Journal of Structural Engineering

Steel eccentrically braced frames (EBFs) combine the advantages of both moment-resisting frames and concentrically braced frames and provide an attractive seismic design solution. Shear-critical replaceable links were developed about a decade ago to improve the performance, design process, construction, and postearthquake repair process in EBFs. However, replaceable shear links are still susceptible to the commonly observed limit states in EBF links such as web fracture close to web stiffeners, local buckling, and lateral torsional buckling. This paper presents the experimental validation of a new generation of optimized cast steel replaceable yielding links for use in EBFs, which address the shortcomings of conventional and fabricated replaceable links. The performance of the proposed cast steel links is investigated through nine large-scale component-level and system-level experiments, covering a range of link sizes and loading conditions, while also studying the impact of other phenomena influencing the response such as the presence of axial load, the level of axial restraint in the links and the presence of a concrete slab. The tested series of cast links demonstrated enhanced ductility levels and low-cycle fatigue life when compared to fabricated links, achieving up to 0.21 radians of link rotation under the AISC protocol used for the qualification of EBF links.

The possible failure modes of cold-formed steel (CFS) lipped angle (LA) compression members are yielding, local, flexural torsional, or flexural buckling, and any possible interaction among these buckling modes. In general, the strength estimated by current design guidelines are conservative for these members when flexural-torsional buckling (FTB) is the first global buckling mode because the postbuckling strength of this mode is not accounted for in the global buckling strength equations. The initial part of this paper reports the results of an experimental and numerical study of CFS-LA members undergoing independent FTB. Modifications are suggested to global buckling strength equations based on these results. Subsequently, the reduction in the ultimate strength from strength corresponding to independent buckling modes for LA members undergoing interaction between buckling modes such as local-flexural torsional, flexural-flexural torsional, local-flexural, and local-flexural torsional-flexural are studied systematically using finite-element analysis results. A simple and more accurate interaction equation that accounts for these interactions among buckling modes in CFS-LA compression members is proposed.

Abstract

A physical model of the simplest three-dimensional tensegrity unit was built at human scale out of aluminum. Self-stress implementation and static loading tests were performed on this model. At each step, accurate measurements were obtained for all nodal positions and element forces. For the prestressing phase, elongations were imposed, via mechanical devices, in different combinations of elements, called prestress scenarios. Experimental results are compared to the theoretical self-stress state obtained by singular value decomposition of the equilibrium matrix and to numerical simulations using the dynamic relaxation method. It is shown that internal forces follow the same linear trend for all prestress scenarios even if the geometry is significantly impacted. Compressive tests were conducted by hanging masses from the top nodes. It is shown that there exists a unique load-displacement relation that follows the infinitesimal mechanism direction for a finite distance, which depends on the self-stress level. The paper provides a detailed overview of the simplex’s structural behavior using both experimental and numerical results while discussing the limitations of the analysis methods explored.

Practical Applications

Tensegrity structures are composed of compressive elements floating inside a network of prestressed cables. Their unique aesthetics and mechanical properties have always amazed architects, scientists, and engineers. However, the number of tensegrity structures built for civil purposes remains limited. Reasons behind this include a nonintuitive structural behavior with occurrences of insufficient stiffness and lack of robustness as well as a complex construction process that requires introduction of prestressing forces. Consequently, tensegrity structures are often distrusted in favor of other structural systems. Many studies have focused on finding the conditions required for the existence of self-equilibrated prestressing forces that provide stability and stiffness in tensegrity structures. However, few studies have focused on how these prestressing forces can be implemented in a structure, and the discrepancy between theoretical and numerical approaches. For these reasons, a full-scale physical model of a tensegrity module was built and tested with extreme care on the design and experimental testing. This paper presents a comparison of experimental results using two established analysis methods discussing the differences between experimental measurements and numerical models.

