Diaphragm Design — Chord Forces, Collectors, and Seismic Fpx

A diaphragm is the horizontal structural element (typically a floor or roof) that distributes lateral forces to vertical bracing elements (shear walls, braced frames, or moment frames). In steel buildings, diaphragms are formed by metal deck with or without concrete fill. Diaphragm design is governed by ASCE 7-22 Sections 12.10 and 12.10.1-3 for seismic forces, and by SDI (Steel Deck Institute) standards for deck shear capacity.

Diaphragm classification

Rigid diaphragm: Maximum diaphragm deflection is less than 2x the average story drift (ASCE 7-22 Section 12.3.1). Distributes forces in proportion to the stiffness of the vertical elements. Most concrete-on-metal-deck floors in steel buildings qualify as rigid.

Flexible diaphragm: Maximum diaphragm deflection exceeds 2x the average story drift. Distributes forces in proportion to tributary area, like a simply supported beam. Bare metal deck roofs (without concrete fill) and wood diaphragms are typically flexible.

Semi-rigid: Analysis must account for diaphragm flexibility (rare in practice; usually classified as one or the other).

The classification affects lateral force distribution, accidental torsion calculations, and redundancy provisions.

Seismic diaphragm forces (ASCE 7-22 Section 12.10)

Floor diaphragm force Fpx

Fpx = (sum(Fi, i=x to n)) / (sum(wi, i=x to n)) * wpx    [Eq. 12.10-1]

Subject to bounds: 0.2SDSIewpx <= Fpx <= 0.4SDSIewpx.

Where Fi = story force from vertical distribution, wi = story weight, wpx = weight tributary to the diaphragm at level x.

For a 5-story building with SDS = 1.0 and Ie = 1.0, the minimum diaphragm force is 0.2 _ 1.0 _ wpx = 0.2wpx (20% of floor weight). The upper bound of 0.4wpx often governs at the roof level.

Transfer forces

At levels where vertical elements of the SFRS are discontinuous or change stiffness, transfer forces must be added to the diaphragm design forces. These can be much larger than the Fpx forces and often govern the diaphragm and collector design at podium levels and setbacks.

Chord forces

The diaphragm acts as a deep beam spanning between vertical bracing lines. The top and bottom edges resist the bending moment as a tension-compression couple:

T = C = M_diaphragm / d

Where M_diaphragm = wL^2/8 (for uniform lateral load w, span L between bracing lines), and d = diaphragm depth (building width perpendicular to the force direction).

Chord members are typically the perimeter beams or angles at the slab edge. They must be designed for the chord tension force plus any gravity loads. Connections splicing chord members must transfer the full chord tension through the splice.

Collector design (drag struts)

Collectors gather diaphragm shear and deliver it to the vertical bracing elements. They are required whenever the bracing element does not extend the full depth of the diaphragm.

Collector force diagram: The collector force equals the accumulated difference between the applied diaphragm shear and the shear that enters the bracing element. It varies linearly, peaking at the edge of the bracing element.

ASCE 7-22 Section 12.10.2: Collector elements in SDC C through F must be designed for the overstrength seismic load (Omega_0 * Fpx), where Omega_0 = 2.0 to 3.0 depending on the SFRS type. This requirement often governs collector size and connection design.

Collector connections to braced frames must transfer the full collector force. Bolted or welded connections at the brace-beam-column intersection must be checked for the amplified force.

Metal deck diaphragm shear capacity

SDI DDM04 and AISI S310 provide diaphragm shear strength for common deck configurations:

Capacity depends on: deck gauge, attachment pattern (welds, screws, or powder-actuated fasteners), side-lap connections, span, and concrete fill. The SDI Diaphragm Design Manual provides detailed tables.

Worked example — 4-story office building diaphragm

Given: 4-story steel building, 150 ft x 100 ft plan, typical floor weight wpx = 1500 kips, braced frames on each 100-ft side (2 frames per side). SDS = 0.90, Ie = 1.0, Omega_0 = 2.0 (SCBF). Seismic story force at 3rd floor F3 = 180 kips. Sum of Fi above level 3 = 360 kips, sum of wi above = 4500 kips.

Step 1 — Diaphragm force Fpx: Fpx = (360/4500) _ 1500 = 0.08 _ 1500 = 120 kips. Check bounds: min = 0.2 _ 0.90 _ 1.0 _ 1500 = 270 kips (governs!). Max = 0.4 _ 0.90 * 1500 = 540 kips. Design Fpx = 270 kips (minimum governs, which is common at mid-height floors).

Step 2 — Unit shear in diaphragm: Each braced frame side resists Fpx/2 = 135 kips. The diaphragm spans 150 ft between bracing lines. Unit shear at the braced frame = 135 / 100 = 1.35 kip/ft = 1350 plf. A 20-ga composite deck with 3.25" LW concrete fill provides approximately 1000-1400 plf capacity. Verify with SDI tables -- may need 18-ga deck or closer fastener spacing.

