Calculations · 01 · Member design

Floor system & member design

How the structural team picked a mass-timber floor and sized the steel under it: comparing three systems by demand/capacity ratio, checking the CLT panel for deflection and a two-hour fire, then measuring what the redesign saved in steel and carbon.

Thesis sheetsS.1 · S.2 · S.3 · Foundations

CoursesAE 401 · AE 402 · AE 403 · AE 405

Sheet authorsK. Noma (floor & framing) · K. Regep (foundations)

STEP 1

Three floor systems on the table

The owner required mass timber, but "use CLT" isn't a design. The team compared the existing concrete-on-steel-deck floor against two CLT options: one where the topping just sits on the panels, and one where shear studs pass through the CLT and make the topping act compositely with the steel beams.

System	Topping	Deck / panel
Concrete–steel composite (base)	3.5″ NWC, 145 pcf	2″ Vulcraft 2.0D FL deck
CLT non-composite	2″ NWC topping	Structurlam E4M3 139 ESP, 5-ply, t = 5.48″
CLT composite (selected)	3″ NWC topping	SmartLam E4M5.1, 5-ply, t = 5.875″

The selected panel is a 5-ply E4M5.1 layup of 1.375″ / 0.875″ / 1.375″ / 0.875″ / 1.375″ laminations (5.875″ total, 8.875″ with the topping, 17 psf). A single-span layout was used so bays with an odd number of infill members still work. The panel was selected for the worst-case bay, a 10′-9″ span, so one panel covers the whole building.

CLT panels on steel beams with a concrete topping — **S.3 · Fig. S.3.4.** Selected system: topping tied to the steel through the CLT with shear studs.

Table of average deflection demand-capacity ratios for three floor systems — **S.3 · Fig. S.3.2.** Average deflection DCRs by system.

STEP 2

Concrete topping properties

The topping was increased from 2″ to 3″ of normal-weight concrete to add mass for vibration and stiffness for deflection. Its material properties come from standard relationships:

Elastic modulus (ACI 318, normal-weight concrete) E_c = 57,000 √f′_c = 57,000 √4,000 psi = 3,604,997 psi = 3,605 ksi Dynamic modulus for vibration E′_c = 1.35 E_c = 1.35 × 3,605 = 4,867 ksi Shear modulus G_c = E′_c / 2(1 + ν) = 4,866.7 / 2(1 + 0.25) = 1,947 ksi

Values match Fig. S.1.6 on sheet S.1.

STEP 3

Demand / capacity ratios

Each system's steel beams and girders were checked for strength and deflection. The demand/capacity ratio (DCR) says how much of a member's capacity is used. 100% is the limit, and a DCR well under 100% means steel is being wasted.

Definition DCR = demand / capacity (≤ 1.00 required) Total-load deflection, average Concrete–steel composite: beam 56.9% · girder 40.6% CLT non-composite: beam 90.4% · girder 87.1% CLT composite: beam 89.1% · girder 89.1% (worst-case bay) Flexural strength, CLT composite beams and girders ≈ 98% → most efficient system

The base system's 41–57% deflection DCRs showed that the original structure was significantly over-designed. Both CLT systems came in around 90% on deflection. Strength decided between them: the composite system used its members to about 98% in flexure.

Bar chart of average strength DCR for beam shear, beam flexure, girder shear and girder flexure, CLT non-composite vs composite — **S.3 · Fig. S.3.3.** Average strength DCR, non-composite vs. composite CLT.

STEP 4

CLT panel deflection

The steel checks don't cover the timber itself. CLT is orthotropic: its stiffness depends on the direction of each lamination. So the panel was checked separately over its 10.75 ft span, using the shear analogy method (U.S. CLT Handbook, Ch. 3) for effective bending and shear stiffness.

Allowable deflections, L = 10.75 ft = 129 in Live load: Δ_allow = L/360 = 129/360 = 0.36 in Total load: Δ_allow = L/240 = 129/240 = 0.54 in Computed curves (Fig. S.3.5) peak near 0.08 in live and 0.13 in total, well inside both limits.