Large-scale experimental tests were conducted to evaluate the strength of partial joint penetration (PJP) groove welds in axially loaded transverse plate-to-circular hollow section (CHS) X-connections. Six connections, comprising 12 joints, were designed to investigate the influence of branch-to-chord width ratio and chord slenderness on weld strength. Nonuniform strain distributions were observed in the branches adjacent to the joints, indicating that the welds were only partially effective. Results from the experimental tests were used to evaluate design guidance for PJP welds in the American steel design standard, AISC 360-16, and a weld effective length equation is proposed for axially loaded plate-to-CHS connections.

The seismic deflection amplification factor for a series of archetype buildings utilizing cold-formed steel–framed shear walls was investigated. A total of 118 archetype buildings were considered, of which 83 employed cold-formed steel–framed shear walls with steel sheet sheathing, and 35 employed wood structural panel sheathing. Using nonlinear equivalent single-degree-of-freedom (SDOF) models, nonlinear time-history analyses for the 118 archetype buildings subjected to the 44 FEMA P-695 earthquakes were conducted. In these SDOF models, the actual response of shear walls obtained from experimental studies was used to define the nonlinear material parameters. The AISI S400 deflection expression was evaluated using experimental data, and numerically predicted deflection amplification factors were calculated and compared against that recommended in current practice. The results show that current practice may overestimate expected deflections. To address this issue, and to simplify design, a linearization of the AISI S400 deflection expression is recommended. With appropriate choice of the force level, the linearized AISI S400 deflection expression leads to acceptable drift predictions with the currently employed deflection amplification factor.

This paper investigates the potential of using distributed fiber optic sensing (DFOS) to evaluate load distribution and support reactions within a statically indeterminate structure. A multibeam two-span composite model bridge was built and instrumented with DFOS. Three different loading scenarios (full width, concentrated, and offset) and two different slab thicknesses were used to investigate their impact on load distribution and reactions forces. Disturbed regions near the supports meant that shear forces, and thus reactions, could not be measured in this region and thus had to be extrapolated. Two extrapolation techniques (linear and second order) were developed and evaluated using a grillage model. The second-order fitting technique provided more accurate reaction forces for the grillage model and was then used with the distributed strain data from the model bridge to estimate the reactions. Challenges associated with the scale of the experiment were identified that should result in better performance on full-scale structures.

Recent research has shown that seismic design forces for horizontal floor and roof diaphragms that have been in the US building codes for decades are not sufficiently large to protect the diaphragm from inelastic actions. These findings led, in part, to the development of alternative diaphragm design provisions in US standards, which use increased diaphragm force demands, but allow for a reduction of the demands by a unique diaphragm design force reduction factor, $R_s$. In this study, the effect of different diaphragm design philosophies on the behavior of steel buildings is investigated using three-dimensional computational building models that consider nonlinear behavior in both the vertical and horizontal elements of the lateral force–resisting system (LFRS). Objectives include examining the effect of diaphragm inelasticity on building dynamic behavior, understanding seismic diaphragm force demands, investigating collapse probabilities for different diaphragm design approaches, and evaluating proposed $R_s$ values for bare steel deck and concrete-filled steel deck diaphragms. Building parameters were varied such as diaphragm design approach (traditional and alternative design with different $R_s$ values), building height (1-, 4-, 8-, and 12-story archetype buildings), and type of LFRS (buckling restrained braced frames or special concentrically braced frames). Nonlinear response-history analyses were performed, and resulting performance in terms of drift and collapse were evaluated. It was found that traditionally designed building diaphragms can experience substantial inelasticity during earthquake response. Computed adjusted collapse margin ratios for buildings utilizing the alternative diaphragm design procedure with $R_s=2.0$ for concrete-filled steel deck floor diaphragms and $R_s=2.5$ for bare steel deck roof diaphragms satisfy US design criteria for acceptance and are recommended for use in design of these types of structures.

