Tension Ties Research Articles

Espérance Bridge

Espérance Bridge is one of the final infrastructure elements to be delivered on the King’s Cross estate in central London. The 25 metre footbridge spans over the Regent’s Canal to connect the major railway stations and Pancras Square in the south with shopping and eating hotspots, Granary Square and Coal Drops Yard in the north. As part of the original King’s Cross master plan, the bridge strengthens the link between the two halves of the site, enabling visitor flow and giving residents better access to public transport. The bridge also enlivens the canal corridor, providing a platform to observe Camley Street Natural Park to the west and the Ghat Steps to the east. Designed and constructed during a global pandemic and opening in the summer of 2021, the bridge is an innovative take on a traditional warren truss bridge that uses tapering and folded steel plates to create an elegant and sculptural form. The bold pomegranate red carbon steel plates set against the diagonal stainless steel tension ties illustrate the structural behaviour of the warren truss. Re-use of existing foundations to support the bridge ensured a seamless integration of the abutments into the setting, whilst also providing cost and carbon benefits.

Pre-tension design and research of cable net structure for space modular deployable antenna

Modular deployable antennas represent an ideal structural form for the development of large-aperture antennas because of their flexibility, adaptability, and high versatility. To enhance the surface accuracy of the antenna after deployment, a comprehensive pre-tension design method that considers truss deformation and tension uniformity is proposed. First, the configuration design of the antenna cable net is constructed, and the mathematical models for cable length under surface accuracy requirements and boundary nodes are established considering catenary effects. Second, the distribution patterns of cable net structure nodes and segments are analyzed, leading to the creation of node coordinate matrices and cable net connection matrices. A basic model for cable net pre-tension design is developed based on the fundamental principles of force density. Furthermore, a multi-objective optimization of cable net pre-tension is performed using a genetic algorithm, considering truss structure deformation and tension uniformity as dual factors. Finally, the developed model is applied to design a single-module cable net structure, and numerical simulation is used for validation. Research results show that the overall surface form error is 0.32 mm, and the maximum tension ratio of cable net on the front cable net surface is 1.54, whereas the maximum tension ratio of tension ties is 2.28, thereby meeting the design requirements. Numerical simulation shows that the maximum deformation of the cable net structure is 0.16 mm, validating the correctness of the model. This research can provide valuable insights and references for the pre-tension design and research of cable net structures in other antennas.

A unifying strut-and-tie model for conventionally reinforced link beams

Reinforced concrete link or coupling beams are usually cast integral with wall piers to help them act as a unit to resist lateral loads. The use of deep beam design in ACI 318-19 provisions leads to conservative shear designs for link beams which do not follow Euler-Bernoulli beams. Instead, strut-and-tie systems are used. The paper demonstrates the modeling of such beams using strut-and-tie provisions of ACI 318-19 Ch. 23. Alternatively, to using a time-consuming trial-and-error process, a unified general multi-panel strut-and-tie model is proposed, and simple design equations are developed to directly design conventionally reinforced link beams subjected to high shear force demand. As link beams have often a small span-to-depth ratio, the first one- and two-panel strut-and-tie models are considered basic and common. The one-panel model consists of a direct inclined compression concrete strut with horizontal tension ties in addition to the required crack-control web reinforcement and is used wherever the strut-tie angle is greater than the ACI minimum of 25 degrees; one vertical-to-two horizontal. The two-panel model is used when the beam span is too long to use the one-panel model and consists of one vertical tension tie and two steep inclined compression concrete struts. Worked design examples have been presented to justify and demonstrate the ease of implementation of the considered first two simple and direct models of the proposed unified general multi-panel strut-and-tie model. The predictions of the two basic models have been compared with five sample calculations and the comparison shows a good agreement.

Structural design and engineering of Striatus, an unreinforced 3D-concrete-printed masonry arch bridge

