ensures the ductile yielding is confined to the replaceable infill plate rather than damaging the boundary frame.

The expected infill plate shear strength is:

V_expected = 0.42 * Ry * Fy * tp * Lcf * sin(2*alpha)

where Ry is the material overstrength factor (1.3 for A36, 1.1 for A572 Gr 50 and A992).

From the expected plate strength, the forces on boundary elements are computed as distributed loads along the HBE and VBE lengths, resolved from the diagonal tension field. The HBE experiences: (1) axial tension/compression from the horizontal component of the tension field, accumulating from the middle of the wall toward the ends; (2) flexure from the eccentricity of the tension field relative to the HBE centroid; and (3) end moments from frame action. The VBE experiences: (1) axial compression from overturning moment (P/A from the building gravity plus seismic overturning); (2) axial force from the vertical component of the tension field anchorage; and (3) flexure from tension field eccentricity.

AISC 341 F5.5 requires the combined axial-flexural interaction check using AISC 360 Chapter H with the amplified forces from the expected plate strength.

Plate Slenderness Limit

The infill plate slenderness limit h/tw ≤ 2000/√Fy (approximately 333 for A36, 283 for Gr 50) per AISC 341 F5.4 serves several purposes. First, it ensures the plate buckles elastically under service-level wind loads so that the building does not have visible plate buckling under non-seismic conditions. Second, it ensures the post-buckling tension field has adequate stiffness to limit drift under design-level events. Third, for SDC D and above, it ensures the plate yields across its full area rather than developing localized yield bands. Plates that exceed the slenderness limit are permitted with stiffeners dividing the panel into sub-panels meeting the slenderness limit individually.

Worked Example -- 3-Story SPSW Building

Problem: Design an unstiffened SPSW for a 3-story office building in SDC D (SDS = 1.0, SD1 = 0.6). Wall height = 36 ft (3 stories at 12 ft each), wall width = 24 ft. Steel frame: A992 Gr 50 beams and columns, A36 infill plate (Fy = 36 ksi, Fu = 58 ksi). From ELF analysis: base shear V_base = 480 kips distributed as roof = 200 kips, 3rd = 160 kips, 2nd = 120 kips. Overturning moment at base = 5,760 kip-ft.

Step 1 -- Trial infill plate thickness. Try 1/4-inch A36 plate. Check slenderness: h/tw = 144 / 0.25 = 576 >> 333 limit for A36. Plate too slender per F5.4. The 12-ft story height requires either a thicker plate or an intermediate stiffener.

Try 3/8-inch plate: h/tw = 144 / 0.375 = 384 > 333. Still too slender.

Try 7/16-inch (0.438 in): h/tw = 144 / 0.438 = 329 < 333. OK, just within limit.

Step 2 -- Tension field strength at the base story (governing case). Clear distance between VBE flanges: Lcf = 24 x 12 - 2 x (12.4 in flange width for W14x132 VBEs, assumed) = 288 - 24.8 = 263.2 in.

For initial iteration, assume alpha = 42 degrees (typical for symmetric SPSW with balanced HBE/VBE stiffness). Vn = 0.42 x 36 x 0.438 x 263.2 x sin(84) = 0.42 x 36 x 0.438 x 263.2 x 0.995 = 1,733 kips.

Design shear strength: phi_Vn = 0.90 x 1,733 = 1,560 kips. This is the wall shear capacity. The base story shear demand is 480 kips. DCR = 480/1,560 = 0.31. Passes. The infill plate at 7/16 in has substantial overstrength.

Step 3 -- Tension field angle refinement. Assume W14x132 VBEs (Ag = 38.8 in^2) and W18x86 HBEs (Ag = 25.3 in^2). tan(2alpha) = (1 + 0.438 x 263.2 / (2 x 38.8)) / (1 + 0.438 x 144 / (2 x 25.3)) = (1 + 115.3/77.6) / (1 + 63.1/50.6) = (1 + 1.486) / (1 + 1.247) = 2.486 / 2.247 = 1.106 2alpha = arctan(1.106) = 47.9 degrees alpha = 24.0 degrees

With alpha = 24.0 degrees: sin(2*alpha) = sin(47.9) = 0.742. Vn_revised = 0.42 x 36 x 0.438 x 263.2 x 0.742 = 1,290 kips. phi_Vn = 0.90 x 1,290 = 1,161 kips. DCR = 480/1,161 = 0.41. Still passes.

Step 4 -- VBE design (capacity-based). Expected plate strength: V_expected = 0.42 x 1.3 x 36 x 0.438 x 263.2 x 0.742 = 1,678 kips.

Vertical component of tension field on VBE per unit height: w_v = 0.42 x Ry x Fy x tp x cos^2(alpha) = 0.42 x 1.3 x 36 x 0.438 x cos^2(24.0) = 0.42 x 1.3 x 36 x 0.438 x 0.835 = 7.20 kips/in.

VBE axial force at base from tension field (accumulated over wall height): P_tf = w_v x 36 x 12 / 2 = 7.20 x 216 = 1,555 kips (each VBE, tension side; compression VBE carries the same magnitude plus gravity).

Gravity load on VBE: P_gravity = 100 kips per story x 3 = 300 kips. P_overturning = M_ot / L_wall = 5,760 / 24 = 240 kips.

Total VBE axial demand (compression side): Pu = 1.2 x 300 + 240 + 1,555 = 2,155 kips.