Starting from a recently developed variational principle for the lateral torsional buckling analysis of steel I-beams strengthened with cover plates, this study formulated an energy-based solution that quantifies the lateral torsional buckling resistance of simply supported strengthened I-beams. The solution captures the detrimental effect of loads that may act on the beam prior to strengthening through an interaction relation combining the prestrengthening and poststrengthening peak moments. Additionally, it captures the effects of moment gradient and load height for pre and poststrengthening loads, as well as prebuckling deformation effects through a series of design-oriented coefficients. A systematic comparison of the solution to finite-element analysis (FEA) predictions demonstrated its accuracy for a wide range of cross sections, strengthening plate geometries, spans, pre and poststrengthening load distributions, and load heights. The use of the proposed solution in typical strengthening design scenarios was illustrated through two examples. The simplicity of the solution compared with the FEA, the universality implied by its dimensionless format, and its predictive accuracy make it attractive in a design environment.

This paper presents the seismic performance of the moment-resisting timber frame (MRTF). In Japanese urban areas, there are many urban small houses, and it is difficult to design a wooden building to ensure both the seismic performance and the comfortable plan that effectively makes use of small and constrained sites, and it also lacks flexibility in the design. Therefore, expectations are rising for high performance of MRTF using residential members. In this study, to clarify the seismic performance and the dynamic behavior under the heavy seismic wave, we conducted a full-shaking table test of the 2-story MRTF composed of residential members with short sides. The structure was designed by the allowable stress design (ASD) to resist 1.5 times the earthquake ground motion required in Japanese Building Standard Law (BSL) and linear analysis under frequent loading conditions (snow, wind, and earthquake events corresponding to a return period of approximately 50 years), and the unidirectional full-scale shaking table tests were conducted. The structure did not collapse up to a peak ground acceleration of $0.87g$ and experienced $\sim 1/20\mathrm{rad}$ of maximum interstory drift. This indicates that an MRTF designed by the method can secure the seismic performance for a large earthquake. The time-response analysis was also conducted based on the joint tests, but the stiffness of the analytical result is little lower than the experimental result. Then, we tried the parameter identification using quality engineering to reproduce the experimental behavior. The results indicated that the moment resistance of the joint was higher because of the stressed-skin effect of the floor.

The application of steel castings in earthquake engineering has increased significantly in recent years, and steel casting technology has been proven as a viable solution for the design and development of energy dissipative yielding elements. The first-generation of cast steel replaceable modular yielding links were recently proposed as an off-the-shelf energy dissipative product line for use in steel eccentrically braced frames (EBF). The performance of the links was validated through an extensive full-scale experimental program. These links featured a design approach in which the effective length of all links across the product line was identical. As a result of this design approach, a wide range was observed in the ductility capacity, with the smaller- to medium-capacity links achieving larger rotation capacities than the larger-capacity links. This paper presents the design and experimental validation of an alternative design of cast steel replaceable yielding links where, rather than ensuring equal length across the product line, a similar link ductility capacity is targeted for all link sizes. The new cast steel links with targeted ductility capacity are presented, and the performance of two link sizes is validated through large-scale experiments to confirm that the proposed design achieved the targeted design ductility. Each link size was tested twice: once as a standalone element and once as part of a one-story EBF system that imparted a large axial load to the link. Based on the results, the effect of axial load on the performance of EBF links is discussed.

The structural response of earth block masonry is characterized by cracking patterns and inelastic behavior distributed across masonry units, mortar joints, and unit-mortar interfaces. This behavior is different from that exhibited by masonry built with fired clay bricks, concrete blocks, or regularly shaped stones, which are commonly characterized by cracking patterns and inelastic behavior within the mortar joints and unit-mortar interfaces and are typically analyzed using finite element (FE) simplified micro-models (SMMs). This paper presents a new detailed micromodel (DMM) specifically tailored for earth block masonry systems. The proposed DMM enables the accurate simulation of the experimentally-measured mechanical response of earth block wallettes subject to combined shear-compression diagonal loads, whereas the SMMs produce inaccurate results. Through a series of FE simulations of representative masonry elements, this study shows that the proposed DMM and different types of SMMs provide consistent predictions of mechanical behavior only under specific conditions, depending on the relative strength of masonry units and mortar as well as the loading conditions. The outcomes of this research provide a new tool for accurate prediction and simulation in instances where the compressive strength of the masonry units is similar to or lower than that of the mortar.

