Orthogonal Horizontal Directions Research Articles

Magnification factor for pile internal forces of pile‐supported wharves under bi‐directional ground motions

AbstractIn order to determine the pile internal forces of wharf under simultaneous seismic excitation in orthogonal horizontal directions with ease, the total internal forces can be obtained by multiplying the pile forces of two‐dimensional model under transverse earthquake loading with a magnification factor. The factors were computed from the seismic response of wharves having various aspect ratios (length to width) and eccentricity ratios when subjected to 30 pairs of bi‐directional earthquake records. Mean magnification factors and their corresponding dispersion are presented for all ground motion ensembles. The influence of aspect ratio and eccentricity ratio is evaluated and discussed. It is concluded that the magnification factor can be expressed as the function of aspect ratio and eccentricity ratio, and follows lognormal distribution. The proposed equation of magnification factor can be an alternative for internal force analysis of wharves under bi‐directional ground motion.

Microstructural effects on the unconfined mechanical behavior of a tectonically deformed calcareous shale, a study case in the Santiago Formation, México

Microstructural properties play a crucial role in the mechanical response of shale rocks. This work examines the impact of fabric anisotropy on the strength and elastic behavior of a highly deformed Jurassic calcareous shale from the Santiago Formation in eastern México by means of unconfined compression strength tests (UCS). The Santiago Formation is attracting considerable interest for the development of unconventional resources of shale gas and shale oil in México. However, the effect of tectonic deformation on the mechanical properties of these Mexican Shales has not been addressed in detail. The anisotropy of the shale was evaluated by means of rock samples cored in the direction normal to layers and two horizontal directions defined along the foliation planes. Petrography of oriented thin sections, X-ray diffraction, scanning electron microscopy (SEM), and petrophysical properties (porosity and permeability), were used to assess the rock composition and microstructural properties. UCS tests results revealed different mechanical responses between the normal direction (V) and the direction parallel to layers, but also differences between the two mutually orthogonal horizontal directions (H1, H2). Tangent Young's modulus (E) showed higher values in the H2 direction (13–22 GPa) and lower values in the H1 and V directions (8–10 GPa). All the specimens yielded very low Poisson's ratios (<0.11). H2 samples displayed the highest strength (48–84 MPa) and reached higher axial strains at failure (0.4–0.7%). Specimens in the H1 direction presented the lowest strength and axial strains (15–29 MPa and 0.22–0.35%, respectively). Compared to H1 samples, vertical samples yielded slightly higher strengths (26–33 MPa) and axial strains (0.31–0.40%). The results reported here confirm that microstructure strongly influenced the mechanical anisotropy and fracture mechanisms of the Santiago Shale. A direct relation was documented between fabric anisotropy, elastic response, UCS, and brittle failure modes validating the importance of fabric characterization for a complete description of anisotropy in tectonically deformed shale rocks.

Fragility and risk assessment for sliding artifacts in artifact-showcase-museum systems subjected to three-component ground motions

Vertical ground motions may increase irregularity of sliding response, while the subsequent impact on the sliding fragility of building contents is not clear. Moreover, seismic risk of structural collapse contributes to the total sliding risk of building contents, while it is usually ignored. This paper first introduces a seismic fragility and risk assessment method for the sliding artifact in the artifact-showcase-museum (ASM) system subjected to three-component ground motions. In this method, the square roots of the sums of the squares of peak ground accelerations and peak sliding displacements in two orthogonal horizontal directions are implemented as the intensity measurement and the engineering demand parameter, respectively. Incremental dynamic analysis using the nonlinear three-dimensional finite element model of the ASM system is performed to generate seismic fragility curves of sliding artifacts. The total sliding risk of the artifact is estimated as the sum of the sliding risk of the artifact on the premise of no structural collapse and the structural collapse risk. Then, the seismic fragility and risk of the sliding artifacts within a four-story frame structure and an existing museum is assessed when the systems are subjected to three-component ground motions, respectively. Effects of vertical ground motions, freestanding and restrained showcases, floor levels, sliding thresholds, structural collapse and different structures on the sliding fragility and risk of the artifact are investigated. Results show that the influence of vertical ground motions on the sliding fragility of artifacts in different structures may be significant or marginal depending on the ratios of peak vertical to horizontal floor acceleration. Moreover, the artifact in the freestanding showcase is less fragile than that in the restrained showcase regarding sliding failure. Furthermore, neglecting the structural collapse risk and estimating the sliding risk of the artifact by not removing the structural collapse data would underestimate the total sliding risk of the artifact.

