Journal articles: 'Strut-and-tie model design'

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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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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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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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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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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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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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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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Ghaisas, Kunal V., Dhiman Basu, Svetlana Brzev, and Juan José Pérez Gavilán. "Strut-and-Tie Model for seismic design of confined masonry buildings." Construction and Building Materials 147 (August 2017): 677–700. http://dx.doi.org/10.1016/j.conbuildmat.2017.04.200.

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Abdalla, K. M., A. Alshegeir, and W. F. Chen. "Analysis and design of mushroom slabs with a strut-tie model." Computers & Structures 58, no. 2 (January 1996): 429–34. http://dx.doi.org/10.1016/0045-7949(95)00135-4.

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Ghoraba, Ahmed K., Salah E. El-Metwally, and Mohamed E. El-Zoughiby. "The strut-and-tie model and the finite element - good design companions." Journal of Structural Engineering & Applied Mechanics 3, no. 4 (December 31, 2020): 244–75. http://dx.doi.org/10.31462/jseam.2020.04244275.

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The strut-and-tie method (STM) can serve as a tool for a safe design of concrete structures or members. It aids to trace the flow of forces, appropriately lay-out the reinforcement, and safely predict the structure capacity. On the other hand, the linear elastic finite element can be utilized as an alternative in the development of the strut-and-tie models besides the load path method. In addition, the nonlinear finite element analysis assists in the optimization of the design results obtained from the STM. Hence, the two methods work well as companions in structural design. In order to demonstrate such understanding, different examples which include a deep beam with large opening and recess, continuous deep beams with and without openings, and beam ledges, have been utilized. In the STM solutions, the ACI 318-14 failure criteria have been adopted. In the nonlinear finite element analysis, material nonlinearity has been accounted for. The obtained solutions from the two methods, along with the experimental data of the selected examples of this study, revealed the reliability of the STM in obtaining a safe solution. Besides, the nonlinear finite element proved to be an efficient tool in obtaining an economic design.

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Araújo, José Milton de. "Design of Rigid Pile Caps through an Iterative Strut-and-Tie Model." Journal of Advanced Concrete Technology 14, no. 8 (August 23, 2016): 397–407. http://dx.doi.org/10.3151/jact.14.397.

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ÖZKAL, FATİH MEHMET, and HABİB UYSAL. "A FULLY STRESSED DESIGN METHOD TO DETERMINE THE OPTIMUM STRUT-AND-TIE MODEL FOR BEAM–COLUMN CONNECTIONS." International Journal of Computational Methods 09, no. 03 (September 2012): 1250035. http://dx.doi.org/10.1142/s0219876212500351.

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Topology optimization and strut-and-tie model methods have a remarkable success in the detailing of reinforced concrete structures, especially for discontinuity regions of the beam–column connections. However, it has always been complicated to determine an optimum design throughout all the offers of an optimization process, since it is not obvious which of the decision variables should be considered in order to select the optimum design. This paper presents the application of a new selection method on topology optimization and strut-and-tie modeling of the beam–column connections. A performance index formulation assists the selection of the optimum design from the process by considering the fully stressed design concept unlikely other performance indices. Former indices take just one of the structural criterions into consideration such as stress, strain energy, displacement, etc. The efficiency and capability of the approach have been demonstrated by the comparison of element removal criterions and different parameter values on several bidimensional design examples.

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Zargarian, Mahsa, and Alireza Rahai. "Theoretical and Experimental Studies of Two-Span Reinforced Concrete Deep Beams and Comparisons with Strut-and-Tie Method." Advances in Civil Engineering 2021 (February 8, 2021): 1–16. http://dx.doi.org/10.1155/2021/8880067.

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Regarding the complicated behavior of continuous deep beams, a research program including three parts was conducted. First part: three continuous concrete deep beams with different shear span-to-depth ratios (a/h) were tested. The effects of varying a/h ratio on ultimate strength and failure modes were investigated. Second part: the nonlinear finite element (FE) analyses were performed to simulate the experimental specimens and 21 large-scale continuous deep beams. The main parameters investigated were a/h ratio from 0.33 to 2 and f c ′ considered 40 MPa, 60 MPa, and 80 MPa. Third part: the strut-and-tie modeling of different design codes and indeterminate strut-tie method were studied for continuous deep beams. Regardless of the a/h ratio, all beam specimens failed in shear mode with main diagonal cracks. Although EC2 load prediction was conservative for all beam models, the ACI and CSA predictions for concrete deep beams with high compressive strength were unsafe. The indeterminate truss model showed closer results to FE analysis in comparison with ACI, EC2, and CSA strut-and-tie method.

