Journal articles: 'Strut and tie model'

1

Yun, Young Mook, and Julio A. Ramirez. "Strength of Struts and Nodes in Strut-Tie Model." Journal of Structural Engineering 122, no. 1 (January 1996): 20–29. http://dx.doi.org/10.1061/(asce)0733-9445(1996)122:1(20).

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Gong, Hao Jun, and Min Su. "The Preliminary Calculation Process of Strut-and-Tie Model." Applied Mechanics and Materials 351-352 (August 2013): 325–28. http://dx.doi.org/10.4028/www.scientific.net/amm.351-352.325.

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By briefly introducing the main steps of using strut-and-tie (STM) , this paper showing the preliminary calculation process. In this paper, defining D-region is the very first step in design.Then paper gives the method to calculate the reinforcement needed to meet required tie capacities. In addition, checking the room for struts is also an important step in the calculation. Since it can examine the correctness of the STM designed by engineer.

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Yang, Chun, Ming Ji He, Jian Cai, Yan Sheng Huang, and Yi Wu. "Study on Mechanical Behaviors and Calculation of Shear Strength of Steel Truss Reinforced Concrete Deep Beams." Advanced Materials Research 243-249 (May 2011): 514–20. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.514.

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Based on strut-and-tie model (STM) in deep beams, steel truss reinforced concrete (STRC) deep beam was developed. Experimental investigations of mechanical performances of STRC deep beams were carried out, and results show that STRC deep beam is of high ultimate bearing capacity, large rigidity and good ductility; Strut-and-tie force transference model is formed in STRC deep beams, and loads can be transferred in the shortest and direct way. Then Steel reinforced concrete (SRC) strut-and-tie model (SSTM) for determining the shear strength of STRC deep beams is proposed. The contribution of SRC diagonal strut, longitudinal reinforcements, stirrups and web reinforcements to the shear strength of STRC deep beams are determined with consideration of softened effects of concrete, and for safe consideration, superposition theory is employed for SRC struts. Computer programs are developed to calculate the shear strength of STRC deep beams and verified by experimental results.

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Yun, Young Mook, and Youjong Lee. "Strengths of Struts and Nodal Zones for Strut-and-Tie Model Design of Reinforced Concrete Corbels." Civil Engineering Journal 7, no. 8 (August 1, 2021): 1275–89. http://dx.doi.org/10.28991/cej-2021-03091725.

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The strut-and-tie model (STM) method is useful for the limit state design of reinforced concrete (RC) corbels. However, for the rational design of RC corbels, designers must accurately determine the strengths of concrete struts and nodal zones to check the strength conditions of a selected STM and the anchorage of reinforcing bars in nodal zones. In this study, the authors suggested a numerical process for determining the strengths of concrete struts and nodal zones in RC corbel STMs. The technique incorporates the state of two-dimensional (2-D) stresses at the strut and nodal zone locations, 2-D failure envelope of concrete, deviation angle between the strut orientation and compressive principal stress trajectory, and the effect of concrete confinement by reinforcing bars. The authors also proposed the strength equations of struts and nodal zones that apply to the typical determinate and indeterminate STMs of RC corbels. The authors considered the effects of the shear span-to-effective depth ratio, the horizontal-to-vertical load ratio, and the primary tensile and horizontal shear reinforcement ratios in developing the strength equations. The authors predicted the failure strengths of 391 RC corbels tested to examine the appropriateness of the proposed numerical process and strength equations. The predicted failure strength compares very well with experimental results, proving that the rational analysis and design of RC corbels are possible by using the present study's strut and nodal zone strengths. Doi: 10.28991/cej-2021-03091725 Full Text: PDF

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Yun, Young Mook, and Hyun Soo Chae. "An optimum indeterminate strut-and-tie model for reinforced concrete corbels." Advances in Structural Engineering 22, no. 12 (May 8, 2019): 2557–71. http://dx.doi.org/10.1177/1369433219845689.

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The failure behavior of a reinforced concrete corbel is complicated due to the shear span-to-effective depth ratio, reinforcement patterns, load conditions, and material properties. In this study, an optimum first-order indeterminate strut-and-tie model that reflects all characteristics of the failure behavior is proposed for the rational design of reinforced concrete corbels with a shear span-to-effective depth ratio of less than 1.0. A load distribution ratio that transforms the indeterminate strut-and-tie model into a determinate model is also developed to help structural designers design reinforced concrete corbels using the strut-and-tie model methods of current design codes. For the development of the load distribution ratio, a material nonlinear finite element analysis of the proposed first-order indeterminate strut-and-tie model was conducted repeatedly by changing the combination of primary design variables of the corbels. To examine the validity of our results, the ultimate strengths of 294 reinforced concrete corbels tested to failure by other investigators were predicted using the proposed strut-and-tie model with the load distribution ratio, the existing determinate strut-and-tie models representing arch and truss load transfer mechanisms, and the American Concrete Institute 318 conventional design method based on a shear friction theory. The ultimate strengths predicted by the proposed strut-and-tie model agreed fairly well with the experimental results. The ratio of the experimental strength to the predicted strength (and coefficient of variation) was 1.09 (28.0%), implying that the proposed strut-and-tie model can represent the load transfer mechanisms of corbels most appropriately.

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Chae. "Effective Strengths of Concrete Struts in Strut-Tie Models of Reinforced Concrete Corbels." Journal of the Korean Society of Civil Engineers 34, no. 4 (2014): 1081. http://dx.doi.org/10.12652/ksce.2014.34.4.1081.

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SOUZA, R. A., and S. BREÑA. "Behavior predictions of deep beams with short straight bar anchorages using strut-and-tie models and nonlinear analysis." Revista IBRACON de Estruturas e Materiais 9, no. 5 (October 2016): 710–21. http://dx.doi.org/10.1590/s1983-41952016000500004.

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Abstract This paper investigates the laboratory test results of 12 deep beams available in the literature, where the longitudinal reinforcement was anchored into the support using short straight bar anchorages. Four different specimen groups with three different shear span-to-depth ratios (a/d) were selected and most of the deep beams failed by strut crushing after yielding of the main longitudinal reinforcement. In order to investigate the behavior of the selected deep beams, an enhanced strut-and-tie model assuming geometrical adaptability (possibility of update in the dimensions of the struts and ties as the main tie starts to yield) is proposed. The analytical results obtained using this approach may be considered as much as accurate than some conducted complex nonlinear analysis considering smeared fixed cracking model and bond-slip behavior. However, an improvement on the effective strength factor of bottle-shaped struts by means of an iterative strut-and-tie model is needed, once the effective strength factor prescribed by NBR6118 (2014) has shown to be over conservative for all ranges of span-to-depth ratio (a/d) investigated. Finally, the obtained results indicated that short bar anchorages did not seem to influence significantly the shear strength of the deep beams investigated, especially the strength of bottled-shaped struts when appropriate crack control reinforcement is present.

