Rooftop Unit on a 25-Year-Old Composite Beam

Loads on one beam (tributary 8 ft):

• Slab + deck: 58 × 8 = 464 plf
• Superimposed dead: 45 × 8 = 360 plf
• Beam self-weight: 35 plf → total D = 859 plf = 0.859 klf
• Live: 50 × 8 = 400 plf = 0.400 klf

Demand (1.2D + 1.6L + 1.6P, P = 12 k at midspan):

• MD = 0.859 × 32²/8 = 110 ft-k → 1.2 × 110 = 132 ft-k
• ML = 0.400 × 32²/8 = 51 ft-k → 1.6 × 51 = 82 ft-k
• MP = 12 × 32/4 = 96 ft-k → 1.6 × 96 = 154 ft-k
• Mu ≈ 368 ft-k, plus an added 6 kip reaction at each end.

Capacity:

• Steel alone: φMn = 0.9 × 50 × 66.5/12 = 249 ft-k → overstressed (DCR 1.48).
• Composite: effective width = 8 ft = 96 in; T = AsFy = 10.3 × 50 = 515 kip; compression block a = 515/(0.85 × 4 × 96) = 1.58 in, which fits within the 2.5 in of concrete above the ribs. Lever arm ≈ 12.5 in → φMn ≈ 480 ft-k, DCR ≈ 0.77.

So the beam works only if composite action is real. Stud check: 32 studs, Qn ≈ 21.5 kip each (governed by the AscFu cap) = 688 kip > Vh = 515 kip, so full composite is available if the studs are where the drawings say.

No shoring of this beam is required for the reason shoring exists. Shoring on composite beams is a construction-phase issue: it carries wet concrete on the steel alone before the slab cures. Here the slab has been composite for 25 years, so the 12 kip is added to a fully composite section - it is not a construction-load case. A crane's outrigger loads, however, are a different and often larger problem, and must be checked against the joist/deck capacity separately.

Conditions I would attach:

1. Verify the unit: confirm the 12,000 lb operating weight (not shipping weight) and the actual center of gravity; confirm whether the curb spans between two beams or lands on one. The analysis above is the single-beam, midspan worst case.
2. Verify the studs in the field: confirm ribs are perpendicular to the beam (one stud per rib counted), and spot-check that studs were not burned off during prior roof work. The whole answer is a DCR of 0.77 only with 32 effective studs.
3. End connections: factored reaction goes from about 22 kip to 31 kip. Check the beam-to-girder connection and the girder/column below for the added 6 kip.
4. Local slab check: 12 kip on a curb footprint - check the deck and slab for the patch load and do not cut the deck.
5. Deflection: the unit adds 96 ft-k of sustained dead moment; check that the added long-term deflection will not pond or bind the unit's connections.

Stud count halves: 16 studs × 21.5 kip = 344 kip of horizontal shear capacity, so Vh′ = 344 kip against AsFy = 515 kip - about 67% composite. With partial composite, the plastic neutral axis stays in the steel and the lever arm shrinks only slightly, so φMn ≈ 344 × 12.5/12 × 0.9 ≈ 320 ft-k, roughly 12% below the 368 ft-k demand. The beam fails, and it fails on connection, not on steel.

Adding studs through a 25-year-old finished slab is not realistic. Practical options, in order of intrusiveness:

• Reinforce the steel: weld a bottom-flange cover plate over the middle third. A ½ × 6 in plate adds roughly 3 in² at 16 in from the centroid - enough to recover the missing 50 ft-k with the partial-composite section.
• Add a post or hanger: pick up the unit with a new column from the floor below, or a pair of channels spanning to the adjacent beams so the load is shared three ways.
• Relocate the unit: move it to a quarter point, which cuts MP from 96 to 72 ft-k and brings the demand under the partial-composite capacity without new steel.

The judgment point: the answer is sensitive to a field detail that is invisible in the calculations, and the fix should be one that does not rely on composite action.