Assessing the Impact of Ground Motion Duration on Losses in Typical Modern Steel Moment Frames

Abstract

This research was undertaken to study the duration effects on the seismic economic risk of steel moment frame (SMF) buildings, a prominent class of buildings in commercial stock. Firstly, a modified version of FEMA P-695 ground motion scaling, tailored for seismic loss estimation purposes and incorporating two sets of spectrally matched bi-directional short- and long-duration ground motions, is proposed to study code-compliant plan-symmetrical SMFs with different heights (i.e., two to 20 stories). It is shown that long-duration ground motions increase the collapse risk of SMFs, on average, by 28.0% at the MCE level. Next, a component-based loss estimation methodology was adopted for evaluating the seismic losses under each set of ground motions. These losses are studied separately for building components (i.e., structural and nonstructural) and contents. Moreover, we propose an approach for calculating average annualized loss (AAL) as a prominent risk meter that segregates contributions of short- and long-duration ground motions to attain hazard consistency. Loss analyses showed the minimal impact of building height on the contribution of these two types of earthquakes. The seismic risk analysis of buildings also revealed that collapse risk is influenced mainly by duration effects followed by building and content losses.

1. Introduction

Duration is a key characteristic of ground motions. The strong shaking during a moderate or large earthquake typically lasts 10 to 30 s; however, at certain seismic zones (e.g., subduction), faulting systems can trigger strong ground motions that typically have a much longer duration, e.g., greater than 1 min. Modern buildings are designed in accordance with seismic codes and regulations that generally do not take long-duration earthquakes into consideration [1]. Extensive destruction to buildings and infrastructures brought about by long-duration seismic events, like those occurring in Maule, Chile, in 2010 and Tohoku, Japan, in 2011, has raised considerable concerns among researchers, insurance carriers, business owners, authorities, and property managers. A quick look at a world map showing major subduction faults reveals that large cities and associated critical infrastructures, including important metropolitan areas on the west coast of the United States (e.g., Seattle, WA, USA), are highly exposed to long-duration severe ground shaking. Loss assessment methodologies, however, such as FEMA’s HAZUS-MH methodology [2], do not explicitly consider the ground-motion duration effects on seismic losses.

Over the past decades, various researchers have studied the effects of ground motion duration on the seismic performance of buildings. An early study conducted by van de Lindt and Goh revealed the significant impact of long-duration ground motions on the reliability of structural systems [3]. More recently, researchers have employed incremental dynamic analysis (IDA) more extensively to study the impact of ground motion duration on the seismic performance of structural systems. However, to quantify the impact of long-duration compared with short-duration shakings, the spectral shape effect needs to be isolated by considering two separate representative ensembles of spectrally matched ground motions. In this way, insights can be obtained into the relative impact of ground motion duration. Many researchers have utilized this approach to gauge duration effects using single degree of freedom (SDOF) modeling [4,5,6,7] on the seismic performance of different structural systems, including bridges [8], reinforced concrete structures [9,10,11], and light-frame wood constructions [12,13,14,15]. In terms of steel moment frames, the focus of the current study, Liapopoulou et al. [7], Chandramohan et al. [16], and Hwang et al. [17] found that long-duration ground motions resulted in a relatively 20%, 29%, and 43% reduction in median collapse capacity (i.e., median spectral acceleration of collapse at the fundamental period of buildings), respectively. Additionally, Zengin et al. [18] reported that long-duration earthquakes amplify the mean annual frequency of collapse of SMFs by 3.5 times when compared to corresponding short-duration earthquakes. Overall, these studies prove the detrimental impact of long-duration earthquakes on structural systems in terms of collapse fragility and damage index.

As briefly mentioned above, a comprehensive literature review showed that most studies conducted on duration effects stopped short of studying seismic losses, particularly nonstructural and content damage and loss. Understanding how duration affects seismic losses could be of great significance in assessing seismic risk and the resilience of communities. Hence, this study proposes an overall seismic performance-based assessment framework that considers spectrally matched long-duration earthquakes.

