Case Study

Multi-story composite building

An 11-story residential building with steel-concrete composite structure is considered as a case study. A lifetime cost assessment is completed to compare the costs and benefits of various structural fire designs for the building. The layout and design of the building is consistent with the NIST full-scale fire experiments, conducted on a two-story, six-bay structure. For the prescriptive solution, the structural elements are designed to meet a 2-hour fire rating for both beams and columns, in compliance with the International Building Code (IBC).

Story height (ft)	12
Floor load in fire compartment (psf)	108
Bay size (ft × ft)	30x20
Compartment area (sq. ft)	600
Number of stories	11
Projection size (ft × ft)	180x240
Total floor area (sq. ft)	475,200

Four different structural fire designs

Four variations of fire designs are compared for the floor systems. The designs vary in fire protection applied to the central beam and in steel reinforcement in the concrete slab, as shown in the table below. Designs 1 to 3 directly align with the specimens tested in the respective three NIST experiments. Design 1 follows the prescriptive approach in the U.S. for a 2-hour fire rating. Design 2 has the same fire protection as Design 1, but the concrete slab reinforcement is increased from a welded wire mesh of 60 mm²/m in S755 to steel reinforcement bars (rebars) of 230 mm²/m in S480. In Design 3 and Design 4, no fire protection is applied on the central (secondary) beams. In Design 3, the slab reinforcement is the same as Design 2. In Design 4, the amount of steel reinforcement is reduced to 142 mm²/m in S480, which corresponds to the minimum amount specified in Annex G of the upcoming Eurocode 4 Part 1-2 for steel and concrete composite floors under tensile membrane action.

	Design 1	Design 2	Design 3	Design 4
Design approach	Prescriptive U.S. code	Prescriptive enhanced	PBSFD for membrane action	PBSFD minimum rebar
Central beam	Protected	Protected	Unprotected	Unprotected
Rebar area in S755 (value in bracket is for S480)	60 (94)	146 (230)	146 (230)	90 (142)

Two different building locations

Two building locations are considered here. Cost variations due to location are accounted for by adjusting material and labor expenses using City Cost Index (CCI). For example, the fire protection material and labor costs in New York City (NYC) are factored by the CCI of 1.105 and 1.652 compared to the National Average value of 1, indicating higher material costs. Furthermore, to evaluate the potential rent income due to variation in construction schedule and rent loss due to fire, the unit rent costs are set as $2.64 and $6.15 per sq. ft per month for the two selected location based on data from CommercialCafe. The unit relocation costs are used to evaluate the relocation expenses the property owner would incur due to a fire event. The national average value of relocation cost is obtained from the Hazus Inventory Technical Manual, with the NYC value factored proportionally based on the difference in rent cost.

Fire load distribution

The expected fire load in the building influences the severity of the fire. Here, the selected fire load follows the Gumbel type 1 distribution for dwellings with a mean value of 780 MJ/m² and standard deviation of 234 MJ/m², based on the Eurocode.

Components of the lifetime cost evaluation

Construction costs

The total construction cost is estimated based on the developed construction cost database.

The total construction cost for the building is about $54.5M when using national average cost data and about $70M with NY data. For Design 3 and Design 4, only 76% of the steel beams are protected with SFRM, as the central beams are left unprotected.

It is assumed that 8 crews of 4 workers are assigned to apply the SFRM, which requires a total of 19 days for completion for Design 1 and 2, and 16 days for Design 3 and 4.

The building lifetime is set as 50 years, and a 3% discount rate is considered. The annual maintenance cost of the floor SFRM is assumed to be a constant ratio (3% in this study) of the total floor SFRM construction cost.

	National Average				NYC
	D1	D2	D3	D4	D1	D2	D3	D4
Total building construction cost (m$)	54.5	54.5	54.4	54.4	70.4	70.3	70.3	70.3
Square foot construction cost ($)	114	114	114	114	148	148	147	147
Floor fire protection construction cost (k$)	409	409	311	311	579	579	440	440
Extra cost in rebar (k$)	–	193	193	67	–	239	239	83
Labor days in fire protection	19	19	16	16	19	19	16	16
Extra rent income (k$)	–	–	(69)	(69)	–	–	(160)	(160)
Maintenance (k$)	317	317	241	241	450	450	342	342
Net initial construction associated costs (k$) *	726	919	676	550	1,028	1,267	860	705

*: The net initial construction associated costs are calculated by summing the costs of floor fire protection, extra reinforcement in the slab, and lifetime maintenance, and deducting the extra rent income.

