Nominal Tension Research Articles

Experimental and numerical investigation on failure behaviour of aluminum-polymer friction stir composite joints

Friction stir composite joints between an aluminum alloy (AA6082-T6) and reinforced polymer (NorylTM GFN2) were studied regarding their failure characteristics. A comprehensive analysis on the mechanical behaviour of the joints was carried out, assessing the resulting deformed shape, the associated strain field and the observed failure modes using a digital image correlation (DIC) system and comparing with a finite elements method (FEM) model. The numerical model evidenced a good fitness to the experimental results since both the displacements and strain fields were found to be very similar. Both numerical and experimental strain fields in the longitudinal direction exhibited a localized spot of highly strained material, clearly indicating the nucleation site. Since secondary bending occurs in structural elements under tension due to geometrical and stiffness asymmetries, as is the case of overlap composite joints, a bending stress is induced, increasing the local stress compared to the nominal tension stress values. The ultimate tensile stress of the joints was found to range between 60.2 and 70.4 MPa, leading to an average joint efficiency of 82.6 %. The bending factor (kb) at the failure region was found to be 2.0, which means that the bending stress accounts for 2/3 of the total stress, acting as main failure catalyst.

Trans-scale characterization of the thickness-dependent interfacial strength of adhesively bonded cylindrical scarf joints

Numerous experiments have revealed that the interfacial strength of adhesive bonding systems increases when the adhesive layer thickness decreases from several millimeters to hundreds of microns. On the basis of the strain gradient elasticity and the nominal-strain failure criterion, a trans-scale model is proposed to characterize the thickness-dependent interfacial strength of the cylindrical scarf joints. The interfacial strengths predicted by this model match well with the previous experimental results. For a given adhesive layer thickness but varying scarf angles, the relation between the interfacial tension and shear strengths can be depicted by a circle, while the relation between the critical nominal tension and shear strains is described by an ellipse. As the adhesive gets thinner, the strength circle and the critical strain ellipse expand outward, indicating larger interfacial strength and critical strain due to the stronger strain gradient effect. The present study reveals the crucial role of the strain gradients, induced by the adherend constraints, in elevating the interfacial strength of adhesive bonding systems. The corresponding results are helpful to achieve ultra-strong interface bonding via constrained micro-scale adhesive layers.

Using biogas for energy cogeneration: An analysis of electric and thermal energy generation from agro-industrial waste

Society strongly relies on energy to develop and maintain its basic activities. The demand for electricity expanded in the last 30 years, increasing the need for more diverse energy supply sources. The biogas produced from industrial, urban-organic, and agro-industrial waste is an alternative renewable energy source that can be used for bioenergy generation. This study aims to evaluate the electric and thermal energy generated in a cogeneration system, using biogas produced by the anaerobic digestion of agro-industrial waste as fuel. The cogeneration system included a shell-and-tube heat exchanger attached to an engine generator with nominal power of 60kVA and nominal tension of 380 V. Biogas with three methane concentrations was used to conduct the experiments in an engine generator connected to an electric power grid, using a heat exchanger to measure the generated heat. In experiment I (68.54% methane), the raw biogas went through a desulfurization process and the system generated 2.04 kWh/m3 and 1.15 kWh/m3 of electric and thermal energy, respectively. In experiment II (83.46% methane), the methane concentration was increased by PSA, and the system generated 3.21 kWh/m3 and 1.57 kWh/m3 of electric and thermal energy, respectively. In experiment III (92.33% methane), the system generated 3.57 kWh/m3 and 1.67 kWh/m3 electric and thermal energy, respectively. Our experiments demonstrated that biogas with a high methane concentration can be efficiently used in the cogeneration of electric and thermal energy, boosting the energy potential of the fuel.