Step 3 — Chord force: Diaphragm moment M = (270/150) _ 150^2 / 8 = 1.80 _ 150^2 / 8 = 1.80 _ 2812.5 = 5062.5 kip-ft. Wait -- distribute total force as uniform load over the 150-ft span: w = 270/150 = 1.80 kip/ft. M = 1.80 _ 150^2 / 8 = 5063 kip-ft. Chord force T = M/d = 5063/100 = 50.6 kips in the perimeter beams along the 100-ft edges. A W18x35 perimeter beam has phiTn = 0.90 _ 50 _ 10.3 = 464 kips >> 50.6 kips. Chord force is easily carried.

Step 4 — Collector force (amplified): If each braced frame is 25 ft wide within the 100-ft building width, the collector must drag forces from the remaining 75 ft. Maximum collector axial force = unit shear _ unbraced width / 2 = 1.35 _ (100-25)/2 = 50.6 kips. Amplified for overstrength: Omega*0 * 50.6 = 2.0 _ 50.6 = 101.3 kips. The collector beam and its connections must resist this axial force in addition to gravity loads.

Metal Deck Diaphragm Design per SDI

The Steel Deck Institute (SDI) Diaphragm Design Manual (DDM04) provides the primary reference for metal deck diaphragm shear capacity. Diaphragm capacity depends on four key variables: deck profile, steel gauge, connection pattern, and concrete fill.

Diaphragm Shear Capacity by Deck Type

The following table provides typical diaphragm shear strengths for common configurations (values are approximate; always verify with SDI DDM04 tables for specific products):

Key observations: (1) Concrete fill increases capacity 3-5x over bare deck. (2) Increasing gauge from 22 to 18 roughly doubles bare deck capacity. (3) The fastener pattern (number and spacing of welds/screws per foot) has a major effect.

Fastener Pattern and Capacity

SDI uses a notation system to describe the fastener pattern. For example, "36/4" means 36-inch deck span with 4 connections per foot of width. Common patterns and their relative capacities:

Side-lap connections (screws or welds at the deck seam between supports) improve diaphragm performance by forcing the deck to act as a continuous shear panel rather than individual flutes.

Flexible vs Rigid Diaphragm Classification

ASCE 7-22 Section 12.3.1 provides the classification criteria:

Flexible diaphragm condition: A diaphragm is flexible if the maximum diaphragm deflection exceeds 2 times the average story drift of the associated vertical elements. This can be determined by comparing calculated diaphragm deflection (using SDI DDM04 methods) with the story drift from the lateral analysis.

Rigid diaphragm condition (concrete-on-deck): Concrete-filled metal deck diaphragms are almost always classified as rigid. The concrete fill provides high in-plane stiffness, and the deflection is typically a fraction of the story drift.

For flexible diaphragms, lateral forces are distributed to vertical elements in proportion to their tributary area. For rigid diaphragms, forces are distributed in proportion to the relative stiffness of the vertical elements. This distinction can dramatically affect the design forces on individual braced frames, particularly in buildings with asymmetrically placed lateral elements.

Chord and Collector Design — Detailed Procedure

Chord Force Calculation

The diaphragm chord force follows from the maximum bending moment in the diaphragm:

T = C = M_max / d_diaphragm

For a simple span diaphragm with uniform lateral load w: M_max = w x L^2 / 8. The chord members (perimeter beams or slab edge angles) must resist this axial force in addition to their gravity loads.

Chord Splice Design

Chord members are typically spliced at beam-to-beam connections. Each splice must transfer the full chord tension force. For a chord force of 50 kips:

• Bolted splice: 50 / 17.9 = 2.8, use 4 bolts (3/4" A325-N) with a splice plate area of 50 / (0.90 x 50) = 1.11 in^2 minimum.
• Welded splice: 50 / (0.75 x 70 x 0.707) = 1.35 in of 1/4" fillet weld per inch of force, so a 6" long x 1/4" fillet weld on each side (2 x 6 x 0.75 x 70 x 0.707 x 0.25 = 111 kips capacity).

Collector Design with Overstrength

For SDC C through F, ASCE 7-22 Section 12.10.2 requires collectors to be designed for Omega_0 x Fpx. The amplified collector force often exceeds 100 kips for mid-rise buildings:

The amplified collector force often requires heavy connections at the collector-to-brace-frame interface. Standard single-plate shear connections are rarely adequate. Bolted flange plates, welded flanges, or special collector connections designed per AISC 358 principles are typically required.

Concrete-Topped Diaphragm Design

Concrete fill on metal deck dramatically increases diaphragm shear capacity and stiffness. Two fill types are common:

The concrete fill acts as a deep shear panel with the metal deck serving as tensile reinforcement. Cracking of the concrete under service-level seismic loads is expected but does not represent failure; the deck continues to carry shear through membrane action.

