The behavior of Tilted RC Beams Under Biaxial Shear and Torsion: A Finite Element Approach

The behavior of Tilted RC Beams Under Biaxial Shear and Torsion: A Finite Element Approach | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The behavior of Tilted RC Beams Under Biaxial Shear and Torsion: A Finite Element Approach Hassan Hussein Majeed, Saad Khalaf Mohaisen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5347044/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In recent years, there has been an urgent need to find unconventional solutions to meet the architectural requirements in designs to produce larger spaces using relatively small or proportionate sections that do not negatively affect the aesthetic appearance of the design. From this standpoint, research and study were conducted on inclined beams and the difference between them and regular beams, studying their behavior and capacity and whether the American ACI code specifications apply to them or require a unique code. This research is based on analyzing the behavior of beams under the influence of biaxial shear forces and torsional moments by designing three groups of models to compare them with regular beam models and compare their behavior and the amount of their resistance to loads. Three methods of analysis were used to apply a load; the first method was to apply biaxial shear force, which had eccentricity from the shear center on a notch at the mid-section of the tilted beam to cause biaxial shear and torsion on the longitudinal span. The second method applied pure torsion on the mid-span of the tilted beam, and the third method used a lever system at the mid-span of the tilted beam to cause biaxial shear and torsion. The results of the analysis help to understand the behavior of tilted beams under torsion and the differences between them and the standard beams. Tilted beam tilting angle torsional moment biaxial shear finite element analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Tilted reinforced concrete (RC) beams refer to structural elements sloped or slanted in elevation relative to the horizontal plane. These beams are used to achieve architectural requirements, such as providing sloping soffits and creating aesthetically pleasing appearances. The study of tilted RC beams is essential due to the several applications of such structural elements in modern construction. For parallel cases, tilted beams are commonly used to construct ramps in car parks and tilted roof slabs in Amphitheatre construction. (Li et al., 2023) Tilted beams aren’t just a design choice but a practical solution. They are used to create modern building spaces, delineate between different internal areas, or create a property, such as a vertical edge to depart a flat roof. Modern structures often use a combination of horizontal and tilted beams, ensuring a continuous and efficiently supported load path from the top of the building to the foundations. This design strategy helps prevent unplanned differential settlements or moving within the structure, reassuring structural engineers and designers. (van Nimwegen & Latteur, 2023) Tilted RC beams, or flanged walls, are commonly found and widely used in buildings. They are under-researched, and their structural behavior under load is complex. Over the past two decades, a few studies have been done on tilted beams in shear or torsional cases; studying tilted RC beams is crucial for several reasons. Torsional behavior evaluation is a complex phenomenon in RC beams, and understanding it is essential for safe and efficient design; traditional analytical approaches struggle to model torsional fracture mechanisms accurately. For structural safety, torsion affects the overall stability and safety of structures. RC beams subjected to torsion may experience shear cracking, diagonal tension, and twisting deformation. (Zhou et al., 2022) In structural engineering, the twisting moment of the structural elements is referred to as the torsional moment. When a structural member is subjected to a torque or twisting of one end relative to the other, the member twists or rotates. The resisting force of a structural member to this type of loading is called torsional moment. The torsional moment is one of the three-moment types in the materials' mechanics, including the bending moment and shear force. A torsional moment acts about the longitudinal axis of a structural member. It is also known as "twisting" or "twisting moment" because it can cause a member's section to twist about its longitudinal axis. The unit of torsional moment is usually expressed in Nm or Newton meters. Understanding the distribution of the torsional moment around the cross-section of a structural member is crucial, as it helps to understand the material's property in torsion. The torsional moment will be generated in the circular cross-section by applying a torque (twisting force) on one of the surfaces. The magnitude of the torsional moment at a specific location is controlled by the distribution of material around the cross-section and the value of torque applied. Unlike bending and axial movement effects, the position of the maximum torsional moment and the distribution pattern of the torsional moment within a structural member cannot be easily predicted, and they are geometry and loading-specific. The torsion calculation is a common step in checking the design of structures. It is also critical for material selection and analyzing the structural stiffness under different loading conditions. Many structural components, such as shafts, transmission poles, and beams, are theoretically designed to resist the torsional moment. (Bhasker & Menon, 2020) 2. Mechanism of load transfer in tilted beam The load transfer mechanism of titled RC beams starts with a certain percentage of applied load from the slab transferred to the beam. This percentage will depend on the magnitude of the vertical loads and the system's stiffness. The rest of the load is directly transferred to the beam. The force transfer from the slab to the beam occurs through the top portion section. When the beam and the slab are cast monolithically, negative moments will develop as the applied load from the slab to the titled beam increases. This will rotate the slab in a downward direction, and as a result, the propped cantilever action will form, and the moment in