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Park, JungWoong, Daniel Kuchma, and Rafael Souza. "Strength predictions of pile caps by a strut-and-tie model approach." Canadian Journal of Civil Engineering 35, no. 12 (December 2008): 1399–413. http://dx.doi.org/10.1139/l08-062.

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In this paper, a strut-and-tie model approach is presented for calculating the strength of reinforced concrete pile caps. The proposed method employs constitutive laws for cracked reinforced concrete and considers strain compatibility. This method is used to calculate the load-carrying capacity of 116 pile caps that have been tested to failure in structural research laboratories. This method is illustrated to provide more accurate estimates of behavior and capacity than the special provisions for slabs and footings of the 1999 American Concrete Institute (ACI) code, the pile cap provisions in the 2002 CRSI design handbook, and the strut-and-tie model provisions in either the 2005 ACI code or the 2004 Canadian Standards Association (CSA) A23.3 standard. The comparison shows that the proposed method consistently well predicts the strengths of pile caps with shear span-to-depth ratios ranging from 0.49 to 1.8 and concrete strengths less than 41 MPa. The proposed approach provides valuable insight into the design and behavior of pile caps.

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Chen, Haitao, Lai Wang, and Jitao Zhong. "Study on an Optimal Strut-And-Tie Model for Concrete Deep Beams." Applied Sciences 9, no. 17 (September 3, 2019): 3637. http://dx.doi.org/10.3390/app9173637.

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The optimal strut-and-tie models (STMs) of two typical irregular concrete deep beams were constructed using evolutionary structural optimization and compared with those of previous studies. The reinforced concrete deep beam specimens were cast according to the reinforcement designs guided by different STMs. Eight irregular concrete deep beam specimens were experimentally investigated under stepped loading, and the differences in the amount of steel used, the load-carrying capacity, and the failure pattern of the different specimens were analyzed. The results show that the optimal STMs proposed in this study have significant advantages in terms of cost-effectiveness and can simultaneously ensure the load-carrying capacity, delay the crack propagation of irregular concrete deep beams, and reduce the amount of steel used in structural members. Therefore, they have an important engineering application value for the reinforcement design of irregular concrete deep beams.

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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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Lu, W. Y. "A Study on the Safety of the Shear Capacity Design of Reinforced Concrete Beam-Column Joints." Journal of Mechanics 22, no. 4 (December 2006): 311–20. http://dx.doi.org/10.1017/s1727719100000964.

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AbstractThe shear failure probabilities of reinforced concrete beam-column joints have been investigated by Monte Carlo method. The theoretical shear strength of joints is based on the softened strut-and-tie model proposed by Hwang and Lee (2002). The random variables included in this study are the strengths of concrete, the ultimate compression strain of concrete, the strengths of reinforcement, the dimensions of cross-section, and the model error of theoretical shear strength of joints. The shear failure probabilities of joints with SD 280 flexural reinforcement in the beams designed using the ACI Code are all higher than 0.04. The joints designed according to the softened strut-and-tie model are safer than those designed according to the ACI Code. The shear failure probabilities of exterior joints are higher than those of interior joints. The shear failure probabilities of joints with SD 280 flexural reinforcement in the beams are higher than those of joints with SD 420 flexural reinforcement.

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LANES, R. M., M. GRECO, and M. B. B. F. GUERRA. "Strut-and-tie models for linear and nonlinear behavior of concrete based on topological evolutionary structure optimization (ESO)." Revista IBRACON de Estruturas e Materiais 12, no. 1 (February 2019): 87–100. http://dx.doi.org/10.1590/s1983-41952019000100008.

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Abstract The search for representative resistant systems for a concrete structure requires deep knowledge about its mechanical behavior. Strut-and-tie models are classic analysis procedures to the design of reinforced concrete regions where there are stress concentrations, the so-called discontinuous regions of the structure. However, this model is strongly dependent of designer’s experience regarding the compatibility between the internal flow of loads, the material’s behavior, the geometry and boundary conditions. In this context, the present work has the objective of presenting the application of the strut-and-tie method in linear and non-linear on some typical structural elements, using the Evolutionary Topological Optimization Method (ESO). This optimization method considers the progressive reduction of stiffness with the removal of elements with low values of stresses. The equivalent truss system resulting from the analysis may provide greater safety and reliability.

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Kassem, Wael. "Shear strength of squat walls: A strut-and-tie model and closed-form design formula." Engineering Structures 84 (February 2015): 430–38. http://dx.doi.org/10.1016/j.engstruct.2014.11.027.

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Tur, Viktar, and Volha Sannikava. "Shear resistance of self-stressing concrete elements expanded under 2D restraint conditions." E3S Web of Conferences 212 (2020): 02018. http://dx.doi.org/10.1051/e3sconf/202021202018.

