Fragility analysis of long-span lightweight steel structures subjected to combined earthquake and non-uniform snow loads

Abstract

Lightweight steel structures are commonly used in industrial facilities due to their low weight, high strength, and excellent performance. The design of these structures for cold regions not only has to consider the effects of earthquakes but also the negative impact of snow loads. Industrial structures often have long spans, and the effects of uneven snow loads cannot be underestimated. However, relatively few studies have focused on the performance of lightweight steel structures under the influence of combined earthquake and non-uniform snow loads. Therefore, this study assessed the seismic fragility of a typical single-span, double-sloped lightweight steel factory under combined earthquake and non-uniform snow loads using incremental dynamic analysis. Non-uniform snow loads, as compared to uniform snow loads, substantially increase the structural displacement responses, thereby increasing the structural failure risk. The improved structural design developed in this study effectively decreases the impact of adverse loading scenarios and enhances the multi-hazard resilience of the structure. Accordingly, these results can serve as an important theoretical guide for enhancing the safety of lightweight steel structures subjected to multiple hazards in cold regions.

Keywords

Lightweight steel structure building safety multi-hazard conditions incremental dynamic analysis seismic fragility

Introduction

Lightweight steel structures are characterized by their reduced weight, which alleviates the foundational load and allows for quicker and more efficient construction processes. Notably, lightweight steel structures demonstrate excellent seismic performance, making them a safer choice in seismic regions. The design flexibility and ability to achieve long spans make lightweight steel structures ideal for various building types, including industrial facilities, residential buildings, commercial spaces, and public infrastructure. Lightweight steel structures have gained significant popularity in the construction industry due to their numerous advantages. Earthquakes and snow are two typical disasters occurring in seismic zones in cold regions that must be carefully considered in structural designs and analyses. Investigations have been conducted individually on each type of load.

Structural collapses due to snow loads, including the fatal collapse of the Katowice Trade Fair building (Biegus and Rykaluk, 2009) and structural failures of multiple high school gymnasiums and sports halls (Geis et al., 2012; Piskoty et al., 2013; Tanzer, 2011), are relatively common. More than 200 roof system collapses occurred in certain regions of Russia between 2001 and 2021 due to snow loads (Lobkina, 2021). Fırat Alemdar and Alemdar, 2021 studied the collapse performance of steel industrial buildings under snow loads in western Turkey. The results indicated that design errors, construction defects, and the insufficient load-bearing capacity of structural components are the main causes of collapse. Heki (2003) found that snow loads during spring melting can exacerbate the seismic response of some buildings in Japan. Ueda et al. (2024) suggested that inland seismic activity in northeastern Japan is influenced by seasonal stress variations caused by annual snow loads, which may trigger earthquakes in Japan. Tian et al. (2021) conducted progressive collapse tests on single-layer latticed dome structures under non-uniform snow loads, revealing that a higher degree of snow load non-uniformity increases the chance of structural collapse. Lee and Rosowsky (2005) proposed a new method for assessing the impact of snow loads and predicted the probability of snow loads with a return period of 10,000 years. These studies demonstrate that the impact of snow loads on structures is significant and cannot be ignored.

However, the combined effects of snow and earthquakes in cold regions are factors that designers must consider (Karamanos and Karamanos, 1997). Researchers, including Ellingwood and Redfield (1983) and O'Rourke and Speck (1992), studied methods for calculating the transfer of snow loads from the ground to the roof and accounting for snow loads combined with seismic effects (Ellingwood and Rosowsky, 1996). The inclusion of snow loads generally exacerbates the seismic response of structures. Among these studies, research on the combined impact of snow and seismic events on lightweight timber structures represents one of the earliest and most extensive areas of study. Wang and Rosowsky (2016) investigated the seismic fragility of lightweight timber structures under moderate snow loads and seismic events. Yin and Li (2011) proposed a risk assessment method for lightweight timber frame structures under the combined effects of earthquakes and snow, demonstrating that snow loads increase the risk of seismic damage to lightweight timber frame structures.