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Hou, Liqun, Weiming Yan, Shicai Chen, Ruiyun Zhang, and Yue Qi. "Shear Strength Prediction of RC Beam-column Sandwich Interior Joints Based on Simplified Softened Strut-and-Tie." Open Civil Engineering Journal 11, no. 1 (December 20, 2017): 933–39. http://dx.doi.org/10.2174/1874149501711010933.

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Introduction: The sandwich joints casted core area with weaker strength concrete of beam, has more advantages than the traditional joints casted core area with higher strength concrete of column, such as the simple construction and quality assurance, while China design codes are too simple about the sandwich joints and have no clear calculation methods. Methods: Due to the scarcity of rational models for predicting the strength of RC beam-column sandwich joints, a modified simplified softened strut-and-tie model suggests a more rational calculation method for the effective compressive strength and the height of the joint concrete based on the simplified softened strut-and-tie. The shear strength of existing tested 15 sandwich interior joints is calculated by using the modified simplified softened strut-and-tie model. Furthermore, the theory results are compared with those of the code method and those of the simplified softened strut-and-tie model. Results and Conclusion: The results indicate that the code method is more conservative, and the modified simplified softened strut-and-tie can more precisely predict the joint shear strength than that of the softened strut-and-tie model and more secure than that of the code method. Thus, the modified simplified softened strut-and-tie model can reasonable reveal the failure mechanism of RC beam-column sandwich interior joints.

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Yun, Young Mook. "Effective Strengths of Concrete Struts in Strut-Tie Models of Reinforced Concrete Deep Beams." Journal of the Korean Society of Civil Engineers 33, no. 6 (2013): 2195. http://dx.doi.org/10.12652/ksce.2013.33.6.2195.

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Tuchscherer, Robin G., David B. Birrcher, and Oguzhan Bayrak. "Strut-and-tie model design provisions." PCI Journal 56, no. 1 (January 1, 2011): 155–70. http://dx.doi.org/10.15554/pcij.01012011.155.170.

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Sedayu, Maulana Agung, Djoko Sulistyo, and Akhmad Aminullah. "EKSPERIMEN PADA STRUKTUR PILE CAP TIGA TIANG DENGAN METODE STRUT AND TIE MODEL." INERSIA: lNformasi dan Ekspose hasil Riset teknik SIpil dan Arsitektur 15, no. 2 (December 7, 2019): 31–43. http://dx.doi.org/10.21831/inersia.v15i2.28619.

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ABSTRACTIn general, the design of the pile cap structure still uses conventional method assuming all regions experience linear strain. However, in reality the strain distribution in the cross section of the structure is not always linear so that a rational analysis method is needed with the assumption that is close to the actual condition using the strut and tie model method. This study aims to determine the behavior of crack pattern in the pile cap designed using the strut and tie model method (SNI 2847:2013 Appendix A) compared to conventional methods (SNI 2847:2013 Article 15). The specimen is the pile cap with three-piles and concentrated load, each of which has three methods. Loading is a static load that is channeled through a column located centric towards the structure of the pile cap. The results show that: the entire test object based on the two methods have flexural crack pattern. The average load capacity of the first crack (Pcr) on the specimen was designed using the strut and tie model and the conventional method were 239.0 kN and 193.7 kN. The average of crack width on the specimen using the strut and tie model and the conventional method were 0.68 mm and 3.88 mm.Keywords: crack pattern, pile cap, three-piles, strut and tie model ABSTRAK Pada umumnya perancangan struktur pile cap masih menggunakan metode konvensional dengan asumsi semua daerah mengalami regangan linier. Akan tetapi pada kenyataannya distribusi regangan pada penampang struktur tidak selalu linier sehingga diperlukan suatu metode analisis yang rasional dengan asumsi yang mendekati kondisi sebenarnya yaitu menggunakan metode strut and tie model. Penelitian ini bertujuan untuk mengetahui perilaku pola retak pada pile cap yang dirancang dengan metode strut and tie model (SNI 2847:2013 Lampiran A) dibandingkan dengan metode konvensional (SNI 2847:2013 Pasal 15). Pada setiap metode terdiri dari tiga buah benda uji berupa pile cap tiga tiang dengan beban sentris. Pembebanan berupa beban statis yang disalurkan melalui kolom yang terletak sentris terhadap struktur pile cap. Hasil pengujian menunjukkan bahwa keseluruhan benda uji berdasarkan kedua metode mempunyai pola retak lentur (flexural crack). Untuk rata-rata kapasitas beban saat retak pertama (Pcr) pada benda uji yang dirancang menggunakan metode strut and tie model dan metode konvensional adalah sebesar 239,0 kN dan 193,7 kN. Kemudian rata-rata lebar retak pada benda uji menggunakan metode strut and tie model dan metode konvensional adalah sebesar 0,68 mm dan 3,88 mm. Kata kunci: pola retak, pile cap, tiga tiang, strut and tie model

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Putri, Mutmainnah Rahman, Djoko Sulistyo, and Andreas Triwiyono. "Reinforced Concrete Corbel’s Behavior using Strut and Tie Model." Journal of the Civil Engineering Forum 4, no. 2 (May 13, 2018): 97. http://dx.doi.org/10.22146/jcef.28221.

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Reinforced concrete (RC) corbel is one of a disturbed region of elements of the structure. SNI 2847: 2013 as a guideline from Ministry of Public Works provides the design of RC corbels by the conventional method and with Strut and Tie Model (STM). The aim of this study is to determine and compare the behaviors of corbels experimentally that designed with both methods. The testing was conducted on two series of specimens and each series consisted of two specimens. Group 1 was designed using conventional method while group 2 designed using Strut and Tie Model. The axial column was tested under 50 kN fixed axial loads and corbels was tested under monotonic loads gradually increased up to failure. The results showed that with the provided steel and compressive strength of concrete, the shear capacity using the conventional method by analysis and experimental respectively were 363.164 kN and 345.7 kN, while the shear capacity using Strut and Tie Model by analysis and experimental respectively were 306.953 kN and 299.35 kN. The shear capacity of specimens using conventional method was 13.40 % greater than by using Strut and Tie Model and the shear capacity for each conventional and STM method were 1.9232 and 1.6653 greater than designated load.