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An analytical design model for estimation the shear resistance of plane self-stressing concrete elements with orthogonal reinforcement is presented. The design model is based on the strut-and-tie model concept and takes into consideration the restrained expansion strains and selfstresses as a result of self-stressing concrete expansion. The results of theoretical investigations were finally compared to the experimental ones showing the suitability of proposed design method.

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R., Balamuralikrishnan, and Saravanan J. "Finite Element Analysis of Beam – Column Joints Reinforced with GFRP Reinforcements." Civil Engineering Journal 5, no. 12 (December 1, 2019): 2708–26. http://dx.doi.org/10.28991/cej-2019-03091443.

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Glass Fibre Reinforcement Polymer (GFRP) reinforcements are currently used as internal reinforcements for all flexural members due to their resistance to corrosion, high strength to weight ratios, the ability to handle easily and better fatigue performance under repeated loading conditions. Further, these GFRP reinforcements prove to be the better alternative to conventional reinforcements. The design methodology for flexural components has already come in the form of codal specifications. But the design code has not been specified for beam-column joints reinforced internally with GFRP reinforcements. The present study is aimed to assess the behaviour of exterior beam-column joint reinforced internally with GFRP reinforcements numerically using the ABAQUS software for different properties of materials, loading and support conditions. The mechanical properties of these reinforcements are well documented and are utilized for modelling analysis. Although plenty of literature is available for predicting the joint shear strength of beam-column joints reinforced with conventional reinforcements numerically, but no such study is carried for GFRP reinforced beam-columns joints. As an attempt, modelling of beam-column joint with steel and with GFRP rebars is carried out using ABAQUS software. The behaviour of joints under monotonically increasing static and cyclic load conditions. Interpretation of all analytical findings with results obtained from experiments. The analysis and design of beam-column joints reinforced with GFRP reinforcements are carried out by strut and tie model. Strut and Tie models are based on the models for the steel reinforced beam-column joints. The resulting strut and tie model developed for the GFRP reinforced beam-column joints predicts joint shear strength. Joint shear strength values obtained from the experiments are compared with the analytical results for both the beam-column joints reinforced with steel and GFRP reinforcements. The joint shear strength predicted by the analytical tool ABAQUS is also validated with experimental results.

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Lymei, Uy, and Byung-Jik Son. "Design Comparison of Strut Tie Model and ACI Traditional by Clear Span-to-Depth Ratio." Journal of the Korea Academia-Industrial cooperation Society 15, no. 4 (April 30, 2014): 2406–13. http://dx.doi.org/10.5762/kais.2014.15.4.2406.

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Cho, Young-Sang, Hyun-Suk Jang, and Geun-Seok Jeong. "Development of Automatic Rebar Placement System of Structural BIM applied Strut and Tie Model Design." Journal of the Architectural Institute of Korea Structure & Construction 32, no. 8 (August 30, 2016): 19–26. http://dx.doi.org/10.5659/jaik_sc.2016.32.8.19.

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Tantipidok, Patarapol, Dinara McLaughin, and Petr Štemberk. "Study of Accelerated Production of Prestressed Concrete Sleepers Using Strut-and-Tie Model." Advanced Materials Research 1054 (October 2014): 122–27. http://dx.doi.org/10.4028/www.scientific.net/amr.1054.122.

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When designing the technological process for producing prestressed concrete sleepers on a large scale, it is especially important to achieve substantial reduction of production time due to the economic aspect. In this study, an estimation of the earliest possible time to release prestressing force from the wire with respect to bond development is presented, thus, allowing earlier removal and reuse of a prestressed concrete sleeper formwork. Time-dependent development of concrete compressive and tensile strength is defined according to fib Model Code 2010. A Strut-and-Tie Model has been adapted as a design method for establishing the transmission length required for anchoring prestressed wires in a prestressed concrete sleeper in accordance with the bond stress. Additional calculations have established that the method is consistent with the Eurocode approach.

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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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Bołbotowski, Karol, Michał Knauff, and Tomasz Sokół. "Applications of truss topology optimization in the design of reinforced concrete structures using „Strut and Tie” models." Budownictwo i Architektura 12, no. 1 (March 11, 2013): 091–98. http://dx.doi.org/10.35784/bud-arch.2178.

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Although Strut and Tie models are often used in practical design due to their apparent concept based on truss analysis, the creation of a model consistent with behaviour of the real structure is not an easy task. Frame corner model considered in the paper and presented in code [7] and article [8] exemplifies the problem. The authors proposed a method of automatic generating of ST models by making use of truss topology optimization (volume minimization problem). The method is based on classical ground structure approach. The authors introduced a method of including the cost of nodes in the objective function, which allowed to obtain solutions consisting of rationally small number of bars (unlike Michell’s structures). Moreover, algorithms ensuring consistency with Eurocode requirements were developed. The method was implemented in computer program. With the use of the software the authors proposed an alternative ST model for the frame corner, which requires considerably less reinforcement steel in comparison with the model suggested by the code. The versatility of the program was well proven in several other examples of plane stress problems in reinforced concrete design.

