Lateral Restraint Research Articles

Finite prism approach for stability analysis of laminated glass fins

The use of laminated glass (LG) as a structural material for load-bearing components within buildings has been growing over the last decades. LG can be obtained by bonding two or more pieces of glass by means of polymeric interlayers (e.g., poly vinyl butyral – PVB). This building process gives LG elements a huge advantage over the same ones made of fully monolithic glass with respect to safety, since after breakage the fragments usually remain attached to the interlayer, reducing the risk of injuries. As LG members usually present a high slenderness, they are susceptible to flexural buckling under compression, requiring specific calculation methods and verification procedures in order to guarantee appropriate and safe structural performance. Compared to literature, this work presents a novel approach that is focused on the prediction of the elastic critical buckling load of LG columns without any lateral restraints at the tensioned edges. The buckling loads of LG columns have been determined using Finite Element Method, generally using shell elements, or analytical models. Usually, such approaches make use of the concept of effective thickness, in which the thickness of a monolithic element with equivalent bending properties in terms of stress and deflection is employed. However, the effective thickness approach is either difficult to apply or inaccurate. Therefore, this work presents an efficient and accurate approach to evaluate elastic critical buckling loads of LG columns applying Finite Prism Method (FPM). The accuracy of the proposed approach is assessed comparing the results obtained using solid finite element and analytical models for fully monolithic glass columns, as well as LG columns composed by multiple glass layers.

Geosynthetic-stabilized aggregate: quantitative modulus evaluation via Bender Element

Geosynthetics, mainly geogrids and geotextiles, are commonly used to mechanically stabilize unbound aggregate layers in paved road applications. They provide lateral restraint to aggregates to initially increase the layer modulus during construction and minimize its time-dependent decrease under vehicular traffic loading. Different types of geosynthetics may provide different improvement mechanisms and stiffness enhancement levels. Quantitative evaluation of various stabilization geosynthetics is presented herein to compare modulus improvement trends and help incorporate geosynthetic benefits into state-of-the-art mechanistic-empirical (M-E) pavement design procedures. Five geogrids (three extruded, one woven, and one welded) and two geotextiles (one woven and one nonwoven) were studied with a dense graded aggregate in laboratory triaxial testing. Geosynthetics were placed at specimen mid-height and three pairs of Bender Element (BE) sensors were placed at various heights above the geosynthetic to collect shear waves and quantify the degree of mechanical stabilization during resilient modulus testing. While resilient moduli did not distinguish effectiveness of different geosynthetics, shear wave measurements could clearly show local stiffness increases achieved with geosynthetic inclusions. Meanwhile, trends observed in shear modulus profiles at various distances from the geosynthetic, when compared to that of control specimen, properly established the modulus enhancement level achieved in mechanical stabilization with geosynthetics.

Application of one-dimensional periodic layers with elastomeric seismic isolators for three-dimensional isolation

Three-dimensional (3D) seismic isolation is an appealing idea to protect structures and their components from earthquake-induced horizontal and vertical ground motions. Past attempts to develop 3D isolation systems were ineffective due to their complexity and reliability issues. One-dimensional periodic material-based isolation systems (1D-PIS) have been extensively researched for applications as raft foundations due to their simple and construction-friendly unit cell designs. These systems aim to attenuate seismic excitations in both horizontal and vertical directions. However, the effectiveness of 1D-PIS in mitigating 3D excitations may be limited due to the potential mismatch between the frequency content of horizontal and vertical vibrations. The present study proposes to combine a conventional horizontal isolation system with a 1D-PIS in the vertical direction to achieve a simple, passive, and efficient three-dimensional isolation system for structures and components. The 1D-PIS is strengthened by incorporating steel shims within the rubber layers and implementing steel casings at its periphery, enabling its utilization as an isolated system. Small-scale experimental and numerical investigations were conducted on strengthened 1D-PIS to study its isolation characteristics in the vertical directions. The study reveals that infinite boundary conditions required for the efficacy of 1D-PIS were achieved through lateral restraint provided by steel shims and steel casings. Notably, the individual isolation characteristics of the conventional and the 1D-PIS are not compromised in the combined isolation system. Nonlinear time history analysis on a prototype combined isolation system confirms its effectiveness in attenuating the seismic response under simultaneous horizontal and vertical ground motions.