Incremental dynamic analysis (IDA) is a nonlinear dynamic analysis method that can comprehensively assess the performance of a structure from the elastic to plastic states until collapse. Selecting an appropriate intensity measure (IM) is crucial for evaluating the seismic fragility of structures. He and Lu (2019) suggested that the peak ground velocity (PGV) is not only suitable for the IDA analysis of high-rise buildings but is also highly effective in fragility assessments. Liu et al. (2016) and Pan et al. (2023) found that PGV is also appropriate as an IM for underground structures. The peak ground acceleration (PGA) is widely used by researchers to analyze steel structures because it effectively captures the record-to-record variability of earthquake motions (Guo et al., 2024; Zhou et al., 2018). Vahdani et al. (2017) employed the IDA method to investigate the seismic fragility of steel frame structures under near- and far-fault earthquake motions and found that near-fault earthquake motions more significantly impact structures. Venneri et al. (2023) numerically investigated the response of multi-story moment-resistant steel frames under seismic action and indicated that semi-rigid joints affect the overall seismic performance of multi-story steel buildings. Luo et al. (2021) evaluated the probabilistic seismic performance of wood-steel hybrid structures under main shock-aftershock sequences and suggested that higher wall-bracing stiffness ratios are advantageous for reducing the exceedance probability of wood-steel hybrid structures.

Sensitivity studies of multi-hazard impacts on lightweight steel frame structures have recently become a focal research topic. Peng et al. (2023) assessed the reliability of long-span roof structures under wind-snow coupling and multiple hazards. The conclusive findings highlighted fluctuating wind as the primary factor causing deformation and failure of long-span roof structures. Song et al. (2024) proposed a multi-hazard fragility assessment framework suitable for long-span spatial structures and evaluated multi-hazard risks to facilities under the combined effects of wind-induced fatigue and earthquakes. Ciabattoni et al. (2024) proposed an innovative approach employing low-damage structural systems and a combination of engineered wood and steel connections in the preliminary design stage to withstand wind and earthquake loads using a steel-wood hybrid structure. Guo et al. (2024) established a multi-hazard performance assessment method applicable to various structures and disasters, selecting two common low-rise cold-formed steel structures to investigate their dynamic responses under earthquake and wind loads with and without inclined braces. Lu et al. (2024) analyzed the fragility of the supertall buildings in Suzhou under combined seismic and wind actions. The findings revealed that the structural fragility increases under the joint action of earthquakes and wind. Earthquakes primarily induce structural damage. The likelihood of moderate, severe, and collapse damage under combined seismic and wind actions exceeds that under isolated earthquakes. Kozak and Liel (2015) investigated the reliability of two steel roof systems and considered snow, dead loads, and uncertainties in the capacities of the two roof systems. They demonstrated that the roof reliability is highly dependent on the building location and seasonal snowfall patterns. Additionally, Aghdam et al. (2023) studied the deformation of space frame domes under asymmetric snow loads and seismic vibrations, which indicated that certain dome types exhibit higher deformation rates under asymmetric snow load conditions. Gong et al. (2023) numerically studied the structural performance of extra high voltage long-span truss structures (LSTSs) under multiple hazards, such as earthquakes and icing, to mitigate disaster losses. The seismic response of LSTSs decreases and its total response (caused by conductor tension, ice loads, and earthquakes) increases with an increasing ice thickness. Zelleke et al. (2024) introduced a reliability-based multi-hazard optimization framework for base-isolated buildings to meet predefined reliability performance standards considering various hazards.

In summary, research has been conducted on lightweight steel and timber structures under the individual actions of snow loads and earthquakes, combined wind and earthquake effects, and multi-hazard scenarios. However, research on the combined effects of earthquakes and snow loads on structures remains relatively scarce. The inherent characteristics, such as long spans and low weight, make lightweight steel industrial buildings sensitive to both snow loads and earthquakes. Therefore, conducting fragility analyses on these structures under the combined effects of snow loads and earthquakes is crucial for ensuring structural safety. Therefore, this study primarily aimed to assess the seismic fragility of single-span double-sloped lightweight steel structures under seismic and non-uniform snow loads using IDA to enhance our understanding of this subject. Additionally, the study analyzed measures to improve the performance of lightweight steel factory structures, focusing on structural interventions to enhance their ability to withstand the combined effects of severe snow loads and earthquakes.

Description of structural models

Structural modeling

A typical single-span double-tilted lightweight steel factory structure was selected as the research subject. Figure 1 shows the architectural floor plan. The building floor area was 60 m × 30 m and consisted of nine rigid frames placed at 7.5 m intervals. The roof slope was 1:15, with ridge and eaves heights of 9.4 and 8.4 m, respectively. H-section steel was used for the equally sectioned steel columns (GJ), beams (GL),

Figure 1.

Structural layout diagram. All units in mm. (a) Plan. (b) Horizontal roof supports arrangement. (c) Elevation. (d) Pediment.