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Cattaneo, Sara, Pietro Crespi, and Luigi Biolzi. "Structural Analysis and Design of Reinforced Concrete Bridge Corbels." Applied Sciences 10, no. 19 (September 25, 2020): 6727. http://dx.doi.org/10.3390/app10196727.

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Post-installed systems for the anchorage of safety barriers to bridge corbels are widely used today thanks to their flexibility and easiness of installation. Because of commonly found in situ boundary constraints, however, the design requirements for post-installed fasteners and rebars are frequently not satisfied or only partially satisfied. This paper assesses the mechanical response of a corbel where an innovative solution concerning the placement of post-installed reinforcement in reinforced concrete members was suggested. With reference to the refurbishment of bridge curbs, which usually requires concrete removal in the damaged top layers, the proposed method was based on the introduction of additional U-shaped post-installed rebars connecting the existing portion of the corbel to the newly cast top layer, in order to allow the transfer of the tension pull-out force exerted by the posts restraining the safety barrier. The layout investigated in this paper consisted of three anchors connecting the baseplate of the post supporting the safety barrier to the corbel (a layout commonly found in Italy). These anchors transfer the external actions (bending moment and shear) to the corbel thanks to the formation of a strut-and-tie system where the U-shaped rebars and the existing reinforcement play a crucial role. A strut-and-tie model of the corbel was presented to allow the use of a simplified approach to assess the safety of the corbel. The tests on real-scale specimens were also modeled numerically and additional models were considered to evaluate the effect of characteristics parameters (i.e., size of the corbel, existing shear reinforcement, etc.) on the overall response of the corbel.

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Ng, Chee Khoon, Alex Mee Kuei Tiong, and See Hung Lau. "Analytical Model for RC Beams with Externally Bonded Laminates Using Strut-and-Tie Method." Advanced Materials Research 446-449 (January 2012): 3218–28. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.3218.

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An analytical model for RC beam strengthened with externally bonded laminates based on the strut-and-tie method is reported herein for predicting the strength and mode of failure of the strengthened RC beam. From the proposed model, four inequality equations were derived corresponding to four possible modes of failure. These four inequality equations define a safe domain. When the loading path up to the ultimate flexural limit state of a beam is plotted on the same diagram, the mode of failure and strength of the beam can be identified. The possible modes of failure consist of both flexure-type and shear-type failures. Flexure-type failure is due to the yielding of internal longitudinal reinforcement or the yielding of externally bonded laminates, whereas shear-type failure is due to the crushing of the diagonal compressive concrete strut or the yielding of the shear reinforcement. The failure mode initiated by one flexure-type followed by another is possible. Mode of failure initiated by one flexure-type followed by a shear-type is also possible but not otherwise. In short, this model describes the mode of failure and the corresponding strength of an RC beam strengthened with externally bonded laminates, which can be used to verify the adequacy of design for beam strengthening.

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Li, Lungui, Zhiqi He, Zhongguo John Ma, and Lingkan Yao. "Development of strut-and-tie model and design guidelines for improved joint in decked bulb-tee bridge." Structural Engineering and Mechanics 48, no. 2 (October 25, 2013): 221–39. http://dx.doi.org/10.12989/sem.2013.48.2.221.

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Barros, R., and J. S. Giongo. "Shear force and torsion in reinforced concrete beam elements: theoretical analysis based on Brazilian Standard Code ABNT NBR 6118:2007." Revista IBRACON de Estruturas e Materiais 5, no. 5 (October 2012): 576–95. http://dx.doi.org/10.1590/s1983-41952012000500002.

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Reinforced concrete beam elements are submitted to applicable loads along their life cycle that cause shear and torsion. These elements may be subject to only shear, pure torsion or both, torsion and shear combined. The Brazilian Standard Code ABNT NBR 6118:2007 [1] fixes conditions to calculate the transverse reinforcement area in beam reinforced concrete elements, using two design models, based on the strut and tie analogy model, first studied by Mörsch [2]. The strut angle θ (theta) can be considered constant and equal to 45º (Model I), or varying between 30º and 45º (Model II). In the case of transversal ties (stirrups), the variation of angle α (alpha) is between 45º and 90º. When the equilibrium torsion is required, a resistant model based on space truss with hollow section is considered. The space truss admits an inclination angle θ between 30º and 45º, in accordance with beam elements subjected to shear. This paper presents a theoretical study of models I and II for combined shear and torsion, in which ranges the geometry and intensity of action in reinforced concrete beams, aimed to verify the consumption of transverse reinforcement in accordance with the calculation model adopted As the strut angle on model II ranges from 30º to 45º, transverse reinforcement area (Asw) decreases, and total reinforcement area, which includes longitudinal torsion reinforcement (Asℓ), increases. It appears that, when considering model II with strut angle above 40º, under shear only, transverse reinforcement area increases 22% compared to values obtained using model I.