Different Couplings Between Precipitation and Deformation at the Same Site: A Case Study at Central Pyrenees (Spain)

AbstractImpact of hydrology‐associated deformation spans from the study of the rock hydrological properties and aquifer dynamics to the identification of geological disaster precursors. We analyze a comprehensive set of hydrology‐associated deformation signals, recorded by two underground 70 m long strainmeters (GAL16 and LAB780) operating under the Central Pyrenees (Spain) from the end of 2011 to the end of 2018. The two strainmeters measure extensional strain at the picostrain (10−12) level along two nearly orthogonal horizontal directions. Sign (compression or extension along any of the two directions), size, and time evolution of hydrology‐associated deformation vary considerably from season to season. We identify four classes of signals, related to summer rainfalls (producing compression along both GAL16 and LAB780), late‐spring and autumn rainfalls (producing extension along GAL16 and compression along LAB780), snow melting (producing opposite diurnal cycles along GAL16 and LAB780), and winter snowfalls (producing extension along both GAL16 and LAB780). Similar precipitations of the same class can give rise to differently sized signals; differences may be due to infiltration and/or surface load inhomogeneities as well as to complexities of the underground hydrogeological set up, which can lead to nonlinear, intrinsically time‐dependent, responses. Our modeling sheds light on the diverse effects associated with different environmental conditions. The variety of hydrology‐associated deformation we report is warning for the interpretation of all kinds of deformation data, as for their difficult modeling, the causative physical mechanisms, and the extreme care that is needed when removing hydrologically induced effects. Our insights are particularly useful in mountain areas.

Proposal of orientation-independent measure of intensity for earthquake-resistant design

A new measure of ground motion intensity in the horizontal direction is proposed. Similarly to other recently proposed measures of intensity, the proposed intensity measure is also independent of the as-installed orientation of horizontal sensors at recording stations. This new measure of horizontal intensity, referred to as MaxRotD50, is defined using the maximum 5%-damped response spectral ordinate of two orthogonal horizontal directions and then computing the 50th percentile for all non-redundant rotation angles, that is, the median of the set of spectral ordinates in a range of 90°. This proposed measure of intensity is always between the median and maximum spectral ordinate for all non-redundant orientations, commonly referred to as RotD50 and RotD100, respectively. A set of 5065 ground motion records is used to show that MaxRotD50 is, on average, approximately 13%–16% higher than Rot50 and 6% lower than RotD100. The new measure of intensity is particularly well suited for earthquake-resistant design where a major concern for structural engineers is the probability that the design ground motion intensity is exceeded in at least one of the two principal horizontal components of the structure, which for most structures are orthogonal to each other. Currently, design codes in the United States are based on RotD100, and hence using MaxRotD50 for structures with two orthogonal principal horizontal components would result in a reduction of the ground motion intensities used for design purposes.

Investigation of the Influence of Dynamic Loads of Industrial Equipment on the Occurrence of Prolonged Yielding of their Foundation Soils

The parameters of oscillations of the foundations and structures of the dynamic equipment of the new production workshop located in the Kharkiv region were experimentally investigated. For this purpose, appropriate measurements of the amplitude of oscillations in the vertical and orthogonal horizontal directions were performed. To compare the parameters of the amplitudes of forced oscillations and determine the damping properties of the applied rubber spacers placed between the frame and the slides, as well as the quenching effect of the foundation massif, several measurements of oscillation parameters were performed at the locations mentioned above. The amplitude of oscillations of the vertical component of the vibration load on different sides of the rubber dampers was reduced by 2-3 times, the horizontal component was completely attenuated. It was also established that there was no transmission of vibrations to the foundations of the production workshop. The safety of the measured parameters of oscillations from the point of view of long significant unstabilized subsidence of the foundations, both equipment and building, was determined. Recommendations for monitoring are given from the point of view of the possible deterioration of the properties of the used rubber dampers over time.