Check W14x132 at 12 ft unbraced height: KLy = 12 ft (assuming HBE provides lateral bracing). phi_Pn for W14x132 at KLy = 12 ft = phi x Fcr x Ag. With KLy/r_y = 144/3.76 = 38.3, Fcr ≈ 0.658^(50/Fe) x 50. Fe = pi^2 x 29,000/38.3^2 = 195 ksi. Fcr = 0.658^(50/195) x 50 = 45.3 ksi. phi_Pn = 0.90 x 45.3 x 38.8 = 1,582 kips.

DCR = 2,155 / 1,582 = 1.36 -- FAILS for the trial W14x132. Try W14x193 (Ag = 56.8 in^2, ry = 4.05 in): KL/r = 144/4.05 = 35.6, Fe = 226 ksi, Fcr = 46.1 ksi. phi_Pn = 0.90 x 46.1 x 56.8 = 2,356 kips. DCR = 0.91. Passes.

Step 5 -- HBE design (capacity-based). Horizontal component of tension field on HBE per unit length: w_h = 0.42 x Ry x Fy x tp x sin^2(alpha) = 0.42 x 1.3 x 36 x 0.438 x sin^2(24.0) = 0.42 x 1.3 x 36 x 0.438 x 0.165 = 1.43 kips/in.

HBE axial force at wall ends (accumulated from midspan): P_hbe = w_h x Lcf/2 = 1.43 x 131.6 = 188 kips.

HBE also resists gravity beam bending from floor loads. Assume W18x86 composite beam carrying 20 psf dead + 40 psf live at 24 ft tributary: Mu_gravity ≈ 150 kip-ft (approximate, depending on number of infill beams).

Combined check per AISC 360 H1.1: Pr/Pc = 188/(0.90 x 50 x 25.3) = 188/1,138 = 0.165 < 0.2, so use Eq H1-1b: Pr/(2*Pc) + Mrx/Mcx + Mry/Mcy ≤ 1.0. With W18x86 phi_Mnx ≈ 540 kip-ft: 0.083 + 150/540 = 0.36. Passes.

Step 6 -- Drift check. Assume first-order roof drift from 480 kips base shear = 0.75 in (calculated from frame analysis). Second-order drift amplification: theta = P x delta_s / (H x h_tot) = (3 x 300) x 0.75 / (480 x 36 x 12) = 675 / 207,360 = 0.0033. B2 = 1/(1-0.0033) = 1.003 (negligible).

Drift limit: 0.025 x hsx for SDC D = 0.025 x 144 = 3.6 in per story. Roof drift limit: 0.025 x 36 x 12 = 10.8 in. 0.75 in << 10.8 in. Passes.

Result: SPSW with 7/16-inch A36 infill plate, W14x193 VBEs, W18x86 HBEs. The infill plate thickness is governed by the h/tw slenderness limit, not by strength, which gives considerable overstrength reserve. VBE section is governed by capacity-based axial force from the expected infill plate yield strength.

Frequently Asked Questions

What is the difference between steel plate shear walls and conventional braced frames?

SPSW provides higher ductility and more uniform stiffness over the building height compared to braced frames. The infill plate yields in shear across the entire panel, distributing energy dissipation over the full wall height. Braced frames concentrate inelastic action at specific braces. SPSW also provides better architectural flexibility since the wall can be concealed within a partition. SPSW has a higher R factor (R = 7 per ASCE 7-22 Table 12.2-1 for SPSW in SDC D-F) compared to SCBF (R = 6), reflecting its superior ductility.

What is the minimum infill plate thickness for SPSW?

AISC 341-22 Section F5.4 limits infill plate slenderness to h/tw ≤ 2000/√Fy. For a 12-ft story with A36 steel, h/tw = 144/tw ≤ 333, so tw ≥ 0.43 in (7/16 in minimum). For 50 ksi steel, h/tw ≤ 283, so tw ≥ 0.51 in (9/16 in would be next standard). Practically, infill plates are typically 3/16 to 3/8 inch thick for low-rise buildings and up to 1/2 inch for mid-rise. Very thin plates (under 3/16 inch) are difficult to weld without distortion.

How are HBEs and VBEs designed for SPSW?

HBEs (horizontal boundary elements -- beams) and VBEs (vertical boundary elements -- columns) are designed using capacity design principles per AISC 341 Section F5.5. The boundary elements must remain elastic under the forces generated by the fully yielded and strain-hardened infill plate. This requires designing HBEs and VBEs for 1.2 times the forces from the expected infill plate strength (Ry x Fy). The combined axial-flexural interaction is checked using AISC 360 Chapter H. HBE-to-VBE moment connections must be designed as fully restrained (FR) moment connections capable of developing the HBE plastic moment.

When are intermediate stiffeners required for SPSW infill plates?

Intermediate stiffeners (horizontal or vertical) are required when the unstiffened plate slenderness h/tw exceeds the 2000/√Fy limit. Stiffeners divide the panel into sub-panels that individually satisfy the slenderness limit. Stiffeners also increase the elastic shear buckling stress, which increases stiffness under service-level wind loads. At least one intermediate stiffener per panel is common for walls taller than 15 ft per story. The stiffener moment of inertia must satisfy Is ≥ 2.0 x tp^3 x h per AISC 341 F5.4b.

Does this calculator cover coupled SPSW systems?

The current calculator handles single SPSW panels. Coupled SPSW (two walls connected by coupling beams) can be analyzed by modeling each wall independently and then applying the coupling beam forces as point loads at the connection levels. The coupling beam itself acts as a ductile fuse, similar to coupled reinforced concrete shear wall systems, and must be designed per AISC 341 Section F3 for EBF link beams.

Disclaimer (Educational Use Only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All structural designs must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) registered in the project jurisdiction. The site operator disclaims all liability for any loss or damage arising from the use of this page or the associated calculator tool. Results are preliminary -- not for construction.