Optimization of a novel lateral energy dissipation system for cable-stayed bridge with short piers based on seismic vulnerability analysis

Cable-stayed bridges with short piers are susceptible to becoming the structural weak link in seismic resistance during strong earthquakes. Traditional lateral restraint systems, such as fixed and sliding bearing systems, may impose substantial lateral forces and displacement demands, affecting the entire bridge's seismic safety. A butterfly-shaped steel plate damper has been developed and integrated into a lateral energy dissipation system along with elastoplastic cables to address this. Given the significant computational challenges and the complexity of identifying the optimal parameters for the energy dissipation system, this paper combines the probabilistic seismic demand model (PSDM) with the response surface method (RSM) to propose the seismic vulnerability fitting optimization method (SVFOM). Based on SVFOM, utilizing a central composite design (CCD), 17 analysis scenarios that account for the parameter variations of the lateral energy dissipation system are established. By developing response surface functions for bearing damage (ys) and pier damage (yp) through the seismic response fitting of the structure across all scenarios, we determined the optimal parameters for the lateral energy dissipation system to minimize damage to both bearings and piers. The finite element model validation analysis, which demonstrated significant reductions in pier displacement and the probability of bearing damage, confirms the effectiveness of the SVFOM. Optimized parameters showed that the new lateral energy dissipation system can significantly enhance the lateral seismic performance of cable-stayed bridges with short piers. Compared to scenarios without energy dissipation and with lateral sliding bearings, they demonstrated that this optimized system reduces the relative displacement of the piers and girders by 56 % and the probability of complete bearing failure by 87 % while maintaining pier damage within acceptable limits. This optimized system offers a valuable reference for the seismic design of similar bridge structures.

Wall sandwich panels with steel facings and PUR foam core under transverse loading: Experimental testing and numerical model calibration

Light weight panels are largely used for the envelope (wall assembly, roofing system) of different kind of buildings. Under extreme loading conditions, like external explosions, the walls may suffer extensive damage, under either positive or negative pressures. The study presented in the paper describes the results obtained on wall sandwich panels tested for transverse loading until complete failure. The panels are arranged as single span systems supported on side rails and loaded at the mid-span. After a quasi-linear response, the maximum bending capacity is reached. At this point, the panels have a sudden drop in capacity, associated with the rapid wrinkling of the face in compression. If the end fasteners have adequate resistance, catenary stage develops, and the ultimate capacity can be significantly higher than the peak bending capacity. Flexibility of the lateral restraints significantly influence the initiation of catenary action and the ultimate capacity of sandwich panels. Numerical models were calibrated using the structural analysis and design program SAP2000. This may allow professionals to integrate more quickly the wall models into the structural design even for extreme loading conditions.

Study on the Effects of Influence Factors on the Stress and Deformation Characteristics of Ultra-High CFRDs

A sensitivity analysis was conducted to evaluate several factors, including dam height, bank slope gradient, water storage times, and phased panel filling, on concrete-faced rockfill dams (CFRDs). The analysis identified the three most significant factors to examine their impacts on the stress-deformation characteristics of CFRDs. The results show that the order of influence on the dam body’s stress and deformation characteristics is as follows: dam height > bank slope gradient > water storage times > panel phased construction. From the perspective of stress-deformation of the face slab, water storage times predominantly affect tensile stress, while the bank slope gradient exerts the greatest influence on compressive stress. As the bank slope gradient decreases, the panel’s lateral restraint diminishes, leading to a decrease in the panel’s extrusion efficacy. Consequently, there are notable variations in the panel’s compressive stresses. An increase in dam height correlates with escalating stress and deformation in both the dam and face slab. As the bank slope gradient decreases, the deformation of the dam and face slab, as well as the range of tensile stress of the face slab, also increase. In contrast to a single water storage scenario, the face slab has experienced greater stress and deformation during the initial impoundment under multiple impoundment conditions. Therefore, multiple water storage schemes result in reduced deflection, axial horizontal displacement, and tensile stresses both along the slope and axial in the face slab. Furthermore, the tensile area at the bottom of the face slab transitions into a compressive area.