Purlins (LT), and ridge beams (WL), as shown in Figure 2. Four horizontal (ZC) and eight column (SC) braces were installed at the roof ends. Additionally, three wind-resistant columns (SQZ) were installed at the gable wall with a purlin between each beam and column at 1.5 m intervals. GJ, GL, LT, WL, ZC, SC, and SQZ are abbreviations used in architectural drawings. Table 1 provides a summary of the cross-sectional dimensions of the components.

Figure 2.

Cross-sections of the main components.

Table 1.

Cross-Sectional Dimensions of the Main Components.

Classification	Height (mm)	Width (mm)	Diameter (mm)	Thickness 1 (mm)	Thickness 2 (mm)
Steel columns	350	750	—	10	14
Steel beams	350	600	—	8	14
Wind columns	180	400	—	8	10
Ridge beams	125	200	—	4.5	6
Supports	—	—	20	—	—
Purlins	125	200	—	4.5	6

Finite element modeling

A finite element model of the structure was established using the ABAQUS platform, as shown in Figure 3. RS is a structure that incorporates additional construction measures beyond GS. RS, as compared with GS, has additional rigid column braces in the central area. The spacing of the roof purlins in GS was 1.5 m, whereas that in RS was 0.75 m. The primary objective of this study was to preliminarily investigate the impact of these two simple construction measures on the resistance of the structure to combined snow and earthquake loads. B31 beam elements were used to model the beams, columns, purlins, and supports. Table 2 lists the first three fundamental periods of the two models obtained through modal analysis.

Figure 3.

Finite element models. (a) GS skeleton. (b) RS skeleton. (c) GS model. (d) RS model.

Table 2.

Results of the Modal Analysis.

Structure	Vibrational mode	Period (s)
GS	1st	0.62
	2nd	0.57
	3rd	0.44
RS	1st	0.59
	2nd	0.51
	3rd	0.43

Material modeling

YX35-125-750 profiled steel sheets simulated using S4R shell elements were employed as the structural roof panels. The simplified calculations of the roof panels accounted for isotropy and employed an ideal elastic-plastic model. A bilinear kinematic hardening model was employed for the framing steel. The bilinear kinematic hardening model was adopted due to its simplicity, computational efficiency, and accuracy in representing cyclic behavior. The bilinear kinematic hardening model balances accuracy and complexity, making it suitable for structural analysis and design. Additionally, the bilinear kinematic hardening model, which can be expressed as equation (1), is widely validated and has been included in many design standards to ensure reliability.

σ_{p} = {\begin{array}{c} E_{s} ε_{s} & ε_{s} < ε_{y} \\ f_{y} + k (ε_{s} - ε_{y}) & ε_{y} < ε_{s} \leq ε_{u} \\ 0 & ε_{s} > ε_{u} \end{array}

(1)

where

σ_{p}

is the stress at that point,

ε_{s}

is the strain at that point,

k

is the hardening coefficient,

E_{s}

is Young’s modulus,

f_{y}

is the yield stress,

ε_{y}

is the yield strain, and

ε_{u}

is the ultimate strain. The elastic modulus, yield strength, ultimate tensile strength, and Poisson’s ratio of the steel were set to 2.06 × 10⁵ MPa, 160 MPa, 240 MPa, and 0.3, respectively. Moreover, the von Mises yield criterion was employed.

Multiple hazards

Selection of snow load

The equation for calculating the standard snow load recommended in the Code for Design of Building Structures Load (GB50009, 2012) is defined in equation (2):

S_{k} = μ_{r} S_{0}

(2)

where S_k is the standard snow load (kN/m²), S₀ is the basic snow pressure (kN/m²), and

μ_{r}

is the snow distribution coefficient.

Table 3 lists the specific values for these variables.

μ_{r}

= 1.0 was used in this study because the slope angle was <25°. The snow distribution coefficients for non-uniform snow loads were taken as 0.75

μ_{r}

and 1.25

μ_{r}

. Figure 4 illustrates the slope angle of the roof and snow load distributions.

Table 3.

Snow Distribution Parameters.

$α$	<25°	30°	35°	40°	45°	50°	55°	>60°
$μ_{r}$	1.0	0.85	0.7	0.55	0.40	0.25	0.10	0

Figure 4.

Roof slope angle and snow load distribution.

The uniformly distributed snow load data for the return periods of 10, 50, and 100 years in Shenyang (the typical representative city in Liaoning province) were selected with corresponding basic snow pressures (S₀) of 0.30, 0.50, and 0.55 kN/m², respectively. The site of the prototype structure is classified as a Class 1 site according to the Chinese Seismic Design Code (GB50011, 2010), and the quasi-permanent value coefficient was set to 0.5 (because a uniformly distributed snow load is an idealized situation).

