Abstract: In this study, a novel vision-based bolt-loosening monitoring technique is proposed for bolted joints connecting tubular steel segments of the wind turbine tower (WTT) structure. Firstly, a bolt-loosening detection algorithm based on image processing techniques is developed. The algorithm consists of five steps: image acquisition, segmentation of each nut, line detection of each nut, nut angle estimation, and bolt-loosening detection. Secondly, experimental tests are conducted on a lab-scale bolted joint model under various bolt-loosening scenarios. The bolted joint model, which is consisted of a ring flange and 32 sets of bolt and nut, is used for simulating the real bolted joint connecting steel tower segments in the WTT. Finally, the feasibility of the proposed vision-based technique is evaluated by bolt-loosening monitoring in the lab-scale bolted joint model.

Abstract: For high-speed railways (HSR) in wind prone regions, wind barriers are often installed on bridges to ensure the running safety of trains. This paper analyzes the effect of wind barriers on the running safety of a high-speed train to cross winds when it passes on a bridge. Two simply-supported (S-S) PC bridges in China, one with 32 m box beams and the other with 16 m trough beams, are selected to perform the dynamic analyses. The bridges are modeled by 3-D finite elements and each vehicle in a train by a multi-rigid-body system connected with suspension springs and dashpots. The wind excitations on the train vehicles and the bridges are numerically simulated, using the static tri-component coefficients obtained from a wind tunnel test, taking into account the effects of wind barriers, train speed and the spatial correlation with wind forces on the deck. The whole histories of a train passing over the two bridges under strong cross winds are simulated and compared, considering variations of wind velocities, train speeds and without or with wind barriers. The threshold curves of wind velocity for train running safety on the two bridges are compared, from which the windbreak effect of the wind barrier are evaluated, based on which a beam structure with better performance is recommended.

Abstract: To overcome the drawbacks of the traditional contact-type sensor for structural displacement measurement, the vision-based technology with the aid of the digital image processing algorithm has received increasing concerns from the community of structural health monitoring (SHM). The advanced vision-based system has been widely used to measure the structural displacement of civil engineering structures due to its overwhelming merits of non-contact, long-distance, and high-resolution. However, seldom currently-available vision-based systems are capable of realizing the synchronous structural displacement measurement for multiple points on the investigated structure. In this paper, the method for vision-based multi-point structural displacement measurement is presented. A series of moving loading experiments on a scale arch bridge model are carried out to validate the accuracy and reliability of the vision-based system for multi-point structural displacement measurement. The structural displacements of five points on the bridge deck are measured by the vision-based system and compared with those obtained by the linear variable differential transformer (LVDT). The comparative study demonstrates that the vision-based system is deemed to be an effective and reliable means for multi-point structural displacement measurement.

Abstract: A numerical model for analyzing airtraintrack interaction is proposed to investigate the dynamic behavior of a high-speed train running on a track in crosswinds. The model is composed of a traintrack interaction model and a trainair interaction model. The traintrack interaction model is built on the basis of the vehicletrack coupled dynamics theory. The trainair interaction model is developed based on the train aerodynamics, in which the Arbitrary LagrangianEulerian (ALE) method is employed to deal with the dynamic boundary between the train and the air. Based on the airtraintrack model, characteristics of flow structure around a high-speed train are described and the dynamic behavior of the high-speed train running on track in crosswinds is investigated. Results show that the dynamic indices of the head car are larger than those of other cars in crosswinds. From the viewpoint of dynamic safety evaluation, the running safety of the train in crosswinds is basically controlled by the head car. Compared with the generally used assessment indices of running safety such as the derailment coefficient and the wheel-load reduction ratio, the overturning coefficient will overestimate the running safety of a train on a track under crosswind condition. It is suggested to use the wheel-load reduction ratio and the lateral wheelrail force as the dominant safety assessment indices when high-speed trains run in crosswinds.