Active roof-contacted combined backfill mining technology based on a modified magnesium slag-based cementitious material

Backfill mining technology is an inevitable choice for sustainable green mining. Full roof-contact of backfill is a key issue to ensure the long-term stability of the backfill mining technology, but no effective measures have been proposed. Based on the expansion characteristics of the modified magnesium slag-based filling material (MCM) and the shrinkage characteristics of the ordinary cement-bonded filling material (CFM), an active roof-contacted combined backfill mining technology (MCM-CFM) was proposed. The expansion characteristics and the uniaxial compressive strength (UCS) of the modified magnesium slag-based cementitious material (MC) were compared and analyzed. And the analytical expressions of the main control parameters as the axial force and the filling height of the backfill were derived, with or without lateral restraints. Then the sensitivity and the influence rule of the parameters were also investigated. The results show that: (1) the expansion rate of MC can reach 0.21% and increases rapidly in the early stage. At 28d and 40d, 84% and 95% of the total expansion deformation are reached, respectively, and the maximum expansion rate is 0.21%. (2) With or without lateral restraints, the height ratio of the upper and the lower filling parts is about 0.72 or 0.18, respectively. (3) The force subjected on the backfill is mainly controled by the parameters of the filling width, the elastic modulus and the expansion rate. (4) With or without lateral restraints, the height ratio of the two filling materials is controlled by the elastic modulus, the density or the elastic modulus, the Poisson’s ratio, the expansion rate, respectively. MCM-CFM can solve the problem of active roof-contact for backfill mining technology, and has the potential for large-scale application in mine backfilling.

A Simplified Analytical Model for Strip Buckling in the Pressure-Assisted Milling Process.

A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries.

Performance of the bond between recycled concrete and steel bars subject to transverse stirrup constraints after exposure to high temperatures

This study investigates and assesses the bond performance between steel reinforcement and recycled concrete, subject to the confining effect of transverse stirrups post high-temperature exposure. A series of 24 specimen groups was examined, with variations in parameters including transverse stirrup ratios (0 %, 0.24 %, 0.67 %, 1.34 %), recycled concrete aggregate (RCA) replacement ratios (0 %, 50 %, 100 %), and temperatures (300 °C, 500 °C, 700 °C). Central pull tests were administered to discern the impact of each parameter on the bond integrity of steel-reinforced recycled concrete. The results revealed that high temperatures reduced the thickness of the critical cover, altering the failure mode of the specimen. With rising temperatures, the bond strength of steel-reinforced recycled concrete weakened. Nonetheless, an increase in stirrup ratio served to counteract the detrimental effects of high temperatures. In contrast, a higher RCA replacement ratio exacerbated these effects. For example, specimens with a 1.34 % stirrup ratio showed a 30 % decrease in the adverse impacts of high temperature on bond strength compared to those with no stirrups. A comprehensive computational model, devised from experimental data and theoretical analysis, predicts the bond-slip behavior of steel-reinforced recycled concrete, incorporating the constraint coefficient k, temperature T, and replacement ratio r as pivotal parameters. The model’s predictive curve corresponds closely with the experimental findings, effectively capturing the influence of high temperature, lateral restraint, and RCA replacement ratio on the bond performance of steel-reinforced recycled concrete.

Experimental and Numerical Study on the Anchoring Mechanism of an Anchor Bolt Considering its Lateral Restraint Effect

Experimental and Numerical Study on the Anchoring Mechanism of an Anchor Bolt Considering its Lateral Restraint Effect