The impact of non-uniform snow load distributions was also examined in this study. Existing studies have reported that normal, lognormal, and Gumbel distributions perform well in simulating ground and roof snow loads, although their applicability varies across scenarios (Ceribasi, 2020; Li et al., 2023; O’Rourke and Stiefel, 1983; Zhou et al., 2022). The snow load distributions can typically be approximated using a normal distribution, especially with a large number of samples. The central limit theorem states that the distribution of the sum of multiple random variables tends towards a normal distribution. Therefore, this study modeled the distribution of snow loads using the probability density function of the normal distribution, which better represents snow loads on roofs. The roof panels were divided into 4 × 8 blocks for these loads. Assuming that the snow loads for these 32 blocks followed a normal distribution, the probability distribution of the snow loads was modeled using equation (3):

f (x) = \frac{1}{\sqrt{2 π}} e^{- \frac{{(x - u)}^{2}}{2 σ^{2}}}, - \infty < x < + \infty

(3)

where μ and σ² are the mean and variance of the normal distribution, respectively.

Twelve different snow load distributions (labeled S1‒S12) representing various scenarios (10-, 50-, and 100-year return periods, each with standard deviations ( $σ$ ) of 0.01, 0.02, 0.03, and 0.04) were simulated using MATLAB, as shown in Figure 5. S1‒S4, S5‒S8, and S9‒S12 correspond to snow loads with return periods of 10, 50, and 100 years, respectively, with corresponding standard snow load values of 0.3, 0.5, and 0.55 kN/m². Each snow load distribution was divided into 32 regions, and the snow load variation in each region was random with corresponding standard deviations of 0.01, 0.02, 0.03, and 0.04. The degree of snow load non-uniformity and load magnitude increased with the standard deviation and return period. Individual seismic activities, uniform snow loads, and non-uniform snow loads are denoted in this paper by E, SR, and UN, respectively. For example, E + SR10 represents seismic activity combined with a uniform snow load with a 10-year return period while E + UN10-0.01 represents seismic activity combined with a 10-year return period with a non-uniform snow load and standard deviation of 0.01.

Figure 5.

Distribution of the snow load on roof panels.

Selection of earthquake ground motion

Basic information on the site and seismic design group for the building researched in this study was used to analyze the target response spectrum according to the relevant standards. Twenty as-recorded earthquake ground motion records that match the target response spectrum were selected from the PEER database and are listed in Table 4. Figure 6 compares the design spectrum with the earthquake response spectrum of the ground motion records in terms of the acceleration response spectra.

Table 4.

Earthquake Ground Shaking Records.

Serial number	Ground motion	Year	Magnitude	Fault distance	PGA
E01	Humbolt bay	1937	5.8	71.28	0.0363
E02	Northwest Calif-02	1941	6.6	91.15	0.0631
E03	Northern Calif-01	1941	6.4	44.52	0.1148
E04	Borrego	1942	6.5	56.88	0.0659
E05	Imperial Valley-03	1951	5.6	24.58	0.0307
E06	Northwest Calif-03	1951	5.8	53.73	0.1080
E07	Kern county	1952	7.4	81.3	0.0897
E08	Kern county	1952	7.4	38.42	0.1589
E09	Southern Calif	1952	6	73.35	0.0360
E10	Northern Calif-03	1954	6.5	26.72	0.1634
E11	Parkfield	1966	6.19	17.64	0.0536
E12	Parkfield	1966	6.19	12.9	0.1250
E13	Parkfield	1966	6.19	63.34	0.0117
E14	Parkfield	1966	6.19	15.96	0.3565
E15	Borrego Mtn	1968	6.63	45.12	0.1327
E16	San Fernando	1971	6.61	19.33	0.0268
E17	San Fernando	1971	6.61	25.58	0.0068
E18	San Fernando	1971	6.61	22.77	0.0122
E19	San Fernando	1971	6.61	35.54	0.0270
E20	San Fernando	1971	6.61	52.64	0.0196

Figure 6.

Seismic response spectrum.

Seismic response analysis

Limit state definition

Four structural damage limit states and their corresponding ISDA_max were classified according to the Chinese Seismic Design Code (GB50011, 2010), as listed in Table 5. PGA and ISDA_max were selected as the IM and damage measure, respectively.

Table 5.

Classification of the Limit States of the Structure.