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Almeida, V. S., H. L. Simonetti, and L. Oliveira Neto. "The strut-and-tie models in reinforced concrete structures analysed by a numerical technique." Revista IBRACON de Estruturas e Materiais 6, no. 1 (February 2013): 139–57. http://dx.doi.org/10.1590/s1983-41952013000100008.

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The strut-and-tie models are appropriate to design and to detail certain types of structural elements in reinforced concrete and in regions of stress concentrations, called "D" regions. This is a good model representation of the structural behavior and mechanism. The numerical techniques presented herein are used to identify stress regions which represent the strut-and-tie elements and to quantify their respective efforts. Elastic linear plane problems are analyzed using strut-and-tie models by coupling the classical evolutionary structural optimization, ESO, and a new variant called SESO - Smoothing ESO, for finite element formulation. The SESO method is based on the procedure of gradual reduction of stiffness contribution of the inefficient elements at lower stress until it no longer has any influence. Optimal topologies of strut-and-tie models are presented in several instances with good settings comparing with other pioneer works allowing the design of reinforcement for structural elements.

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SANTOS, D. M., M. L. CARVALHO, and F. R. STUCCHI. "Design of deep pile caps by strut-and-tie models." Revista IBRACON de Estruturas e Materiais 12, no. 4 (August 2019): 832–57. http://dx.doi.org/10.1590/s1983-41952019000400007.

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Abstract There are many methods for designing pile caps, but there is still no consensus on which one provides the best approach for the practical engineers. In Brazil, many structural designers use the classical Blévot method; however, the applicability of the method has been questioned after the revision of the NBR 6118 standard for design of concrete structures in 2014. To support structural designers, a strut-and-tie model has recently been developed that relates the classical method to the most current concepts of strut-and-tie models. The theoretical bearing capacity of four-pile cap obtained through several strut-and-tie models are compared with experimental tests. The results show that this recently developed model is suitable for the design of deep pile cap.

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Aihara, Aya, Victor Mendoza, Anders Goude, and Hans Bernhoff. "Comparison of Three-Dimensional Numerical Methods for Modeling of Strut Effect on the Performance of a Vertical Axis Wind Turbine." Energies 15, no. 7 (March 24, 2022): 2361. http://dx.doi.org/10.3390/en15072361.

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This paper compares three different numerical models to evaluate their accuracy for predicting the performance of an H-rotor vertical-axis wind turbine (VAWT) considering the influence of struts. The strut of VAWTs is one factor that makes the flow feature around the turbine more complex and thus influences the rotor performance. The focus of this study is placed on analyzing how accurately three different numerical approaches are able to reproduce the force distribution and the resulting power, taking the strut effect into account. For the 12 kW straight-bladed VAWT, the blade force is simulated at three tip speed ratios by the full computational fluid dynamics (CFD) model based on the Reynolds-averaged Navier–Stokes (RANS) equations, the actuator line model (ALM), and the vortex model. The results show that all the models do not indicate a significant influence of the struts in the total force over one revolution at low tip speed ratio. However, at middle and high tip speed ratio, the RANS model reproduces the significant decrease of the total tangential force that is caused due to the strut. Additionally, the RANS and vortex models present a clear influence of the struts in the force distribution along the blade at all three tip speed ratios investigated. The prediction by the ALM does not show such distinctive features of the strut impact. The RANS model is superior to the other two models for predicting the power coefficient considering the strut effect, especially at high tip speed ratio.

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TUCKER, VANCE A. "Measuring Aerodynamic Interference Drag Between a Bird Body and the Mounting Strut of a drag Balance." Journal of Experimental Biology 154, no. 1 (November 1, 1990): 439–61. http://dx.doi.org/10.1242/jeb.154.1.439.

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1. The drag of a bird body mounted on the strut of a drag balance in a wind tunnel is more than the sum of the drags of the isolated strut and the isolated body. The strut changes the air flow around the body and generates additional drag, known as interference drag. This paper describes practical methods for measuring the drag of bird bodies: a strain-gauge drag balance, dimensions for struts made with machine or hand tools, and a procedure for correcting drag measurements for interference drag. 2. Interference drag can be measured by extrapolating a relationship between the drag of isolated struts with different crosssectional sizes and shapes and the drag of a body mounted on those struts. The interference length the length of an isolated strut that produces drag equal to the interference drag is a usefulquantity for predicting interference drag. 3. The relationship mentioned above is a straight line for a model peregrine falcon (Falco peregrinus L.) body mounted on smooth struts struts with convex cross-sectional shapes ranging from streamlined to circular. This finding simplifies the determination of interference drag in three ways: (i) the line can be found from measurements with just two struts a standard strut with low drag and a calibration strut with high drag; (ii) the two struts need not have the same shape for example, the standard strut can be changed to a calibration strut by attaching a spoiler without disturbing the body mounted on the strut and (iii) a single value of interference length (33.1mm) describes smooth struts with a range of shapes and sizes. These struts had drag coefficients between 0.33 and 0.91 at Reynolds numbers between 2100 and 10800. 4. The interference length of a strut supporting the actual falcon body with a feathered surface is not significantly different from that of the strut supporting the model body with a rigid surface. 5. As a hypothesis, interference length (hI, in metres) of a smooth strut varieswith the size of the body mounted on it: hI=0.0365m0.333 where m is the body mass (in kg) of the intact bird.

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Wong, T. N., and R. K. L. Su. "Design criteria for strut-and-tie modelling in Hong Kong practice." Special Issue with Awarded and Shortlisted Papers from the HKIE Outstanding Paper Award for Young Engineers/Researchers 2022 29, no. 4 (December 16, 2022): 229–43. http://dx.doi.org/10.33430/v29n4thie-2022-0002.