Geosynthetic stabilization of road pavements, railroads, and airfields

Geosynthetics provide sustainable alternatives for enhanced performance, durability and cost-effectiveness of road pavements, railways, and airfields. Even when the same geosynthetic products are used for constructing these different transportation facilities, an optimal approach is needed to match the properties of soils or unbound aggregate geomaterials and the geosynthetic products to establish an effective mechanical stabilization. This Proctor lecture keynote paper presents the state-of-the-practice on the transportation applications of geosynthetics, design methods, and the recent research findings on geosynthetics used in road and airfield pavements and ballasted railway tracks. The paper introduces first the transportation applications of commonly used geosynthetic products, i.e., geogrids, geotextiles, and geocells, with special emphases to subgrade restraint and unbound aggregate stabilization applications and discusses in detail the related unpaved and paved design procedures. Next, the focus is directed towards establishing a better understanding of geosynthetic mechanisms governing stabilization applications. To summarize, this keynote paper reports on two decades of developments and research findings at the University of Illinois and elsewhere on the topic of geosynthetic stabilization using the latest technologies to quantify the stiffness enhancement in the vicinity of a geosynthetic material via the bearing capacity improvement and lateral restraint mechanisms. Recent research at the University of Illinois focused on the successful use of bender element shear wave transducer technology is discussed in detail with several examples given related to the laboratory and field efforts of unbound aggregate base and railroad ballast geosynthetic stabilization including full-scale instrumentation of stabilization geosynthetics used in actual road and airfield pavements constructed in the United States.

Finite element analysis and simplified envelope curve model for RC shear key under earthquake-tsunami actions

Coastal bridges are vulnerable to the compounded effects of earthquakes and subsequent tsunamis. Their limited lateral restraints can result in critical risks such as the deck unseating or overturning. To this end, reinforced concrete (RC) shear keys are often integrated to enhance the superstructure resilience. While previous studies have investigated their seismic performance, their effects under seismic-tsunami actions remains relatively unexplored yet. This study employed finite element (FE) analysis to examine shear key properties under such conditions, with emphasis on hysteretic curves, concrete damage, and strain evolution. The FE model was developed in accordance with precedent tests, and the modeling results were also compared with tests. A simplified envelope curve model was developed using both geometry and rebar configuration, with various damage states included to reckon their seismic damages after initial earthquakes. The proposed model was validated and aligned well with test results. Further, a framework was proposed to determine the envelope curve for bridges at different damage stages. This study aims to provide insights into the seismic-tsunami analysis on coastal bridges by considering their varying properties under seismic and tsunami actions.

Fatigue and monotonically-loaded reinforced concrete specimens subjected to partial area loading

The degradation of concrete structures is often due to the continuous application of compressive fatigue loads. Understanding of concrete behaviour in different environmental conditions and under especial fatigue loading arrangements, particularly in cases where the loaded area is smaller than loaded element, herein referred to as partially loaded area, is of utmost importance to make a realistic prediction of the concrete fatigue life for a reliable design of civil engineering infrastructure. This paper focuses on investigating the fatigue performance of reinforced concrete specimens subjected to partially loaded areas, considering the influences of steel fibres, reinforcement arrangement, and the environmental factor of water submergence. A typical example of a partially loaded concrete component subjected to fatigue loading is circular spread footings used as concrete foundations for typical wind turbines. In these types of elements, the compressive strength of the concrete can be enhanced due to the confinement provided by way of lateral restraint stemming from surrounding concrete and reinforcement. However, design codes primarily address static loading and lack specific criteria for fatigue loading in these partially loaded regions. To address this research gap, results from a comprehensive experimental study, which in total included 111 concrete specimens subjected to monotonic loading and 25 specimens tested under cyclic loading, were used to study this problem. The investigation aimed to evaluate the effects of steel fibres and reinforcement arrangement on both static and fatigue capacity. Additionally, the impact of submerging concrete structures in water on their fatigue performance was examined, revealing a decrease in their fatigue life. The experimental results demonstrated that the presence of steel fibres and splitting reinforcement significantly increased both static and fatigue capacity. Most current design codes neglect the environmental factor of water submergence, leading to reduced fatigue capacity in concrete structures. Consequently, the validity of the design codes DNV-OS-C502 and fib Model Code 2010 was evaluated, and a new environmental factor for partially loaded areas subjected to cyclic loading is proposed. To evaluate the experimental results and understand the mechanical response, nonlinear finite element analyses were conducted using a smeared-crack continuum modelling procedure coupled with high cycle fatigue material models to assess its applicability for estimating fatigue performance of partially loaded reinforced concrete elements. It was found that a plane stress modelling procedure was capable of estimating fatigue capacity for dry concrete components, however, overestimated the fatigue capacity of wet concrete components.

