Calculations · 02 · Analysis

Structural analysis & modeling

How load gets through the building and how it was modeled: the gravity load path, a RAM finite element model tuned for an orthotropic floor, the walking-vibration check, and torsion in the beams that carry the façade.

Thesis sheetsS.1 · S.2 · S.4 · Torsion

CoursesAE 308 · AE 430 · MATH 220

Sheet authorsK. Noma (gravity, model) · K. Regep (torsion) · T. Alenezi (drift)

STEP 1

Loads into the model

Floor live loads come from ASCE 7-22 Ch. 4 by occupancy, reduced where the code allows. Mechanical and electrical rooms were set to a uniform 100 psf to allow for the extra equipment that three more stories bring. Façade weights from the enclosure design are applied as perimeter line loads.

Program	Live load (psf)	Reduction
Corridor (1st floor / above)	100 / 80	Yes
Classrooms / lecture hall	60	Yes
Storage	125	Yes
Bathroom	60	No
Stairs	100	Yes
Open seating	100	No
Computer lab	100	Yes
Penthouse	20	No
Mechanical / electrical	100	No
Curtain wall line load	0.295 klf	from AP.3
Fiber cement wall line load	0.231 klf	from AP.2

Live loads: Fig. S.1.7 on sheet S.1. The highlighted line loads are Tamara's assembly weights, rounded. See how they were calculated.

STEP 2

Gravity load path & takedown

Load goes from the CLT deck to the secondary beams, then to the primary girders at each level, then down the columns to the foundation. The axial load in each column builds up story by story. Columns on the perimeter also pick up the façade line loads. RAM Structural System's Builder module did the member sizing and load takedown.

Frame model with load path arrows — **S.2 · Fig. S.2.4.** Orange: deck → beams → girders. Blue: column axial load building toward the foundation.

Typical floor framing plan with open-web joists highlighted — **S.2 · Fig. S.2.3.** Typical floor framing. Joists (blue) in Zone 3.

The framing layout also took constructability into account: repeating bay spacing for fabrication and erection, and as little angled framing as possible to avoid complicated connections and irregular load paths.

STEP 3

Modeling an orthotropic floor in RAM

Modeled as a plain isotropic plate, a CLT–concrete floor is too stiff in one direction and too soft in the other. So the team derived orthotropic shell stiffness modifiers to scale the plate's bending (m), membrane (f), shear and torsion stiffness separately in each direction, using the Mass Timber Floor Vibration Design Guide (Ch. 9).

Property	Value	Property	Value
Effective thickness	11.625 in	Elastic modulus	2,000 ksi
Poisson's ratio	0.20	Self-weight	45 psf
f₁₁ (membrane, strong)	1.02	m₁₁ (bending, strong)	1.129
f₂₂ (membrane, weak)	0.597	m₂₂ (bending, weak)	0.294
f₁₂ (in-plane shear)	1.121	m₁₂ (torsion)	0.511

Knowing the tool's limits. RAM's shell modifiers assume the CLT and concrete act as separate (non-composite) layers. Scaling one homogeneous plate this way doesn't capture the stiffness that true composite action adds. The sheet states this as a modeling caveat.

RAM structural model isometric — **S.4 · Fig. S.4.2.** RAM model.

RAM deck property dialog with stiffness modifiers — **S.4 · Fig. S.4.3.** Modifiers that mimic the hybrid concrete–CLT floor.

STEP 4

Walking vibration

CLT has a high strength-to-weight ratio, low mass and little damping. A floor can pass every strength check and still feel bouncy. The FPInnovations method (U.S. CLT Handbook, Ch. 7) gives a maximum vibration-controlled span, and the 3″ topping was partly chosen to add mass.

vibration-controlled span = 16.38 ft maximum span in building = 10.75 ft utilization = 10.75 / 16.38 = 65.6% headroom = 5.63 ft ✓

Bars comparing max span 10.75 ft with vibration-controlled span 16.38 ft, headroom 5.63 ft — **S.4 · Fig. S.4.1.** Vibration doesn't govern the final design.

STEP 5

Spandrel beam torsion

The heaviest façade (full-story GFRC framing, 230 plf) hangs off the slab edge, eccentric to the spandrel beam's shear center, so it twists the beam. Following AISC 360 and Design Guide 9, the team checked rotation of the controlling W18×40 spandrel and designed kickers back to the slab.

Eccentricity e = 3.0 (½ flange) + 2.0 (slab edge clearance) + 1.5 (½ bearing) = 6.5 in = 0.542 ft Applied torsion m_t = w·e = 0.230 k/ft × 0.542 ft = 0.1246 k·ft/ft T = m_t·L = 0.1246 × 26.5 ft = 3.30 k·ft Section torsional parameter (DG 9) a = √(E·C_w / G·J) = √(29,000 × 1,440 / 11,200 × 0.810) = 67.9 in Rotation check, θ_allow = 0.5° no kickers: θ = 0.733° ✗ exceeds limit kickers @ 8 ft (30°): θ = 0.067° ✓ (max spacing 21.88 ft)

Torsion design spreadsheet: inputs, applied torsion and design summary — **S. Façades.** DG 9 torsion workbook.

Spandrel detail with GFRC panel, bearing and tie-back attachments and a kicker to the slab — **S. Façades.** Final framing: bearing, tie-back and kicker.

Torsion sheet authored by K. Regep.

STEP 6

Drift: analysis meets enclosure

Lateral analysis returns interstory drift, and the façade is what has to tolerate it. Tamara set the drift each enclosure system must accommodate under the 10-year service wind (D + 0.7W): h/600 at the ground floor and h/400 above. With h = 208 in, that's 0.35 in and 0.52 in.

See the drift compatibility calculation →