Abstract: In the current study, dynamic and quasi-static analyses were performed to investigate the response of multiple-spanned and single-spanned transmission line conductors under both downburst and synoptic winds considering different wind velocities and different length spans. Two critical downburst configurations, recommended in the literature and expected to cause maximum conductor reactions, were considered in the analyses. The objective of the study was to assess the importance of including the dynamic effect when predicting the conductor\'s reactions on the towers. This was achieved by calculating the mean, the background and the resonant reaction components, and evaluating the contribution of the resonant component to the peak reaction. The results show that the maximum contribution of the resonant component is generally low (in the order of 6%) for the multiple-spanned system at different wind velocities for both downburst and synoptic winds. For the single-spanned system, the result show a relatively high maximum contribution (in the order of 16%) at low wind velocity and a low maximum contribution (in the order of 6%) at high wind velocity for both downburst and synoptic winds. Such contributions may justify the usage of the quasi-static approach for analyzing transmission line conductors subjected to the high wind velocities typically used for the line design.

Abstract: Characterization of wind flows over a complex terrain, especially mountain-gorge terrain (referred to as the very complex terrain with rolling mountains and deep narrow gorges), is an important issue for design and operation of long-span bridges constructed in this area. In both wind tunnel testing and numerical simulation, a transition section is often used to connect the wind tunnel floor or computational domain bottom and the boundary top of the terrain model in order to generate a smooth flow transition over the edge of the terrain model. Although the transition section plays an important role in simulation of wind field over complex terrain, an appropriate shape needs investigation. In this study, two principles for selecting an appropriate shape of boundary transition section were proposed, and a theoretical curve serving for the mountain-gorge terrain model was derived based on potential flow theory around a circular cylinder. Then a two-dimensional (2-D) simulation was used to compare the flow transition performance between the proposed curved transition section and the traditional ramp transition section in a wind tunnel. Furthermore, the wind velocity field induced by the curved transition section with an equivalent slope of 30 was investigated in detail, and a parameter called the \'velocity stability factor\' was defined; an analytical model for predicting the velocity stability factor was also proposed. The results show that the proposed curved transition section has a better flow transition performance compared with the traditional ramp transition section. The proposed analytical model can also adequately predict the velocity stability factor of the wind field.

Abstract: Full scale measurement on the structural dynamic characteristics and Vortex-induced Vibrations (VIV) of a long-span suspension bridge with a central span of 1650 m were conducted. Different Finite Element (FE) modeling principles for the separated twin-box girder were compared and evaluated with the field vibration test results, and the double-spine model was determined to be the best simulation model, but certain modification still needs to be made which will affect the basic modeling parameters and the dynamic response prediction values of corresponding wind tunnel tests. Based on the FE modal analysis results, small-scaled and large-scaled sectional model tests were both carried out to investigate the VIV responses, and probable Reynolds Number effects or scale effect on VIV responses were presented. Based on the observed VIV modes in the field measurement, the VIV results obtained from sectional model tests were converted into those of the three-dimensional (3D) full-scale bridge and subsequently compared with field measurement results. It is indicated that the large-scaled sectional model test can probably provide a reasonable and effective prediction on VIV response.

Abstract: Open decks are a widely used deck configuration in long-span cable-stayed bridges; however, incorporating aerodynamic countermeasures are advisable to achieve better aerodynamic performance than a bluff body deck alone. A sectional model of an open deck cable-stayed bridge with a main span of 400 m was selected to conduct a series of wind tunnel tests. The influences of five practical aerodynamic countermeasures on flutter and vortex-induced vibration (VIV) performance were investigated and are presented in this paper. The results show that an aerodynamic shape selection procedure can be used to evaluate the flutter stability of decks with respect to different terrain types and structural parameters. In addition, the VIV performance of Π-shaped girders for driving comfortableness and safety requirements were evaluated. Among these aerodynamic countermeasures, apron boards and wind fairings can improve the aerodynamic performance to some extent, while horizontal guide plates with 5% of the total deck width show a significant influence on the flutter stability and VIV. A wind fairing with an angle of 55° showed the best overall control effect but led to more lock-in regions of VIV. The combination of vertical stabilisers and airflow-depressing boards was found to be superior to other countermeasures and effectively boosted aerodynamic performance; specifically, vertical stabilisers significantly contribute to improving flutter stability and suppressing vertical VIV, while airflow-depressing boards are helpful in reducing torsional VIV.