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Zhao, Jian-li, Shui-long Shen, and Yang Sun. "Application of strut-and-tie model for design of interior anchorage zone in post-tensioned concrete structure." Journal of Shanghai Jiaotong University (Science) 15, no. 3 (May 28, 2010): 273–78. http://dx.doi.org/10.1007/s12204-010-1002-6.

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Li, Shengyu, Erwin Lim, Linbai Shen, Yu Hong, and Qianhui Pu. "Strut-and-Tie Model-Based Prestress Design for the Cable–Pylon Anchorage Zone of Cable-Stayed Bridges." Journal of Bridge Engineering 26, no. 9 (September 2021): 04021069. http://dx.doi.org/10.1061/(asce)be.1943-5592.0001771.

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Cavers, William, and Gordon A. Fenton. "An evaluation of pile cap design methods in accordance with the Canadian design standard." Canadian Journal of Civil Engineering 31, no. 1 (January 1, 2004): 109–19. http://dx.doi.org/10.1139/l03-075.

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There are a number of design methods that have been described for the design of pile caps, but there has been no consensus on which method provides the best approach for the working designer. This paper describes a study conducted to establish the performance of several pile cap design methods, particularly with respect to the Canadian standard, CSA A23.3-94. Previous research was examined to determine the basis of the design methods and the state of current research. The design methods identified were then applied to pile caps for which test data were available. The theoretical loads obtained using the various design methods were compared with the experimental loads. The results of this study indicate that two design models of the five examined are the most suitable. This study also indicates that the provisions of the Canadian design standard are adequate. A possible refinement of the strut-and-tie model incorporating a geometric limit is also outlined.Key words: building codes, footings, pile caps, reinforced concrete, structural design.

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Chetchotisak, Panatchai, Jaruek Teerawong, Danaipong Chetchotsak, and Sukit Yindeesuk. "Efficiency Factors for Reinforced Concrete Deep Beams: Part 2 - Code Calibration." Advanced Materials Research 931-932 (May 2014): 514–19. http://dx.doi.org/10.4028/www.scientific.net/amr.931-932.514.

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This paper presents the limit state shear design formulas for both normal and high-strength reinforced concrete deep beams using strut-and-tie model (STM). The proposed equations are based on the STMs with six state-of-the-art efficiency factors. These STMs were improved by correcting the bias and quantifying the scatter using a Bayesian parameter estimation method. The statistical parameters of material properties, dimensions, and the accuracy of design equations are considered to develop the resistance models obtained by Monte Carlo simulations. The reliability analysis is performed to determine the strength reduction factors. The calculated values of strength reduction factors are proposed for each of the considered efficiency factors.

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Kuebler, Michael, and Maria Anna Polak. "Critical review of the CSA A14-07 design provisions for torsion in prestressed concrete poles." Canadian Journal of Civil Engineering 41, no. 4 (April 2014): 304–14. http://dx.doi.org/10.1139/cjce-2013-0211.

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This paper focuses on the effect of the transverse reinforcement in concrete poles and its influence on torsional strength in an effort to simplify the governing Canadian prestressed concrete pole code (CSA A14-07). The rationale behind the CSA code values for amount, spacing, and direction of the transverse reinforcement is not apparent. A testing program consisting of 14 concrete pole specimens were produced to investigate the torsional response. The specimens were divided into two groups with different tip diameters. Within each group the spacing and direction of the wound helical transverse reinforcement varied. Experimental cracking torque values were compared with calculated theoretical cracking torques from ACI 318, Eurocode 2, and various journal articles. The theoretical predictions were generally unconservative. Post-cracking behaviour was modelled using the Compression Field Theory (CFT) and Softened Truss Model (STM) for torsion. It was found that the CFT predicts the post-cracking response with reasonable accuracy. The failure mode in pure torsion is brittle and sudden, and the transverse reinforcement provides no post-cracking ductility. The primary function of the transverse reinforcement is to minimize the longitudinal precracking due to prestressing transfer forces. CSA A14 transverse reinforcement spacing requirements were compared against code minimum spacing requirements and a strut and tie model of the prestressing force transfer zone. Based on the strut and tie model of the transfer zone it was concluded that the CSA A14 helical reinforcement spacing values were insufficient to resist the transfer forces. New helical reinforcement spacing values were recommended to simplify the current CSA A14 code requirements. In addition concrete mix designs, prestressing levels, and wall thicknesses all have a large impact on torsional capacity and therefore quality assurance of these factors should be emphasized in CSA A14.