This paper describes the structural design and engineering of “Striatus”, a 3D-concrete-printed unreinforced masonry pedestrian bridge built in Venice in 2021 as part of the Time Space Existence exhibition organised by the European Cultural Centre. The project combines the latest developments in 3D concrete printing with the structural principles of historic unreinforced masonry. Typically, the structural applications of 3D concrete printing are limited to elements such as columns and walls loaded vertically, perpendicularly to the horizontal printing layers, to formwork elements or secondary structural elements. Indeed, fabrication constraints, delamination issues and the low tensile strength of the concrete have been seen as limiting factors to 3D concrete printing for structural applications demanding resistance to bending or predominant loading directions not perpendicular to the printing layers. By using unreinforced-masonry structural principles, this paper shows that structural elements spanning space horizontally, such as a pedestrian bridge, can be built by using the 3D concrete printing components as the main structure, working only in compression, loaded perpendicularly to the printed layers. Furthermore, as a compression-only structure following masonry principles, Striatus enabled the use of unreinforced concrete without any mechanical or chemical connections between the elements and the separation of concrete and steel, only used for the supports and to equilibrate the horizontal thrust of the arch effect through the tension ties. This work shows how the application of unreinforced masonry principles to 3D concrete printing offers new opportunities in terms of structural design and represents a strategy to increase sustainability by reducing material consumption and allowing reusability and recyclability of the structure. Finally, this paper discusses the critical aspects related to the design of Striatus from an engineering and construction point of view.

Construction of strut‐and‐tie models for members under complex stress states based on topology optimization

AbstractThe construction of strut‐and‐tie models (STMs) is the key, but also the difficulty when the model is used to describe the force mechanism and guide the reinforcement layout design of concrete disturbed regions (D‐regions). Topology optimization is a promising way to guide STMs construction. Different from the existing construction methods of predetermining nodes, the angle of inclination of the truss elements is first determined to ensure that it is consistent with that of the principal stresses in a 2D finite element model of the structure. The constructed model can well reflect the force transmission path of structural members, and it is better than the existing methods when it is evaluated through the principle of minimum strain energy. To verify the validity of the STM, a reinforcement layout scheme is adopted completely according to the position of the tension ties. On this basis, another reinforcement layout scheme adds additional transverse reinforcements in the bottle‐shaped stress field. The nonlinear finite element comparative analysis of an irregular deep beam designed by the two schemes is carried out. The results show that the two ultimate loads are close. Brittle failure occurs in the former, while the latter has higher deformability and eventually ductile failure occurs.

Form-finding and shape adjustment of cable-membrane reflectors

Cable-membrane reflector is a highly nonlinear flexible structure, which can represent a specific surface shape under the proper combination of cable tension and membrane stress. AstroMesh reflector is a representative of cable membrane reflector, which has advantages of large aperture, easy folding, and light weight, and is increasingly utilized in space antenna reflectors. In this paper, a finite element model of the cable-membrane structure is established together with the corresponding incremental equilibrium equation which provides the sensitivity of the nodal position with respect to the geometric parameter of the cables and triangular membranes. A form-finding strategy is detailed, which aims at a configuration with the reflector nodes locating on a specified paraboloid while all cables and membranes are tensioned uniformly as possible. In addition, the surface precision of the reflector is reduced due to the inevitable errors in the manufacturing process. Therefore, the tension ties in the cable network is designed to be adjustable to solve this problem. Carefully changing the length of these cables can increase the reflector surface precision, which is referred as shape adjustment. An adjustment strategy with model updating is proposed. The model updating using the measured positions of the reflector nodes can dramatically reduce the discrepancy of the finite element model with respect to the actual reflector, thus remarkably improving the efficiency of shape adjustment. Numerical example and physical experiment demonstrate the effectiveness of the proposed method.

Digitally fabricated weak interfaces to reduce minimum reinforcement in concrete structures

AbstractCrack initiators in reinforced concrete structures can facilitate fulfilling the serviceability requirements. They can be used as a design parameter to diminish the minimum reinforcement for members subject to imposed deformation and exposed to the environment as they reduce the crack spacing and width when arranged close enough. While crack initiators in conventional concrete construction are cumbersome to provide (e.g., by construction joints or taperings), they are inherent to layered extrusion processes with digital fabrication technologies: the tensile strength is typically reduced locally in interfaces between layers. Rather than trying to avoid these weak interfaces, this paper discusses the potential of taking advantage of them to act as crack initiators reducing the minimum reinforcement content. A tension chord‐based model is developed to (i) account for the local strength reduction and (ii) predict the effect of weak interfaces on the expected crack spacing and width. As a key finding, the model predicts a reduction of the required minimum reinforcement ratio proportional to the locally decreased concrete tensile strength for a specified maximum crack width requirement under imposed deformations. An experimental campaign on five layered and three reference tension ties confirmed the clearly positive impact of weak interfaces on crack spacings and widths.