Limit states	Level of damage	Descriptions	ISDA _max
LS1	Slight	Minor damage (e.g., minor localized cracking or minor displacement within small areas); overall structural stability maintained	1/100
LS2	Moderate	Noticeable damage (including localized damage to structural components or significant displacement in certain areas); overall load-bearing capacity retained	1/50
LS3	Severe	Extensive damage to multiple structural components or entire structure significantly tilted; overall load-bearing capacity substantially reduced	1/20
LS4	Collapse	Complete collapse; unable to continue bearing loads	2/25

Seismic response under uniform snow loads

The earthquake ground motion was applied longitudinally along the structure, parallel to the direction of column bracing, to examine the influence of the added column bracing on the structure. Twenty sets of IDA curves for earthquake only (E) and uniform snow loads (E + SR) were statistically analyzed, and the 50^th percentile curve is presented in Figure 7 and indicated by bold lines. The ISDA_max values at the 50^th percentile under isolated seismic action with PGA values of 0.2 g, 0.4 g, and 0.6 g, were 1/207, 1/95, and 1/55, respectively. When considering the effect of snow loads, the displacement response of the structure under seismic action increases significantly. For example, the ISDA_max values at the 50^th percentile with a PGA of 0.2 g and under snow loads with return periods of 10, 50, and 100 years were 1/169, 1/153, and 1/148, respectively, representing corresponding increases of 22.48, 35.29, and 39.86%, as compared with the isolated seismic action. The ISDA_max values at the 50^th percentile with a PGA of 0.4 g and under snow loads with return periods of 10, 50, and 100 years were 1/77, 1/67, and 1/65, respectively, representing corresponding increases of 23.37, 41.79, and 46.15%, as compared with the isolated seismic action. The ISDA_max values at the 50th percentile with a PGA of 0.6 g and under snow loads with return periods of 10, 50, and 100 years were 1/41, 1/31, and 1/29, respectively, representing corresponding increases of 34.15, 77.42, and 89.66%, as compared with the isolated seismic action.

Figure 7.

IDA curves for various return periods of the uniform snow load. (a) E. (b) E + SR10. (c) E + SR50. (d) E + SR100.

Seismic response under non-uniform snow loads

Table 6 lists the ISDA_max values of the structure under the combined effects of non-uniform snow loads and earthquakes with different standard deviations. Figure 8 presents the 50th percentile curves for four standard deviations under different return periods. Figure 8 illustrates that as the standard deviation increases, the ISDA_max increases with the degree of non-uniformity of the snow loads. Taking the 50-year return period snow load as an example, the ISDA_max values at PGA = 0.2 g was 1/152 for uniform snow loads (

σ

= 0) and 1/147, 1/140, 1/131, and 1/122 for non-uniform snow loads (

σ

= 0.01‒0.04), representing corresponding increases of 3.40, 8.57, 16.03, and 24.59%. The ISDA_max value at PGA = 0.4 g was 1/67 for uniform snow loads (

σ

= 0) and 1/63, 1/60, 1/55, and 1/50 for non-uniform snow loads (

σ

= 0.01‒0.04), representing corresponding increases of 6.35, 11.67, 21.82, and 34.00%. The ISDA_max value at PGA = 0.6 g was 1/30 for uniform snow loads (

σ

= 0) and 1/29, 1/27, 1/24, and 1/22 for non-uniform snow loads (

σ

= 0.01‒0.04), representing corresponding increases of 3.45, 11.11, 25.00, and 36.36%. Non-uniform snow loads, as compared with uniform snow loads, have a greater impact on the displacement response of this type of long-span lightweight steel structure.

Table 6.

Seismic Responses for Non-uniform Snow Loads With Various Return Periods.

Return periods (years)	PGA (g)	ISDA _max
Return periods (years)	PGA (g)	0	0.01	Rate of increase (%)	0.02	Rate of increase (%)	0.03	Rate of increase (%)	0.04	Rate of increase (%)
10	0.2	1/169	1/167	1.20	1/164	3.05	1/159	6.29	1/151	11.92
	0.4	1/77	1/74	4.05	1/73	5.48	1/70	10.00	1/65	18.46
	0.6	1/41	1/39	5.13	1/38	7.89	1/36	13.89	1/35	17.14
50	0.2	1/152	1/147	3.40	1/140	8.57	1/131	16.03	1/122	24.59
	0.4	1/67	1/63	6.35	1/60	11.67	1/55	21.82	1/50	34.00
	0.6	1/30	1/29	3.45	1/27	11.11	1/24	25.00	1/22	36.36
100	0.2	1/169	1/140	20.71	1/133	27.07	1/126	34.12	1/120	40.83
	0.4	1/65	1/61	6.56	1/56	16.07	1/52	25.00	1/49	32.65
	0.6	1/29	1/27	7.41	1/25	16.00	1/23	26.09	1/21	38.10

Figure 8.