Characterising the mechanical properties of haematopoietic and mesenchymal stem cells using micromanipulation and atomic force microscopy

BackgroundImproving stem cell (SC) deformability using pre-treatment strategies, or isolating more deformable sub-populations, may prevent non-specific entrapment of injected cells, maintain circulating numbers and thus increase the likelihood of capture by microvessels in injured organs. However, nothing is currently known about the basic mechanical properties of SCs, particularly with regards their elastic characteristics. This study therefore aimed to determine the mechanical characteristics of haematopoietic stem cells (HSCs) and mesenchymal stem cells (MSCs) with comparisons made to neutrophils. MethodsMicromanipulation and atomic force microscopy (AFM) were used to quantitate mechanical properties following large and small deformations respectively of neutrophils, MSCs and naïve and stromal cell-derived factor-1α (SDF-1ɑ) or hydrogen peroxide (H2O2) pre-treated HSCs. ResultsNeutrophils and HSCs underwent rupture at ∼80% deformation. Nominal rupture stress (σR), nominal rupture tension (TR) and the Young's/elastic modulus at large deformations was significantly higher for neutrophils indicating they were stiffer and less deformable than HSCs. Surprisingly, MSCs did not rupture and were as deformable as HSCs despite their large size. Pre-treatment increased HSC deformability as indicated by lower rupture force, σR, TR and Young's modulus at large deformations. AFM demonstrated that pre-treatment increased the Young's modulus at smaller deformations indicating the HSC surface stiffened. This was accompanied by increased F-actin accumulation and its localisation in the cell cortex. ConclusionThis is the first study to precisely demonstrate that mechanical distinctions exist amongst different therapeutic SCs with regards their deformability and rupture response to applied stress. This can potentially be utilized as label-free markers in microfluidic cell sorting systems to separate sub-populations of potentially more therapeutic SCs.

ON DETERMINATION OF THE NOMINAL TENSION IN BOLT CONNECTION WITH RADIAL TENSION

ON DETERMINATION OF THE NOMINAL TENSION IN BOLT CONNECTION WITH RADIAL TENSION

Droplet retraction in the presence of nanoparticles with different surface modifications

We studied the influence of nanoparticles with different surface modifications on the interfacial tension and relaxation of model polymer blend after cessation of different strains. The droplet retraction experiments were carried out on a model system composed of polydimethylsiloxane (PDMS) as the suspending fluid and polyisobutylene (PIB) as droplet at room temperature in the presence of hydrophobic and hydrophilic nanosilica. Different weight fractions of particles were dispersed in the PIB droplet before forming a dispersed droplet by using a microsyringe in shear cell. We found that applied strain, nanoparticle concentration and their thermodynamically preferred localization affect both nominal interfacial tension and droplet retraction process. By addition of nanoparticles at a concentration as low as 0.2%wt, the nominal interfacial tension decreases from 3.12 ± 0.15 mN/m for neat PIB-PDMS interface depending on the surface characteristics of nanosilica. Hydrophilic nanosilica has the most effect on nominal interfacial tension and decreases it as low as 0.2 ± 0.21 mN/m at 1 wt.% loading under a strain of 7. The results show that the retraction process in this system is mainly controlled by interfacial phenomena rather than bulk rheological properties. Additionally, the shape evolution of droplets changes and the retraction rate slows down in the presence of nanoparticles.

An evaluation of the Gent and Gent-Gent material models using inflation of a plane membrane

The Gent material model is the simplest extension of the neo-Hookean material model that can describe the finite extensibility of the polymeric chains comprising the elastomer network. However, it is known that its fitting to experimental results of uniaxial tension is not satisfactory for moderate values of stretch, and the Gent-Gent model was proposed to remedy this deficiency. In this paper we provide further evidence on the good performance of the Gent-Gent model by using it to study the inflation of a circular plane membrane. For this problem, the deformation near the pole is equibiaxial and the associated nominal tension is a monotonic function of the stretch, but the pressure as a function of the stretch has both a maximum and a minimum. The Gent and Gent-Gent models are first fitted to our own experimental data for the nominal tension, and then used to predict variation of the pressure with respect to the stretch. By comparison with the experimental data, it is shown that the Gent-Gent model gives much better predictions than the Gent model.