Polarization-Controllable Dual-Band Antennas Using Nonbianisotropic Complementary Split Ring Resonator-Loaded Metasurfaces

In this work, compact polarization-controllable dual-band antennas are designed, prototyped, and experimentally verified, which are composed of a planar monopole on top of a dual-layer truncated metasurface (MS) containing patches and nonbianisotropic complementary split ring resonators. By tailoring the dispersive properties of the MS, the relative phase difference of resonances associated with surface waves supported along two orthogonal horizontal directions can be independently engineered at two separate frequency bands, thereby giving rise to compact dual-band antennas with controllable polarization in each band. Three proof-of-concept example antennas with a form factor on the order of 0.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ×0.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ×0.04λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> were designed and measured. The first one provides circularly polarized (CP) radiation with the same sense of polarization in both bands, the second one offers linearly polarized (LP) radiation in the lower band and CP radiation in the higher band, while the last one achieves CP radiation in the lower band and LP radiation in the higher band. The measured results agree well with the simulation predictions, thus verifying the proposed concept and specific antenna designs.

Axial Load Variation of Columns in Symmetrical RC Buildings Subject to Bidirectional Lateral Actions in Regions of Low to Moderate Seismicity

ABSTRACT Columns in building frame systems are subjected to the combined action of bidirectional horizontal loading and axial load variation during an earthquake. Whilst the behaviour of RC columns under unidirectional and bidirectional lateral loading with constant axial load is understood well, the behaviour under bidirectional lateral loading with axial load variation is rarely studied, especially for limited ductile RC columns prevalent in regions of low to moderate seismicity. This paper begins with a numerical study that aims to obtain the generalised patterns and range of axial load variation in RC building columns. To this end, a case study building is subjected to a suite of 15 ground motions, representative of low to moderate seismic regions, in OpenSees. This is followed by an experimental study in which limited ductile high-strength RC columns are tested under bidirectional lateral loading and two different axial load variation protocols, namely synchronous and nonsynchronous variable axial loading protocols. The results of the numerical study demonstrated that axial load variation of the columns in an RC building is primarily dependent on the response spectral acceleration corresponding to the fundamental period of the structure in the two orthogonal horizontal directions and/or the vertical direction. The results of the experimental testing showed that nonsynchronous axial loading (compared to constant and synchronous axial loading) results in the lowest collapse drift capacity and energy dissipation of the RC columns.

A two degree of freedom stable quasi-zero stiffness prototype and its applications in aseismic engineering

In this paper, an archetypal aseismic system is proposed with 2-degree of freedom based on a smooth and discontinuous (SD) oscillator to avoid the failure of electric power system under the complex excitation of seismic waves. This model comprises two vibration isolation units for the orthogonal horizontal directions, and each of them admits the stable quasi-zero stiffness (SQZS) with a pair of inclined linear elastic springs. The equation of motion is formulated by using Lagrange equation, and the SQZS condition is obtained by optimizing the parameters of the system. The analysis shows that the system behaves a remarkable vibration isolation performance with low resonant frequency and a large stroke of SQZS interval. The experimental investigations are carried out to show a high sonsistency with the theoretical results, which demonstrates the improvement of aseismic behavior of the proposed model under the seismic wave.

A simplified methodology for the seismic assessment of masonry buildings with RC slabs

The present paper aims to contribute to the knowledge concerning the seismic assessment of load bearing masonry buildings with reinforced concrete slabs. The final goal of the present research was to propose a simple, yet accurate, methodology to assess the seismic safety of existing masonry buildings. The methodology here presented was based on the so-called ICIST/ACSS methodology with major improvements such as the extension to load bearing masonry wall buildings and the consideration of the effects of one of the most common strengthening solutions for masonry walls, here referred to as reinforced plastering mortar, as well as the possibility of considering four levels of increasing refinement: global, by alignment, by wall panel and by wall element. An extended research was performed on the existing methodologies to evaluate the seismic structural risk of load bearing masonry buildings, briefly describing methodologies similar to the one proposed, namely all of those that have in common the fact that they are based in the physical comparison between the resisting and acting shear forces at all storeys and along the two orthogonal horizontal directions. A case study is presented to check the applicability of the proposed methodology. The case study showed that the proposed methodology is relatively simple to apply and has a sufficiently good accuracy when compared with alternative methodologies. The degree of refinement of the analysis (global, by alignment, by wall panel and by wall element) must be taken into consideration and successively more complex analyses may be required when the results of simpler analyses are inconclusive.