More recently, Hwang et al. [17] studied the effects of long-duration earthquakes on the seismic collapse risk and losses of four modern steel structures utilizing the ground motions from work by Chandramohan et al. [16]. The current authors’ similar study on light-frame wood buildings revealed the considerable impact ground motions had on incurred losses [19]. It is worth mentioning that these studies incorporate two sets of ground motions in which horizontal components of different ground motions are mixed and matched. Even though such ground motion ensembles are utilized for loss estimation [17], this practice does not seem sound because seismic loss estimation requires predicting seismic responses in the two main orthogonal directions. Belejo et al. extended Chandramohan et al.’s approach for 3D structural analyses by spectrally matching the geomean of two orthogonal rotated short-duration components with the as-recorded long-duration components [20]. Although this strategy seems promising, it may not be effective for all ground motions, especially unpolarized ones, as defined by Shahi and Baker [21]. As a result, this study proposes a modified version of the well-known FEMA P-695 scaling procedure that incorporates a spectral matching approach by matching the geometric means of both horizontal components of short-duration and long-duration pairs [21]. Furthermore, Otarola et al. investigated the influence of ground motion duration on seismic losses in SDOFs and RC frames through a simplified approach utilizing damage-to-loss ratios and system-level fragility functions—similar to the HAZUS-MH approach. However, they did not differentiate between losses attributed to structural, non-structural, and content elements [22,23].

To address the issue under research, an understanding is needed of the effects of subduction earthquakes on steel structures of different heights as well as the loss associated with two primary insurance coverages (i.e., building and content) of a building property. The current study was undertaken on modern commercial buildings with steel moment frames, one of the leading commercial construction types. As high-rise buildings are unlikely to collapse, how building height affects financial losses from events other than collapse is a critical issue [24]. At the outset, this paper proposes a modified version of the FEMA P-695 [25] ground motion scaling procedure to pave the way for studying the influence of ground motion duration on the expected loss. First, a bi-directional, spectrally matched database of 50 ground motions corresponding to 25 long- and 25 short-duration ground motions is designated. Thereafter, the modified approach is employed to conduct IDA on steel moment frame archetypes with heights ranging from two to 20 stories designed for a high seismic region. Next, the structural analysis results are relayed to a building-specific loss assessment framework developed based on FEMA P-58 provisions [26] to assess the impact of different ground motion durations on structural and nonstructural components as well as content losses, separately. Average annual loss (AAL) is a vital risk index applied to quantify losses and make financial-related decisions (e.g., determining insurance rates). This paper proposes an effective approach to computing AAL, which segregates the contribution of short- and long-duration earthquakes and helps derive a hazard-consistent estimate of AAL, as urged in an earlier study [17].

2. Selecting and Scaling Ground Motions

Selecting and scaling ground motions are crucial for predicting a building’s seismic response to quantify its seismic performance. FEMA P-695 provisions are widely used in IDA, which recommends a selecting and scaling method consisting of two main steps, i.e., normalizing and group scaling. The P-695 approach, however, does not account for long-duration (i.e., subduction zone) ground motions. Moreover, the spectral matching technique is used to study duration effects [16], whereby each horizontal component of long-duration ground motions is matched with a horizontal component of short-duration ground motions based on spectral shape. This study proposes a modified version of FEMA P-695 suitable for spectral matching technique and seismic loss analysis.

2.1. Selection of Ground Motions

Twenty-five bi-directional ground motion records were collected from the PEER NGA-West2 [27], K-Net, and Kik-net databases [28], and the Consortium of Organizations for Strong-Motion Observation Systems (COSMOS) Virtual Data Center [29]. Subduction earthquakes included long-duration earthquakes from nine events. The records are characterized by significant durations of 5% to 95% (D_5–95%); this parameter is defined as the time interval between accumulated Arias intensity (I_a) of 5.0% and 95.0%, as described elsewhere [16], as shown in Figure 1.

Records with a significant duration of D_5–95% longer than 30 s were classified as long-duration [16]. The proposed methodology for the selection of the short-duration records comprises the following steps:

Step 1: Select a source (e.g., PEER NGA-West2 database) for short-duration ground motions. The short-duration records are classified as those with a significant duration (D_5–95%) of less than 30 s.