Fire-induced losses

The evaluation of the cost components associated with fire damage , including the direct loss and indirect loss, requires assessing the response of the structure in the event of a fire. This assessment is conducted using fire fragility functions given the uncertainties in both fire and materials. The fragility functions characterize the probability to reach predefined damage levels as a function of the fire intensity. These damage levels are used to estimate the severity of the building after a fire event. Therefore, the lifetime damage estimation begins with the selection of fragility functions based on the structural fire design data. As the probability defined in the fragility functions are conditional to the occurrence of a structurally significant fire, the fire data including fire frequency and fire load distribution must be specified to evaluate the lifetime damage loss.

	DS1	DS2	DS3	DS4
Criterion	1/240 ≤ < 1/120	1/120 ≤ < 1/60	1/60 ≤	1/60 ≤ and steel failure or: simulation stops due to large deflection
Fire spread status	Fire is confined to the compartment of origin			Fire spreads

Fire Frequency

The fire frequency adopted here is estimated from the National Fire Incident Reporting System (NFIRS) database for all residential fires with story >=4, with a value of 2.6e-9/ft²/year. For the considered the prototype, the fire frequency is 0.0012/year.

Direct damage losses

Direct structural losses associated with damage states DS1 to DS3 are evaluated based on the damaged structural components identified in reference. Non-structural costs are assumed to be 50% of the compartment construction cost at DS1 to DS3. For DS4, which entails structural integrity failure and fire spread scenario. The structural and nonstructural losses at different damage states, normalized by the initial compartment construction cost, with values of 0.54, 0.63, 0.76, and 200 for DS1, DS2, DS3 and DS4, respectively.

Injury losses are conditional to fire spread status and derived based on NFIRS database. The calculated injury losses at different damage states are $136,750 and $281,730 corresponding to different fire spread statuses.

Indirect damage losses

		Average structural and non-structural loss per fire (k$)	Injury loss per fire (k$)	Annual loss (given fire rate of 0.0012/year) (k$)	Lifetime loss (k$)
National Average	D1	3,785	176	5	245
	D2	71	137	0.3	13
	D3	153	138	0.4	18
	D4	1,313	150	2	90
NYC	D1	4,673	174	6	299
	D2	93	137	0.3	14
	D3	212	138	0.4	21
	D4	1,699	150	2	114

The demolition costs are assumed to be 50% of the installation costs. The sum of installation and demolition costs are then used to evaluate the labor days needed to repair the components. The maximum number of workers on-site is limited to 118 . Additionally, it is assumed that a maximum of four workers are allocated per 1,000 sq. ft. in each compartment. It is assumed that the entire building will remain closed until the structural components are repaired when the fire spreads (damage state DS4). These closed areas and days can be interpreted as indirect consequences, ranging from unavailability of 600 sq. ft in the building for half a month at DS1 up to unavailability of the whole building for about 3 years at DS4.

		Relocation cost (k$)	Rent loss (k$)	Average loss per fire (k$)	Annual loss (k$)	Lifetime loss (k$)
National Average	D1	155	7,455	7,610	9	470
	D2	2	65	67	0.08	4
	D3	5	202	207	0.26	13
	D4	53	2,548	2,602	3	161
NYC	D1	362	17,371	17,732	22	1,096
	D2	4	152	156	0.19	10
	D3	11	475	483	0.60	30
	D4	125	5,938	6,062	7	375

Co-benefits associated with the fire design

A medium-density SFRM (minimum 22 pounds per cubic foot) is considered, which produces 493 kg of CO₂ emissions per 1,000 kg of SFRM.