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He, Zhi-Qi, Zhongguo John Ma, Cheryl E. Chapman, and Zhao Liu. "Longitudinal Joints with Accelerated Construction Features in Decked Bulb-Tee Girder Bridges: Strut-and-Tie Model and Design Guidelines." Journal of Bridge Engineering 18, no. 5 (May 2013): 372–79. http://dx.doi.org/10.1061/(asce)be.1943-5592.0000378.

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Hou, Dong-Wei, Jian-Li Zhao, Jack Shui-Long Shen, and Jun Chen. "Investigation and improvement of strut-and-tie model for design of end anchorage zone in post-tensioned concrete structure." Construction and Building Materials 136 (April 2017): 482–94. http://dx.doi.org/10.1016/j.conbuildmat.2017.01.033.

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Aswin, M., Sonny, and Tonny. "Design and analysis of RC corbel based on SNI 2847:2019 and analysed using computer aided strut-and-tie model." IOP Conference Series: Materials Science and Engineering 1122, no. 1 (March 1, 2021): 012024. http://dx.doi.org/10.1088/1757-899x/1122/1/012024.

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Lu, W. Y. "Failure Probabilities of Reinforced Concrete Square Pile Caps." Journal of Mechanics 23, no. 2 (June 2007): 173–80. http://dx.doi.org/10.1017/s1727719100001192.

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AbstractAn analytical model for determining the shear strength of concrete pile caps under the failure mode of diagonal-compression originally based on the softened strut-and-tie model is proposed. The failure probabilities of reinforced concrete pile caps are investigated by Monte Carlo method. The results indicate that the proposed model can accurately predict the shear strength of the pile caps. The distribution of the failure probabilities for pile caps designed to ACI 318-02 Appendix A and the proposed design method are more uniform than that designed to the ACI 318-99. The ACI 318-99 is very conservative and cannot provide a consistent safety for pile caps design. It is suggested that the procedures in the ACI 318-02 Appendix A should be moved to the main body of ACI 318-02 and the proposed design method should be incorporated into the current reinforced concrete pile cap design methods.

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Hu, Zhangqi, Weirong Lv, Yusheng Wu, and Miao Zhang. "Analysis of Stiffness Reduction Coefficient of Conventionally Reinforced Concrete Coupling Beams on the Bias of Strut-and-Tie Model." Journal of Engineering Science and Technology Review 13, no. 5 (2020): 82–89. http://dx.doi.org/10.25103/jestr.135.11.

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Stiffness reduction coefficient of coupling beams (κ) can reflect the stiffness degradation degree at yield and significantly affect the seismic response and the internal force distribution. However, existing calculation methods do not consider the influencing factors comprehensively and have a limited application scope. To effectively predict the stiffness reduction coefficient of conventionally reinforced concrete coupling beams (CCBs), a simplified analysis model was established, and analysis and parameter modification were also implemented. Then, an equation with comprehensive consideration, wide application, and high accuracy was proposed. The proposed equation was verified by comparison with existing test data and calculation methods, and parametric analysis was performed to investigate the independent factors, including the span–depth ratio, longitudinal reinforcement ratio, stirrup ratio and concrete compressive strength. Results show that the independent factors are related to each other, and the span–depth ratio has the greatest influence on the stiffness reduction coefficient of CCBs. Furthermore, κ significantly increases with the longitudinal reinforcement ratio when the coupling beam has a large span–depth ratio, but the stirrup ratio has a bigger role when the span-depth ratio is small. Finally, on the basis of the analysis results, suggestions are made to improve the stiffness reduction coefficient of CCBs. The study results provide a reference for the design and optimization of shear wall and core tube structures.

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Wang, Guo Lin, and Shao Ping Meng. "Experimental Study on Shear Behavior of Prestressed Concrete Deep Beams with Draped Tendons." Advanced Materials Research 163-167 (December 2010): 1339–42. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.1339.

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Two simply supported deep beams were tested, one with draped prestresssing tendons and the other without for reference. Shear behavior and the prestressing effect were focused on. The test results showed that deep beams with the longitudinal reinforcement ratio of a normal amount were inclined to fail in flexural-shear, and the prestressing could greatly increase both the cracking load and the shear strength. Beside, the Modified Strut-and-Tie Model (MSTM) and the sectional design method from China Code (GB02) have also been adopted for predictions. The comparisons indicates that the MSTM can not only well predict the shear strengths of deep beams, but also well account for the prestressing effect, while the sectional design method seems so conservative due to its not properly considering the shear mechanism of deep beams. It can be concluded that the MSTM is capable of predicting the shear strength of PC deep beams with draped tendons and thus can be employed in practical designs.

