Shear Wall — Engineering Reference

SPSW tension field angle, plate shear capacity φVn, HBE/VBE capacity design, stiffness requirements per AISC 341 Chapter F5. Interactive calculator.

Overview

Steel plate shear walls (SPSW) use thin steel web plates infilled within a boundary frame to resist lateral forces. The web plate is designed to buckle in shear under lateral loading, developing a diagonal tension field that resists story shear — similar to the tension field action in plate girder webs but applied as a lateral-force-resisting system. AISC 341-22 Chapter F5 governs the design of SPSW systems.

The SPSW system consists of three key components:

• Web plate — thin steel plate (typically 1/8 to 3/8 in.) welded to the boundary frame, designed to yield in tension field action
• Horizontal Boundary Elements (HBE) — beams at each floor level that anchor the tension field forces from the web plates above and below
• Vertical Boundary Elements (VBE) — columns at each end that resist the horizontal component of the tension field and carry overturning forces

SPSW provides high stiffness and ductility with R = 7.0 per ASCE 7, making it competitive with SMF (R = 8) and SCBF (R = 6) for seismic applications.

Tension field action in SPSW

When the thin web plate buckles in shear, a diagonal tension field develops at an angle alpha from the vertical:

alpha = arctan(sqrt((1 + t_w x L / (2 x A_c)) / (1 + t_w x h_s x (1/(A_b) + h_s^3/(360 x I_c x L)))))

where t_w is the web plate thickness, L is the bay width, h_s is the story height, A_c and I_c are the VBE area and moment of inertia, and A_b is the HBE area. For typical proportions, alpha is approximately 35-50 degrees from the vertical.

The shear strength of the web plate is:

V_n = 0.42 x F_y x t_w x L_cf x sin(2 x alpha)

where L_cf is the clear distance between VBE flanges. The design strength is phi x V_n with phi = 0.90.

HBE and VBE capacity design

The boundary elements must be designed for the forces generated when the web plates yield at their expected strength (R_y x F_y). This is a capacity design requirement — the boundary elements must remain elastic while the web plate yields.

HBE design forces: The HBE must resist the vertical components of the tension field from the web plates above and below. The net force creates a distributed load on the HBE. For an interior HBE between two story plates:

• Vertical distributed load: w_y = R_y x F_y x (t_w,above x sin^2(alpha_above) - t_w,below x sin^2(alpha_below))
• Axial force from horizontal component of tension field

VBE design forces: The VBE must resist the horizontal component of the tension field as a distributed lateral load plus the axial overturning forces. The VBE is analyzed as a beam-column with the distributed tension field load and the accumulated axial force from all stories above.

Worked example — single-story SPSW

Given: Single-story SPSW, bay width L = 20 ft, story height h = 13 ft, V_u = 300 kip, A36 web plate (R_y = 1.50, F_y = 36 ksi).

1. Web plate thickness: Assume alpha = 42 degrees. V_n = 0.42 x 36 x t_w x (20 x 12 - 2 x 6) x sin(84°) = 0.42 x 36 x t_w x 228 x 0.995 = 3432 x t_w kip. For V_u = 300 kip: t_w = 300 / (0.90 x 3432) = 0.097 in. Use 1/8 in. (0.125 in.) plate.
2. HBE design: Vertical load from tension field = R_y x F_y x t_w x sin^2(alpha) = 1.50 x 36 x 0.125 x sin^2(42°) = 1.50 x 36 x 0.125 x 0.449 = 3.03 kip/ft distributed along the HBE. The HBE must carry this as a uniformly loaded beam plus any gravity loads.
3. VBE design: Horizontal load = R_y x F_y x t_w x sin(alpha) x cos(alpha) = 1.50 x 36 x 0.125 x sin(42°) x cos(42°) = 1.50 x 36 x 0.125 x 0.669 x 0.743 = 3.37 kip/ft distributed along the VBE height. The VBE acts as a cantilever column with this distributed lateral load.

SPSW vs. other lateral systems

Key design considerations

• Web plate material — A36 steel (F_y = 36 ksi) is preferred over A992 for web plates because lower yield strength produces thinner plates that develop tension field action more efficiently. Thinner plates also reduce the capacity design forces on the boundary elements.
• Web plate connections — the web plate is typically connected to the boundary frame with fillet welds or fish plate details. The connection must develop the expected yield strength of the plate (R_y x F_y x t_w per unit length).
• VBE stiffness requirement — AISC 341 F5.4b requires the VBE moment of inertia to be at least: I_c >= 0.0031 x t_w x h_s^4 / L. This ensures the VBE is stiff enough to develop the full tension field across the web plate width.
• Openings — openings in the web plate (for doors, windows, mechanical penetrations) interrupt the tension field and must be reinforced or accounted for by reducing the effective plate area. Circular openings up to approximately D/h_s = 0.30 can be accommodated with local reinforcement.

Common mistakes to avoid

• Designing the web plate for shear without tension field action — the web plate is designed to buckle. Using conventional plate shear capacity (0.60 x F_y x t_w x h) without tension field action drastically underestimates the wall capacity and results in unnecessarily thick plates.
• Under-designing the VBE — the VBE must resist the full horizontal component of the expected tension field forces from all stories above. This creates very large column moments and axial forces. VBE sizing often requires W14x370+ columns for multi-story buildings.
• Using high-strength steel for web plates — higher F_y means thicker plates are needed for the same shear capacity (counterintuitive). Thicker plates also increase the capacity design forces on the boundary elements. A36 is optimal.
• Ignoring the net HBE load from unequal plates — at intermediate floors, the web plates above and below may have different thicknesses. The net vertical pull on the HBE from the difference in tension field forces must be resisted by the HBE in bending.
• Not providing adequate anchorage at the foundation — the base HBE and VBE connections to the foundation must transfer the full tension field forces. The foundation must resist overturning, base shear, and the vertical pull-down from the web plate tension field.

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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.