The self-centering technical approach is used widely to improve building resiliency. This paper presents a double activation self-centering brace (DA-SCB) with two groups of disc springs activated successively. Compared with current self-centering braces (SCBs), the DA-SCB is first activated under small displacement excitation to dissipate energy, and reactivated under large displacement excitation, leading to a higher bearing capacity. Cyclic loading tests were conducted on the SCB and the DA-SCB in order to comparatively study their energy dissipation and the self-centering behaviors and to validate the hysteretic performance of the DA-SCB. Moreover, the double flag–shaped model was developed to predict the hysteretic behavior of the DA-SCB. Fifteen-story steel frame models with SCBs (SCBF) and DA-SCBs (DA-SCBF) were analyzed to study the influence of the reactivation behavior on the seismic resilience of these structures. The test results showed that the bearing capacity and the energy dissipation ability of the DA-SCB were highly consistent with those of the SCB within the same design parameters. Comparisons of the prediction and test results indicated that the proposed model can accurately replicate hysteretic responses of the DA-SCB and the SCB. The DA-SCBF and SCBF have equivalent self-centering behavior. However, the seismic performance of the DA-SCBF is higher than that of the SCBF, and the economic loss of the DA-SCBF after earthquakes decreased by 8.08% compared with the SCBF. Moreover, compared with the SCB, the DA-SCB uses fewer disc springs and can attenuate the weak story effect. To sum up, the seismic resilience level of the DA-SCBF first increases and then decreases with an increased gap length.

Three desirable features of a seismic-resisting system’s hysteresis are ductile behavior, consistent dissipation during loading cycles, and negligible residual displacements after earthquakes. A self-centering, pinching-free connector (PFC) was developed to attempt to meet these demands. The tension-only PFC uses a linear ratchet made from unified/metric screw threads to absorb the slack generated when a dissipator deforms/elongates monotonically. Nondestructive ratcheting tests were conducted to support the equations derived to predict the ratcheting behavior. Although the PFC can recenter unimpeded during tension (half) cycles, the ratcheting persisted on the compressive stroke during full tension-compression cycles and subsequently hindered its ability to recenter. Therefore, additional hook and ratchet stoppers were incorporated into the PFC to control the ratcheting and allow recentering from any position. This was verified in a preliminary test of a diagonally braced frame that demonstrated self-centering when unloaded. An incremental numerical procedure was able to predict the cyclic response of the frame satisfactorily from just the backbone curve of the PFC, which is mostly a reflection of the dissipator’s backbone. This paper highlights an alternate means to self-centering dissipative systems through a linear ratchet that precludes the need for buckling restraints or substantial prestressing/poststressing. One implication is that very slender braces could be used in moderate-to-high seismicity regions because the pinching is no longer an issue and the dissipative potential is restored for monotonic dissipators.

Reinforced concrete (RC) walls containing openings are usually stiffened by boundary elements (or boundary flanges) in the form of columns on one or both sides. Both thickness and longitudinal reinforcement ratio of such boundary members generally exceed those of enclosed walls. Such boundary elements also contribute to an improvement in the strength of enclosed walls. As a result, the strength of RC walls with openings with boundary elements is higher than those without them. In this paper, an analytical approach based on the softened strut-and-tie model is proposed to evaluate the shear strength of RC walls with a central opening and enclosed by boundary elements. The combined behavior of the wall and boundary elements under a simultaneous bending moment and axial loading is considered in the sectional analysis to calculate neutral axis depth for evaluating strut capacity. Shear strength predictions through the proposed approach showed reasonable accuracy when verified against the test data from eleven RC walls with a single central opening. Comparisons are also made with strength estimations based on American and Japanese code provisions. Finally, a simplified equation for the evaluation of neutral axis depth is presented to enable design engineers to conduct preliminary design of RC walls with openings that are enclosed by boundary elements.