Step 2: Compute 5% damped elastic response spectra for each pair of as-recorded short-duration and as-recorded long-duration records. Then, find the geometric mean of the orthogonal response spectra for both long- and short-duration pairs. Finally, select a matching factor (MF) that yields the minimum sum of the squared error (SSE) as follows:

$$SSE={\sum }_{i=1}^N\left(\right(MF\left){Sa}_{gm}^{LD}\right(T_i)-{Sa}_{gm}^{SD}(T_i\left)\right)$$

(1)

where ${Sa}_{gm}^{LD}\left(T_i\right)$ is the geomean spectral acceleration ordinate at each discretized period T_i corresponding to as-recorded long-duration components, ${Sa}_{gm}^{SD}\left(T_i\right)$ is the geomean spectral acceleration ordinate at each discretized period T_i corresponding to the as-recorded short-duration records, and N is the number of the period intervals. The period range of interest is 0.05 < T < 5.0 s to include low-, mid-, and high-rise structures.

Step 3: For the short-duration set, normalize the short-duration pairs according to the FEMA P-695 procedure. For each short-duration record (j), find the peak ground velocity (PGV_j) for both orthogonal components. Then, determine the geometric mean of both components (PGV_gm,j). The normalization factor (NM_j) is:

$${NM}_j=\frac{\widehat{{PGV}_{gm}}}{{PGV}_{gm,j}}$$

(2)

where $\widehat{{PGV}_{gm}}$ is the median of PGV_gm,j values for the set of ground motions. Normalization reduces record-to-record variability, which alleviates the need for a large number of ground motion records. Both short-duration orthogonal components are multiplied by the same normalization factor to preserve the relative strength of each ground motion component [25]. Figure 2 presents the natural log of response spectra of 50 individual short-duration records (25 pairs), the natural log median, and two natural log standard deviations (LnSTRDev).

Step 4: Repeat Step 2, but this time for each pair of the normalized short-duration and as-recorded long-duration records, compute the elastic response spectra at 5% damping, then find the geometric mean of the orthogonal response spectra for both long- and short-duration pairs. Finally, select the new matching factor (MF) that yields the minimum SSE. Figure 3 displays the matched geometric response spectra of the third pair of long- and short-duration ground motions and those corresponding to components.

Appendix A lists the selected pairs of long-duration and short-duration earthquake records as well as normalization and matching factors. In this work, we adopted predefined matched pairs of long and short records handpicked from the previous literature. It is worth mentioning that pulse-like ground motions are eliminated. Figure 4 presents an overview of various key characteristics of selected short- and long-duration ground motions in terms of D_5–95%, magnitude (M_w), and rapture distance (R_rup). Figure 5 shows the median of the geometric mean of long- and short-duration spectra, revealing a good match between them.

2.2. Group Scaling

FEMA P-695 scaling procedure requires the spectrum of normalized selected ground motions to be scaled altogether to a series of select incrementally increasing spectral accelerations using group factor (GF) to conduct the IDA and evaluate the collapse capacity of the building. In a nutshell, the final scaling factor (SF) can be calculated from:

$${{STH}^{LD}=SF}_{LD}·{TH}^{LD}=MF·GF·{TH}^{LD}$$

(3)

$$S{TH}^{SD}{=SF}_{SD}·{TH}^{SD}=NM·GF·{TH}^{SD}$$

(4)

where SF_SD and SF_LD are defined as the final short-duration and long-duration scaling factors, respectively; TH^SD and TH^LD are the time history of each component and each short- and long-duration ground motion, respectively; and GF is the group factor. STH^SD and STH^LD are the scaled time history of each component and each short- and long-duration ground motion, respectively. More details can be found in FEMA P-695.