the beam will start to decrease from mid-span to the ends. Near the support, positive moments will develop due to the negative moments in the slab. According to Sutherland's studies, the magnitude of the end moment will increase with a higher tilt angle. Also, the transfer of slab load to the beam is generally more efficient with a lower tilt angle. This is because a higher tilt angle results in a larger free-body diagram for the slab. When an applied load from the slab reaches the potential of the maximum negative moment, this forms what we call a 'breaking' joyous moment at the ends near the support. From there, the load is directly transferred from the slab to the beam and the moment the beam starts to increase from mid-span to the ends. (Yu et al., 2020)(Quadri & Fujiyama, 2021) 3. Torsional cracks Torsional cracks are tensile stress cracks inclined at an angle toward maximum principal stress. They are caused by shear stress exceeding the shear strength of the affected material. Tensile stresses then cause cracks to form at 45° in the direction of the shear force, essentially in a torsional mode. Torsional cracks occur in concrete when combined shear and compressive forces result in tensile stress exceeding the material's tensile strength. This can occur, for example, when a column is subjected to eccentric loading, resulting in the column sliding against its base. Torsional cracks can also occur in welds, often at the interface between the weld and parent material. Indicate a severe loss of material strength, which must be prevented wherever possible. (Figueiredo et al., 2021) 4. Theoretical of analysis Previous research revolved around studying tilted beams at an angle of 45 degrees with an eccentricity of the load applied from the shear center of the concrete section. In these studies, models with a rectangular concrete section were used, with different dimensions for each survey.(Chaisomphob et al., 2003)(Waryosh et al., 2014) In the other research, work was done on changing the inclination angle pattern on models with a square concrete section and loading without eccentricity of the load from the shear center to test biaxial shear on the sides, whether equally when using a tilted angle of a 45-degree or unevenly when using other angles.(Tinini et al., 2016) Research related to torsion focused on highlighting pure torsion and studying its effects on the behavior of concrete beams. The research was based on static loading on beams using simultaneous biaxial shear, torsional moments, and pure torsion for one group. 5. program analysis As shown before, this research started with the specimen shape of previous research in the first group using a notch to make biaxial shear, biaxial flexural, and torsion, as field tests had been done previously. For pure torsional analysis, in the second group, just a tilted rectangular section with the same span subjected to pure torsional moment at mid-section, at the end proposed and worked on specimens using a lever system to make case simulate real cases to action all load types in the same time to analyze and study the behavior of tilted beam in this case. To conduct a comprehensive study of the analysis aspects, it was decided to adopt various types of analysis on the ABAQUS program, starting with models tilted at an angle of 45˚ degrees using a lever system to analyze specimens in the form of static analysis to study the linear and nonlinear behavior of the properties of the concrete section for the tilted beam section and study the effect of tilted angle on section strength. Group - A Use a tilted rectangular beam with a notch that carries a point static load with three types of reinforcements: Specimen-1 (B1) Primary reinforcements 8 bar Ø 20 mm stirrups Ø 12 mm @ 100 mm C/C Group - B Use a tilted rectangular beam without a notch and use pure torsional moment on the longitudinal section of the beam with the same three types of reinforcements : - Specimen-4 (B4) Primary reinforcements 8 bar Ø 20 mm stirrups Ø 12 mm @ 100 mm C/C Group - C Use a tilted rectangular beam angle of 45˚ degrees (b 200 mm & h 500 mm) with a cantilever (b 200mm & h 200 mm) carry point load that causes shear & torsional stresses on a tilted beam longitudinal section with the same three types of reinforcements: - Cantilever reinforcement Primary reinforcements 4 bar Ø 20 mm stirrups Ø 12 mm @ 80 mm C/C Specimen-7 (B7) Primary reinforcements 8 bar Ø 20 mm stirrups Ø 12 mm @ 100 mm C/C 6. ACI limitation design The models are designed according to the requirements of the ACI code by calculating the ultimate torsional moment and checking the shear and flexural design to avoid failure under shear force or bending moments so that the models can be tested and analyzed in the ABAQUS program. Started calculation for torsion with the minimum spacing between bars and maximum reinforcement area ( S min = 300 – d/4 – d/2 ) and from this ultimate torsional moment can calculate the load needed to be subjected to the lever arm to make torsion action plus the by axial shear and flexural. d = 460 / S min = 300–460/4–460/2 / S min = 300–115 – 230 so for over-designed in shear, use S = (100–200 – 300) 7. Program Analysis Criteria The analysis criteria are divided into several introductory paragraphs, starting from the criteria of the materials used for the sections until reaching the final analysis, which will be presented in detail below. These criteria were fixed according to the static to create the best analysis conditions and be as close as possible to resembling objective reality—the actual loading conditions of the static analysis. This static load is direct. The nonlinear properties of concrete were defined to try to study its behavior well in the theoretical analysis and the extent of its impact on the behavior of structural elements. Material criteria The analysis criteria for the materials were chosen based on the material properties from the actual sites in the construction work, as also explained in the practical analysis chapter, without any reduction or safety factors to reach the maximum limits of the material. Because the first step in the research was based on theoretical analysis, the concrete properties were taken from a ready file of the program library uploaded on public sites. These properties were fixed in all the models used in the theoretical static analysis to study