Stochastic model for simulation of near‐fault ground motions

SummaryA parameterized stochastic model of near‐fault ground motion in two orthogonal horizontal directions is developed. The major characteristics of recorded near‐fault ground motions are represented. These include near‐fault effects of directivity and fling step; temporal and spectral non‐stationarity; intensity, duration, and frequency content characteristics; directionality of components; and the natural variability of ground motions. Not all near‐fault ground motions contain a forward directivity pulse, even when the conditions for such a pulse are favorable. The proposed model accounts for both pulse‐like and non‐pulse‐like cases. The model is fitted to recorded near‐fault ground motions by matching important characteristics, thus generating an ‘observed’ set of model parameters for different earthquake source and site characteristics. A method to generate and post‐process synthetic motions for specified model parameters is also presented. Synthetic ground motion time series are generated using fitted parameter values. They are compared with corresponding recorded motions to validate the proposed model and simulation procedure. The use of synthetic motions in addition to or in place of recorded motions is desirable in performance‐based earthquake engineering applications, particularly when recorded motions are scarce or when they are unavailable for a specified design scenario. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Assessment of Spatial Coherency Using Tri-directional Ground Motions

Structures and infrastructure are subject to spatial varying seismic ground motions. The commonly available empirical lagged coherency models are for the record components along the same orientation at spatially distributed recording stations; the lagged coherency for record components in two orthogonal horizontal directions was reported recently. It appears that the lagged coherency between a vertical and a horizontal record component has not been systematically investigated. The assessment of the lagged coherency among tri-directional ground motion components at a single or multiple recording stations is presented in this study using ground motion records from dense arrays (i.e., LSST and SMART-1 arrays) in Taiwan. The results indicate that the lagged coherency between vertical record components at different recording stations is systematically lower than that between horizontal record components in the same direction; and as a first-order approximation the lagged coherency between any two orthogonal record component components can be modeled as a linear function of frequency and is insensitive to separation between the recording stations. A simple-to-use lagged coherency model is suggested and illustrated for simulating array of tri-directional ground motions.

Simulation of Horizontal Ground Motions with Spatial Coherency in Two Orthogonal Horizontal Directions

Most available spatial coherency models are for the excitations along the same orientation. However, the coherency for excitations in two orthogonal horizontal directions may not be neglected, at least for recording stations with a separation distance, Δ, greater than 100 m. An assessment of this coherency using the records from a dense array in Taiwan with Δ < 100 m is presented and an empirical model is suggested. Use of the model to simulate spatial varying excitations is presented by applying the spectral representation method with both Cholesky and square-root decompositions, and the method by adjusting the phase angle to match the coherency characteristics.