Time‐dependent elongation and cracking behavior of fiber reinforced concrete tension chords

AbstractThe long‐term (LT) tension stiffening effect in fiber reinforced concrete (FRC) tension chords is investigated in this paper. Six tension tie specimens with varying fiber types (either no fibers, polypropylene, or steel fibers) and reinforcement ratios were subjected to a sustained tensile in‐service load for 560 days. The LT specimens were fitted with gauges to monitor their elongation over the test period. In addition, 12 specimens were subjected to instantaneous loading to capture the entire load‐deformation response of the tension ties, up to and beyond the yielding of the reinforcement. A complete suite of material characterization tests were conducted in conjunction with the tension tie testing. The results from this investigation indicate that the inclusion of the fiber types and dosages adopted in this program improve the short‐term performance with respect to stiffness, tension stiffening, and cracking. Steel fibers improved the LT behavior, while the polypropylene fibers used in this study led to mixed results. Models previously developed by the authors have been shown to describe the behavior with good accuracy.

FRP Tension Ties: State-of-the-Art Review of Existing Design Guidance for Debonding Capacity and Applicability to Concrete Diaphragm Seismic Strengthening

FRP Tension Ties: State-of-the-Art Review of Existing Design Guidance for Debonding Capacity and Applicability to Concrete Diaphragm Seismic Strengthening

Numerical investigation of RC exterior beam-column connection with different joint reinforcement detailing

The proper detailing of joint reinforcement plays an essential role in ensuring adequate performance of reinforced concrete frames in terms of strength and ductility. The influence of various options of joint reinforcement detailing on joint performance has been numerically investigated using the nonlinear finite element analysis software, ABAQUS. Two sets of beam-column connections of various joint reinforcement detailing with greater spacing between the stirrups at two different locations have been modeled for achieving this purpose, considering validated experimentally tested specimen as reference. This study reveals that achieving the minimum requirments of joint reinforcement ratio according to the ACI 318-19 and ACI 352R-02 codes utilizing both internal cross ties and outer stirrups with greater spacing between the stirrups rather than closely spaced outside stirrups only is more efficient in terms of joint strength and deformation capacity. This implies that the contribution of the inner cross ties considering their configuration and location in the shear strength resistance should be considered. Therefore, the joint stirrups' main role should be considered as tension ties and a crack-control reinforcement that requires less steel and wider spacing for the joint details rather than the confinement of the concrete. Furthermore, it has been observed that both the joint strength and deformation capacity have been significantly improved with the use of three layers of stirrups with two closed rectangular cross ties or one polygon cross tie. However, the employment of only two layers of stirrups with two crossed rectangular cross ties located at the middle third of the joint as well as diagonal bars at the corners between the beam and column of the joint core successfully controlled the joint cracks and improved the performance of the connection.

Experimental investigation on cracking behavior of reinforced concrete tension ties

The safe design of modern structures against earthquake excitation is a matter that troubles consultant engineers worldwide. Given the random nature of crack formation, research into reinforced concrete members, in the context of cracking behavior, has proved difficult. Sometimes, depending on the crack width and spacing, cracking can affect general behavior and, specifically, the seismic behavior of reinforced concrete in multi-story buildings. Widely accepted methodologies for predicting crack characteristics, e.g. crack width and spacing and number of cracks, have not been developed yet. Furthermore, the phenomenon of cracking in highly-strained members, which takes place during earthquakes, needs to be investigated more. The characteristics of cracks affect the appearance of catastrophic phenomena, e.g. transverse buckling of reinforced concrete structural walls. In the context of the present work, the impact of the mechanical factors of tensile deformation is investigated, in terms of cracking behavior. Eight test specimens were divided into two groups according to their longitudinal reinforcement ratio (1.79% and 3.19%) and strained under uniaxial tensile loading. The degrees of elongation used were equal to 10‰, 20‰, 30‰ and 50‰. Extreme tensile strains were also used, e.g. 30‰ and 50‰, in order to take into account the cases of extreme seismic excitations. Apart from the investigation of the tensile strain factor, this work also examines the influence of the rebar content. The test results can be used to establish an experimental database, in order to develop an empirical equation that can forecast the quantity of cracks, their width and spacing. The experimental study is followed by an analytical investigation that aims to develop an empirical equation, predicting the average width of cracks. The results are basically given in terms of diagrams showing the development of cracking characteristics in relation to the tensile strain applied. Useful conclusions concerning cracking behavior are derived.