Abstract: In this paper, a novel methodology is proposed to obtain optimum location of outriggers. The method utilizes genetic algorithm (GA) for shape and size optimization of outrigger-braced tall structures. In spite of previous studies (simplified methods), current study is based on exact modeling of the structure in a computer program developed on Matlab in conjunction with OpenSees. In addition to that, exact wind loading distribution is calculated in accordance with ASCE 7-10. This is novel since in previous studies wind loading distributions were assumed to be uniform or triangular. Also, a new penalty coefficient is proposed which is suitable for optimization of tall buildings .Newly proposed penalty coefficient improves the performance of GA and results in a faster convergence. Optimum location and number of outriggers is investigated. Also, contribution of factors like central core and outrigger rigidity is assessed by analyzing several design examples. According to the results of analysis, exact wind load distribution and modeling of all structural elements, yields optimum designs which are in contrast of simplified methods results. For taller frames significant increase of wind pressure changes the optimum location of outriggers obtained by simplified methods. Ratio of optimum location to the height of the structure for minimizing weight and satisfying serviceability constraints is not a fixed value. Ratio highly depends on height of the structure, core and outriggers stiffness and lateral wind loading distribution.

Abstract: A three-dimensional aerodynamic model and a vehicle dynamics model are established to investigate the effect of noise barrier on the dynamic performance of a high-speed train running on an embankment in crosswind in this paper. Based on the developed model, flow structures around the train with and without noise barrier are compared. Effect of the noise barrier height on the train dynamic performance is studied. Then, comparisons between the dynamic performance indexes of the train running on the windward track and on the leeward track are made. The calculated results show that the noise barrier has significant effects on the structure of the flow field around the train in crosswind and thus on the dynamic performance of the high-speed train. The dynamic performance of the train on the windward track is better than that on the leeward track. In addition, various heights of the noise barrier will have different effects on the train dynamic performance. The dynamic performance indexes keep decreasing with the increase of the noise barrier height before the height reaches a certain value, while these indexes have an inverse trend when the height is above this value. These results suggest that optimization on the noise barrier height is possible and demonstrate that the designed noise barrier height of the existing China Railway High-speed line analysed in this article is reasonable from the view point of the flow field structure and train dynamic performance although the noise barrier is always designed based on the noise-related standard.

Abstract: In this study, the feasibility of vibration-based damage detection methods for the wind turbine tower (WTT) structure is evaluated. First, a frequency-based damage detection (FBDD) is outlined. A damage-localization algorithm is visited to locate damage from changes in natural frequencies. Second, a mode-shape-based damage detection (MBDD) method is outlined. A damage index algorithm is utilized to localize damage from estimating changes in modal strain energies. Third, a finite element (FE) model based on a real WTT is established by using commercial software, Midas FEA. Several damage scenarios are numerically simulated in the FE model of the WTT. Finally, both FBDD and MBDD methods are employed to identify the damage scenarios simulated in the WTT. Damage regions are chosen close to the bolt connection of WTT segments; from there, the stiffness of damage elements are reduced.

Abstract: This study investigated aerodynamic characteristics of an inclined square prism experimentally. Pressure measurements were performed on a static square prism with a series of inclinations including forward inclinations (inclined to the upwind direction) and backward inclinations (inclined to the downwind direction). The prism with a vertical attitude was also tested for comparisons. Based on the pressure data, influences of the inclinations on aerodynamic characteristics (e.g., force coefficients, pressure distributions on the surfaces, and vortex shedding features) of the square prism were evaluated in detail. The results show that the inclinations have significant effects on these aerodynamic characteristics. Furthermore, the influences of the forward and backward inclinations are quite different.

Abstract: 【This paper investigates the effects of Reynolds number (Re) on the aerodynamic characteristics of a twin-deck bridge. A 1:36 scale sectional model of a twin girder bridge was tested using the Wall of Wind (WOW) open jet wind tunnel facility at Florida International University (FIU). Static tests were performed on the model, instrumented with pressure taps and load cells, at high wind speeds with Re ranging from $1.3{\times}10^6$ to $6.1{\times}10^6$ based on the section width. Results show that the section was almost insensitive to Re when pitched to negative angles of attack. However, mean and fluctuating pressure distributions changed noticeably for zero and positive wind angles of attack while testing at different Re regimes. The pressure results suggested that with the Re increase, a larger separation bubble formed on the bottom surface of the upstream girder accompanied with a narrower wake region. As a result, drag coefficient decreased mildly and negative lift coefficient increased. Flow modification due to the Re increase also helped in distributing forces more equally between the two girders. The bare deck section was found to be prone to vortex shedding with limited dependence on the Re. Based on the observations, vortex mitigation devices attached to the bottom surface were effective in inhibiting vortex shedding, particularly at lower Re regime.】