Vibration Decoupled Modeling and Robust Control of Redundant Cable-Driven Parallel Robots

Trajectory tracking and vibration control of redundant cable-driven parallel robots (CDPR) attracted the attention of different researchers; however, the effects of the CDPRs end-effectors disturbing force/moment on the undesired vibrations and minimization of such effects has received few attention. A new general dynamic modeling and robust control structure for redundant CDPR is proposed in this paper, which evaluates such factors and tries to minimize their effects on the performance of CDPRs. Considering the effects of redundant cables on the CDPRs’ stiffness improvement, we neglect the second and higher order terms of motion errors that helps to separate the moving platform's undesired vibration equation from its desired (nominal) equation of motion. The obtained vibration model forms a linear parametric variable (LPV) dynamic system that lets us investigate the effects of external disturbances on the undesired vibration in different directions, and use a wide class of well-established robust and optimal vibration control techniques. Consequently, in order to minimize the effect of disturbances on the moving platform trajectory tracking performance, a robust and optimal vibration compensator is designed using the $LPV-H_\infty$ control design techniques. Based on the platform's desired trajectory, the proposed control scheme calculates the cables’ nominal tension required for trajectory tracking and further generates the auxiliary signals to augment these tensions to counteract the undesirable vibrations. Based on the obtained dynamic model, the developed approach is simplified for kinematically-constrained redundant CDPRs as a new actuation method with restricted rotational degrees of freedom. Via numerical analysis and experimental tests of a planar kinematically-constrained CDPR, the proposed modeling and robust control design approach are examined and compared with other common control design methodologies. Moreover, the effectiveness of kinematically-constrained actuation method in vibration elimination and control design simplification of CDPRs is demonstrated.

Twine Tension in High-Density Large Square Bales

Abstract.When greater density bales are made, baler manufacturers recommend using twine with greater knot strength. When twine fails, bale integrity is lost, harvesting costs increase, and productivity suffers. Twine failure typically occurs in the knot on the top strand of the twine. A better understanding of twine tension in the top strands could help reduce failures, allow for improved knot strength recommendations, and ultimately lower baling costs. A system was developed to measure the tension of the top strands while baling a variety of crops with a high-density large square baler. Depending on the bale chute design, twine tension was greatest as the bale cantilevered from the chamber but had not yet touched the chute or just as the bale fully exited the bale chamber. In either case, the absolute maximum recorded tensions were typically less than 60% of the twine specified knot strength. Pulses in synchronization with the plunger frequency were superimposed on the nominal twine tension. Tension was usually greatest in the outer left twine and the other right twine because for each, there was only one neighboring twine to share the load. Average twine tension over the first 60 s after the bale rested on the ground was linearly related to bale density. Crop stress relaxation reduced tension up to 20% within 20 min after the bale was placed on the ground. Top strand tension approached 60% of knot strength for only a short duration as the bale exited the chamber and after that, the tension was much less than the specified knot strength. Therefore, design changes or strategies that reduce tension during the critical period when the bale exits the chamber could reduce maximum knot strength requirements and lead to lower baling costs. Keywords: Bales, Density, Tension, Twine.

Testing and design of cold-formed steel clip angles in tension: Pull-over and serviceability

A cold-formed steel (CFS) clip angle is a common connector used in CFS building structures. This research project was conducted to investigate the behavior of the CFS clip angles in tension and to develop the corresponding design methods. The test program included two phases of testing: Phase I of program focused on the pull-over strength of screw connections on the anchored leg of the clip angles, and Phase II of program concentrated on the tensile strength of the anchored leg of the clip angles within the service deflection limit. Design methods for determining the nominal pull-over strength as well as the nominal tension strength of the clip angles with consideration of the serviceability were developed based on the test results. The Allowable Strength Design safety factors and the Load and Resistance Factor Design, Limit State Design resistance factors were also produced to support the proposed design methods.

Interfacial activity of reactive compatibilizers in polymer blends

The influence of a reactive block copolymer compatibilizer on the breakup of polymer fibers in the quiescent conditions is investigated using the breaking thread method (BTM). The compatibilizer is either localized at the interface of two polymers or incorporated in the bulk of thread phase. Moreover, the nominal interfacial tension between two polymers is estimated as a function of compatibilizer concentration for both types of samples using Tomotika theory. It is shown that assembling of compatibilizer molecules at the interface of two immiscible polymers can result in very different dynamic of thread breakup compared to samples containing the compatibilizer in the bulk phase. We observe a reduction in the rate of thread breakup (kinetic of stabilization) when compatibilizer is incorporated in the bulk of thread phase. Such effect is more significant when compatibilizer is localized at the interface of two fluids. Additionally, the mode of thread breakup is sensitive to the compatibilizer location since a beads-on-a-string (BOAS) morphology is observed when compatibilizer is localized at the interface. In conclusion, the usual attribution of interfacial activity of compatibilizer in polymer blends may be originated from their random presence at the interface rather than thermodynamically favored diffusion to the interface.

