Seismic nonstructural components
The horizontal seismic design force Fp on an architectural, mechanical or electrical component and its attachments by ASCE/SEI 7-22 Chapter 13, with the height factor Hf, the structure ductility factor Rμ, the component factors CAR and Rpo, the limits of Eqs. 13.3-2 and 13.3-3, the vertical force, the overstrength force for anchors, the anchor forces of a rigid component on four supports and the relative displacement DpI. It is an analysis: the result reads Calculated.
Inputs of the nonstructural component #
- Seismic hazard and structure: SDS; the seismic design category of the structure the component is in or on (13.1.2; it drives the Table 13.1-1 exemptions); the risk category of the structure (Ie of Table 1.5-2, used in Rμ and DpI); the seismic force-resisting system of the structure (R and Ω0 of Table 12.2-1 for Rμ, not specified or not listed for Rμ = 1.3, or entered; with several systems choose the one that gives the lowest Rμ); the average roof height h; and Hf by Eq. 13.3-4 with the approximate period Ta (Ct hn^x of Table 12.8-2 with hn taken as h, or entered: the lowest Ta of the two directions) or by Eq. 13.3-5 where the period is not known.
- Component: the row of Table 13.5-1 (architectural) or Table 13.6-1 (mechanical and electrical components, vibration-isolated components, equipment support structures and platforms, distribution system supports and distribution systems) giving CAR (at or below grade plane, or above grade plane by a structure), Rpo and Ω0p, or entered values. For vibration-isolated rows, the restraint air gap over 0.25 in. doubles the design force (Table 13.6-1 note a). The component importance factor Ip (13.1.3: 1.5 for life-safety components such as sprinklers and egress stairs, hazardous contents, or Risk Category IV operation; yours), the operating weight Wp, where it is supported (above grade plane: Hf and Rμ apply; at or below grade plane: Hf = Rμ = 1.0 and the grade CAR), the height of the point of attachment z, and the CAR of a supporting platform (13.3.1.3: the component's CAR is not less than the platform's).
- Anchorage: for a rigid component on four support points at the corners of an a × b rectangle, the spacings a and b, the height of the center of gravity above the attachments hcg and the number of anchors per support point.
- Relative displacement: none, Eq. 13.3-10 from the height between attachments and the allowable drift ratio of Table 12.12-1, or Dp entered (Eq. 13.3-9 or 13.3-11).
Checks performed #
| Check | Basis |
|---|---|
| Height factor Hf | Eq. 13.3-4, Hf = 1 + a1 (z/h) + a2 (z/h)^10 with a1 = 1/Ta ≤ 2.5 and a2 = 1 − (0.4/Ta)² ≥ 0, or Eq. 13.3-5, Hf = 1 + 2.5 (z/h); z/h ≤ 1.0; 1.0 at or below grade plane (13.3.1.1) |
| Ductility factor Rμ | Eq. 13.3-6, Rμ = (1.1 R / (Ie Ω0))^½ ≥ 1.3; 1.3 where the system is not specified or not listed; 1.0 at or below grade plane (13.3.1.2) |
| Component factors | CAR and Rpo (13.3.1.3, 13.3.1.4), Ω0p (13.4.2) from Tables 13.5-1 / 13.6-1; CAR not less than the platform's |
| Fp | Eq. 13.3-1, Fp = 0.4 SDS Ip Wp (Hf / Rμ)(CAR / Rpo), not more than 1.6 SDS Ip Wp (Eq. 13.3-2) nor less than 0.3 SDS Ip Wp (Eq. 13.3-3); 2Fp for isolated components with an air gap over 0.25 in. |
| Vertical force | Ev = 0.2 SDS Wp concurrent with Fp (13.3.1.6, Eq. 12.4-4a); Fp is QE with ρ = 1.0 (13.2.2) |
| Design forces | Eh, Ω0p Eh (13.4.2, where the overstrength is required for anchors in concrete or masonry), 0.7 Eh for ASD (2.4, 13.1.8) |
| Anchorage forces | Overturning Eh hcg resisted by the support points: force along either side (M/2b, M/2a) or diagonally ((M/2)(cos θ/b + sin θ/a), θ = tan⁻¹(b/a), the FEMA P-2192 method); tension with (0.9 − 0.2 SDS)D (LRFD) or (0.6 − 0.14 SDS)D (ASD), compression with (1.2 + 0.2 SDS)D or (1.0 + 0.14 SDS)D; shear Eh / 4; with and without Ω0p |
| Relative displacement | Eq. 13.3-10, Dp = (hx − hy) ΔaA / hsx, or entered; DpI = Dp Ie (Eq. 13.3-8) |
| Exemptions | The Table 13.1-1 row that may exempt the component (SDC A; SDC B; SDC C to F weight, attachment and Ip conditions), named for you to confirm |
The drawings show the building elevation (schematic) with the attachment height z and the roof height h, and the component elevation (schematic outline: its size is not an input) with the center of gravity, the design force and the gravity and vertical force, the support spacing, hcg and the anchor forces.
