The biggest change from ASCE 7-16 to 7-22 in nonstructural design is the replacement of the old (1 + 2z/h) height term and the lumped ap/Rp coefficients with two distinct factors: Hf for height amplification and Rμ for the host building's ductility. This article explains where the new factors come from, how to read Table 13.3-1, and why a chiller on the roof of a stiff building is now significantly more demanding than the same chiller under ASCE 7-16.

What replaces what

  • (1 + 2 z/h) → Hf per Eq. 13.3-4 (now period-dependent).
  • ap → CAR from Tables 13.5-1/13.6-1 (component resonance amplification).
  • Rp → Rpo · Rμ (component over-strength × structure ductility).

The split exposes two effects that were previously buried in one coefficient: how stiff the host building is (Rμ) and how the floor accelerates with height (Hf).

Hf — height amplification factor (Eq. 13.3-4)

Hf is computed from the building's approximate fundamental period Ta per Section 12.8.2.1, the elevation of the component z, and the building height h:

  • For Ta ≤ 2.5 s: Hf = 1 + a1·(z/h) + a2·(z/h)10, where a1 = 1/Ta ≤ 2.5 and a2 = (1 − (0.4/Ta)2) ≥ 0.
  • For Ta > 2.5 s: Hf = 1 + 2.5·(z/h).

Practical numbers for typical buildings:

  • 4-story stiff steel building, Ta ≈ 0.4 s → at z/h = 0, Hf = 1.0; at z/h = 0.5, Hf ≈ 2.25; at z/h = 1.0 (roof), Hf = 3.5 (capped if > 2.5).
  • 10-story moment frame, Ta ≈ 1.0 s → at z/h = 1.0, Hf ≈ 2.0.
  • 30-story flexible building, Ta = 3.0 s → at z/h = 1.0, Hf = 1 + 2.5·1 = 3.5.

Note that the cap at 2.5·(z/h) keeps very tall flexible buildings from producing unbounded amplification.

Rμ — structure ductility reduction factor

Rμ is from Table 13.3-1 indexed by the host building's SFRS (Seismic Force-Resisting System):

  • Stiff systems (cantilever column, ordinary plain masonry) → Rμ close to 1.0 — meaning Fp goes UP because the building does not absorb energy.
  • Ductile special moment frames → Rμ ≈ 1.5 — meaning Fp goes DOWN because the building absorbs more energy in its own yielding.
  • Steel buckling-restrained brace frames → Rμ ≈ 1.4.
  • Special concrete shear walls → Rμ ≈ 1.4.

The two-factor effect on Fp

From Eq. 13.3-1, Fp scales linearly with Hf/Rμ. The same chiller on the roof has Fp ratio:

  • Stiff steel building, Ta = 0.4 s, ordinary moment frame Rμ = 1.0 → factor = 2.5/1.0 = 2.50.
  • Same building height with special moment frame, Rμ = 1.5 → factor = 2.5/1.5 = 1.67.
  • Tall flexible MF, Ta = 2.0 s → Hf ≈ 1 + 0.5·1.0 + 0 = 1.5; Rμ = 1.5 → factor = 1.0.

The same equipment on the same roof has 2.5× the demand in a stiff building vs the flexible one. This is why your old-OPM tables that do not encode the SFRS are inadequate under ASCE 7-22.

Worked example — rooftop chiller, hospital, special moment frame

  • SDS = 1.5 g, Ip = 1.5, Wp = 5,000 lb.
  • Building Ta = 0.6 s; z/h = 1.0.
  • a1 = min(1/0.6, 2.5) = 1.67; a2 = max(0, 1 − (0.4/0.6)2) = 1 − 0.444 = 0.556.
  • Hf = 1 + 1.67·1.0 + 0.556·1.0 = 3.22.
  • Rμ = 1.5 (special MF). CAR = 1.0; Rpo = 1.5.
  • Fp = 0.4 · 1.5 · 1.5 · 5,000 · (3.22/1.5) · (1.0/1.5) = 6,440 lb.
  • Fp,max = 1.6 · 1.5 · 1.5 · 5,000 = 18,000 lb (does not govern).
  • Fp,min = 0.3 · 1.5 · 1.5 · 5,000 = 3,375 lb (does not govern).
  • Design Fp = 6,440 lb.

Why this changes the OPM-style tables

Old OPM tables indexed by SDS and z/h alone are no longer sufficient under ASCE 7-22. The same z/h on a stiff vs ductile building yields different demands. HCAI's PIN 62 update reflects this — see our PIN 62 guide.

Common mistakes

  • Using the old (1 + 2 z/h) instead of computing Hf from Ta.
  • Using Rμ = 1.5 by default, ignoring the SFRS.
  • Dropping the a2·(z/h)10 term — at the roof, it can add 0.5 to Hf.
  • Using Hf > 2.5 on a building with Ta > 2.5 s — the cap applies.

How PANACHE ENGINEERING handles this

Our calculator pulls Ta and the SFRS from the project's structural drawings, computes Hf and Rμ, and propagates them into Fp for every component. See our ASCE 7-22 Chapter 13 guide or request a stamped calculation.