Abstract: This study focuses on the amplitude dependency of damping of tall structures by the random decrement technique (RDT). Many researchers have adopted RDT to establish the amplitude dependency of damping ratios in super-tall buildings under strong wind loads. In this study, a series of simulated examples were analyzed to examine the reliability of this method. Results show that damping ratios increase as vibration amplitudes increase in several cases; however, the damping ratios in the simulated signals were preset as constants. This finding reveals that this method and the derived amplitude-dependent damping ratio characteristics are unreliable. Moreover, this method would obviously yield misleading results if the simulated signals contain Gaussian white noise. Full-scale measurements on a super-tall building were conducted during four typhoons, and the recorded data were analyzed to observe the amplitude dependency of damping ratio. Relatively wide scatter is observed in the resulting damping ratios, and the damping ratios do not appear to have an obvious nonlinear relationship with vibration amplitude. Numerical simulation and field measurement results indicate that the widely-used method for establishing the amplitude-dependent damping characteristics of super-tall buildings and the conclusions derived from it might be questionable at the least. More field-measured data must be collected under strong wind loads, and the damping characteristics of super-tall buildings should be investigated further.

Abstract: In recent years, high-rise buildings received a renewed interest as a means by which technical and economic advantages can be achieved, especially in areas of high population density. Taller and taller buildings are being built worldwide. These types of buildings present an asset and typically are built not to fail under wind loadings. The increase in a building\'s height results in increased flexibility, which can lead to significant vibrations, especially at top floors. Such oscillations can magnify the overall loads and can be annoying to the top floors\' occupants. This paper shows that increased stiffness in high-rise buildings may not be a feasible solution and may not be used for the design for comfort and serviceability. High-rise buildings are unique, and a vibration control system for a certain building may not be suitable for another. Even for the same building, its behavior in the two lateral directions can be different. For this reason, the current study addresses the application of hybrid tuned mass and magneto-rheological (TM/MR) dampers that can work for such types of buildings. The proposed control scheme shows its effectiveness in reducing floors\' accelerations for both comfort and serviceability concerns. Also, a dissipative analysis carried out shows that the MR dampers are working within the possible range of optimum performance. In addition, the design loads are dramatically reduced, creating more resilient and sustainable buildings. The purpose of this paper is to stimulate, shape, and communicate ideas for emerging control technologies that are essential for solving wind related problems in high-rise buildings, with the objective to build the more resilient and sustainable infrastructure and to optimally retrofit existing structures.

Abstract: Experiments on two-dimensional rectangular prisms with various side ratios (B/D=2, 3, and 4, where B is the along-wind dimension, and D is the across-wind dimension) and rounded corners (R/D=0%, 5%, 10%, and 15%, where R is the corner radius) are reported in this study. The tests were conducted in low-turbulence uniform flow to measure the wind pressures on the surfaces of 12 models for Reynolds numbers ranging from 1.1x105 to 6.8x105. The aerodynamic force coefficients were obtained by integrating the wind pressure coefficients around the model surface. Experimental results of wind pressure distributions, aerodynamic force coefficients, and Strouhal numbers are presented for the 12 models. The mechanisms of the Reynolds number effects are revealed by analyzing the variations of wind pressure distributions. The sensitivity of aerodynamic behavior to the Reynolds number increases with increasing side ratio or rounded corner ratio for rectangular prisms. In addition, the variations of the mean pressure distributions and the pressure correlations on the side surfaces of rectangular prisms with the rounded corner ratio are analyzed at Re=3.4x105.