This paper presents experimental and numerical investigations on the cross-sectional behavior and compressive capacities of aluminum alloy channel section stub columns after exposure to fire. A testing program was performed, including heating tests, postfire material tests, geometric imperfection measurements, and 16 stub column tests. The testing program was followed by a numerical modeling program. Finite-element models were developed to simulate the test responses and conduct parametric studies to obtain additional numerical data. The obtained test and numerical data were analyzed and adopted to perform design analyses, in which the applicability of the relevant room-temperature design rules in the American, European, and Australian/New Zealand codes to the postfire design of aluminum alloy channel sections under compression were examined. The results of the design analyses reveal that all three examined design codes yield excessively conservative and scattered predictions of postfire strengths, owing to the neglect of significant postfire material strain hardening. Then, a new design approach was proposed by rationally considering the material strain hardening. The new proposal was found to offer greatly improved design accuracy and consistency compared to the American, European, and Australian/New Zealand codes, especially for aluminum alloy channel sections after exposure to elevated temperatures above 400°C.

While collapse mechanisms have received significant attention for conventional buildings, they are less well understood for isolated buildings. Recently, there has been a more concerted effort to quantify the collapse probability of isolated structures; however, the majority of the research has explored the behavior of buildings isolated with concave sliding bearings, also referred to as friction pendulum (FP) bearings. Isolated buildings are expected to perform similarly under defined ground motion levels regardless of the type of bearing used. Yet the collapse probability of isolated buildings is directly dependent on the bearing failure characteristics, which differ by bearing type. Therefore, employing different isolation systems while following the same design guidelines may result in different collapse probabilities. In this study, the collapse probabilities of a 3-story buckling restrained brace frame isolated with either double-concave FP bearings or lead rubber bearings are compared. Different designs at maximum displacement are considered including use of moat walls versus allowing failure of the bearings (or impact of the restraining rims for FP bearings). In the absence of the moat wall, the system-level failure using both bearing types is triggered by exceeding defined displacement capacities. In contrast, with the moat wall, the system-level failure is dominated by either axial component-level failures or excessive yielding of the superstructure. However, when the moat wall limits ultimate displacement, the difference in collapse probabilities is small.

Recent innovations in composite dowels have led to the realization that robust hybrid systems can provide excellent strength and stiffness. In this contemporary era, puzzle-shaped and modified clothoid-shaped shear connectors are attracting interest, particularly in Europe. Their popularity stems from their outstanding shear capacities and their ease of manufacturing by virtue of having a single cutting line. Moreover, earlier studies based on pushout tests have proven this fact. Composite beams in buildings experience fully reversed cyclic stress between compression and tension during seismic events. When the concrete slab starts to crack under tensile stress, the shear capacity of the composite dowel can deteriorate considerably. Nevertheless, the influence of this cyclically applied stress on mechanical performance remains unclear. This study specifically examined puzzle-shaped shear connectors, with cyclic loading tests conducted using a component model of the composite beam, which can carry the various stress histories to the concrete slab. In all, findings obtained from 14 specimens with several influential factors clarified the cyclic behaviors and stress transfer mechanisms of puzzle-shaped shear connectors. Based on the experimentally obtained results, the applicability of existing evaluation equations was investigated with respect to the ultimate shear strength and shear force–slip displacement relation. Results indicate that those formulas overestimate the mechanical capacities of composite dowels under fully reversed cyclic stress. For that reason, this study has led to an evaluation formulation of mechanical performance that reflects the stress history effects. Ultimately, this study has proven that the proposed equations can assess the ultimate shear strength and shear force–slip displacement accurately while embracing simplicity.