Development of overuse tendinopathy: A new descriptive model for the initiation of tendon damage during cyclic loading.

Tendinopathic tissue has long been characterized by changes to collagen microstructure. However, initial tendon damage from excessive mechanical loading-a hallmark of tendinopathy development-could occur at the nanoscale level of collagen fibrils. Indeed, it is on this scale that tenocytes interact directly with tendon matrix, and excessive collagen fibril damage not visible at the microscale could trigger a degenerative cascade. In this study, we explored whether initiation of tendon damage during cyclic loading occurs via a longitudinal compression-induced buckling mechanism of collagen fibrils leading to nanoscale kinkband development. Two groups of tendons were cyclically loaded to equivalent peak stresses. In each loading cycle, tendons in one group were unloaded to the zero displacement mark, while those in the other group were unloaded to a nominal level of tension, minimizing the potential for fibril buckling. Tendons that were unloaded to the zero displacement mark ruptured significantly sooner during cyclic loading (1,446 ± 737 vs. 4,069 ± 1,129 cycles), indicating that significant fatigue damage is accrued in the low stress, toe region of the load-deformation response. Ultrastructural analysis using scanning electron microscopy of tendons stopped after 1,000 cycles showed that maintaining a nominal tension slowed the accumulation of kinkbands, supporting a longitudinal compression-induced buckling mechanism as the basis for kinkband development. Based on our results, we present a new descriptive model for the initiation of tendon damage during cyclic loading. The so-called Compression of Unrecovered Elongation or CUE Model may provide useful insight into the development of tendinopathy. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:467-476, 2018.

Playing a tug of war with integrin and Notch receptors

It is now widely appreciated that cancer cells and stem cells can change their cell fate (differentiation, metastasis, etc.) depending on their mechanical environment. Mechanical sensing is likely to be initiated by individual membrane receptor proteins that are in direct contact with the mechanical environment. In order to understand how molecular level mechanical events trigger a cellular response, we need to examine the forces applied across individual cellular proteins during mechanical signaling.To define the single molecular forces required to activate signaling through a ligand‐receptor bond, we developed the tension gauge tether (TGT) approach in which the ligand is immobilized to a surface through a rupturable tether before receptor engagement. TGT serves as an autonomous gauge to restrict the receptor‐ligand tension. Using a range of tethers with tunable tension tolerances, we showed that cells apply a peak tension of about 40 picoNewtons (pN) to single integrin‐ligand bonds during initial adhesion. This tension value was consistent across different cell types. We then presented a mixture of weak and strong TGTs (12 pN and 54 pN nominal tension tolerance) to the cells in order to better mimic native cellular environments that are likely heterogeneous. Surprisingly, just one or two strong TGTs were sufficient to allow the cells to adhere as long as there is a high density of weak tethers. Therefore, mechanical tugging through one or two integrins is enough to convince the cell that the substrate is stiff enough for adhesion. Even more surprisingly, when we presented a mixture of two different weak TGTs (12 pN and 23 pN), cells adhered to the surface despite the fact that individually neither of the two tethers could support cell adhesion. Furthermore, we found that the 23 pN tether can exert its influence even at very high dilution, down to as few as two tethers per cell. This phenomenon of ‘ultrasensitivity in differential force sensing through integrin’ can be explained by a model where simultaneous rupture of weaker bonds exerts a transient high tension across a single integrin to activate that integrin.Notch signaling, involved in development and tissue homeostasis, is activated at the cell‐cell interface through ligand‐receptor interactions. Previous studies have implicated mechanical forces in the activation of Notch receptor upon binding to its ligand. In our original TGT paper, we showed that Notch signaling is activated even for the weakest TGT (12 pN), suggesting that if Notch activation requires force, it must be less than 12 pN. Subsequently, the Blacklow lab show that the exposure of a Notch cleavage site required for its activation occurs at a tension of ~5 pN39, consistent with our estimate of a 12 pN upper limit. We recently developed LTGT (a low tension gauge tether) utilizing the low unbinding force of ~ 4 pN between single‐stranded (ss)DNA and E. coli ssDNA binding protein (SSB) and showed that Notch activation requires forces between 4 and 12 pN.