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Lyčka, Lukáš, and Petr Štěpánek. "A Method to Predict the Punching Shear Strength of Flat Slabs with Shear Reinforcement Using a Strut-and-Tie Model." Key Engineering Materials 738 (June 2017): 25–35. http://dx.doi.org/10.4028/www.scientific.net/kem.738.25.

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The use of flat slabs in constructions due to its many functional and economic advantages is wide-spread. Behavior of flat slabs in shear and flexure is a fairly complex problem. Therefore, the punching shear failure belongs to one of the most critical aspects in the design of concrete buildings.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. Most of the current codes in force are mainly based on empirical formulation. The proposed method is based on a strut-and-tie model and therefore could be considered as an analytical approach. 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, ACI 318 and Model Code 2010. The comparison consists of results of more than 90 experiments on flat slabs with shear reinforcement, gathered from publications from all around the world.

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MESQUITA, A. C., A. S. ROCHA, R. G. DELALIBERA, and W. A. DA SILVA. "The influence of connecting pile cap-column in the mechanisms of break in the two pile caps." Revista IBRACON de Estruturas e Materiais 9, no. 6 (December 2016): 856–82. http://dx.doi.org/10.1590/s1983-41952016000600004.

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Abstract The paper analyzes the two pile caps with partially embedded socket and subject a center load. Three models were experimentally tested, varying the type of conformation of the column and walls of the socket, with a smooth, the other rough, and a monolithic two pile cap, used for reference. The roughening of the column-socket interface was examined with the aim of verifying the difference of the distribution of compressive and tensile stresses in the strut an tie model used for design. The experimental test to show that the two pile caps with conformation rough of the column and walls of the socket, support more load in comparison with two pile caps with smooth of the column and walls of the socket. Both however underperformed the monolithic two pile cap, with values of 66% and 36% respectively.

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MUNHOZ, F. S., and J. S. GIONGO. "Variation analysis effects of square and rectangular columns section with different longitudinal reinforcement rates in the main reinforcement two pile caps analysis." Revista IBRACON de Estruturas e Materiais 10, no. 3 (June 2017): 760–87. http://dx.doi.org/10.1590/s1983-41952017000300011.

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ABSTRACT The transition between the columns of building and foundation had been used the pile-cap structural elements. The most appropriate method for the pile caps design is the Strut and Tie model. In most cases in the structural project is not considered the influence of certain parameters: the columns cross section and the amount of longitudinal reinforcement columns. This paper studies the effect of the variability of the geometric section of square and rectangular columns, with different longitudinal reinforcement rates, in the main reinforcement traction two pile caps. The basis for study was development experimental program in the Structures Laboratory of EESC-USP . The traction reinforcement bars strains are reduced the pile-caps central section to pile-caps sections that approximate cutting axis shows the experimental results. In models with columns of elongated rectangular section and with great reinforcement rates this reduction is smaller.

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46

Guan, Dongzhi, Hui Yang, Dan Ju, Zhengxing Guo, and Sen Yang. "Cyclic loading test on a locally post-tensioned precast concrete beam–column connection." Advances in Structural Engineering 22, no. 12 (May 22, 2019): 2699–711. http://dx.doi.org/10.1177/1369433219849811.

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A novel precast concrete beam–column connection locally post-tensioned using arc-shaped prestressing bars was proposed for satisfactory seismic performance and rapid construction. Three full-scale cruciform specimens, including one monolithic reference specimen, were tested under reversal cyclic loadings to evaluate the seismic behaviours. Grade 630 steel rods and high-strength deformed steel rebars were used for the arc-shaped prestressing bars in the precast specimens. The results show that the proposed precast connection presents an acceptable seismic performance and that the structural details should be ameliorated to improve the energy dissipation capacity. The design philosophy of strong column-weak beam is applicable to the new precast system. Finally, a strut-and-tie model was developed to investigate the force transfer mechanism of the novel precast connection.

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Wang, Guo Lin, and Wen Sheng Ding. "Experimental Study on Shear Behavior of Prestressed Concrete Beams." Applied Mechanics and Materials 226-228 (November 2012): 1045–48. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.1045.