Limitations #
- Components of 20 % or more of the combined effective seismic weight (13.1.1, 13.2.9) and Eq. 13.3-7 (accelerations from a nonlinear response history analysis) are outside this calculation.
- The anchor design itself (ACI 318-19 Chapter 17 with the 17.10 seismic requirements, TMS 402 for masonry, ACI 355.2 qualification of post-installed anchors), prying (13.4.3), friction clips and power-actuated fasteners (13.4.5, 13.4.6) are yours; use the concrete anchor calculation for anchors in concrete.
- The anchorage forces assume a rigid component on four support points; flexible components, more support points, isolator snubbers and their supporting frames are not analysed.
- The design of the component, its support structure or platform, distribution system braces and hangers is not part of the calculation; the force on a brace is Fp of the tributary weight entered as Wp.
- The 13.2.9 expression for a combined system is garbled in the text copy on file (to confirm against the code text); it is not used.
Verification examples #
Verification status: 77 values compared in 18 examples (15 published, 3 hand calculations from the cited equations): 77 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
FEMA P-2192-V1 (2020 NEHRP Provisions Design Examples, Chapter 8) works its examples with the ASCE 7-22 equations. FEMA prints Hf, Rμ and the coefficients rounded and multiplies with the unrounded values; periods are compared to 0.01 s.
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| 8.3-PANEL | Precast spandrel panel, steel SMF building, z/h = 40.5/67.5, SDS 1.487 (pp. 339 to 349) | Ta 0.81 s, a1 1.23, a2 0.76, Hf 1.74 (2.50 by Eq. 13.3-5), Rμ 1.71, 0.403 Wp, max 2.379 / min 0.446 Wp, Fp 4,570 lb, Ev 3,047 lb | same |
| 8.3-FASTENERS | Fasteners of the connecting system (CAR 2.8, Ω0p 1.0) (p. 350) | 1.129 Wp, Fp 11,568 lb | same |
| 8.4 | Egress stair, Ip = Ie = 1.5, Ta of the braced frame and Rμ of the moment frame (pp. 370 to 378) | Ta 0.484 s, Hf 2.03, Rμ 1.40 (1.48 SCBF), 0.582 Wp; flight 410 / landing 298 lb, Ev 141 / 103 lb; fasteners 1.280 Wp, 903 / 657 lb; DpI 2.52 in. | same |
| 8.5-FAN | HVAC fan on the roof, ordinary masonry walls, SDS 0.474 (pp. 383 to 388) | Ta 0.29 s, a1 2.5, a2 0, Hf 3.5, Rμ 1.3, 0.357 Wp, Fp 1,072 lb, Ev 284 lb, Vu 268 lb, bolt force −409 lb (compression) | same |
| 8.5-ISOLATED | Same fan on spring isolators, 2Fp (pp. 390 to 393) | 0.864 Wp, Fp = Fp,max 2,275 lb, 2Fp 4,550 lb, tension 448 lb, compression 2,023 lb, Vu 1,138 lb; with Ω0p 1,237 / 1,991 lb | same |
| 8.6 | Threaded piping and hot-rolled bracing on a BRBF roof, Ip 1.5 (pp. 405 to 416) | Ta 0.38 s, Hf 3.5, Rμ 1.53, 1.508 Wp (24.7 / 47.8 plf), supports 0.914 Wp, longitudinal brace 2,318 lb | same |
| 8.7 | Elevated vessel and its platform, CAR raised to 1.4 (pp. 432 to 444) | Ta 0.353 s, Hf 2.52, Rμ 1.48, 0.762 Wp, Fp 3,808 lb, Ev 1,200 lb; platform 762 / 240 lb | same |
FEMA's tension case "LC6" uses 1.2D − Ev, which is not an ASCE 7 combination; the program uses (0.9 − 0.2 SDS)D for uplift, and the LC7 tensions and LC6 compressions match. Hand calculations: a component at grade (Hf = Rμ = 1.0, grade CAR, Fp 4,800 lb), a structure system not specified with Eq. 13.3-5 (Hf 2.25, Rμ 1.3, Fp 775.4 lb) and ASD anchor forces (minimum Fp 1,200 lb, −145 lb, 210 lb), all exact.