3. Studied Steel Moment Frame Buildings

The west coast of the United States is prone to long-duration ground shakings because of the proximity of subduction fault systems in the Pacific Ocean. Important cities in the region, like Seattle, WA, are centers of many vital industries. Steel construction in this area is known to play a dominant role in commercial building stock [30]. Studies have also shown that ductile buildings are more drastically influenced by long-duration ground motions than non-ductile buildings [11]. The current study is devoted to modern steel moment frames designed for high seismic regions, or seismic design category (SDC) D [31], and assumes that such buildings are located in Seattle, WA. Modeling is conducted using the OpenSees software package [32]. The lateral system of the buildings is a perimeter moment frame with reduced beam section (RBS) connections, which are widely used prequalified steel moment connections [33].

To investigate the effects of building height, five buildings with 2, 4, 8, 12, and 20 stories were selected and referred to as SMF2, SMF4, SMF8, SMF12, and SMF20, respectively. The building footprint was 42.7 m by 30.5 m; the typical story height was 4 m, but the first story was 4.6 m high. Figure 6 presents the layout and elevation view of the building archetype. The five buildings were simulated with a phenomenological modeling approach incorporating two sets of nonlinear springs, the first of which accounts for the flexural nonlinearities of steel members, including cyclic deterioration through the Ibarra–Medina–Krawinkler (IMK)’s modified deterioration model [34], and the second for the shear nonlinearity of the panel zone region through Gupta and Krawinkler’s trilinear model [34]. The models consider the contributions of the gravity system and composite action. The models also take P-Delta effects into consideration by incorporating leaning columns. Further details about the models, including ductility, mode shapes, and plastic hinge formation, can be found elsewhere [35,36,37].

The fundamental periods for the five models were determined to be 0.68 s, 1.31 s, 1.81 s, 2.45 s, and 3.18 s, respectively, using eigenvalue analysis. IDA was conducted for each building separately for the ensemble of short- and long-duration ground motions. Each ground motion was scaled up incrementally using 5% spectral damping acceleration at the fundamental period of the building until collapse was reached. We adopted the non-simulated collapse strategy, by which the collapse is defined as the maximum story drift ratio exceeding a certain limit (i.e., 10%) or the story shear resistance becoming zero. Figure 7 compares the dynamic capacity curves (i.e., IDA curves) for each building for short- and long-duration ground motions. The IDA curves represent the relationship between the maximum story drift ratio and the fundamental period’s spectral acceleration. The collapse capacity of the buildings is characterized based on the IDA results in terms of median collapse spectral acceleration ($\widehat{S_{CT}}$) and the associated dispersion. As can be seen, all buildings subjected to long-duration sets had a lower collapse capacity than those exposed to short-duration sets. On average, the median collapse spectral acceleration of a building is 28% lower under long-duration ground motions. Generally, SMF4 had a lower median collapse capacity than SMF2, because its overstrength is lower than that of SMF2 [35].

4. Loss Assessments

The seismic loss of the building archetypes was computed using a component-based loss assessment framework which utilizes the FEMA P-58 [26] methodology relying on the framework by the Pacific Earthquake Engineering Research (PEER) Center. The framework partitions the whole risk assessment domain into four subdomains, i.e., hazard, structural, damage, and loss analyses, interconnected in a Markov chain manner. The last two analyses, i.e., loss and damage, were merged and are referred to herein as the loss assessment framework. The framework consists of three separate sequential modules, namely the collapse check, irreparability check, and component-wise loss calculation. Loss assessment was performed using a previously developed MATLAB-based [38] computational platform called Apocalyptic Structural Assessment Program (ASAP) and implemented on the high-performance computing facilities of Clemson University, dubbed the Palmetto Cluster [39]. FEMA P-58 provides minimal content component fragility functions in its database. Therefore, content fragility and consequence functions were developed for this study based on earlier work [40] and added to the ASAP’s clearinghouse. The toolbox was used extensively for loss estimation purposes, e.g., [41]. Losses made by the adopted archetypes’ structural, nonstructural, and content components were studied; however, the losses sustained by the building (i.e., structural and nonstructural components) and its content were treated separately, according to the norm of insurance risk modeling.