Abstract: The wind tunnel test of large-scale sectional model and computational fluid dynamics (CFD) are employed for the purpose of studying the aerodynamic appendices and mechanism on suppression for the vortex-induced vibration (VIV). This paper takes the HongKong-Zhuhai-Macao Bridge as an example to conduct the wind tunnel test of large-scale sectional model. The results of wind tunnel test show that it is the crash barrier that induces the vertical VIV. CFD numerical simulation results show that the distance between the curb and crash barrier is not long enough to accelerate the flow velocity between them, resulting in an approximate stagnation region forming behind those two, where the continuous vortex-shedding occurs, giving rise to the vertical VIV in the end. According to the above, 3 types of wind fairing (trapezoidal, airfoil and smaller airfoil) are proposed to accelerate the flow velocity between the crash barrier and curb in order to avoid the continuous vortex-shedding. Both of the CFD numerical simulation and the velocity field measurement show that the flow velocity of all the measuring points in case of the section with airfoil wind fairing, can be increased greatly compared to the results of original section, and the energy is reduced considerably at the natural frequency, indicating that the wind fairing do accelerate the flow velocity behind the crash barrier. Wind tunnel tests in case of the sections with three different countermeasures mentioned above are conducted and the results compared with the original section show that all the three different countermeasures can be used to control VIV to varying degrees.

Abstract: Long-span cable-stayed bridges exhibit some features which are more critical than typical long span bridges such as geometric and aerodynamic nonlinearities, higher probability of the presence of multiple vehicles on the bridge, and more significant influence of wind loads acting on the ultra high pylon and super long cables. A three-dimensional nonlinear fully-coupled analytical model is developed in this study to improve the dynamic performance prediction of long cable-stayed bridges under combined traffic and wind loads. The modified spectral representation method is introduced to simulate the fluctuating wind field of all the components of the whole bridge simultaneously with high accuracy and efficiency. Then, the aerostatic and aerodynamic wind forces acting on the whole bridge including the bridge deck, pylon, cables and even piers are all derived. The cellular automation method is applied to simulate the stochastic traffic flow which can reflect the real traffic properties on the long span bridge such as lane changing, acceleration, or deceleration. The dynamic interaction between vehicles and the bridge depends on both the geometrical and mechanical relationships between the wheels of vehicles and the contact points on the bridge deck. Nonlinear properties such as geometric nonlinearity and aerodynamic nonlinearity are fully considered. The equations of motion of the coupled wind-traffic-bridge system are derived and solved with a nonlinear separate iteration method which can considerably improve the calculation efficiency. A long cable-stayed bridge, Sutong Bridge across the Yangze River in China, is selected as a numerical example to demonstrate the dynamic interaction of the coupled system. The influences of the whole bridge wind field as well as the geometric and aerodynamic nonlinearities on the responses of the wind-traffic-bridge system are discussed.

Abstract: A wind energy assessment is an integrated analysis of the potential of wind energy resources of a particular area. In this work, the wind energy potentials for Mauritius have been assessed using a Computational Fluid Dynamics (CFD) model. The approach employed in this work aims to enhance the assessment of wind energy potentials for the siting of large-scale wind farms in the island. Validation of the model is done by comparing simulated wind speed data to experimental ones measured at specific locations over the island. The local wind velocity resulting from the CFD simulations are used to compute the weighted-sum power density including annual directional inflow variations determined by wind roses. The model is used to generate contour maps of velocity and power, for Mauritius at a resolution of 500 m.

Abstract: Wind speed is the most important parameter in the design and study of wind energy conversion systems. The weibull distribution is commonly used for wind energy analysis as it can represent the wind variations with an acceptable level of accuracy. In this study, the wind data for 11 cities in Iran have been analysed over a period of one year. The Goodness of fit test is used for testing data fit to weibull distribution. The results show that this data fit to weibull function very well. The scale and shape factors are two parameters of the weibull distribution that depend on the area under study. The kinds of numerical methods commonly used for estimating weibull parameters are reviewed. Their performance for the cities under study was compared according to root mean square and wind energy errors. The result of the study reveals the empirical, modified maximum likelihood estimate of wind speed with minimum error. Also, that the moment and modified maximum likelihood are the best methods for estimating the energy production of wind turbines.

Abstract: The presence of traffic on a slender long-span bridge deck will modify the cross-section profile of the bridge, which may influence the flutter derivatives and in turn, the critical flutter wind velocity of the bridge. Studies on the influence of vehicles on the flutter derivatives and the critical flutter wind velocity of bridges are rather rare as compared to the investigations on the coupled buffeting vibration of the wind-vehicle-bridge system. A typical streamlined cross-section for long-span bridges is adopted for both experimental and analytical studies. The scaled bridge section model with vehicle models distributed on the bridge deck considering different traffic flow scenarios has been tested in the wind tunnel. The flutter derivatives of the modified bridge cross section have been identified using forced vibration method and the results suggest that the influence of vehicles on the flutter derivatives of the typical streamlined cross-section cannot be ignored. Based on the identified flutter derivatives, the influence of vehicles on the flutter stability of the bridge is investigated. The results show that the effect of vehicles on the flutter wind velocity is obvious.