Chloride-induced corrosion in reinforced concrete and fiber reinforced concrete elements under tensile service loads

Corrosion of rebars is one of the main issues affecting the service life of Reinforced Concrete (RC) structures. It is well-known that the use of fibers enhances the mechanical behavior of RC structures at both Serviceability Limit States (SLS) and Ultimate Limit States (ULS). In the former, fibers mainly influence the cracking pattern, leading to narrower and more closely spaced cracks. The crack width is a key parameter for controlling the durability of RC structures along with concrete quality and the thickness of the concrete cover. Even though many research studies have been carried out on this topic, the behavior of RC elements, with and without fibers, in both cracked stage and aggressive environments is still not well understood. This article describes an innovative test procedure specifically developed to evaluate the chloride-induced corrosion in RC elements with and without fibers in service condition (under tensile stress and in the cracked stage). Prismatic specimens 90 × 90 × 830 mm with Ø12 rebar (called hereafter tension ties) were subjected for 280 days both to a tensile load and to wet-dry cycles in a water solution containing 5% of NaCl. Experimental results indicate that this test procedure was suitable to assess the chloride-induced corrosion in tensile elements in the cracked stage. Furthermore, a positive influence of fibers was observed, while no relationship between crack width and pitting depth was found.

APPLICATION OF STRUT-TIE-METHOD (STM) TO RETROFIT AN EXISTING FOUNDATION ANCHORAGE

A strut-and-tie model (STM) is an ultimate strength design method based on the formation of a hypothetical truss elements that transmit forces from loading points to supports. The STM utilizes concrete struts to resist compression and reinforcing ties to carry tension. Design using STM involves calculating the required amount of reinforcement to serve as the tension ties and then checking that the compressive struts and nodal zone (joints) are adequate to support the forces. A key advantage of design using STM is that the designer can visualize the flow of stresses in the member. This paper presents the basic concepts, assumptions and approaches using STM to perform the calculation and design for the existing foundation anchor retrofit based on a real application in high seismic zone. The analysis also includes up-to-date finite element modelling techniques for the machine base plate the anchor rods connection to the concrete foundation subjected to large forces (tension and shear).

Decoupling of arch action and truss action in deep beams by strain energy

It is commonly accepted that deep beams transfer shear forces through a combination of arch action and truss action, but there is disagreement on how to estimate the fraction transferred by each assumed action. This study provides a theoretical method to decouple the two shear-carrying mechanisms from the perspective of strain energy. Through multiple-level least-energy solutions, a two-panel truss consisted of parallel compression diagonals and orthogonal tension ties is obtained for the minimum strain energy. Assuming that vertical ties of the truss model and diagonal ties of the combined model have the same energy, the fraction of load transferred by the truss action is decoupled as 2λ/3–0.5 (where λ is the shear span-depth ratio). It means that the entire shear is carried by the arch action when λ ≤ 0.75, while the entire shear is carried by the truss action when λ ≥ 2.25. Six deep beams were tested with instruments placed along the assumed direct struts and indirect struts, from which the contributions of the two load-transfer mechanisms can be separated experimentally. The theoretical method agrees well with the experimental results of the current study and the others collected from the literature.

A design methodology to reduce the embodied carbon of concrete buildings using thin-shell floors

This paper explores the potential of thin concrete shells as low-carbon alternatives to floor slabs and beams, which typically make up the majority of structural material in multi-storey buildings. A simple and practical system is proposed, featuring pre-cast textile reinforced concrete shells with a network of prestressed steel tension ties. A non-structural fill is included to provide a level top surface. Building on previous experimental and theoretical work, a complete design methodology is presented. This is then used to explore the structural behaviour of the proposed system, refine its design, and evaluate potential carbon savings.Compared to flat slabs of equivalent structural performance, significant embodied carbon reductions (53–58%) are demonstrated across spans of 6–18 m. Self-weight reductions of 43–53% are also achieved, which would save additional material in columns and foundations. The simplicity of the proposed structure, and conservatism of the design methodology, indicate that further savings could be made with future refinements.These results show that considerable embodied carbon reductions are possible through innovative structural design, and that thin-shell floors are a practical means of achieving this.