Loss due to structural collapse is a main contributor to building and content losses. It is predicted by considering the collapse fragility of a structure idealized using the lognormal cumulative distribution function without any adjustment for spectral shape. FEMA P-58 provisions emphasize incorporation with three-dimensional modeling of structures. In this study, two-dimensional nonlinear modeling was adopted because the lateral force resisting system of each building consists of two uncoupled perimeter moment frames. The seismic responses of each building can be reasonably modeled using a separate two-dimensional moment frame in each of the lateral directions (Figure 6). The probability of building collapse at a given intensity measure, assuming the collapses of the two moment frames are statistically independent (S.I.), is computed as:

$$P_{2D}\left(C|IM\right)=\frac{n_{C1}}{n_{GM}}+\frac{n_{C2}}{n_{GM}}-\frac{n_{C1}}{n_{GM}}\frac{n_{C2}}{n_{GM}}$$

(5)

where $P_{2D}\left(C\right|IM)$ is the building collapse probability at a given intensity measure assessed using two-dimensional analysis and S.I. moment frames; n_C1 and n_C2 are the number of collapsed cases in directions 1 and 2, respectively (shown in Figure 6); and n_GM is the total number of selected ground motions (25 for the current study).

In a three-dimensional structure or building, the collapse of a moment frame in one of the lateral directions will result in the collapse of the building. Thus, it is more appropriate to assume the collapses of the two moment frames as fully dependent. The building collapse probability assuming the two moment frames are fully dependent is expressed as follows:

$$P_{P3D}\left(C\right|IM)=\frac{n_{C1\cup C2}}{n_{GM}}$$

(6)

where $P_{P3D}\left(C\right|IM)$ is the pseudo-three-dimensional collapse probability at a given intensity measure, assuming the collapses of the two moment frames are fully dependent, and $n_{C1\cup C2}$ is the number of occurrences of collapse in either direction 1 or direction 2. Equation (6) reflects that the collapse events are not independent in directions 1 and 2 for the studied structural system, even though the structure’s responses can be assumed to be independent for these two directions. The relationship also implies that the collapse of seismic frames in one direction is equivalent to the collapse of the whole structure for these structural systems. Equation (6) might be used to predict collapse probability for similar structural systems that are independent in two directions, like shear walls or bracing, using two-dimensional analysis.

Repairability plays an essential role in the prediction of seismic losses for modern buildings. Repairability, however, is only considered in predicting losses related to the building (i.e., structural and nonstructural components). FEMA P-58 makes use of an irreparability model which relates irreparability probability to residual drifts. As stated earlier, the nonlinear models used in the current course of study are incorporated with the IMK hysteresis model. The residual drifts predicted using this model are known to be less reliable [42].

The current study utilized the repairability model developed by Safiey and Pang, which defines repairability as a state in which “repair cost” exceeds “reconstruction cost”. The great advantage of this model is the ability to account for various exogenous or external factors (e.g., insurance and heritage values) as well as endogenous or internal factors (e.g., structural system). For simplicity, it was assumed that the building was uninsured. The parameters associated with the repairability model were set to L_m = n. 2000 USD, ${\lambda }_D=n. 7000\frac{USD}{day},$ and RCV_T = n. 504000 USD, where n represents the number of stories, L_m is miscellaneous indirect losses, ${\lambda }_D$ is the daily downtime loss, and RCV_T is indirect replacement cost. Refer to [43] for more details. The direct replacement cost of the building was predicted based on the maximum repair cost obtained from the corresponding consequence functions.

A total of 39 structural and nonstructural vulnerable components were identified for the studied buildings. The fragility and consequence functions of these components were chosen based on FEMA P-58 provisions. The quantity of the vulnerable nonstructural components was determined according to FEMA P-58 recommendations. Appendix B presents the list of structural and nonstructural components. Some of the component fragility functions are sensitive to peak floor acceleration and some to inter-story drift ratios.