This study aims to develop a high-performance acrylate viscoelastic damper (HAVED), which is suitable for the low-frequency vibration control of building structures. To reveal the influence of ambient temperature, excitation frequency, and displacement amplitude on the dynamic mechanical performance and energy dissipation capacity of a HAVED, a series of dynamic mechanical performance tests were performed on a HAVED within the extensive temperature ($10°\mathrm{C}–50°\mathrm{C}$), frequency ($0.1–3\mathrm{Hz}$), and displacement ($0.5–4\mathrm{mm}$) range. The analysis results show that a HAVED has excellent energy dissipation capacity and good adaptability to the external environment. The loss factor of a HAVED can reach up to 1.85, and it remains above 0.28 even in a high-temperature environment of 50°C. The dynamic mechanical properties and energy dissipation capacity of a HAVED show strong dependences and obvious coupling effects on temperature, frequency, and displacement amplitude. Based on the experimental research of a HAVED, the micromechanical properties of viscoelastic materials are analyzed, and the high-order fractional derivative model is used to comprehensively describe the mechanical characterization of microscopic molecular chains. The Kraus theory is introduced to consider the influence of filler particles, and the high-order fractional derivative micro–macro cross-scale mathematical model is proposed by combining with the temperature-frequency equivalence principle. Through the experimental results, the prediction capabilities of the model that have been established have been verified. The analysis results show that the proposed model can comprehensively describe the influence of ambient temperature, excitation frequency, displacement amplitude, microscopic molecular chain structure, and filler particles on the mechanical properties of a HAVED.

This paper presents the analytical formulation and computational implementation of a conceptual probabilistic performance-based seismic design (PBSD) framework for ordinary standard bridge (OSB) structures. An updated probabilistic performance-based earthquake engineering (PBEE) assessment methodology is used for the parametric performance assessment of four distinct OSBs in California to investigate the effects of varying key structural design parameters over a primary design parameter space on risk-based structural performance measures. The dire need for a systematic PBSD framework for OSBs is illustrated given the significant variability in risk-based performance levels exhibited by these traditionally designed testbed OSBs. A PBSD methodology involving the design of the bridge piers is proposed wherein a risk-based feasible design domain in the primary design parameter space is identified which facilitates the risk-informed design/decision making process in the face of uncertainty. Sensitivities of risk-based feasible design domains compared with other (secondary) design variables and with the method employed for damage hazard assessment are investigated.

Waffle slabs made of ultra-high performance concrete (UHPC) are now being widely used in bridge deck construction. However, to date, no research has been conducted to study their failure behavior. Two one-way waffle slab strips made of UHPC were load-tested under four-point bending to investigate their strength, ductility, and failure patterns. An identical set made of high strength concrete (HSC) was also tested to provide a comparison to specimens made with traditional construction materials. The UHPC specimens exhibited multiple fine cracks prior to rebar yielding and failed by steel rebar rupture after a single crack localized. In contrast, the HSC slab strips exhibited several large cracks and substantially larger ductility than the UHPC slab strips, although their strength was about 40% less than the corresponding UHPC specimens. The experimental results were used to validate a three-dimensional finite element model, which was then employed to investigate the two-way response of UHPC waffle slabs. The simulation study revealed that the yield line design method is applicable to UHPC waffle slabs despite their markedly different behavior compared to concrete slabs. Like the HSC slabs, the UHPC slabs also exhibited displacements and load carrying capacities well in excess of those predicted by flexural theories, due to formation of membrane action.

Because U-shaped steel beams filled with concrete have the advantages of reduced construction period and superior structural performance, they have been widely used as structural elements. In this study, the flexural behavior of newly developed bolt-connected U-shaped steel and concrete composite beams under a negative bending moment was experimentally evaluated. The main test variables were bolt spacing in bottom steel plates and types of U-shaped steel sections. Test results showed that the flexural behavior of the composite beams is determined by the plate-buckling mode of bolt-connected bottom steel plates. Composite beams with a greater bolt spacing than that in the standard AISI S100-16 experienced early plate buckling of the bottom steel plates, resulting in reduction of flexural stiffness and maximum flexural strength. Thus, the buckling mode of bolt-connected bottom plates should be considered for bolt-connected U-shaped composite beams under a negative bending moment. The longitudinal lips of U-shaped steel sections can increase the flexural performance of composite beams due to anchorage performance of the steel sections with lips.

