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Roof-mounted HVAC fan unit: seismic design force and anchor forces with the governing force direction (FEMA P-751 Section 14.3)

Tool	Seismic Equipment Anchorage
Source	Building Seismic Safety Council (2012). 2009 NEHRP Recommended Seismic Provisions: Design Examples. FEMA P-751, Federal Emergency Management Agency, Washington, DC. Section 14.3.3, pp. 14-23 to 14-25.
Level	Professional

Problem

A 3,000 lb HVAC fan unit sits on the roof of a five-story office building near an active fault (S_DS = 1.487). It is bolted to the slab by four cast-in-place anchors on a 7 ft by 5.5 ft pattern, and its centre of gravity is 2 ft above the slab. With a_p = 2.5, R_p = 6.0 and I_p = 1.0, find the seismic design force, the shear per anchor and whether any anchor goes into tension under the strength combinations.

Inputs to Enter

Mounting: floor-mounted, anchored directly; strength design (LRFD)
S_DS 1.487; a_p 2.5, R_p 6.0, I_p 1.0, overstrength factor 2.0; W_p 3,000 lb; attachment and roof height equal (z/h = 1)
Pattern 7 ft by 5.5 ft, 2 anchors per side (4 in all); centre of gravity 2 ft high, no offset

Open the Seismic Equipment Anchorage tool (loaded with this example)

Answers

F_p = 0.4 × 2.5 × 1.487 × 3,000 × (1 + 2) / 6 = 2,231 lb, between 0.3 S_DS I_p W_p = 1,338 lb and 1.6 S_DS I_p W_p = 7,138 lb (book the same); vertical effect 0.2 S_DS W_p = 892 lb (book 892)
Shear per anchor 2,231 / 4 = 558 lb (book 558)
(0.9 − 0.2 S_DS) D + E_h, force across the 5.5 ft spacing: 46.4 lb of bearing per anchor, no tension (book 46 lb, no tension); force along the 7 ft side: 133 lb of bearing
Tool only, force turned through 360°: the largest tension is 63.8 lb on a corner anchor with the force at 51.8° (tan θ = 7 / 5.5), = F_p h √(1/7² + 1/5.5²) / 2 − 0.6026 W_p / 4
With the overstrength factor 2.0 on the horizontal force (anchor in concrete not governed by a ductile steel element): tension 580 lb, shear 1,115 lb
(1.2 + 0.2 S_DS) D + E_h: largest bearing 1,639 lb per anchor

Notes

The tool's default inputs are this case; press Submit. The book checks the two axes only and finds no tension; the diagonal direction puts a small tension on one corner. The book prints 299 lb for its first combination beside an expression that evaluates to 271 lb. The same unit on spring isolators with snubbers (Mounting = floor-mounted on vibration isolators, R_p = 2.0, gap above 0.25 in) gives F_p = 6,692 lb, 2 F_p = 13,383 lb, 3,346 lb of shear, 2,643 lb of tension and 4,218 lb of compression per isolator at 51.8°, against the book's 6,692, 13,384, 3,346, 2,630 and 4,204 (Section 14.3.4; the book's last two are 13 lb below its own expression).