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Strut-and-tie modelling has proved a very useful method in the analysis and design of non-flexural components of reinforced concrete members. Examples of design codes encompassing the strut-and-tie model (STM) provisions include Eurocode 2 (EC2), the fib Model Code 2010 (MC2010), the Canadian Standard (CSA A23.3-04), the American bridge design specifications (AASHTO LRFD 2020), the American Standard (ACI 318-14 and -19) and the Australian Standard (AS 3600:2018). Nevertheless, the application of different assumptions, model types and methodologies means that the strength acceptance criteria for struts, nodes and bearings vary within the literature and design codes. Unifying the STM design criteria is thus encouraged, to facilitate worldwide use of the STM in the design of non-flexural components, particularly for places such as Hong Kong that have not yet developed the localised design criteria for the STM. In this paper, the proposals set out in the literature and the provisions in the above-stated design codes are reviewed and compared with each other. Calibrating with the existing literature and design provisions, unified STM design criteria for struts, nodes and bearings with localisation are proposed for application in Hong Kong. The proposed design criteria are then applied to the STM design of a cantilever deep beam.

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Panjehpour, Mohammad, Hwa Kian Chai, and Yen Lei Voo. "Strut Deformation in CFRP-Strengthened Reinforced Concrete Deep Beams." Scientific World Journal 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/265879.

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Strut-and-tie model (STM) method evolved as one of the most useful designs for shear critical structures and discontinuity regions (D-regions). It provides widespread applications in the design of deep beams as recommended by many codes. The estimation of bottle-shaped strut dimensions, as a main constituent of STM, is essential in design calculations. The application of carbon fibre reinforced polymer (CFRP) as lightweight material with high tensile strength for strengthening D-regions is currently on the increase. However, the CFRP-strengthening of deep beam complicates the dimensions estimation of bottle-shaped strut. Therefore, this research aimed to investigate the effect of CFRP-strengthening on the deformation of RC strut in the design of deep beams. Two groups of specimens comprising six unstrengthened and six CFRP-strengthened RC deep beams with the shear span to the effective depth ratios (a/d) of 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00 were constructed in this research. These beams were tested under four-point bending configuration. The deformation of struts was experimentally evaluated using the values of strain along and perpendicular to the strut centreline. The evaluation was made by the comparisons between unstrengthened and CFRP-strengthened struts regarding the widening and shortening. The key variables werea/dratio and applied load level.

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Yang, Haiwei, Xue Liu, Yuyang Bian, and Ge Wang. "Numerical Investigation on the Mechanism of Transpiration Cooling for Porous Struts Based on Local Thermal Non-Equilibrium Model." Energies 15, no. 6 (March 13, 2022): 2091. http://dx.doi.org/10.3390/en15062091.

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Struts as an important structure in the combustion chamber of hypersonic flight vehicles to inject fuel into main flow face a severe thermal environment. Transpiration cooling is considered as a potential method to provide a thermal protection for struts. This paper presents a numerical investigation on transpiration cooling for a strut based on Darcy–Forchheimer model and the local thermal non-equilibrium model and analyzes the mechanism of transpiration cooling. A coolant film and a velocity boundary layer are formed on the strut surface and the shock wave is pushed away from the strut, which can effectively reduce the heat load exerted on the strut. The temperature difference between coolant and solid matrix inside the porous strut is analyzed, a phenomenon is found that the fluid temperature is higher than solid temperature at the leading edge inside the porous strut. As flowing in the porous medium, the coolant absorbs heat from solid matrix, and the fluid temperature is higher than solid temperature at the stagnation point of the strut. The influence of coolant mass flow rate and various coolants on transpiration cooling is studied. As mass flow rate increases, the cooling efficiency becomes higher and the temperature difference between fluid and solid in the porous medium is smaller. The coolant with a lower density and a higher specific heat will form a thicker film on the strut surface and absorbs more heat from solid matrix, which brings a better cooling effect for strut.

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Marzouk, H., E. Rizk, and R. Tiller. "Design of shear reinforcement for thick plates using a strut-and-tie model." Canadian Journal of Civil Engineering 37, no. 2 (February 2010): 181–94. http://dx.doi.org/10.1139/l09-120.

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The strut-and-tie method is a rational approach to structural concrete design that results in a uniform and consistent design philosophy. A strut-and-tie model has been developed to model the punching-shear behaviour of thick concrete plates. This model provides a quick and simple approach to check the punching-shear behaviour. Thick concrete slabs (250–500 mm) without shear reinforcement can exhibit brittle shear failure under a central force and an unbalanced moment. Shear reinforcement has proven to be very effective in preventing such failures. The developed strut-and-tie model has also been used to evaluate the minimum shear reinforcement required to prevent brittle shear failure of two-way slabs in the vicinity of concentrated loads. The strut-and-tie model for symmetric punching consists of a “bottle-shaped” compressive zone in the upper section of the slab depth, leading to a “rectangular-stress” compressive zone in the lower section of the slab depth. Inclined shear cracking develops in the bottle-shaped zone prior to failure in the lower zone. Cracking in the bottle-shaped zone is related to the splitting tensile strength of concrete.

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Chae. "An Indeterminate Strut-Tie Model and Load Distribution Ratio for Reinforced Concrete Corbels." Journal of the Korean Society of Civil Engineers 34, no. 4 (2014): 1065. http://dx.doi.org/10.12652/ksce.2014.34.4.1065.

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Yun, Y. M., and J. A. Ramirez. "Strength of Concrete Struts in Three-Dimensional Strut-Tie Models." Journal of Structural Engineering 142, no. 11 (November 2016): 04016117. http://dx.doi.org/10.1061/(asce)st.1943-541x.0001584.

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Nazila, Kamila Shaomi, Yulita Arni Priastiwi, and Sukamta Sukamta. "STRUT AND TIE MODEL STRUKTUR BALOK TINGGI BERLUBANG." TERAS JURNAL 11, no. 1 (April 1, 2021): 41. http://dx.doi.org/10.29103/tj.v11i1.362.

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Park, Hong-Gun, Yun-Gon Kim, and Tae-Sung Eom. "Direct Inelastic Strut-Tie Model Using Secant Stiffness." Journal of the Korea Concrete Institute 17, no. 2 (April 1, 2005): 201–12. http://dx.doi.org/10.4334/jkci.2005.17.2.201.

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Yun, Young Mook. "Computer Graphics for Nonlinear Strut-Tie Model Approach." Journal of Computing in Civil Engineering 14, no. 2 (April 2000): 127–33. http://dx.doi.org/10.1061/(asce)0887-3801(2000)14:2(127).