Deflection along the 10.75 ft CLT span: live and total load curves well inside the L/360 and L/240 limit curves — **S.3 · Fig. S.3.5.** CLT layup deflection vs. limits along the span.

STEP 5

Two-hour fire: residual section

Instead of spray fireproofing, the team used the inherent charring method (NDS Ch. 16 with the manufacturer's guide). The panel is sized so that after two hours of burning, the wood that hasn't charred can still carry the load. It's predictable, needs no applied protection, and leaves the timber exposed.

Char depths for the 5.875″ layup, 2-hour exposure a_char = 3.708 in a_eff = 1.2 a_char = 1.2 × 3.708 = 4.45 in (adds a zero-strength layer) residual depth = 5.875 − 4.45 = 1.43 in Residual capacity vs. demand Flexure: 2.265 ≤ 16.36 kip·ft/ft → DCR = 0.14 ✓ Shear: 0.843 ≤ 1.99 → DCR = 0.42 ✓

Serviceability isn't checked after a fire because the panels would be replaced. Strength is, to make sure the floor holds up for safe egress and panel replacement.

Diagram of the CLT layup before and after charring, showing the effective char zone and the inherent char zone — **S.3 · Fig. S.3.5.** Layup and char zones.

Bar chart: residual section capacity vs demand for flexure and shear — **S.3.** Capacity vs. demand, 2-hour residual section.

STEP 6

Steel tonnage

A lighter deck lowers gravity load all the way down the building, so beams, girders and columns could all be resized. In Zone 3, where loads were light, open-web steel joists replaced wide-flange beams. The average number of members per bay dropped from about 3 to 2.5.

	Columns (lb)	Joists (lb)	Braces (lb)	Beams (lb)	Total (lb)
Original	239,840	—	45,302	1,933,260	2,218,402
Redesign	156,897	152,230	64,045	828,735	1,201,907

reduction = 1 − 1,201,907 / 2,218,402 = 45.8%

Stacked bar chart of steel weight by member type, original vs redesign — **S.2 · Fig. S.2.1.** Steel superstructure weight.

STEP 7

Embodied carbon

Each material's weight (converted to kg) is multiplied by its global warming potential (GWP) factor, in kg CO₂e per kg of material. CLT adds carbon back in, but much less than the steel it replaces.

Material	GWP (kg CO₂e/kg)	Weight, old (lb)	Weight, new (lb)	CO₂e old (kg)	CO₂e new (kg)
Concrete	0.30	930,417	930,417	126,591	126,591
Steel	1.16	2,218,402	1,201,907	1,167,088	632,316
CLT	0.20	0	374,000	—	33,924
Total				1,293,680	792,832

Method CO₂e = Σ (W_i × 0.4536 kg/lb × GWP_i) table totals: 1 − 792,832 / 1,293,680 = 38.7% S.2 chart (Fig. S.2.2): 1,293,680 → 774,747 kg = 40.1%

Either way the target is met. The sheet's table and chart give slightly different totals (38.7% and 40.1%). Both clear the project's 30% embodied-carbon reduction target comfortably.

Stacked bar chart of embodied carbon by material for the old and new design — **S.2 · Fig. S.2.2.** Gravity system embodied carbon.

STEP 8

Foundations: the procedure

Three extra stories and a new coastal site meant the foundations had to be reconsidered. The foundation sheet sets out the design procedure the team followed:

Determine soil parameters from the geotechnical report.
Select the foundation systems to analyze.
Identify loading from the structure: base axial and base shear (RAM reactions).
Axial capacity design.
Settlement analysis, evaluating the controlling settlement conditions.
Lateral capacity design, spot-checking elements for gravity and lateral performance.
Acoustics and vibration review of construction (OSHA limits on equipment use).
Compare results to design goals and justify the best system.

Governing references: ASCE 7-22 Ch. 11, 12 and 20 (seismic parameters and site class), FBC 2023 Ch. 17–18 (testing, inspection and deep foundations), ACI 318-19, ASTM D1143 / D3966 (axial and lateral load tests) and ACI 336.1-24 (drilled shafts).