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Two simply supported beams with a shear span to depth ratio of 2.2 were tested, one with straight prestresssing tendons and the other without for reference. The shear behavior and the prestressing effect are focused on. The test results showed that the prestressed concrete (PC) beam has a significant arch effect, and the prestressing could greatly increase both the cracking load and the shear strength. Besides, the Modified Strut-and-Tie Model (MSTM) and the sectional design method from China Code (GB10) and ACI318-08 have also been adopted for predictions. The comparisons indicates that the MSTM can not only well predict the shear strengths of PC beams with a small shear span to depth ratio, but also well account for the prestressing effect, while the sectional design method seems so conservative due to its not properly considering the shear mechanism of such beams. It can be concluded that the MSTM is capable of predicting the shear strength of PC beams with significant arch effect and thus can be employed in practical designs.

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Deniaud, Christophe, and JJ Roger Cheng. "Review of shear design methods for reinforced concrete beams strengthened with fibre reinforced polymer sheets." Canadian Journal of Civil Engineering 28, no. 2 (April 1, 2001): 271–81. http://dx.doi.org/10.1139/l00-113.

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This paper reviews the different shear design methods found in the literature for reinforced concrete beams strengthened externally with fibre reinforced polymer (FRP) sheets and compares the adequacy of each method by using the test results from the University of Alberta. The FRP shear design methods presented include the effective FRP strain and the bond mechanism criteria, the strut-and-tie model, the modified compression field theory, and a mechanical model based on the strip method with shear friction approach. Sixteen full-scale T-beam test results were used in the evaluation. Two web heights of 250 and 450 mm and two ready mix concrete batches of 29 and 44 MPa were used in the test specimens. Closed stirrups were used with three spacings: 200 mm, 400 mm, and no stirrups. Three types of FRP were used to strengthen externally the web of the T-beams: (i) uniaxial glass fibre, (ii) triaxial (0/60/60) glass fibre, and (iii) uniaxial carbon fibre. The results showed that the mechanical model using the strip method with shear friction approach evaluates better the FRP shear contribution. The predicted capacities from this mechanical model are also found conservative and in excellent agreement with the test results.Key words: beams, carbon fibres, composite materials, fibre reinforced polymers, glass fibres, rehabilitation, reinforced concrete, shear strength, sheets, tests.

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Aswin, Muhammad, Zubair Imam Syed, Teo Wee, and Mohd Shahir Liew. "Prediction of Failure Loads of RC Dapped-End Beams." Applied Mechanics and Materials 567 (June 2014): 463–68. http://dx.doi.org/10.4028/www.scientific.net/amm.567.463.

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Shear failure remains the governing mode of failure for reinforced concrete (RC) dapped-end beams. Dapped-ends are commonly classified as disturbed regions (D-regions). Strut and tie model (STM) is a simple and rational way that can be applied to analyze D-regions. The current design codes such as ACI-318-08, Euro Code 2 and BS 8110 facilitate STM to predict the failure loads. In addition, the failure loads may be also predicted using the empirical method proposed in PCI Design Handbook. In this paper, the failure loads were predicted for 24 RC dapped-end beams following different codes. The significant parameters such as concrete compressive strength, dapped-end section size, shear span-depth ratio, type and effective range of stirrups, bent form of the longitudinal reinforcement, amount of dapped-end reinforcements and hanger reinforcements were varied to study their effects against the predicted failure load for RC dapped-end beams according to different codes. These predicted results were compared with the available experimental results to investigate the ability of various codes to predict the failure load reliably. In this study, the comparison shows that PCI Design Handbook and ACI-318-08 can predict the failure loads for RC dapped-end beams more accurately.

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Chetchotisak, Panatchai, Jaruek Teerawong, Danaipong Chetchotsak, and Sukit Yindeesuk. "Efficiency Factors for Reinforced Concrete Deep Beams: Part 1 - Improved Models." Advanced Materials Research 931-932 (May 2014): 506–13. http://dx.doi.org/10.4028/www.scientific.net/amr.931-932.506.

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A strut-and-tie model (STM) has been used as a rational and simple method for analysis and design of reinforced concrete deep beams. The STM idealizes the discontinuity regions in such members as a truss-like structure consisting of compression struts and tension ties. The strength of a deep beam is usually controlled by the capacity of the diagonal concrete struts which is generally proposed in terms of the concrete strength and the efficiency factor. The efficiency factor accounts for the variation of the concrete material and the compression softening effect. One has been used in many STMs and often exhibit biases and uncertain errors in prediction of the shear strengths of deep beams. This uncertainty is due to the imperfection of formulation, missing parameters, and insufficient experimental data. Based on a database of 406 test results and six state-of-the-art formulations of the efficiency factors found in the international building codes and literature, this paper proposes improved STMs for accurate prediction of shear strength of simply supported reinforced concrete deep beams by correcting the bias and quantifying the scatter using a Bayesian parameter estimation method.

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