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Won, Dae-Yon. "Design of Rigid Joints Using Strut-Tie Model." Journal of the Korea institute for structural maintenance and inspection 18, no. 1 (January 30, 2014): 31–39. http://dx.doi.org/10.11112/jksmi.2014.18.1.031.

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Drobiec, Łukasz, Wojciech Mazur, and Tomasz Rybarczyk. "Analysis of confined masonry with Strut and Tie models." MATEC Web of Conferences 323 (2020): 02002. http://dx.doi.org/10.1051/matecconf/202032302002.

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Strut & Tie (S-T) models are used quite commonly for the analysis of reinforced concrete structures and in the calculation of masonry structures. Creating the S-T model of the confined masonry is slightly different from models of reinforced concrete or models of classic masonry structures. These models should take into account different stiffness of concrete and masonry. This article proposes a Strut & Tie model for the analysis of confined masonry. The results of calculations were compared with the results of tests of full scale masonry walls with and without opening. Good compliance of the calculation results of S-T models with the test results was obtained.

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Ji, Lei, and Xin Sheng Yin. "Strut- and- Tie Model Method for Partial Compression about Prestressed Tendon Constraint Concrete." Applied Mechanics and Materials 351-352 (August 2013): 1004–7. http://dx.doi.org/10.4028/www.scientific.net/amm.351-352.1004.

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Prestressed tendon constraint partial compression concrete is a new approach to solve the phenomenon of insufficient bearing capacity in partial compression concrete members .The keystone of Strut-and-tie theory is presented.The development of strut-and-tie model is in-depth analyzed based on the description of the stress distribution in the members , the author considers that this theory can yet be regard as an ideal calculation method in partial compression members which is constrained by prestressed tendon or steel mesh.

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R. Farhat, N. Gluck, and U. Tzadka. "Inclined struts variation and its effect in reinforced concrete design." Electronic Journal of Structural Engineering 10 (January 1, 2010): 57–65. http://dx.doi.org/10.56748/ejse.10125.

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Cracks developing in high intensive shear areas are largely dictated by the effect of variable levels of flexural moments and their direction at the supports regions. Changes in developing crack inclinations, lead to changes in developing strut inclinations available for pressure, creating a sort of truss and allowing the transfer of forces for equilibrium. Strut and tie model analysis of reinforced concrete elements is considered an alternative to the usual approaches of analysis and design, and is applied effectively in regions of discontinuity. This analysis follows the truss analogy approach. Inclined concrete compression struts between parallel inclined cracks are assumed. The variation of the struts’ angle of inclination, depending on the shear and flexure levels, and its effect in reinforced concrete design are researched. This research introduces a rapid and approximated methodology for the representation of struts’ angle of inclination in analytical modelling of shear computations as customary in codes of practice

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Wang, Ji Yang, Yi Lin Sun, and Masanobu Sakashita. "Direct Strut-and-Tie Model for Ultimate Shear Strength of Reinforced Concrete Structural Walls." Advanced Materials Research 255-260 (May 2011): 89–93. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.89.

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A direct strut-and-tie model to calculate the ultimate shear strength of structural walls based on an interactive mechanical model (C.Y.Tang et al.) is presented. Two common failure modes, namely, diagonal splitting and concrete crushing, are examined in this paper. Ultimate shear strengths of structural walls are governed by both the transverse tensile stresses perpendicular to the diagonal strut, and the compressive stresses in the diagonal strut. Such proposed model is verified aganist three experimental case studies of structural walls. Generally, predictions by the proposed model are not only accurate and consistent in each case study, but also conservative.

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Somraj, Amornthep, Kazunori Fujikake, and Bing Li. "Study on Dynamic Shear Resistance of RC Beams." Applied Mechanics and Materials 566 (June 2014): 211–16. http://dx.doi.org/10.4028/www.scientific.net/amm.566.211.

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The aim of this study was to investigate the dynamic shear failure behavior of RC beams under rapid loading through an experimental study and also to set up a strut-and-tie model with loading rate effect to predict the dynamic shear resistance of RC beams. Thus, rapid loading test with 24 RC beams with a shear span-to-deep ratio of 1.9 was performed, in which shear reinforcement ratio and loading rate were variable. All of the RC beams exhibited shear compression failure. Although the shear resistance increases with increasing loading rate, the influence of loading rate on the shear resistance clearly depends on shear reinforcement ratio. The strut-and-tie model with loading rate effect was finally developed, in which the thickness of the compression strut was formulated to be increased with an increase in loading rate. The developed strut-and-tie model was good agreement with the experimental results.

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Tasenhod, Piyoros, and Jaruek Teerawong. "Shear Strength Prediction of Reinforced Concrete Deep Beams Using Strut-and-Tie Model." Advanced Materials Research 931-932 (May 2014): 468–72. http://dx.doi.org/10.4028/www.scientific.net/amr.931-932.468.

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Shear strength prediction of simple deep reinforced concrete beams by method of strut-and-tie model is presented in this paper. The tested specimens were designed according to Appendix A of ACI 318-11 code with variations of shear span-to-effective depth ratios and ratios of horizontal and vertical crack-controlling reinforcement. Test results revealed that at the same shear span-to-effective depth ratio, the various crack-controlling reinforcements significantly influenced on strength reduction coefficients of strut and failure modes. When the shear span-to-effective depth ratios were increased, failure modes changed from splitting diagonal strut to flexural-shear failure. Based on the test results, the proposed model was compared with Appendix A of ACI 318-11code.

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Fric, T. F., R. Villarreal, R. O. Auer, M. L. James, D. Ozgur, and T. K. Staley. "Vortex Shedding From Struts in an Annular Exhaust Diffuser." Journal of Turbomachinery 120, no. 1 (January 1, 1998): 186–92. http://dx.doi.org/10.1115/1.2841380.

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Results from scale-model experiments and industrial gas turbine tests show that strut vortex shedding in an annular exhaust diffuser can effectively be modified by adding tapered chord to the struts. The struts are bluff bodies at full-speed, no-load conditions, when inlet swirl is close to 60 deg. Data from wind tunnel tests show that wake Strouhal number is 0.47, larger than that expected for an isolated cylinder wake. This value of Strouhal number agrees with those measured in full-scale exhaust diffusers. Wind tunnel tests showed that a strut with tapered chord most effectively reduced wake amplitudes and shifted shedding frequency. The tapered strut was also effective in reducing shedding amplitude in a scale-model diffuser. Finally, gas turbine tests employing a tapered strut showed significant reductions in unsteady pressure and noise. A major benefit of strut taper is a reduction of noise by uncoupling of vortex shedding from acoustic resonant response.