Buildings contain at each floor approximately 1302 square m (14,015 square ft) of office space and are assumed to accommodate fifteen office units, or so-called consequence areas, measuring 71 square m (768 square ft), as shown in Figure 6. A total of 113 content objects from 31 groups are included in one consequence area. The normative quantity for each component, i.e., the quantity for each component per unit gross square area, is estimated based on engineering judgment. The replacement cost is estimated based on the Xactimate 2019 database [44], computer software that estimates the cost of property repairs. The contents and their normative quantities are listed in Appendix C. The component fragility functions for content are developed for two independent major failure modes, namely, sliding or overturning, which are sensitive to peak floor acceleration (more information about fragility function derivation can be found in [40,45]). Heavy and electrical content components are herein considered anchored based on engineering judgment [40,45]. Figure 8 presents fragility functions for one anchored (bookcase) and one unanchored component (chair) under both failure modes. Each content component is assumed to have one damage state if unanchored (DS1); DS1 is defined as excessive sliding (when the maximum displacement exceeds a certain displacement threshold) or overturning. If anchored, however, each content component is assumed to have two damage states (DS1, DS2); DS1 is defined as restraint breakage due to sliding or rocking, and DS2 is defined as excessive sliding or overturning. Each content component loss is determined by first calculating the loss due to each failure mode and then considering the maximum of the two modes.

Each component is also represented by a consequence function. Based on engineering judgment, the content consequence function is assumed to be normally distributed with the damage ratio as a median and 20% variance to define the uncertainty of the repair cost. In the case of restraint breakage (DS1 for anchored components), the damage ratio is the restrainer replacement cost ratio for all anchored components. In the case of excessive sliding or overturning (DS2 for anchored components or DS1 for unanchored components), the damage ratio depends on the content type. For example, glassware is expected to have 100% damage if overturned, whereas chairs will incur less damage. The damage ratio is assigned to contents as follows: 30% for furniture, 80% for electrical components, and 100% for glassware [46]. Figure 8 presents the consequence function for the two selected components (chair and bookcase).

In the first step, the vulnerability function of each archetype, defined as the mean economic losses versus the spectral acceleration as an intensity measure, is studied. Figure 9 presents the vulnerability of each archetype separately for long- and short-duration shakings. Each plot includes the collapse losses together with content and building vulnerability functions. The building or content loss ratio is the mean total loss divided by the total replacement cost (replacement value). Broadly speaking, the trends of collapse, content, and building losses are similar. The predicted mean values of content and building losses are similar for different heights under long- and short-duration shakings. To be more specific, building losses are higher than content losses for the 2-story building; however, this trend is the opposite for 4- and 8-story buildings. For taller buildings, higher content losses are observed at lower levels of shaking. Nonetheless, this trend was reversed for this building archetype at spectral accelerations between 0.4 to 0.6 g, except for SMF20 under long-duration ground motions.

To facilitate studying the relationship between height and incurred losses at different levels of ground shaking, three ground motion levels (SLE, DBE, and MCE_R) were chosen to represent different severity levels of seismic events. Figure 10 presents the collapse losses for the studied steel frame buildings at these three levels of shaking. Notably, long-duration shaking resulted in higher collapse losses than short-duration shaking. The collapse risk is highest for a 4-story building, as discussed earlier. Figure 10 and Figure 11 also reveal that the trend of content loss from SLE and DBE levels is not downward for heights greater than 4-story. As discussed earlier, the content components are solely sensitive to acceleration. The contribution of collapse to content loss is negligible for these buildings at SLE and DBE. Another observation indicates that short-duration losses at these levels are higher than long-duration losses, because longer shaking durations and longer periods resulted in lower peak floor accelerations (PFAs) compared with short-duration ground motions, which is consistent with the results of an earlier study [47]. This is because of the expeditious release of energy for short-duration shakings (crustal faults), as reported in other studies [47,48].