Estimating seismic demands for performance-based engineering of steel buildings

Author(s): Reyes, Juan Carlos | Advisor(s): Chopra, Anil K | Abstract: Earthquake engineering practice is increasingly using performance-based procedures for evaluating existing buildings and proposed designs of new buildings. Both nonlinear static and nonlinear response history analyses (RHA) are used for estimating engineering demand parameters (EDPs)--floor displacements, story drifts, internal forces, hinge rotation, etc--in performance-based engineering of buildings. Topics related to both analysis procedures are investigated in this dissertation.In the first part, the original modal pushover analysis (MPA) to estimate seismic demands due to one component of ground motion is extended to consider two horizontal components simultaneously in three-dimensional analysis of buildings, and to estimate internal forces and plastic hinge rotations directly from pushover analyses. Subsequently, the accuracy of MPA in estimating EDPs for tall buildings and unsymmetric-plan buildings is evaluated. Seismic demands for recently designed and built 48- and 62-story buildings with ductile concrete core walls--designed according to the alternative provisions of the 2001 San Francisco Building Code (SFBC)--due to an ensemble of 30 ground motions are computed by MPA and nonlinear RHA, and compared. We demonstrate that MPA procedure shows degree of accuracy that is sufficient for practical application in estimating median values of EDPs for tall buildings subjected to two horizontal components of ground motion. The accuracy of the extended MPA procedure is also evaluated for low- and medium-rise unsymmetric-plan buildings with ductile frames designed in accordance with the 1985 Uniform Building Code (UBC85) and the 2006 International Building Code (IBC06). Seismic demands are computed for six unsymmetric-plan buildings due to 39 ground motions acting simultaneously in two orthogonal horizontal directions. Comparing these results with those from nonlinear RHA, we demonstrate that MPA provides good estimates of EDPs whereas the procedures specified in the ASCE/SEI 41-06 standard and the Eurocode 8 are not satisfactory for estimating seismic demands for unsymmetric-plan buildings.The second part of the dissertation concerns nonlinear response history analysis of buildings. With the goal of developing effective procedures for selection and scaling of multi-component ground motions to be used in nonlinear RHA, a modal-pushover-based-scaling (MPS) procedure is developed in this investigation. The developed MPS procedure is an extension of the original MPS procedure for one component of ground motion to two horizontal components. In this investigation, each horizontal component of ground motion is scaled by a factor selected to match the deformation of its inelastic SDF system to a target inelastic deformation that may be estimated using a design (or response) spectrum. The properties of the inelastic SDF system are determined by pushover analysis of the building using the first-mode distribution. Based on the results for medium-rise symmetric-plan and unsymmetric-plan buildings with ductile frames, we demonstrate that the MPS procedure provides much superior results than the scaling procedure specified in the ASCE/SEI 7-05 standard.

Response of an isolated structure with deteriorating hysteretic isolator model

Cyclic motion of lead rubber bearings (LRBs) leads to increasing temperature in lead core initiating the reduction in strength of LRB. This reduction results in a deteriorating bi-linear force deformation relation for LRB. In this study, response of LRBs (with deteriorating hysteresis loops due to temperature change) subjected to near-field ground motions with distinct pulse-type behavior is studied. Ground motions are applied bi-directionally and LRBs are modeled with due consideration of coupled behavior in the two orthogonal horizontal directions. Response of LRBs with deteriorating hysteresis is compared with that of non-deteriorating ones by considering bounding analyses (upper and lower bound). Thus, nonlinear response history analyses are performed for each selected ground motion record. Bounding analyses result in over predicted displacement demands for LRBs compared to results obtained by implemented deteriorating bi-linear LRB model. By means of new deteriorating model, engineers may come up with more efficient isolation system designs.

Unscented Kalman Filter for Non-Linear Identification of a New Prototype of Bidirectional Tuned Vibration Absorber: A Numerical Investigation

Several nonlinear system identification methods have been presented in the past, such as the Extended Kalman Filter, the H filter and the Sequential Monte Carlo methods. One of the most promising ones is the Unscented Kalman Filter (UKF) recently proposed for the on-line identification of structural parameters. In the present study the UKF is proposed to the purpose of the nonlinear identification of a new prototype of rolling-pendulum tuned vibration absorber which, relying on an optimal three-dimensional guiding receptacle, can simultaneously control the response of the supporting structure along two orthogonal horizontal directions. Unlike existing ball vibration absorbers, mounted on spherical recesses and used in axial-symmetrical structures, the new device can be bidirectionally tuned to both fundamental structural modes even when the corresponding natural frequencies are different, by virtue of the optimum shape of the rolling cavity. Based on preliminary numerical simulations, the UKF is shown to be effective in identifying the structural parameters of the new device and particularly the nonlinear rolling friction dissipation mechanism at the interface between the ball bearing and the rolling surface.

A numerical shoreline model for shorelines with large curvature

This paper presents a new numerical model for shoreline change which can be used to model the evolution of shorelines with large curvature. The model is based on a one-line formulation in terms of coordinates which follow the shape of the shoreline, instead of the more common approach where the two orthogonal horizontal directions are used. The volume error in the sediment continuity equation which is thereby introduced is removed through an iterative procedure. The model treats the shoreline changes by computing the sediment transport in a 2D coastal area model, and then integrating the sediment transport field across the coastal profile to obtain the longshore sediment transport variation along the shoreline. The model is used to compute the evolution of a shoreline with a 90° change in shoreline orientation; due to this drastic change in orientation a migrating shoreline spit develops in the model. The dimensions of the spits evolving in the model compare favorably to previous model results and to field observation of the Skaw Spit in the north of Denmark.