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Hussein, L. T., and R. M. Abbas. "A Semi-Empirical Equation based on the Strut-and-Tie Model for the Shear Strength Prediction of Deep Beams with Multiple Large Web Openings." Engineering, Technology & Applied Science Research 12, no. 2 (April 9, 2022): 8289–95. http://dx.doi.org/10.48084/etasr.4743.

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The behavior and shear strength of full-scale (T-section) reinforced concrete deep beams, designed according to the strut-and-tie approach of ACI Code-19 specifications, with various large web openings were investigated in this paper. A total of 7 deep beam specimens with identical shear span-to-depth ratios have been tested under mid-span concentrated load applied monotonically until beam failure. The main variables studied were the effects of width and depth of the web openings on deep beam performance. Experimental data results were calibrated with the strut-and-tie approach, adopted by ACI 318-19 code for the design of deep beams. The provided strut-and-tie design model in ACI 318-19 code provision was assessed and found to be unsatisfactory for deep beams with large web openings. A simplified empirical equation to estimate the shear strength for deep T-beams with large web openings based on the strut-and-tie model was proposed and verified with numerical analysis. The numerical study considered three-dimensional finite element models, in ABAQUS software, that have been developed to simulate and predict the performance of deep beams. The results of numerical simulations were in good agreement and exhibited close correlation with the experimental data. The test results showed that the enlargement in the size of web openings substantially reduces the elements' shear capacity. The experiments revealed that increasing the width of the openings has more effect than the depth at reducing the load-carrying capacity.

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Admono, Tri, Yoyon Ahmudiarto, Amma Muliya Romadoni, Iman Abdurahman, Agus Salim, Teguh Tri Lusijarto, and Mochammad Agoes Mulyadi. "Numerical investigation of the effect of triangle strut in vertical axis wind turbine (VAWT)." Journal of Mechatronics, Electrical Power, and Vehicular Technology 11, no. 2 (December 22, 2020): 95. http://dx.doi.org/10.14203/j.mev.2020.v11.95-101.

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Strut is used in vertical axis wind turbine (VAWT) to restraint the framework. In this study, struts are analyzed to show the pressure losses in VAWT. ANSYS computational fluid dynamics (CFD) software is used to investigate triangle strut in VAWT. This study aims to show a CFD simulation of struts, which affects the aerodynamic of VAWT. In CFD software, the aerodynamic of VAWT can be analyzed in terms of pressure losses in the struts. The simulation method starts by making a struts model, then meshing and setting up ANSYS's boundary conditions. The last iteration runs in ANSYS until convergence. Our results show the percentage of pressure losses with the variation of the angle of wind 0°, 20°, 40°, and 60° are 0.67 %, 0.52 %, 0.48 %, and 0.52 %. The effect of triangle strut in VAWT did not affect the wind flow to the VAWT blade. The results also indicated that the triangle strut could be applied in the multi-stage of VAWT system.

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Sattar, Siamak, and Abbie B. Liel. "Seismic Performance of Nonductile Reinforced Concrete Frames with Masonry Infill Walls—I: Development of a Strut Model Enhanced by Finite Element Models." Earthquake Spectra 32, no. 2 (May 2016): 795–818. http://dx.doi.org/10.1193/90914eqs139m.

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Reinforced concrete (RC) frames with masonry infill walls are prevalent in high-seismicity areas worldwide and have experienced significant damage in earthquakes. This paper proposes a finite element–enhanced strut model to simulate the in-plane seismic response of masonry-infilled RC frames through time-history analysis. The strut backbone defining the behavior of the wall is developed from the response extracted from the finite element (FE) model(s) for the infill and frame configuration of interest. These struts are combined with models capturing flexural and shear failures of beam-columns to simulate building response. The strut model takes advantage of the accuracy of the FE modeling results, yet is computationally efficient for use in nonlinear dynamic analysis. The robustness of the proposed strut model is examined through comparison with experimental results for frames with different failure modes. This modeling approach is used in the companion paper to simulate the collapse response of 1920s-era California frames.

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Al-Bayati, Ahmed Faleh. "Alternative Strut and Tie Model for Reinforced Concrete Deep Beams." Al-Nahrain Journal for Engineering Sciences 21, no. 1 (February 10, 2018): 86. http://dx.doi.org/10.29194/njes21010086.

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This paper presents a simple strut and tie model to calculate the shear strength of reinforced concrete deep beams. The proposed model assumes that the shear strength is the algebraic sum of three strength components: concrete diagonal strut, vertical stirrups, and horizontal web reinforcements. The contribution of each strength components was calibrated with the test results of 305 deep beams compiled from previous studies with wide range of geometrical and material properties. The predictions of the proposed model were compared with those of the current codes of practice (ACI-318-14 and ASHTOO 2014) and those of existing model in the literature. Comparisons revealed that the proposed model provided better predictions than other models. The mean of predicted strength to test of the proposed model, the ACI-318-14 model, the ASHTOO 2014 model were 0.98, 0.79, and 0.75, respectively. The corresponding standard deviations were 0.17, 0.28, and 0.49, respectively.

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Mabrouk, Rasha T. S., Mahmoud A. S. Mahmoud, and Magdy E. Kassem. "Behavior of Reinforced Concrete Deep Beams with Openings under Vertical Loads Using Strut and Tie Model." Civil Engineering Journal 7 (May 11, 2022): 148–70. http://dx.doi.org/10.28991/cej-sp2021-07-011.

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This research aims to study the effects of the size and location of openings on deep beams. The analysis of deep beams with openings presents a rather complex problem for engineers, as there are currently no guidelines within the design codes for this problem. Using the strut and tie model is a feasible solution, but also gives some uncertainties due to the various models that can be used. This paper proposes using a strut and tie model for the deep beams with openings where reinforcement is laid out in the form of embedded struts and ties. The study is divided into an experimental and a numerical part. The experimental study was conducted on eight reinforced concrete deep beams under vertical loads. Seven of the beams had web openings of different sizes and locations, while the eighth specimen was a reference beam without any openings. The beams had the same concrete dimensions with the size of the openings in the web taken as 150 150 mm and 300 300 mm, and the location of the opening in the horizontal direction was varied between 0.11 to 0.4 the span. The experimental results were analyzed in terms of cracking pattern, mode of failure, and load-deflection behavior and then compared to numerical analysis conducted using a finite element program. A parametric study followed to investigate the influence of reinforcement arrangement and reinforcement around the openings on the behavior of deep beams. The results showed that large web openings that directly interrupted the compression strut had the most reduction in beam capacity and that the location of the opening did not significantly affect the strength of the beam in the case of small openings. Doi: 10.28991/CEJ-SP2021-07-011 Full Text: PDF

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Tan, K. H., K. Tong, and C. Y. Tang. "Direct Strut-and-Tie Model for Prestressed Deep Beams." Journal of Structural Engineering 127, no. 9 (September 2001): 1076–84. http://dx.doi.org/10.1061/(asce)0733-9445(2001)127:9(1076).