A further step is taken by calculating and comparing each archetype’s AAL, which can be computed using the following relationship inferred from FEMA P-58 provisions:

$$AAL=\int \lambda \left(L\right)dL=\iint P\left(L>l|IM\right)d\lambda \left(IM\right)dL$$

(7)

where AAL stands for average annual loss, $\lambda \left(L\right)$ is the annual frequency of exceedance at a given loss, $P\left(L>l|IM\right)$ is the probability of exceeding a certain amount of loss at a specific shaking intensity, and $\lambda \left(IM\right)$ is the annual frequency of exceedance of a given shaking intensity, which is known as the hazard curve of the site of the building. To estimate the total average annual loss (AAL_T), we propose breaking it down into two parts, the first being AAL_LD, defined as the contributions of long-duration shakings (i.e., subduction faults), and the second one being AAL_SD, defined as the contributions of short-duration shakings (i.e., crustal faults). This approach separates the contribution of long- and short-duration earthquakes considered earlier by researchers to determine the annual collapse rate [11]. The described relationship can be mathematically expressed as:

$${AAL}_T={AAL}_{LD}+{AAL}_{SD}$$

(8)

Contributions of long- and short-duration ground motions to the total AAL can be estimated separately using Equation (7) substituted into Equation (8), as follows:

$${AAL}_T=\iint P_{LD}\left(L>l|IM\right)d{\lambda }_{LD}\left(IM\right)dL+\iint P_{SD}\left(L>l|IM\right)d{\lambda }_{SD}\left(IM\right)dL$$

(9)

where $P_{LD}\left(L>l|IM\right)$ and $P_{SD}\left(L>l|IM\right)$ can be predicted using the building-specific loss assessment for each building under long- and short-duration ground shaking sets, respectively. ${\lambda }_{LD}\left(IM\right)$ and ${\lambda }_{SD}\left(IM\right)$ are hazard curves for the building site for long-duration (i.e., subduction) and short-duration (i.e., crustal) ground motions. The event-type-specific hazard curve of Seattle, WA, with soil type D [49] was used to compute AALs for the studied buildings. Figure 12 shows the seismic hazard curves for the building site disaggregated as the short-duration (crustal) and long-duration (subduction) hazard curves for a building with a period of 1.31 s. Crustal events consist of gridded and fault event types, while subduction events encompass interface and slab event types [50]. Bradley et al.’s parametric hazard model is utilized to facilitate the numerical implementation of the proposed method [51]. The annual frequency of collapse (${\mathsf{\lambda }}_{\mathrm{C}}$) of the buildings is determined using the same strategy:

$${\lambda }_C=\int P_{CLD}\left(IM\right)d{\lambda }_{LD}\left(IM\right)dIM+\int P_{CSD}\left(IM\right)d{\lambda }_{SD}\left(IM\right)dIM$$

(10)

wherein P_CLD(IM) and P_CSD(IM) are the collapse fragility functions for the building obtained from IDA and expressed in the format of the lognormal cumulative distribution function under long- and short-duration sets of ground motions, respectively. Figure 13 presents the annual frequency of collapse and AAL for each building. Clearly, the trends of content and building AALs under short- and long-duration ground motions are similar to those of corresponding annual frequencies of collapse.

The following two ratios are introduced to quantify the contribution of long-duration ground motions on the total AAL and annual frequencies of collapse:

$$R_{AAL-LD}=\frac{{AAL}_{LD}}{{AAL}_T}$$

(11)

$$R_{C-LD}=\frac{{\lambda }_{C-LD}}{{\lambda }_C}$$

(12)

where $R_{AAL-LD}$ and $R_{C-LD}$ are the contributions of long-duration ground motions on AAL_T and ${\lambda }_C$, respectively. Figure 13 provides the estimates of these two ratios for all studied buildings. As can be seen, the contribution of long-duration earthquakes to the annual frequency of collapse is always more significant than that of short-duration earthquakes, which can be explained through the higher energy dissipation from a larger number of cycles which results in more deterioration and, accordingly, higher collapse rates induced by long-duration ground motions.