Active Balancing of Super-Capacitors

В данной статье рассматривается решение одной из проблем использования суперконденсаторов, в связи с которым их применение является затруднительным в настоящее время. Как известно, из-за низкого номинального напряжения суперконденсаторов использование происходит при их последовательном соединении. При производстве суперконденсаторов имеется некоторый разброс параметров по емкости. В связи с этим возникает проблема разной скорости заряда суперконденсаторов, а именно: возникает вероятность перезаряда суперконденсатора, что может вызвать его пробой. Появляется необходимость ограничения напряжения на суперконденсаторе при заряде. Для проверки теоретических сведений проведено моделирование заряда последовательно соединенных суперконденсаторов в программной среде Multisim. В статье рассматриваются ключевые этапы разработки схемы устройства для ограничения напряжения на суперконденсаторах, которая будет являться активной балансировкой. Содержится расчет основных параметров данной балансировки. Для подтверждения работоспособности предложенной схемы проведено моделирование последовательно соединенных суперконденсаторов с использованием разработанной активной балансировки. Описаны результаты проведенных моделирований. Для наглядного представления принципа работы активной балансировки при моделировании были дополнительно выведены осциллограммы напряжений внутренних узлов схемы. В качестве доказательства важности правильного расчета параметров схемы проведено моделирование с неверно выбранными параметрами активной балансировки. Проведены описание и анализ результатов данного моделирования. В заключение раскрывается эффективность решения проблемы заряда последовательно соединенных суперконденсаторов. Раскрывается вопрос надежности и энергоэффективности использования модулей суперконденсаторов. С помощью приведенной статьи раскрывается вопрос ускорения внедрения использования суперконденсаторов в качестве накопителей энергии.

Biomechanical properties of human T cells in the process of activation based on diametric compression by micromanipulation

A crucial step in enabling adoptive T cell therapy is the isolation of antigen (Ag)-specific CD8+ T lymphocytes. Mechanical changes that accompany CD8+ T lymphocyte activation and migration from circulating blood across endothelial cells into target tissue, may be used as parameters for microfluidic sorting of activated CD8+ T cells. CD8+ T cells were activated in vitro using anti-CD3 for a total of 4 days, and samples of cells were mechanically tested on day 0 prior to activation and on day 2 and 4 post-activation using a micromanipulation technique. The diameter of activated CD8+ T cells was significantly larger than resting cells suggesting that activation was accompanied by an increase in cell volume. While the Young's modulus value as determined by the force versus displacement data up to a nominal deformation of 10% decreased after activation, this may be due to the activation causing a weakening of the cell membrane and cytoskeleton. However, nominal rupture tension determined by compressing single cells to large deformations until rupture, decreased from day 0 to day 2, and then recovered on day 4 post-activation. This may be related to the mechanical properties of the cell nucleus. These novel data show unique biomechanical changes of activated CD8+ T cells which may be further exploited for the development of new microfluidic cell separation systems.

Effect of pre-strain on susceptibility of Indian Reduced Activation Ferritic Martensitic Steel to hydrogen embrittlement

The role of pre-strain on hydrogen embrittlement susceptibility of Indian Reduced Activation Ferritic Martensitic Steel was investigated using constant nominal strain-rate tension test. The samples were pre-strained to different levels of plastic strain and their mechanical behavior and mode of fracture under the influence of hydrogen was studied. The effect of plastic pre-strain in the range of 0.5–2% on the ductility of the samples was prominent. Compared to samples without any pre-straining, effect of hydrogen was more pronounced on pre-strained samples. Prior deformation reduced the material ductility under the influence of hydrogen. Up to 35% reduction in the total strain was observed under the influence of hydrogen in pre-strained samples. Hydrogen charging resulted in increased occurrence of brittle zones on the fracture surface. Hydrogen Enhanced Decohesion (HEDE) was found to be the dominant mechanism of fracture.