Concrete-topped diaphragms are required in most seismic applications (SDC C and above) because bare metal deck does not provide sufficient stiffness or capacity for the amplified forces.

Seismic Diaphragm Requirements per ASCE 7

ASCE 7-22 imposes several additional requirements for diaphragms in seismic design categories C through F:

1. Minimum force: Fpx >= 0.2 x SDS x Ie x wpx (Eq. 12.10-1 lower bound)
2. Maximum force: Fpx <= 0.4 x SDS x Ie x wpx (Eq. 12.10-1 upper bound)
3. Collector amplification: Omega_0 x collector force in SDC C-F (Section 12.10.2)
4. Transfer forces: additive to Fpx at discontinuity levels (Section 12.10.3)
5. Redundancy factor: rho = 1.3 for non-redundant systems (Section 12.3.4)
6. Diaphragm design: must be designed for the greater of Fpx or story shear from analysis
7. Connection requirements: diaphragm-to-LFRS connections must develop the design force (Section 12.12)

For buildings in SDC D, E, and F, the diaphragm design forces are typically 20-40% of the floor weight, which can produce significant collector and chord forces requiring careful connection design.

Multi-code comparison

ASCE 7-22 (USA): Diaphragm forces per Section 12.10 (Eq. 12.10-1) with 0.2SDS and 0.4SDS bounds. Collectors amplified by Omega_0 in SDC C-F per Section 12.10.2. Rigid/flexible classification per Section 12.3.1. New ASCE 7-22 alternative diaphragm design provisions in Section 12.10.3 provide a more rational force distribution based on diaphragm ductility (Rs and Cd,dia factors).

AS 1170.4-2007 (Australia): Diaphragm design forces are derived from the equivalent static method (Section 6.3) or dynamic analysis. There is no explicit Fpx equation with upper/lower bounds like ASCE 7. Instead, the diaphragm must resist the story shear from the lateral analysis. AS 4100 Clause 9.1.4 addresses diaphragm connections. Collector (drag strut) design follows from equilibrium; no explicit overstrength amplification factor is prescribed, though capacity design principles apply in high-seismicity regions (as per NZS 1170.5 in New Zealand).

EN 1998-1 (Europe): Clause 4.4.2.5 requires that floor diaphragms distribute seismic forces to vertical elements. Diaphragms are assumed rigid if their deformation does not significantly affect force distribution (Clause 4.3.1(3)). No tabulated Fpx formula -- forces come from the modal analysis or lateral force method. Collector elements must satisfy capacity design requirements: their strength must exceed the overstrength plastic resistance of the connected dissipative elements (Clause 6.5.5). gamma_ov = 1.25 for capacity design in DCM/DCH frames.

NBCC 2020 / CSA S16-19 (Canada): Diaphragm design forces per NBCC Clause 4.1.8.15. CSA S16 Clause 27.1.5 requires diaphragms to transfer seismic forces between stories. Capacity design applies: collectors and their connections must be designed for the probable resistance (R_y*Fy) of the braces or frame elements. CSA S16 Clause 27.5.4.2 requires collector connections in ductile braced frames to develop the probable brace resistance.

Common mistakes

1. Forgetting the minimum diaphragm force. The Fpx lower bound (0.2SDSIe*wpx) often governs at upper floors where the vertical distribution force Fi is small. In many buildings, the minimum force governs at every floor except the roof, meaning the diaphragm design force is significantly higher than the story shear from vertical distribution.

2. Not designing collectors for overstrength. In SDC C-F, collectors must use Omega_0 amplified forces (ASCE 7-22 Section 12.10.2), which can be 2-3x the basic seismic force. Standard shear connections at the collector-to-brace-frame interface are almost never adequate for the amplified collector force -- bolted flange plates or welded flanges are typically required.

3. Ignoring transfer forces at discontinuities. Podium levels, setbacks, and bracing offsets generate large transfer forces that must pass through the diaphragm. Transfer forces are additive to the Fpx forces and frequently govern the diaphragm and collector design at transition levels. They are not subject to the 0.2*SDS lower bound.

4. Using bare deck capacity for a filled deck (or vice versa). Concrete fill dramatically increases diaphragm shear capacity (typically 3-5x bare deck). Using unfilled capacity for a composite deck wastes material; using filled capacity for an unfilled deck is unconservative and dangerous.

5. Not detailing chord splices for tension. Standard beam splices designed for gravity loads may not transfer the diaphragm chord tension force. At each splice, the bolted or welded connection must be checked for the chord tension (often 20-80 kips for typical buildings) in combination with the gravity shear.

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Related references

• Load Combinations ASCE 7
• Braced Frame Design
• Gusset Plate Design
• Steel Connection Types
• Load Path
• How to Verify Calculations

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against ASCE 7-22 Section 12.10 and SDI DDM04. The site operator disclaims liability for any loss arising from the use of this information.