Determination of New Zealand Ocean Bottom Seismometer Orientation via Rayleigh-Wave Polarization

Online material: Complete list of earthquakes used in this study. Three-component ground-motion recordings are critical to modern seismic analysis techniques such as receiver functions and body- and surface-wave polarization studies. Modern three-component seismometers typically resolve three axes of ground motion into one vertical and two orthogonal horizontal directions. The standard convention for installation is to orient the instrument such that one of the horizontal components is aligned with true north, taking into account the current local magnetic declination at the station. This practice can be difficult in the case of borehole instruments and practically impossible for ocean-bottom seismometers (OBS). Some deployments of OBS have used airgun shots to determine sensor orientation (Anderson et al. , 1987; Duennebier et al. , 1987); however, this is not an error- or cost-free procedure and is not always available. In these cases, determination of sensor orientation is necessary independent of human interaction with the physical instrument. The elliptical particle motion of Rayleigh waves is exploited here to calculate sensor orientation based on the statistical analysis of earthquakes recorded on OBS deployed around the south island of New Zealand. This robust method is computationally fast because synthetic seismograms are not generated and accurate source parameters are not necessary. The technique is compared with body-wave orientation results and full-waveform surface-wave orientation results. Application of this method to waveforms recorded on land stations and synthetic waveforms confirms its reliability. Surface-wave arrival azimuth is determined via polarization analysis of the Rayleigh wave recorded on a three-component sensor. Rayleigh waves exhibit retrograde elliptical particle motion, theoretically only observed on the vertical and radial components. Because it is more stable to quickly determine a linear relationship than to measure ellipticity, the polarization analysis is performed by cross correlating the vertical component with the Hilbert-transformed radial component. The 90° phase …

Response of an isolated cable-stayed bridge under bi-directional seismic actions

This paper investigates the effectiveness and limitations of seismic isolation for the earthquake protection of a cable-stayed bridge under bi-directional seismic actions. A simplified lumped mass finite element model of the Quincy Bay-view Bridge at Illinois is developed for the investigation. The deck of the bridge is isolated from the towers by using elastomeric and sliding isolation systems. For the non-linear isolation systems, the interaction between the restoring forces in two orthogonal horizontal directions is duly considered in the response analysis. The seismic response of the bridge is obtained by solving the governing equations of motion in the incremental form using an iterative step-by-step method. A parametric study is also performed by varying important parameters of the isolation systems. The seismic response of the isolated cable-stayed bridge is compared with the corresponding response of the bridge without isolation systems. The results of the investigation indicate that the peak base shear response of the towers and deck accelerations are significantly reduced by the isolation. The displacement response of the hysteretic isolation systems is found to be increased when the bi-directional interaction of the bearing force is considered in the response analysis. Furthermore, it is also found that the response of the bridge is significantly affected by the variation in the parameters of the isolation systems.

A new passive rolling‐pendulum vibration absorber using a non‐axial‐symmetrical guide to achieve bidirectional tuning

AbstractA new, passive, vibroprotective device of the rolling‐pendulum tuned mass damper type is presented that, relying on a proper three‐dimensional guiding surface, can simultaneously control the response of the supporting structure in two mutually orthogonal horizontal directions. Unlike existing examples of ball vibration absorbers, mounted on spherical recesses and effective for axial‐symmetrical structures, the new device is bidirectionally tuneable, by virtue of the optimum shape of the rolling cavity, to both fundamental structural modes, even when the corresponding natural frequencies are different, in such a case recurring to an innovative non‐axial‐symmetrical rolling guide.Based on Appell's non‐holonomic mechanics, a non‐linear dynamic model is first derived for the bidirectional absorber mounted on a 1‐storey 3‐degrees‐of‐freedom linear structure translating under the effect of both imparted base motion and applied dynamic forces. A laboratory‐scaled prototype of the device is then tested to experimentally demonstrate the bidirectional tuning capability and to validate the mathematical model. The design procedure and the seismic performance of the absorber are finally exemplified through numerical simulation. Copyright © 2009 John Wiley &amp; Sons, Ltd.