Abstract: Excessive motions in buildings cause occupants to become uncomfortable and nervous. This is particularly detrimental to the tenants and ultimately the owner of the building, with respect to financial considerations. Serviceability issues, such as excessive accelerations and inter-story drifts, are more prevalent today due to advancements in the structural systems, strength of materials, and design practices. These factors allow buildings to be taller, lighter, and more flexible, thereby exacerbating the impact of dynamic responses. There is a growing need for innovative and effective techniques to reduce the serviceability responses of these tall buildings. The current study considers a case study of a real building to show the effectiveness and robustness of the TLD in reducing the coupled lateral-torsional motion of this high-rise building under wind loading. Three unique multi-modal TLD systems are designed specifically to mitigate the torsional response of the building. A procedure is developed to analyze a structure-TLD system using High Frequency Force Balance (HFFB) test data from the Boundary Layer Wind Tunnel Laboratory (BLWTL) at the University of Western Ontario. The effectiveness of the unique TLD systems is investigated. In addition, a parametric study is conducted to determine the robustness of the systems in reducing the serviceability responses. Three practical parameters are varied to investigate the robustness of the TLD system: the height of water inside the tanks, the amplitude modification factor, and the structural modal frequencies.

Abstract: The characteristics of the coherence functions of X axial, Y axial, and RZ axial (i.e., body axis) wind forces on the Shanghai World Trade Centre - a 492 m super-tall building with section varying along height are studied via a synchronous multi-pressure measurement of the rigid model in wind tunnel simulating of the turbulent, and the corresponding mathematical expressions are proposed there from. The investigations show that the mathematical expressions of coherence functions in across-wind and torsional-wind directions can be constructed by superimposition of a modified exponential decay function and a peak function caused by turbulent flow and vortex shedding respectively, while that in along-wind direction need only be constructed by the former, similar to that of wind speed. Moreover, an inductive analysis method is proposed to summarize the fitted parameters of the wind force coherence functions of every two measurement levels of altitudes. The comparisons of the first three order generalized force spectra show that the proposed mathematical expressions accord with the experimental results well. Later, the influences of coherence functions on wind-induced dynamic responses are analyzed in detail based on the proposed mathematical expressions and the frequency-domain method of random vibration theory.

Abstract: Aerodynamic forces of vortex-induced vibration and galloping are going to be coupled when their onset velocities are close to each other, which will induce the cross-wind amplitudes of the structures increased continuously with ever-increasing wind velocities. The main purpose of the present work is going to propose an empirical formula to predict the response amplitude of VIV-galloping interaction. Firstly, two typical mathematical models for the coupled oscillations, i.e., Tamura & Shimada model and Parkinson & Corless model are comparatively summarized. Then, the key parameter affecting response amplitude is determined through comparative numerical simulations with Tamura & Shimada model. For rectangular cylinders with the side ratio from 0.5 to 2.5, which are actually prone to develop the VIV and galloping induced interaction responses, an empirical amplitude prediction formula is proposed after regression analysis on comprehensively collected experimental data with the predetermined key parameter.

Abstract: To study the vibration frequency of super high-rise buildings in the process of vortex induced vibration (VIV), wind tunnel tests of multi-degree-of-freedom (MDOF) aero-elastic models were carried out to measure the vibration frequency of the system directly. The effects of structural damping, wind field category, mass density, reduced wind velocity (Vr), as well as VIV displacement on the VIV frequency were investigated systematically. It was found that the frequency drift phenomenon cannot be ignored when the building is very high and flexible. When Vr is less than 8, the drift magnitude of the frequency is typically positive. When Vr is close to the critical wind velocity of resonance, the frequency drift magnitude becomes negative and reaches a minimum at the critical wind velocity. When Vr is larger than12, the frequency drift magnitude almost maintains a stable value that is slightly smaller than the fundamental frequency of the aero-elastic model. Furthermore, the vibration frequency does not lock in the vortex shedding frequency completely, and it can even be significantly modified by the vortex shedding frequency when the reduced wind velocity is close to 10.5.