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.

Steel Plate Shear Walls (SPSW) per AISC 341 — Design Philosophy

Steel plate shear walls represent a fundamental departure from conventional lateral-force-resisting systems in that the primary energy-dissipating element — the thin web plate — is designed to buckle and yield rather than remain elastic. This philosophy leverages the post-buckling strength of thin steel plates through diagonal tension field action, providing both high initial stiffness and excellent ductility. AISC 341-22 Chapter F5 codifies this approach for seismic design, requiring capacity design of all boundary elements to remain elastic while the web plates yield at their expected strength.

The design philosophy of SPSW is rooted in three principles:

1. Web plates as structural fuses — the thin web plates are the designated yielding elements, absorbing seismic energy through repeated tension field cycling. Because the plates are thin and easily replaceable, they serve as structural fuses that protect the more costly boundary elements from damage.

2. Capacity-designed boundary elements — all forces used to design HBEs and VBEs are derived from the expected yield strength of the web plates (R_y x F_y), not from the computed seismic forces. This ensures the boundary elements remain elastic even during maximum considered earthquake events, maintaining the structural integrity of the frame.

3. Redundancy and overstrength — the system relies on the distributed yielding across the full web plate area, not on a single hinge or brace. This distributed yielding provides inherent redundancy that improves seismic performance beyond what single-element systems can achieve.

Strip Model for Analysis

The strip model is the standard analytical approach for SPSW design. In this model, the web plate is replaced by a series of inclined tension-only strips that represent the diagonal tension field. Each strip is oriented at the tension field angle alpha and carries only axial tension (no compression), accurately representing the post-buckling behavior of the thin plate.

The strip model procedure involves:

• Dividing the web plate into a minimum of 10 strips spanning between the HBE and VBE flanges
• Assigning each strip an area equal to (t_w x L_cf) / n_strips, where n_strips is the number of strips
• Orienting all strips at angle alpha (computed from the geometry and boundary element stiffness)
• Analyzing the resulting frame-strip system under the applicable load combinations
• Checking that boundary element demands remain below their design strengths

The strip model can be implemented in standard structural analysis software by modeling each strip as a truss element with tension-only behavior. This approach automatically captures the interaction between the boundary frame flexibility and the tension field distribution, providing more accurate results than simplified hand calculations.

For multi-story SPSW, the strip model analysis is essential because the tension field forces from upper stories accumulate in the VBEs, creating column moments and axial forces that cannot be estimated by simple statics alone. The VBE must be designed as a beam-column with the full distributed load from all web plates above.

Capacity Design Requirements

AISC 341 F5 imposes strict capacity design requirements on the boundary elements. The key requirements are:

HBE (Horizontal Boundary Elements):

• Must resist the vertical component of the tension field from web plates above and below, computed using the expected yield stress R_y x F_y
• Must also resist the axial force from the horizontal component of the tension field
• Must be designed for combined bending and axial force as a beam-column
• The HBE flange connection to the VBE must develop the full plastic moment of the HBE (connection must be as strong as the HBE)
• HBE must be compact per AISC 360 Table B4.1b

VBE (Vertical Boundary Elements):

• Must resist the horizontal component of the tension field as a distributed load along the column height
• Must resist the accumulated overturning axial force from all stories above
• Minimum stiffness requirement: I_c >= 0.003 x t_w x h_s^4 / L (ensures uniform tension field development)
• Must satisfy the column stability requirements of AISC 360 Chapter E
• VBE splices must develop the full column strength

Web Plate Connections:

• Must develop the expected yield strength of the web plate: R_y x F_y x t_w per unit length
• Typically achieved with fillet welds on both sides of the plate
• Fish plate details (a thinner connecting plate welded to the boundary element with the web plate bolted to the fish plate) are used when field bolting is preferred over field welding

Concrete Shear Wall vs. Steel Plate Shear Wall — Comparison

The choice between concrete shear walls and steel plate shear walls is driven by structural performance requirements, architectural constraints, construction sequence, and cost. Both systems provide high lateral stiffness and are suitable for medium-to-high-rise buildings, but they differ fundamentally in behavior, construction methodology, and post-earthquake repairability.

Key Behavioral Differences

Concrete shear walls resist lateral forces through a combination of flexural resistance (concentrated at the wall boundary elements) and shear resistance (distributed across the web). Under cyclic seismic loading, concrete walls develop flexural cracks at the base and diagonal shear cracks across the web. While special shear walls (per ACI 318) are detailed for ductility with confined boundary elements, the cracking and spalling that occurs during a design-level earthquake requires significant repair.