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Chae, Hyun Soo, and Young Mook Yun. "An Indeterminate Strut-Tie Model for Prestressed Concrete Beams." Journal of The Korean Society of Civil Engineers 35, no. 4 (August 1, 2015): 801–14. http://dx.doi.org/10.12652/ksce.2015.35.4.0801.

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To, N. H. T., J. M. Ingham, and S. Sritharan. "Strut-and-tie computer modelling of reinforced concrete bridge portal frames." Bulletin of the New Zealand Society for Earthquake Engineering 35, no. 3 (September 30, 2002): 165–89. http://dx.doi.org/10.5459/bnzsee.35.3.165-189.

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Nonlinear inelastic force-displacement response envelopes of full-scale reinforced concrete bridge portal frames are predicted in this paper by representing the frame using strut-and-tie models. The nonlinear strut-and-tie analyses, which included the tension stiffening effect, were performed using the computer program Drain-2DX. Strut-and-tie analytical results were found to correlate satisfactorily with the experimental data and to provide superior prediction to that generated using conventional planar frame models.

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Fan, Guoxi, Debin Wang, Yuhong Diao, Huaishuai Shang, Xiaocheng Tang, and Hai Sun. "Improvement and Application of the Softened Strut-and-Tie Model." IOP Conference Series: Materials Science and Engineering 269 (November 2017): 012016. http://dx.doi.org/10.1088/1757-899x/269/1/012016.

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Ševeček, Oldřich, Jiří Hanák, Zdeněk Majer, Daniel Drdlík, Zdeněk Chlup, and Michal Kotoul. "Prediction of the Ceramic Foam Structure Failure Using a Detailed Finite Element Model." Key Engineering Materials 827 (December 2019): 222–27. http://dx.doi.org/10.4028/www.scientific.net/kem.827.222.

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The contribution deals with modelling and prediction of failure of mechanically loaded open cell ceramic foam structures by using 3D volume FE models constructed from CT scans of real foam specimens. The condition for crack initiation in particular struts comes from the coupled stress-energy criterion which combines two fracture-mechanics parameters of the investigated material – tensile strength and its fracture toughness. By combining of both stress and energy condition one obtains information about the crack initiation length which is later used (together with the tensile strength) for determination of the strut failure in the complex 3D FE model of the ceramic foam structure. The crack onset is considered in the critical location at the moment when the (tensile) principal stress under the strut surface (in a depth corresponding to the crack initiation length) exceeded the tensile strength of the strut. Such approach enables us to define failure also on relatively coarse meshes of the FE models where potential stress concentrations are not described precisely and therefore it is not possible to decide about the failure just based upon the value of tensile stress on the strut surface.

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Hu, Ming Hao, Pu Yang, and Daniel McCrum. "A Deployable Brace Model with Joint Clearance and Strut Eccentricity in Seismic Design." Materials Science Forum 972 (October 2019): 123–28. http://dx.doi.org/10.4028/www.scientific.net/msf.972.123.

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The paper discusses seismic performance of deployable brace member as well as its application in single-story single-bay frame by using finite element method in OpenSees Navigator. Even though deployable structure has wide applications in engineering area, it is almost blank for earthquake (seismic) engineering. A finite element deployable brace model consisting two identical struts and a revolute joint is built in this paper. The model considers joint clearance and initial eccentricity to accord practical situation. Hysteresis analysis has been done on the brace model as well as its application. The results show deployable structure provides sufficient lateral stiffness and ductility. Strut eccentricity is the key factor affecting the capacity of the strut and buckling strength, while joint clearance also has influence on the strut capacity and energy dissipation.

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Lyčka, Lukáš, and Petr Štěpánek. "Strut-and-Tie Model for Predicting the Punching Shear of Flat Slabs with Shear Reinforcement." Solid State Phenomena 259 (May 2017): 178–83. http://dx.doi.org/10.4028/www.scientific.net/ssp.259.178.

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The purpose of this paper is to describe a framework of the proposed method for predicting the punching shear of flat slabs with shear reinforcement. The proposed method is based on a strut-and-tie model. Current methods of predicting the punching shear strength of flat slabs could be divided into these categories: models based on empirical equations, physical models, analytical methods and finite element methods. Most of the current codes in force would be best described as empirical formulations. Physical model for prediction of punching shear is described in Model Code 2010. Proposed method for flat slabs with shear reinforcement is based mainly on a strut-and-tie model and therefore could be considered as an analytical method.For the purpose of demonstrating the effectiveness of the proposed method, the method is compared with some of the main methods currently in use, such as Eurocode EC2, American code ACI 318 and Model Code 2010. The comparison consists of results of more than 98 experiments of punching shear on the flat slabs with shear reinforcement, gathered from publications from all around the world.

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Zheng, Yanfeng, Huiying Cai, Meijia Wang, Junjie Yao, Xian Xu, Chunlin Zhou, and Yaozhi Luo. "Rolling gaits of a strut-actuated six-strut spherical tensegrity." International Journal of Advanced Robotic Systems 17, no. 5 (September 1, 2020): 172988142096090. http://dx.doi.org/10.1177/1729881420960904.