Design and Stability of Laminated Glass Beams and Cantilevers with Continuous Lateral Silicone Restraint

The stability of monolithic glass beams is reasonably well defined; as an elastic material it behaves in a similar manner to other elastic materials such as steel, for which there are many equations of different forms which give similar results. Special care is required for continuous restraint to the tension flange. Equations presented in Australian Standard AS1288 Glass in Buildings – Selection and Installation have been used successfully for many years for monolithic fins when used with the strength model of AS1288 but require a more comprehensive approach when using laminated fins and/or strength models that allow higher levels of stress. A review of equations for cantilevers results in a wider range of approaches with significant variance between the outcomes of various published steel and glass standards. AS1288 has been used as the default standard for stability of glass fins, however for cantilevers it appears to have a misprint which has existed for decades. This paper presents strategies for determining the moment capacity of beams and cantilevers made of laminated glass with continuous flexible buckling restraints, such as structural silicone, which have initial imperfections and a known design strength capacity. Where multiple wave lengths form, the warping stiffness may contribute and formulations for rectangles are presented. The accuracy and validity of the approach is also assessed by means of comparisons with the outcomes of Finite Element numerical analyses.

Flexural–torsional buckling with enforced axis of twist and related problems

The classical lateral–torsional instability of a cantilever beam with continuous elastic lateral restraint and a transverse point-load applied at the free end is discussed here through the lens of asymptotic simplifications. One of our main goals is to provide analytical approximations for the critical buckling load, as well as its dependence on various key non-dimensional groups. The first part of this study is concerned with a scenario in which a doubly symmetric beam is constrained to rotate about a fixed axis situated at an arbitrary height above the shear centroidal axis. The second part examines a beam that features a continuous elastic lateral restraint spanning its entire length. Assuming that the stiffness of the constraint, κ (say), is finite, the buckling equations in the second case are described by a system of two coupled fourth-order differential equations in the lateral displacement and the angle of twist. We show that as κ → ∞ , the problem discussed in the first part provides an outer solution for the aforementioned system; the relevant boundary conditions for the next-to-leading-order outer approximation are also derived using matched asymptotics. Our theoretical findings are confirmed by comparisons with direct numerical simulations of the full buckling problem.

Influence of continuous elastic lateral restraints on beams and beam-columns of steel-timber hybrid structures in fire

With the climate crisis and pursuit of efforts to reduce embodied carbon impacts in the built environment, steel-timber hybrid structures have emerged as a sustainable form of framed construction which offer numerous benefits over the widely used and well-established steel-concrete hybrid structures. However, there are major concerns about the structural fire performance of such systems among various stakeholders in the construction industry, particularly for the design implications in terms of the lateral-torsional buckling behaviour and the degree of lateral restraint mobilised in the steel-to-timber connections. The screws that connect cross-laminated timber slabs to steel beams may provide a certain degree of restraining action in fire. However, further investigations are required to quantify the slip characteristics of such connections. In this study, it was found from existing literature that at the fire limit state, the continuous elastic lateral stiffness available to restrain the beam varies between approximately 500 kN/m/m and 2000 kN/m/m. Relying entirely on the screws and using this practical range of stiffness, a parametric study using Eurocode 3 design buckling resistance equations on 9 m simply supported span steel beams and beam-columns with span-to-depth ratios of about 10, 15, 20 and 25 was performed. The results indicate that designing such members as fully restrained in fire conditions may lead to unrealistic assumptions and unsafe structures.