Effective dynamics of twisted and curved scroll waves using virtual filaments

Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.

부유식 해양플랜트 계류 체인의 면외굽힘 거동에 대한 연구

OPB(out-of-plane bending)-induced failure of mooring chain was firstly addressed by CALM (catenary anchor leg mooring)-type offloading buoy, located approximately one mile away from the bow of the Girassol FPSO which was installed offshore area of Angola in September 2001. This study deals with verifying the load transfer mechanism between the first free chain link and connected two chain links inside the chain hawse. OPB moment to angle variation relationships are proposed by extensive parametric study where the used design variables are static friction coefficients, proof test loads, nominal tension forces, chain link diameters, chain link grades and chain link types. The stress ranges due to OPB moments are obtained using nonlinear FEAs (finite element analyses). Final stress ranges are derived considering ones from IPT (in-plane tension) forces. Also a formula for OPB fatigue assessment is briefly introduced.

Totally implantable robot to treat chronic atrial fibrillation

Chronic atrial fibrillation affects millions of people worldwide. Its surgical treatment often fails to restore the transport function of the atrium. This study first introduces the concept of an atrial assist device (AAD) to restore the pump function of the atrium. The AAD is developed to be totally implantable in the human body with a transcutaneous energy transfer system to recharge the implanted battery. The ADD consists of a motorless pump based on artificial muscle technology, positioned on the external surface of the atrium to compress it and restore its muscular activity. A bench model reproduces the function of a fibrillating atrium to assess the circulatory support that this pump can provide. Atripump (Nanopowers SA, Switzerland) is a dome-shaped silicone-coated nitinol actuator 5 mm high, sutured on the external surface of the atrium. A pacemaker-like control unit drives the actuator that compresses the atrium, providing the mechanical support to the blood circulation. Electrical characteristics: the system is composed of one actuator that needs a minimal tension of 15 V and has a maximum current of 1.5 A with a 50% duty cycle. The implantable rechargeable battery is made of a cell having the following specifications: nominal tension of a cell: 4.1 V, tension after 90% of discharge: 3.5 V, nominal capacity of a cell: 163 mA h. The bench model consists of an open circuit made of latex bladder 60 mm in diameter filled with water. The bladder is connected to a vertically positioned tube that is filled to different levels, reproducing changes in cardiac preload. The Atripump is placed on the outer surface of the bladder. Pressure, volume and temperature changes were recorded. The contraction rate was 1 Hz with a power supply of 12 V, 400 mA for 200 ms. Preload ranged from 15 to 21 cm H2O. Maximal silicone membrane temperature was 55 °C and maximal temperature of the liquid environment was 35 °C. The pump produced a maximal work of 16 × 10−3 J. Maximal volume pumped was 492 ml min−1. This artificial muscle pump is compact, follows the Starling law and reproduces the hemodynamic performances of a normal atrium. It could represent a new tool to restore the atrial kick in persistent atrial fibrillation.

Design of anchor bolts in masonry

AbstractA review of the methods used to design anchors for masonry in Canada, Australia, New Zealand, Europe and the United States was conducted. It was determined that with the exception of the American standard (MSJC), most provisions for connections for masonry require anchors to be designed using some form of performance based criteria.The MSJC uses design equations to predict anchor behavior and an evaluation of these equations using recent published test results suggests that the nominal tension anchor bolt capacity equations appear to give relatively good results at smaller anchor diameters. However, unaccounted for tension splitting/flexural modes appear to be present in larger anchor diameters.The investigations also suggest that the shear load provisions in the MSJC appear to be adequate when predicting the capacity of smaller diameter bolts, but they can be very unconservative for shear load capacities for bolts above 19 mm in diameter. The masonry break out equation does not appear to accurately predict the splitting/prying masonry failures observed with these large diameter anchors. In addition, it appears that splitting failures may occur in smaller masonry assemblies and further work must be conducted to determine if this is a testing protocol artifact or a failure mode that can be realistically expected in the field such as the proposed shear bearing model.Finally, results of combined shear and tension load tests, appear to suggest that the interaction equation for anchors used in grouted cavities in masonry assemblies is a power function, with a value between 1.4 and 1.67.