Following column failure in a reinforced concrete (RC) frame, the beams supported initially by the failed column need to successfully carry the redistributed gravity loads to prevent a progressive collapse. These gravity loads will continuously act on the damaged structure after the column loss. However, it is unknown how the load sustainment would impact the collapse resistance of the beams. This research aimed to experimentally characterize the time-dependent response of axially restrained RC frame beams under compressive arch action, which has been identified from the past short-term loading tests as an important load-carrying mechanism. Five two-span beam-column subassemblies were constructed at a $1/3$-scale for cross sections and tested after 267 to 480 days of concrete casting. Major test variables included sustained load level and beam span-to-depth ratio. Two specimens had a span-to-depth ratio of 10.6 and the remaining three had a ratio of 7.5. Four high sustained load levels were considered: 80%, 90%, 95%, and 100% of the predicted short-term loading capacity. To explore the effects of previous sustained loading on beam behavior during the subsequent sustained loading, two specimens were tested with two increasing levels of sustained load. Two specimens failed after carrying the sustained loads for 3 and 65 min. For other specimens, the sustained loads were applied for 10 to 50 days, depending on the observed deflection rate. The tests suggested that the sustained loading capacity of aged RC frame beams with a span-to-depth ratio of 10.6 and 7.5 can be taken as 90% and 95% of the short-term loading capacity under compressive arch action and the reduced global long-term loading capacity was affected by beam slenderness. However, neither the sustained load level nor duration negatively affected the flexural strength of the critical sections. Moreover, the evolution of Poisson’s ratio of concrete cover indicated the likelihood of creep failure due to the sustained loads.

Wind fragility curves for roof sheathing were developed for single-family building models to investigate the effects of roof shape and roof pitch on the wind performance of roof sheathing. For gable roofs, it was found that more complex roof shapes are more likely to suffer roof sheathing damage when subjected to high winds. The probability of no roof sheathing failure can be up to 36% higher for a simple gable roof than for a complex gable roof. For hip roofs with different configurations, variation in roof shape has minimal effect on roof sheathing fragility. Roof pitch effects were also evaluated for 10 pitch angles, ranging from 14° to 45°. Results suggest that for roof pitches smaller than 27°, the effects of this angle are more substantial on the performance of gable roofs than on hip roofs. For gable roofs, the probability of no roof sheathing failure can be up to 23% higher for a 23° roof pitch than that for an 18° roof pitch. Furthermore, the inclusion of complex roof shapes in a regional hurricane loss model for New Hanover County, North Carolina, accounted for a 44% increase in estimated annual expected losses from roof sheathing damages compared to a scenario in which all roofs are assumed to have rectangular roof shapes. Therefore, to avoid an underestimation of roof damages due to high-wind impact, the inclusion of complex roof geometries in hurricane loss modeling is strongly recommended.

A method to calculate structural functionality for building structures based on structural natural frequency was proposed for seismic loading events. Structural functionality loss and recovery were determined by monitoring the change of structural natural frequency during the earthquake events or repair activities. A shape factor was introduced, structural functionality recovery function (SFRF), to consider the repair strategy and repair speed. As an example, this method was applied to obtain the structural functionality curve and seismic resilience of a half scale two-story reinforced concrete (RC) frame structure. This structure was subjected to a series of ground motions on a shake table and then repaired by carbon fiber cloth a total of four times. The results indicate that the SFRF is able to capture the recovery trend of a structure in the repair process. Meanwhile, a damage index-repair target (DI-RT) curve, representing the 5% difference between the proposed and traditional SFRFs, was used to investigate the impact of structural damage degree and repair target. The areas above the curve indicates that the difference between the proposed and traditional SFRFs cannot be ignored.