Axial compressive performance of cruciform timber-encased steel composite columns: Experimental investigation and buckling analysis through 3D laser scanning

Timber-encased steel composite (TESC) columns have garnered increasing attention owing to their high mechanical performance. However, limited studies have focused on the compressive performance of cruciform TESC columns and accurate evaluations of the full-field deformation of embedded steel components. In this paper, a novel cruciform TESC column embedded with a thin-walled cruciform steel component was proposed. 22 specimens including TESC columns, bare steel columns and bare glulam columns were tested under axial compression. Parameters such as the width and thickness of the cruciform steel component were considered. 3D laser scanning technologies were applied to measure the full-field deformation of 20 steel members, thus quantitatively assessing the reduction in the deformation of steel components resulting from the lateral restraint of timber. Finally, a nonlinear fitting equation was established to predict the load-carrying capacity. The results showed that the TESC columns exhibited significant enhancements in stiffness and load-carrying capacity. The lateral restraint of timber caused the buckling modes of the steel to change from torsional buckling to mainly local buckling. Moreover, the high post-yield stiffness of the steel components before reaching the maximum load indicated that the timber offered sufficient lateral restraint to make full use of the steel strength. The 3D laser scanning method accurately measured the full-field deformation of the steel at the failure state. Compared to bare steel columns, the torsional rotation of the steel components decreased by up to 83.14 %, while the maximum absolute lateral deflection decreased by up to 80.89 %. The suggested strength formula offered sufficient accuracy in predicting the load-carrying capacity of short TESC columns, with ratios between the calculated and experimental values ranging from 0.908 to 1.120.

Lateral-torsional buckling resistance of non-prismatic and prismatic mono-symmetric I-section steel beams based on stress utilization

The lateral-torsional resistance of prismatic double-symmetric I-section beams is accurately predicted using a mechanically consistent Ayrton-Perry approach, combined with a calibrated generalized imperfection. The corresponding design formulation was recently adopted in the revised version of Eurocode 3. However, for prismatic mono-symmetric I-section beams, the General Case shall be used while for non-prismatic beams only the General Method is available. Both methods present a very large scatter and highly underestimate the lateral-torsional buckling resistance. This paper proposes an extension to the General Formulation for non-prismatic beams with arbitrary boundary conditions, partial lateral restraints, and arbitrary loading for mono-symmetric I-sections. Using an advanced numerical model calibrated with experimental test results, a large parametric study is undertaken, and its results are used to assess the available design methodologies and the proposed method. It is concluded that the General Formulation provides excellent safe-sided estimates of the LTB resistance, and it is confirmed the very poor performance of the General Case and the General Method.

Magnified resilient behavior of recycled aggregates due to lateral restraint of geosynthetic under cyclic loading

Recycled aggregate base, usually utilized in permeable roadways, can be stabilized by geosynthetics to reduce rutting. However, the inclusion of geosynthetics would cause a magnified resilient behavior of the aggregate base under cyclic loading and the mechanism is still not well understood. In this study, cyclic triaxial tests were conducted to investigate the effect of the geosynthetic on the performance of the recycled aggregates. Results show that the resilient strains of aggregate samples stabilized by geosynthetics increased; correspondingly, the calculated loading/unloading moduli decreased and volumetric strains increased. However, a significant reduction of the cumulative plastic strains was observed. The main reason for such results is that the lateral confinement provided by geosynthetics was mobilized and caused the major principal stress to vary from the vertical direction to the lateral direction periodically along with the applied cyclic loading. This cyclic variation of the major principal stress would induce a cyclic shear action that causes the structural rearrangement of aggregates, leading to the dilation of samples. The major principal stress in the lateral direction during the unloading process results in a large vertical extension, which not only leads to a magnified resilient strain but also causes a reduced plastic strain.

Research on stability of CLT wall under uniform compression based on orthotropic plate buckling theory

Cross-laminated timber (CLT) has been widely used in the construction of multi-story timber structures, but a method for determining the buckling capability of CLT walls has not been obtained yet. Based on the plate buckling theory and lateral restraints of CLT walls, a method for calculating the uniform-compression buckling capability of CLT walls in cases of elasto-plastic instability and elastic instability is derived in this paper. In addition, equations for determining the boundary between the elasto-plastic instability and elastic instability is also proposed. A numerical model of the CLT wall under uniform compression was established on the basis of previous experiments. The theoretical results were compared with the results of numerical simulations, and the overall error was found to be small. The proposed equations can provide good predictions for the buckling capability of uniformly compressed CLT walls to provide a basis for the design and engineering application of timber structures.