Pipe Trapeze / Strongback Hanger Calculator (Channel Size, Rod Size, Max Spacing) — Sample Report

1 · Design inputs

The rack that prompted the tool: four 30" sch 10 304 SS cooling-tower water headers (water-filled), carried on back-to-back channel strongbacks 144 in wide (pipes on 36" centres), strongbacks every 10 ft, two rods each. What channel, what rod, and is 10 ft spacing OK?

2 · Method

w_rack = Σ n·(w_pipe + w_contents) + extra [lb/ft] → P = w_rack·S per strongback

Pipes are placed at equal centres across the rod-to-rod width W with half-gap edge margins, heaviest nearest midspan. Each rod-to-rod segment is analysed as a simple span (continuity over interior rods ignored — conservative for bending):

M_max from exact point-load statics; V_max = max end reaction; δ_mid = Σ P·b·(3L² − 4b²)/48EI

The channel (half the demand per channel for a back-to-back pair) runs through the full AISC 360-22 member check: F2 flexure with lateral-torsional buckling over L_b = the rod-to-rod span (C_b = 1.0, conservative), G2 shear, and the deflection limit. Auto-select sweeps the C then MC families lightest-first and returns the first section that passes.

Rod: A_root = 0.7854·(D − 1.3/n)² → capacity = A_root·S_allow (default 11.6 ksi)

With two rods the rod load is the exact simple-span reaction; with three or four, rods take tributary width and interior rods carry a 1.25 continuity factor. The default allowable is the carbon-steel hanger-rod practice basis (one-fifth of A36's 58 ksi minimum tensile strength); for 3/8″–1 1/4″ rods the computed capacities land on the published hanger-rod table values.

max spacing = min( pipe span, S / max utilization ) — pipe span from fixed-beam bending (2,300 psi) and sag (0.1 in), both editable

Every hardware demand is linear in the spacing, so the structural spacing limit is the entered spacing divided by the worst utilization; the weakest pipe on the rack governs the pipe-span side. The output names the governor.

3 · Calculation

1. Each header runs π/4·(30² − 29.376²)·501/144 + π/4·29.376²·62.4/144 ≈ 101 + 294 = 395 lb/ft water-filled — the "roughly 390–400 lb/ft" the thread sanity-checked. Four across: 1,579.7 lb/ft of rack.
2. At 10 ft spacing one strongback carries 15,797 lb, laid out as four 3,949 lb point loads at 18 / 54 / 90 / 126 in across the 144 in span.
3. Simple-span statics: R = 7,899 lb per rod; M_max = 7.899·54 − 3.949·36 = 284.4 kip·in → 142.2 kip·in per channel of the pair.
4. Channel sweep at L_b = 144 in: C6 and C8 fail on lateral-torsional buckling; C9X15 passes — elastic-LTB capacity 161.2 kip·in ASD against 142.2 demand (0.882), shear 0.119, deflection 0.213 in vs 0.600 allowed.
5. Rod ladder: 1" (6,403 lb) fails; 1 1/8" carries 0.693 in² × 11.6 ksi = 8,038 lb against 7,899 (0.983 — passing, but tight enough that many crews would stock 1 1/4").
6. Spacing governors: the 30" headers could span 35.28 ft on their own; the hardware hits 1.0 utilization at 10 / 0.983 = 10.18 ft. Rod capacity governs.

4 · Results PASS

5 · Verification statement

The result values above are locked as fixture trapeze-hanger.json, case “4 x NPS 30 sch 10 water-filled 304 SS headers, 144 in rack, 10 ft spacing -> C9X15 pair + 1 1/8 rods, spacing rod-governed at 10.18 ft”, tolerance 0.000001, in the calc-core continuous verification gate (see https://pipingtoolset.com/trust/validation.html). Allowable-stress and factor data are user-supplied inputs; citations: AISC 360-22 — Specification for Structural Steel Buildings (Chapters F, G; ASD). · AISC Shapes Database v16.0 — C and MC section dimensions and properties. · ASME B31.9 ¶921.2.2 — hanger-rod loads on the root area of threads (the rod-capacity practice basis). · MSS SP-58 — Pipe Hangers and Supports: Materials, Design, Manufacture. · ASME B31.1 Table 121.5-1 — suggested support spacing (the span-suggestion context; see the Supports line).