Fiftieth percentile ISDA_max values under different return periods with different standard deviations. (a) 10 years (b) 50 years (c) 100 years.

Seismic fragility analysis

Seismic fragility theory

Seismic fragility analysis was applied to evaluate the response of the structure to different ground shaking intensities. The relationship between the ground shaking intensity and structural damage level can be expressed as equation (4):

F (x) = P (D > C | I M = x)

(4)

where F(x) is the seismic fragility function, D is the deformation demand of the structure, C is the deformation capacity of the structure, and IM is the ground shaking intensity.

Probabilistic seismic demand analyses require a probabilistic seismic demand model based on the results of extensive dynamic time analyses. This model can represent the relationship between the measurement (IM) of the ground motion and the demand parameters of the ground motion and is expressed as equation (5):

\hat{D} = α {(I M)}^{β}

(5)

Seismic fragility analyses assume a normal distribution, and the fragility can be derived from equation (4), which can be expressed as equation (6):

F (x) = P (D > C | I M = x) = Φ (\frac{\ln \hat{D} - \ln \hat{C}}{\sqrt{{β_{D}}^{2} + {β_{C}}^{2}}}) = Φ (\frac{a + b \ln P G A - \ln \hat{C}}{\sqrt{{β_{D}}^{2} + {β_{C}}^{2}}})

(6)

where

\hat{D}

μ_{D} = \ln \hat{D}

, and

β_{D} = σ_{D}

are the median, log mean, and log standard deviation of the structural response (D), respectively, and

\hat{C}

μ_{C} = \ln \hat{C}

, and

β_{C} = σ_{C}

are the median, log mean, and log standard deviation of the structural capacity (C), respectively. The values of

\sqrt{{β_{D}}^{2} + {β_{C}}^{2}}

when the spectral acceleration and PGA were selected as the seismic intensity parameters were 0.4 and 0.5, respectively.

Seismic fragility under uniform snow loads

Figure 9 illustrates the seismic fragility of the structure under uniform snow loads with various return periods. The probabilities of minor damage at PGA = 0.2 g and 0.4 g under the condition E + SR50, as compared with the isolated seismic condition (E), increased by 13.37 and 32.27%, respectively. The probabilities of moderate and severe damage at PGA = 0.4 g under the condition E + SR50 increased by 33.09 and 2.31%, respectively. The probabilities of moderate damage, severe damage, and collapse at PGA = 0.6 g under the condition E + SR50 increased by 44.66, 20.72, and 4.44%, respectively. These results demonstrate that snow loads significantly increase the probability of seismic damage to the structure.

Figure 9.

Influence of uniform snow loads with various return periods. (a) LS1. (b) LS2. (c) LS3. (d) LS4.

Seismic fragility under non-uniform snow loads

Figure 10 illustrates the seismic fragility curves of the structure under different return periods and varying degrees of non-uniform snow load conditions. Taking the example of the 50-year return period snow load from Figure 10(b), the probabilities of minor damage at PGA = 0.2 g and for $σ$ = 0.01, 0.02, 0.03, and 0.04 were 13.19, 13.62, 15.23, and 17.45%, respectively. The probabilities of moderate damage at PGA = 0.4 g and for $σ$ = 0.01, 0.02, 0.03, and 0.04 were 29.39, 30.24, 34.47, and 39.28%, respectively. The corresponding probabilities of severe damage were 0.88, 0.94, 1.28, and 1.77%, respectively. The probabilities of severe damage at PGA = 0.6 g and for $σ$ = 0.01, 0.02, 0.03, and 0.04 were 11.04, 11.51, 14.58, and 18.27%, respectively. The corresponding probabilities of collapse were 1.52, 1.62, 2.30, and 3.25%, respectively. The degree of non-uniform snow loading significantly influences the probability of structural damage. The probabilities of various levels of damage increase with an increasing snow load non-uniformity. Moreover, this effect becomes more pronounced with larger snow load standard deviations.

Figure 10.

Influence of non-uniform snow loads with various return periods. (a) 10 years (b) 50 years (c) 100 years.

Impact of seismic structural measures on the structural fragility under combined snow loads and earthquake conditions

Another structure, labeled RS, was established in the second part of the study to further investigate the influence of simple seismic structural measures for resisting the combined effects of non-uniform snow loads and earthquakes. RS, as compared with the original structure GS, incorporates additional seismic structural measures by introducing intermediate column bracing along the longitudinal direction and reducing the purlin spacing. Similarly, RS was analyzed in the same way as GS for comparative research purposes.