Steel plate shear walls resist lateral forces entirely through tension field action in the web plate. The plate buckles in shear at relatively low loads, after which the diagonal tension field engages and provides both strength and stiffness. Under cyclic loading, the web plate yields in alternating diagonal directions, dissipating energy through repeated plastic straining. Because the boundary elements remain elastic (capacity design), the post-earthquake repair consists of removing the yielded web plates and welding in new ones — a straightforward operation compared to concrete wall repair.

The tension field mechanism also provides inherent damping. As the web plate cycles through tension field reversals, the hysteresis loops are full and stable, providing energy dissipation that is comparable to or better than buckling-restrained braces. This makes SPSW particularly effective for near-fault seismic regions where large velocity pulses demand high energy dissipation.

When SPSW Is Preferred

Steel plate shear walls are the preferred lateral system in the following scenarios:

High Seismic Regions: SPSW provides R = 7 (comparable to SMF at R = 8) with significantly better drift control. In regions of high seismicity (SDC D, E, F), the combination of high ductility and high stiffness makes SPSW competitive with dual systems for buildings 10-30 stories tall.

Architectural Constraints: When the architect requires solid wall panels (for party walls, elevator/stair cores, or acoustic separation), SPSW uses the same bay footprint as a concrete wall but with less depth and much less weight. The wall panels can be finished with drywall directly on the steel plate, or the web plate can serve as backing for architectural finishes.

Retrofit and Strengthening: SPSW is an effective retrofit strategy for existing steel moment frames that require increased lateral stiffness and strength. The web plates can be welded into existing bays without adding significant weight to the structure or increasing foundation demands.

Construction Schedule: In fast-track construction where concrete curing time is a schedule constraint, SPSW can be erected as part of the steel frame with no wet trades, no formwork, and no curing time. The web plates are typically shop-welded to the boundary elements and delivered as prefabricated panels.

Low Foundation Capacity: Because SPSW is much lighter than concrete shear walls, the overturning moment at the foundation is reduced. This is particularly advantageous for buildings on poor soil where foundation costs are a significant portion of the total structural cost.

Post-Earthquake Repairability: In regions where building downtime after an earthquake must be minimized (hospitals, data centers, emergency operations centers), SPSW offers the advantage of rapid web plate replacement without the extensive concrete repair required for cracked shear walls.

Design Example Overview — Multi-Story SPSW

Consider a 5-story office building in SDC D with SPSW as the lateral system. The following outlines the plate thickness selection and boundary element force determination.

Building Parameters:

• Bay width L = 24 ft, story height h_s = 13 ft
• Design story shears (from seismic analysis): V_u = {250, 220, 180, 130, 70} kip (from roof to ground)
• Web plate material: A36 (F_y = 36 ksi, R_y = 1.5)

Plate Thickness Selection:

For each story, the required web plate thickness is determined from:

t_w = V_u / (phi x 0.42 x F_y x L_cf x sin(2 x alpha))

Note: The minimum practical plate thickness is typically 3/16 in. (0.188 in.) for handling and welding. Even though the upper stories only require 0.023-0.058 in., a 3/16 in. plate is specified as the minimum. The ground floor requires a 1/4 in. plate.

Boundary Element Forces (Ground Floor VBE):

The VBE at the ground floor must resist the accumulated horizontal tension field from all five stories:

w_total = R_y x F_y x sum(t_w,i x sin(alpha_i) x cos(alpha_i))

For uniform alpha = 42 degrees:

w_total = 1.5 x 36 x sin(42) x cos(42) x (0.188 + 0.188 + 0.188 + 0.250 + 0.250)
        = 1.5 x 36 x 0.669 x 0.743 x 1.064
        = 28.6 kip/ft per VBE

This distributed load over a 13 ft story height produces a maximum moment in the VBE of approximately w x h_s^2 / 8 = 28.6 x 13^2 / 8 = 604 kip-ft. Combined with the axial force from overturning (approximately 800 kip), this typically requires a W14x370 or larger column for the ground-floor VBE.

The key insight from this example is that the boundary element sizes are driven by the capacity design forces (using R_y x F_y), not the seismic design forces. Even though the web plates are thin, the accumulated tension field forces over multiple stories create very large demands on the VBEs.

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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.