The CO₂emission during construction phase, post-fire CO₂ emissions, annual post-fire CO₂ emissions and lifetime CO₂ emissions are summarized.

PBD methods save approximately 3 tons of CO₂ emissions in SFRM during the construction phase compared to prescriptive methods. During the post-fire recovery phase, Design 1 has the highest CO₂ emissions, around 1,000 tons per fire, whereas Design 3 has significantly lower emissions at approximately 45 tons.

Overall, Design 1 exhibits the highest lifetime CO₂ emissions, followed by Design 4, Design 2, and Design 3.

Economic impact of the structural fire designs

The following table and figure present a detailed breakdown of all cost components, the present value lifecycle costs (PVLCC), and the environmental consequences for the four designs at two different locations. The results indicate that, based on the inputs and assumptions stated above, Design 3 has the lowest economic and environmental costs. Though Design 4 has the lowest construction cost among the four designs, its direct and indirect losses are significantly greater than those of Design 3, resulting in higher PVLCC and lifetime CO₂ emissions. While Design 2 has the lowest direct and indirect losses, the extra investment in reinforcement is not compensated by the reduction in losses, making it less favorable than Designs 3 and 4. Design 1, which represents the current U.S. prescriptive codes, has the highest PVLCC and lifetime CO₂emissions due to the significant lifetime losses. The differences in PVLCC are more pronounced in NYC compared to the national average, primarily due to the higher indirect losses associated with building closures.

		Construction cost (k$)	Maintenance (k$)	Rent Income (k$)	Direct loss (k$)	Indirect loss (k$)	PVLCC (k$) *	CO₂ emission (ton)
National Average	D1	409	317	–	245	470	1,441	254
	D2	602	317	–	13	4	936	192
	D3	504	241	69	18	13	708	162
	D4	378	241	69	90	161	801	182
NYC	D1	579	450	–	299	1,096	2,424	254
	D2	818	450	–	14	10	1,291	192
	D3	679	342	160	23	30	912	162
	D4	523	342	160	114	375	1,193	182

The construction cost includes the investment in the beam fire protection and extra cost in the slab reinforcement.

*: The PVLCC is calculated by summing the costs of construction, maintenance, direct loss, indirect loss, and then deducting the rent income.

Recommendations

The designs based on the PBD (Design 3 and 4) result in lower lifetime costs and reduced environmental impacts compared to the prescriptive design (Design 1). This reflects the lower expected fire-induced losses of the PBD as well as efficiency in construction with lower amount of SFRM, compared to the prescriptive design. The advantage of the PBD is particularly marked for occupancies that have low to medium fire loads (e.g., hospital, school, theatre, etc.). The design based on prescriptive approach with added reinforcement (Design 2) may become more cost efficient for very high expected fire loads (e.g., library). This also illustrates that the proposed method can be used to identify the optimum designs as a function of the parameters specific to a type of building or occupancy.

Lifetime costs (k$) for the four designs at different fire load distributions (with g-value of 200)

Occupancy	Fire load		Prescriptive method		PBD method
Occupancy	mean	sd	D1	D2	D3	D4
Hospital	230	69	727	919	684	559
School	285	85.5	728	920	686	561
Theatre	300	90	729	920	687	561
Hotel	310	93	728	920	687	562
Office	420	126	751	923	688	565
Shopping centre	600	180	952	928	690	615
Dwelling	780	234	1,436	935	706	805
NFPA office [51]	1158	541	2,315	1,015	1,003	1,585
Library	1500	450	3,110	1,102	1,335	2,383

Lifetime CO₂ emissions (ton) for the four designs at different fire load distributions (g-value of 200)

Occupancy	Fire load		Prescriptive method		PBD method
Occupancy	mean	sd	D1	D2	D3	D4
Hospital	230	69	191	191	160	160
School	285	85.5	191	191	160	160
Theatre	300	90	191	191	160	160
Hotel	310	93	191	191	160	160
Office	420	126	192	191	160	160
Shopping centre	600	180	209	191	160	164
Dwelling	780	234	249	192	162	180
NFPA office [51]	1158	541	321	198	185	243
Library	1500	450	387	206	214	311