Diaphragm forces
The in-plane seismic design force of a diaphragm, level by level, to ASCE 7-22 12.10, with the unit shear, chord and collector forces for a rectangular diaphragm spanning between two lines of vertical elements. Results are at strength level, with the 0.7 level beside them for allowable stress work. Copy them into the Wood diaphragm or other material calculation, which does the material checks: nothing links the two. Run one calculation per direction, since wpx and the span differ.
Inputs of the diaphragm forces #
- Design method: 12.10.1 and 12.10.2; the alternative of 12.10.3, which 12.10 requires for precast concrete diaphragms in SDC C to F and permits for others it lists; or 12.10.4, for one-story wood panel or bare steel deck diaphragms on rigid walls within the limitations of 12.10.4.1. Which applies is your decision.
- Seismic parameters: SDS, SD1, Ie and the Seismic Design Category; Ω0 (Table 12.2-1); whether the structure is braced entirely by wood light-frame shear walls (the collector exceptions); for 12.10.3, Cs and the system (zs); for 12.10.4, the diaphragm (Rdiaph, Tdiaph).
- Levels, from the top down: the height, seismic weight w, weight tributary to the diaphragm wpx (0 means w), and the story force Fx from Seismic base shear or your analysis; any transfer force, with the Type 4 box where Ω0 applies to it (12.10.1.1); and Rs for the alternative method (Table 12.10-1, in the table so that a roof and floors can differ). wpx may leave out the walls parallel to the force; the examples do.
- Diaphragm: the span L between the vertical elements, the depth B, the length the collector gathers (0 for none) and a reaction factor over w L / 2 for a share your analysis gives, such as torsion on a rigid diaphragm. It defaults to 1.0.
Checks performed #
| Result | Basis |
|---|---|
| Fpx, traditional | Eq. 12.10-1, not less than Eq. 12.10-2, need not exceed Eq. 12.10-3 |
| Fpx, alternative | Eq. 12.10-4 and the minimum of Eq. 12.10-5; Cpx from Fig. 12.10-2, Eqs. 12.10-6 to -14; Rs of Table 12.10-1 |
| Fpx, one story | Eqs. 12.10-15, -16a, -16b; Rdiaph and Tdiaph by the diaphragm |
| Transfer force | Added at the level; with Ω0 at a Type 4 irregularity (12.10.1.1, 12.10.3.3) |
| Shear, chord | w = Fpx/L; V = w L / 2 × the reaction factor; v = V/B; M = w L²/8; chord = M/B. With 12.10.4: 1.5 v, over the span if L is under 100 ft, else a boundary zone of at least 0.10 L each end (12.10.4.2.2) |
| Collector, traditional | 12.10.2.1: the greatest of the diaphragm's share of Fx (Fx × wpx / w) with Ω0, Eq. 12.10-1 (held to Eq. 12.10-3) with Ω0, and Eq. 12.10-2 without; no Ω0 in SDC B or with the wood light-frame exception |
| Collector, alternative | 12.10.3.4: 1.5 × inertial and transfer forces; a transfer already with Ω0 is not amplified; none in SDC B or with the light-frame exception |
| Collector, one story | 12.10.4.2.4: Ω0-diaph = 2, not over Rdiaph; not combined with the 1.5 shear amplification |
Collector forces are v × length × the amplification, the way the examples work them. Each result reads Calculated. The drawing is a plan of the level with the largest unit shear.
Limitations #
- A rectangular simple span with uniform force. Openings, reentrant corners, multi-span diaphragms and force distribution to more than two lines need your analysis: the reaction factor is the only way in here.
- Material strength, deflection and drift are not checked. The limitations of 12.10.4.1 and Exception 2 of 12.10.3.4 (frame strength as a cap) are yours, and so is the capacity-limited effect of 11.3. Collector forces are horizontal only: combine them with gravity and vertical seismic effects.
- The story forces are entered. So is the upper-level share where the analysis is modal.
- The 12.10-4 minimum and limits use the wpx of the row. 12.3.3.5 and other irregularity rules are not applied, except Type 4 on transfers.
Verification examples #
Verification status: 75 values compared in 11 examples (10 published, 1 hand calculations from the cited equations): 73 within tolerance, 2 recorded deviations. Code basis: the provisions it uses were read in the target edition.
All published values are from FEMA P-2192-V1 (2020), Chapter 7, written to ASCE 7-22. (PDF pages.)
| Example | Pages | Values |
|---|---|---|
| One-story wood hall, 7.4, both directions and both methods | 267 to 272 | Fpx 19,072 and 17,072 lb; limits; 14,647 and 13,111 lb from the equation; ASD 13,350 and 11,950 lb; Cpn 0.576 |
| Six-story steel building, 7.5, traditional | 273 to 278 | Six levels of Eq. 12.10-1, design forces, roof limits, V, v, collector 76 and 127 kips |
| Six-story steel building, 7.5, alternative | 278 to 283 | Γm1, Γm2, Cp0, Cpi, Cs2, Cpn, Cpx and Fpx at each level, roof v, collector 146 kips |
| RWFD, 7.6, traditional | 286 to 290 | Fpx 1,712 and 1,459 kips, v 2.37 klf, moment, chord 356 kips, collector 533 kips |
| RWFD, 7.6, by 12.10.4, both directions | 291 to 294 | Tdiaph, Cs-diaph, Fpx 1,266 and 1,296 kips, v 1.76 and 2.64 klf, chord 264 kips, collector 317 kips |
One documented deviation: at level 6 of the alternative example, P-2192 gets Cpx = 0.60 by dividing by 12 ft, while Fig. 12.10-2 interpolates over the 14.4 ft from 0.8hn to hn. The program gives 0.58 and so about 457 kips where the example has 471 kips.
A hand calculation covers a transfer force with Ω0. No published example here covers a transfer force or the alternative collector rule for it; those rest on the code text.