Strut-and-tie model for shear strength prediction of RC exterior beam–column joints under seismic loading

Based on the Kupfer failure envelope of concrete, an analytical model called the “interactive strut-and-tie model” (ISTM) for predicting the joint shear capacity of exterior beam–column joints (EBCJs) was formulated and is presented in this study. The ISTM consists of the interaction of the strengths of concrete struts and tension ties, and the strength contributions from shear reinforcements consisting of column ties, intermediate column vertical bars and crossed inclined bars are taken into account. The proposed approach was calibrated and validated using a large dataset of 328 EBCJ test results, covering a broad range of important parameters such as the aspect ratio, axial load ratio, beam reinforcement ratio and horizontal joint reinforcement ratio. Finally, the joint shear strengths computed by the ISTM were also compared against those obtained from state-of-the-art models and were found to have resulted in much more precision and uniformity.

Combination hand–instrument tension suture tie

Tying sutures under tension is a common challenge in surgery. Various solutions to this problem include pulley sutures, buried mattress sutures, hand tension ties, towel clamps, and surgical assistant to physically relieve tension on the closure. Disadvantages of these techniques include increased suture waste and additional time involved in suture placement.1 Penetrating towel clamps cause tissue trauma and require an extra instrument on the tray. For various reasons, support staff are not always readily available.

Optimization design method for the cable network of mesh reflector antennas considering space thermal effects

Abstract The mesh reflector antenna is widely used in space satellites for its characteristics of lightweight, large aperture, high precision, and high stiffness. As the form of mesh surface is heavily depended on cable forces and vice versa, the form finding and optimization design of cable networks play an essential role in antenna design. The present methods usually neglect the thermal effects, which is reasonable for ambient temperature. While space thermal loads cause significant variations from the original form finding state, it is essential to investigate and minimize the antenna's on-orbit shape errors caused by the thermal effects. The active shape adjustment on-orbit is far from anticipated, while the preliminary adjustment before launch is also limited by the number of adjustable cables (tension ties) and the engineer's experiences. Under these circumstances, we propose a form finding and design optimization approach for the cable network of mesh reflector antennas considering space thermal effects. In this approach, the cable's thermal deformation and geometric nonlinearity are fully considered at the design stage, and the burden of shape adjustment for thermal errors before launch can be relieved. As all cables instead of adjustable cables are optimized, the improvement of surface accuracy is more obvious than the shape adjustment method. Our work provides a new idea and approach for the optimization design of cable networks and the minimization of on-orbit shape errors.

Minimization of Cable-Net Reflector Shape Error by Machine Learning

During assembly of a cable-net reflector, surface adjustments must be made to meet the stick accuracy requirement of a space mission by changing the lengths of adjustable cables. It is desirable to find the optimum adjustment amount based on the current state of the cable-net reflector. However, all data needed to establish an accurate simulation model for the cable-net reflector cannot be measured. Therefore, the cable-net reflector is treated as a black box, and a machine learning algorithm (support vector machine) is used to develop a prediction model to establish the relationship between cable length adjustments and surface accuracy. The -fold cross-validation method is used to estimate the generalization error. The simulated annealing and grid search are combined to get the optimum hyperparameters for the prediction model. Next, a surface adjustment method is developed to calculate the optimal cable lengths. A tension truss reflector example is used to demonstrate the support vector machine prediction model and the adjustment method. The machine learning algorithm identified the relationships between cable lengths and surface accuracy. Both surface accuracy and tension uniformity can be improved by adjusting the boundary cables and tension ties with this method using only information from the front-side nodes.

Crack development in steel-fibre-reinforced concrete members with conventional rebars

Although concrete performance has increased significantly over the last 20 years, the durability of concrete structures still remains a major concern. In fact, while concrete permeability has been remarkably reduced, aggressive agents can still penetrate concrete structures through cracks, which are generally present due to shrinkage or tensile stresses. A possible solution for crack control in structural members reinforced with conventional steel rebars is represented by fibre-reinforced concrete. In fact, fibre reinforcement improves the tension stiffening in the concrete portions between cracks and allows tensile stresses to be transmitted between the crack faces; both aspects reduce the crack distance and, as a consequence, the crack width. Within this framework, the aim of this paper is to shed new light on the crack control exhibited by steel-fibre-reinforced concrete (SFRC), having high post-cracking residual strength, in combination with steel rebars. In this regard, 32 tension ties under direct tension were tested. Special attention was devoted to the influence of the SFRC post-cracking performance on crack formation and development. The results confirmed a reduction in mean crack spacing compared with reinforced concrete members. However, beyond a nominal residual strength of around 5 MPa, no considerable reduction of the mean crack spacing was found.