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A tensegrity is a self-stressed pin-jointed system consisting of tensile members and compressive members. As its shape can be actively controlled by changing the prestress of its members, it has great potential to be used as a shape-controllable locomotive system. Particularly, the six-strut spherical tensegrity has been studied intensively as a rolling locomotive system. In this study, the rolling gaits of a strut-actuated six-strut spherical tensegrity are investigated. Specifically, a mathematical model for generating the rolling gaits of locomotive spherical tensegrities is presented, and a numerical method combining dynamic relaxation method and genetic algorithm is used to solve the model. Various rolling gaits for the strut-actuated six-strut locomotive spherical tensegrity are identified using this approach. Two basic types of touching-ground triangles, two basic distributions of payload, and six cases for the numbers of used active struts are considered. Several rolling gait primitives are noted, their motion features analyzed, and a simple path-generating strategy is proposed based on idealized rolling gait primitives. A physical prototype of the strut-actuated six-strut locomotive tensegrity is manufactured, and experiments are conducted to verify the rolling gaits and locomotion paths generated by the proposed methods.

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Nguyen, Tong, and Phuong Le. "A Numerical Method for Estimating Strut Forces in Multi-Braced Excavation Systems." Journal of Technical Education Science, no. 75A (February 28, 2023): 78–87. http://dx.doi.org/10.54644/jte.75a.2023.1249.

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The paper discusses the development of a numerical method for a multi-braced excavation to estimate strut forces. Two different software were used in the proposed method. Equivalent strut forces were calculated by plane strain analysis on Plaxis 2D. The number of Etabs models built corresponds to the number of strut levels. Loads acting on waler beams in these structural models were derived from the results of equivalent strut forces on the Plaxis 2D model. The results of the proposed method were compared with those of a full 3D analysis. This method ensures the force equilibrium with an error of less than 5% as compared with the total strut forces in the 3D calculation. Due to the corner effect not take into account, the corner strut internal forces in the proposed method are usually larger than those in the 3D analysis, while the internal forces of the middle struts seem to be the opposite. Although the differences have a wide variation, the average error is 35%. However, the results from the proposed method are conservative. The proposed method is useful for practicing engineers, especially in the primary design stage of multi-braced excavation with a complex-shaped plan.

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Chiang, H. W. D., and M. G. Turner. "Compressor Blade Forced Response Due to Downstream Vane-Strut Potential Interaction." Journal of Turbomachinery 118, no. 1 (January 1, 1996): 134–42. http://dx.doi.org/10.1115/1.2836594.

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A blade forced response prediction system has been developed using an implicit two-dimensional CFD solver to model the rotor blade forced response due to the static pressure distortion (potential disturbance) from the downstream stator vanes and struts. The CFD solver predicts the static pressure distortion upstream of the stator vanes and struts, which is used to calculate the induced velocity perturbation at the rotor inlet. Using the velocity perturbation and the blade’s natural frequencies and mode shapes from a finite element model, the unsteady aerodynamic modal forces and the aerodynamic damping are calculated. A modal response solution is then performed. The results show that the stator vanes cause a significant amplification of the potential disturbances due to the struts. Effects of strut and vane modifications are examined using the analysis. A vane modification with an “optimized” flow angle distribution shows that the disturbance can be greatly reduced. Recent testing of the strut modification shows exceptional correlation with the prediction.

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Dong, Yuxuan, Zhigang Li, Jun Li, and Liming Song. "Effects of struts profiles and skewed angles on the aerodynamic performance of gas turbine exhaust diffuser." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 235, no. 6 (January 5, 2021): 1406–20. http://dx.doi.org/10.1177/0957650920985201.

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The strut structure directly affects the flow field characteristics and aerodynamic performance of the gas turbine exhaust diffuser. The effects of the strut profiles and strut skewed angles on the aerodynamic performance of the exhaust diffuser at different inlet pre-swirls were numerically investigated using three-dimensional Reynolds-Averaged Navier-Stokes(RANS) and Realizable k-ε turbulence model. The numerical static pressure recovery coefficient of the exhaust diffuser is in agreement with the experimental data well. The reliability of the numerical method for the exhaust diffuser performance analysis was demonstrated. Exhaust diffusers with four kinds of vertical strut profiles obtain the highest static pressure recovery coefficient at the inlet pre-swirl of 0.35. The similar static pressure recovery coefficient of exhaust diffusers with four kinds of vertical strut airfoils are observed when the inlet pre-swirl is less than 0.48. The static pressure recovery coefficient of exhaust diffusers with vertical b1 and b2 struts are higher than that with the a1 and a2 struts when the inlet pre-swirl is greater than 0.48. At the inlet pre-swirl of 0.35, The static pressure recovery coefficient of the exhaust diffuser with the a1 strut decreases with the increasing of the strut skewed angles. The static pressure recovery coefficient of the exhaust diffuser with the b1 strut increases with the increasing of the strut skewed angles, and the static pressure recovery coefficient increases by 3.6% compared with the vertical design when the skewed angle of b1 strut is 40[Formula: see text]. At the inlet pre-swirl of 0.64. The static pressure recovery coefficient of the exhaust diffuser with the a1 strut increases by 8.7% compared with the vertical design when the skewed angle of a1 strut is greater than 20°. In addition, the static pressure recovery coefficient of the exhaust diffuser with the b1 strut decreases by 3.8% compared with the vertical design when the skewed angle of b1 strut is 40°. The method to improve the aerodynamic performance of the exhaust diffuser by appropriate increase the strut maximum thickness and design the strut skewed angle is proposed in this work.

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Tan, Kiang Hwee. "FRP Strengthening of Discontinuous Members." Advanced Materials Research 1129 (November 2015): 69–76. http://dx.doi.org/10.4028/www.scientific.net/amr.1129.69.

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Deep beams, corbels, stepped beams, beams with openings and the like are structural members comprising discontinuous regions for which conventional flexural theory does not apply. To strengthen such members using fibre-reinforced polymer (FRP) systems, a rational approach based on strut-and-tie models (STMs) is desirable. This involves the strengthening of struts, ties and nodal zones where required. This study was carried out to illustrate the use of strut-and-tie models in FRP strengthening of reinforced concrete T-beams with a large opening created through the web. Five 3-meter long simply-supported beams were fabricated to simulate existing beams with webs punctured by openings of lengths varying from 180 to 720 mm and located at about 0.5 to 1.5 m from the near support. The depth of the opening was kept constant at 180 mm. Based on strut-and-tie modelling, the beams were strengthened using glass FRP sheets to carry the same ultimate load as a solid beam which had the same dimensions and internal steel reinforcement but without opening, that is, 200 kN. The beams were each subjected to a single load at one-third span from the other support. Test results indicated that all beams with strengthened opening performed as well as the solid beam without opening in terms of cracking and deflection characteristics, in addition to ultimate strength and ductility.

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Journal articles on the topic 'Strut and tie model'

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