The ISDA_max and corresponding PGA were recorded and compared with the sample points under the solitary action of an earthquake, as shown in Figure 11. A log-linear regression was conducted on the sample points in Figure 11 to derive the probabilistic seismic demand model under the combined effects of an earthquake and snow. The ISDA_max values of the RS structure were generally lower than those of the GS structure for all scenarios. The distances between the regression lines of the RS and GS structures under the four scenarios of E, E + SR10, E + SR50, and E + SR100 were 0.080, 0.138, 0.184, and 0.211, respectively. The distances between the regression lines of the RS and GS structures under the four scenarios of E + UN50-0.01, E + UN50-0.02, E + UN50-0.03, and E + UN50-0.04 were 0.223, 0.234, 0.248, and 0.294, respectively. The distances between these lines gradually increased with an increasing standard deviation; however, the slope differences were relatively small. The RS structure with added reinforcement measures exhibited a smaller displacement response than the original GS structure under the combined effects of snow and earthquakes. Additionally, Ethe decrease in the displacement response of the RS structure under the combined effects of non-uniform snow loads and seismic activity was greater, indicating that structural measures can enhance the seismic resistance of lightweight steel structures.

Figure 11.

Regression analysis of engineering demand parameters and IM. (a) E. (b) E + SR10. (c) E + SR50. (d) E + SR100. (e) E + SR50 ( $σ$ = 0.01). (f) E + SR50 ( $σ$ = 0.02). (g) E + SR50 ( $σ$ = 0.03). (h) E + SR50 ( $σ$ = 0.04).

Figure 12 shows the seismic fragility curves of the GS and RS structures under the influence of uniform snow loads in various scenarios. Whether under seismic action alone or combined with uniform snow loads, RS consistently exhibited significantly lower probabilities of damage across all severity levels than GS. For example, under the E + SR50 scenario, the probabilities of minor damage for GS and RS at PGA = 0.2 g were 19.86 and 11.94%, respectively, indicating a 7.92% reduction in the RS minor damage probability. The probabilities of moderate damage for GS and RS at PGA = 0.4 g were 44.46 and 31.92%, respectively, representing a 12.54% decrease in the RS moderate damage probability. The probabilities of severe damage for GS and RS at PGA = 0.6 g were 22.75 and 14.06%, respectively, and the corresponding probabilities of collapse were 4.58 and 2.18%. The severe damage and collapse probabilities for RS, as compared with that for GS, decreased by 8.69 and 2.4%, respectively. These results demonstrate that the incorporation of simple seismic structural measures effectively reduces the combined effects of uniform snow loads and earthquakes on the structure.

Figure 12.

Fragility curves for the RS and GS structures under uniform snow loads with various return periods. (a) E. (b) E + SR10. (c) E + SR50. (d) E + SR100.

Figure 13 shows the seismic fragility curves of the GS and RS structures under non-uniform snow load conditions for the 50-year return period snow load scenario.

Figure 13.

Fragility curves for the RS and GS structures under non-uniform snow loads with a 50-year return period. (a) E + SR50 ( $σ$ = 0.01). (b) E + SR50 ( $σ$ = 0.02). (c) E + SR50 ( $σ$ = 0.03). (d) E + SR50 ( $σ$ = 0.04).

Figure 13 illustrates that the probabilities of damage at all severity levels for both GS and RS increase with an increasing $σ$ . The probabilities of minor damage for GS at PGA = 0.2 g and for $σ$ values ranging from 0.01 to 0.04 were 23.95, 26.74, 30.65, and 34.82%, respectively. In contrast, RS, as compared with GS, exhibited probabilities of 12.46, 14.02, 15.86, and 16.41%, respectively, indicating corresponding reductions in the minor damage probabilities of 11.49, 12.72, 14.79, and 18.41%. The probabilities of moderate damage for GS at PGA = 0.4 g and for $σ$ values ranging from 0.01 to 0.04 were 53.92, 59.68, 65.55, and 71.07%, respectively. However, RS exhibited corresponding probabilities of 36.49, 41.39, 46.23, and 48.73%, which represent corresponding moderate damage probability decreases of 17.43, 18.29, 19.32, and 22.34%, as compared with GS. The probabilities of severe damage for GS at PGA = 0.6 g and for $σ$ values ranging from 0.01 to 0.04 were 32.59, 39.35, 45.36, and 53.47%, respectively. RS, as compared with GS, exhibited corresponding probabilities of 19.53, 23.12, 27.87, and 30.85%, indicating corresponding severe damage probability reductions of 13.06, 16.23, 17.49, and 22.62%. The probabilities of collapse for GS were 8.20, 11.31, 15.12, and 19.68%, whereas those for RS were 3.32, 4.70, 6.34, and 7.49%, respectively, representing corresponding reductions of 4.88, 6.61, 8.78, and 12.19%, as compared with GS. These results demonstrate that RS consistently exhibits lower probabilities of damage across all levels than GS under varying degrees of non-uniform snow load conditions, indicating the effectiveness of incorporating seismic structural measures for mitigating the combined effects of snow loads and earthquakes on structural fragility.