The annual frequency of collapse is the primary concern of design codes like ASCE 7–16 [31], which target a uniform collapse risk to preserve the same level of life safety across the country. Figure 13 also reveals that the contribution of long-duration records to the predicted AAL values for either building or content is always smaller than that of short-duration records. The only exception is SMF2, with an estimated $R_{AAL-LD}$ for the building of slightly greater than 0.5. Moreover, the following relationship can be deduced from Figure 13 for the studied buildings:

$${R_{AAL-LD}^{Content}<R}_{AAL-LD}^{Building}<R_{C-LD}$$

(13)

where $R_{AAL-LD}^{Content}$ and $R_{AAL-LD}^{Building}$ are the contributions of long-duration ground motions to AAL_T predicted for content and building, respectively. The above relationship indicates that long-duration ground motions for the studied buildings contributed less to the AAL of content than that of buildings. AALs are controlled mainly by losses at lower motion levels. Content components are sensitive to peak floor acceleration. Therefore, the higher accelerations developed by short-duration ground motions at the lower levels of shaking, also reported by [47], could explain why long-duration ground motions make the lowest contribution to content losses. Figure 13 further reveals relatively higher losses occurring to the content under short-duration ground motions at SLE, which represents low-level shakings.

Average annual losses are of great importance to managers, stakeholders, and insurance carriers. Two separate coverages of an earthquake insurance policy for building properties typically protect building losses (“coverage A” or “damage to house”) and content losses (“coverage C” or “personal property”). The results show that for the special steel moment frames studied in this paper, regardless of building height, long-duration ground motions had a greater impact on the insured properties of the building than the content.

5. Conclusions

Most prior research has focused almost exclusively on the impact of long-duration ground motion on building collapse, especially in the Pacific Northwest region. Even though several authors have reported that long-duration shakings amplify collapse risk, its impact on non-collapse risk from building and content damages is still lacking in the literature. To fill this knowledge gap, the current study has provided new results on the collapse and non-collapse risk of steel moment frames. This research examined the influence of ground motion duration on the seismic economic risk of five modern steel moment frame buildings with heights ranging from two to 20 stories.

The previous studies highlight the importance of ground motion duration in assessing the performance of structural systems. An approach for selecting and scaling ground motions was proposed for researchers and practitioners when applying the guidelines of FEMA P-695 and FEMA P-58 to quantify the seismic performance of a building. The ground motion selection approach is a FEMA P-695 modified approach in which the spectral shape of the bi-directional components of short-duration ground motions is matched with that of long-duration ones. A component-based loss estimation methodology is adopted to predict seismic losses sustained by buildings impacted by short- and long-duration ground motions. Key results and conclusions can be summarized as follows:

• A simple yet effective approach was proposed to provide a hazard-consistent estimate of AAL for building properties. The approach was used to predict this parameter for studied buildings providing insights into the contribution of long-duration ground motions to the aggregate economic losses;
• The proposed scaling methodology for long-duration ground motions is applied to the FEMA P-695 approach in a way compatible with FEMA P-58 component-based loss modeling. It proves practical for comparisons with the risk associated with short-duration ground motions;
• Long-duration ground motion reduces the collapse capacity for all the studied steel moment frames, where the collapse capacity was 31%, 29%, 31%, 26%, and 23% lower than that of the 2-, 4-, 8-, 12-, and 20-story steel moment frames under short-duration ground motions, respectively. This result aligns with the conclusions of other similar works [7,16,17,18];
• From moderate to extreme ground motion intensities, long duration exerts a higher impact on the building’s total dollar loss. The main reason for this increase is the higher contribution of collapse loss, as long-duration shakings result in higher energy dissipation and deterioration. The influence is more apparent in low- and mid-rise models;
• Contents have higher loss ratios at lower shaking levels than structural and nonstructural components; however, the loss ratios for both building and content are close in value;
• Long-duration ground motion does not play a significant role in the peak floor acceleration of buildings of different heights. Hence, it does not influence content losses, which depend solely on peak floor acceleration;
• The average annual collapse loss is higher for long-duration ground motions than for short-duration shakings. The long-duration ground motions for the studied buildings made a lower contribution to the AALs of content than those of the building.

The scope of this study was only limited to modern steel structures. Therefore, further studies are needed to investigate the influence of long-duration ground motions on economic risk for different structural systems designed for different ductility levels. Furthermore, the study focuses on moment frame buildings with symmetrical floor plans devoid of specific characteristics such as plan irregularities or soft stories. Exploring the impact of such features on a building could be a potential area for future investigation.