Conclusion

This study employed IDA and fragility analyses to investigate the seismic fragility of long-span lightweight steel industrial buildings under combined snow and earthquake loads. Particular attention was given to the impact of the snow load intensity and non-uniform snow load distribution on the structural performance. Additionally, the initial effectiveness of basic seismic structural measures in mitigating the combined impacts of snow loads and seismic events was explored. The main conclusions drawn from this study are as follows:

(1) The presence of snow loads increases both the seismic response and the probability of structural damage. Both the seismic response and probability of different levels of damage increase significantly with an increasing snow load intensity. The impact of non-uniform snow loads further exacerbates this trend, where the seismic response and probability of various damage levels increase significantly with an increasing degree of non-uniformity. For example, the ISDA_max values corresponding to the 50^th percentile under a 50-year return period snow load at a PGA of 0.2 g, 0.4 g, and 0.6gE increased by 35.29, 41.79, and 77.42%, respectively, as compared with that under isolated earthquake conditions. The probabilities of slight, moderate, and severe damage under combined snow and seismic loads with a PGA of 0.4 g increased by 32.27, 33.09, and 2.31%, respectively. The probabilities of moderate damage, severe damage, and collapse at a PGA of 0.6 g increased by 44.66, 20.72, and 4.44%, respectively. The ISDA_max values corresponding to the 50th percentile under non-uniform snow loads (such as $σ$ = 0.04), as compared with uniform snow loads, at PGAs of 0.2 g, 0.4 g, and 0.6 g increased by 24.59, 34.00, and 36.36%, respectively. The probability of slight damage at a PGA of 0.2 g was 17.45%. The probabilities of moderate and severe damage at the PGA of 0.4 g were 39.28 and 1.77%, respectively. The probabilities of severe damage and collapse at a PGA of 0.6 g were 18.27 and 3.25%, respectively.

(2) The simple seismic measures applied to the structure can effectively reduce the impact of both isolated earthquakes and the combined action of snow and earthquakes on structures. RS with additional seismic measures exhibits significantly lower probabilities of seismic damage under all conditions than the original GS structure. The probability of slight damage for RS under a uniform snow load with a 50-year return period at a PGA of 0.2 g was 11.94%, which is 7.92% lower than that for GS. The probability of moderate damage for RS at a PGA of 0.4 g was 31.92%, which is 12.54% lower than that for GS. The probabilities of severe damage and collapse for RS at a PGA of 0.6 g were 14.06 and 2.18%, respectively, which are respectively 8.69 and 2.4% lower than those for GS. The probability of slight damage for RS under non-uniform snow loads (such as $σ$ = 0.04) at a PGA of 0.2 g was 16.41%, which is 18.41% lower than that for GS. The probability of moderate damage for RS at a PGA of 0.4 g was 48.73%, which is 22.34% lower than that for GS. The probabilities of severe damage and collapse for RS at a PGA of 0.6 g were 30.85 and 7.49%, respectively, which are 22.62 and 12.19% lower than those for GS, respectively. These results clearly demonstrate that the reduction in damage probabilities under non-uniform snow loads is more significant, indicating that the simple seismic structural measures discussed in this study are effective in resisting the combined effects of non-uniform snow loads and earthquakes.

(3) Further research is needed to determine if the results for the simple structures investigated in this study apply to complex structures to refine the study of such structures under multi-disaster scenarios. Additionally, the impact of post-earthquake snow on the structure is significant. The residual displacement and damage to the structure after an earthquake will decrease its snow resistance, which is another consequence of multi-disaster effects. Future research efforts should further explore this aspect. The results of this study can serve as an important theoretical guide for enhancing the safety of lightweight steel structures subjected to multiple hazards in cold regions.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclose receipt of the following financial support for the research, authorship, and/or publication of this article: this work was supported by the Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology [2022B08], and Shenyang Young and Middle-aged Science and Technology Innovation Talent Program [RC220171].

ORCID iD

Shiwei Hou

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