the behavior of the tilted beam, as well as to try to study the nonlinear behavior of concrete in these structural elements. All material properties are shown in Appendix C Step criteria The step used: type static, Riks with the maximum number of increments 20 and used equation solver – matrix storage unsymmetric . Made convert severe discontinuity iteration (on) and extrapolation of the previous state as the start of each increment was (parabolic) not linear. Interaction criteria Used embedded interaction between concrete section and rebar reinforcement Mesh criteria For the static analysis, the mesh used for concrete 25 mm was Tet shape, and the geometric order was Quadratic. For bars, reinforcement mesh is used at 50 mm with standard type and linear geometric order with family type truss to ensure the reinforcement is just tension and compression. Boundary conditions criteria Fixed-end faces prevent displacement and rotations at the end to simulate the actual cases of tilted beams in concrete structures with continuous or linked ends in frame structures. The load was divided into several types. For static analysis, 50 KN was used at the end of the lever arm or on the notch, which acts as a 60 KN/m pure torsional moment. 8. The general behavior of static analysis used in ABAQUS The load acted on the cantilever beam, and that point load transferred to the support of the cantilever, which is the tilted beam as a load with a transverse torsional moment at mid-section where the cantilever is linked with the tilted beam as the lever system. “ The lever system is one of the mechanical systems found in nature whose operation requires the presence of a solid physical body, i.e., the lever, capable of rotating around an axis or a fixed fulcrum, and is affected by force (effort) and resistance, and both the line of action of the effort and the line of action are far apart. Resistance is a perpendicular distance from the axis of rotation, where this distance is known as the arm. (Artobolevsky, 1975)”. These combined loads simulate real cases that can affect the tilted beam. This behavior helped make analysis more accessible and took us to known points that calculate displacement and rotation. Perhaps the most common case in structural designs and the most complex models used in this research is when using a cantilever plate supported by an inclined beam that produces a continuous torsional moment along the entire span, and more equations are needed to solve this situation. In addition, ensure that the cantilever beam does not fail before the tilted beam uses a rigid beam (over-designed beam in flexure, shear, and torsion), so ensure no losses approximately when the static load acts on the system and make can three types of cracks (flexural, shear and torsional cracks) when the beam high reinforced for flexural and shear that help to be just torsional crack clear appearance in the field test. At laboratory and program analysis, the foremost parameters to be measured were load displacement at the cantilever, angle of twist at the mid-section, and displacement of the mid-section. 9. Results When the results of both theoretical and practical analysis are delved into in-depth, it becomes clear that the method proposed in this research (creating a cantilever beam on the inclined beam to be examined to solve the torsional loads) is more effective than the methods in previous research if what is required is to produce loads that mimic the objective reality in the structures. Structural (biaxial bending and biaxial shear loads in addition to torsional moment): This impression was evident in both theoretical analysis and practical testing. The purpose of this method is to avoid any imperfections that appeared in previous research made in the same laboratory, whether in the “Bi-axial shear capacity of the tilted solid reinforced concrete beam subject to point loading.”(Waryosh et al., 2014) ” or “Behavior of steel fiber self-compacting concrete hollo deep beams under torque. (Mahdi & Mohaisen, 2021) ” Therefore, one of the main points that was focused on in this research is making the ends of the tilted beams completely fixed, whether in the theoretical program ABAQUS or in the practical test. The second point was how to apply the load to make torsional action and make a rigid cantilever to ensure it did not fail before the tilted beam. Searched on when applying point load at the end caused (shear action, bending moment, and high torsional moment) that simulate the actual case, whether in previous research on torsion used frame at end applied only torsional moment and that not simulate real cases. 9.1 Overall program ABAQUS Static Analysis Results. The result shown in the tables for concrete was a maximum range of stresses at the mid-section of the tilted beam and figures for steel rebar stresses, which can be compared in each group of specimens and between groups. This clear and concise presentation of the results keeps the audience interested in the findings. Before presenting the results, clarifying what they mean and their significance in structural design and analysis is necessary . The results were divided into the stresses of the concrete section at the applied load point (the mid-section of the tilted beam), representing the stresses in the three-dimensional axis, and the three-dimensional plans. This facilitates the comparison of each model's effect and behavior. The steel reinforcement stresses were presented in the figures to clarify the stress distribution at all bars. These practical implications of the results provide valuable insights for future structural designs and analyses. It was decided to display the tilted beam's displacement and angle of rotation for each node. The highest individual displacement for each node is represented by the angle, which also means the node's rotation angle. The significance of these results in the context of structural design and analysis cannot be overstated, as they provide a solid foundation for future research and practical applications. 9.2 Group – A From a first glance at the analysis results with the same loading, as expected, whenever the reinforcement area is reduced, the stresses on the remaining reinforcement increase, and it is noted that the highest stresses in the reinforcement are in the direction of tension-resisting the bending moment. In addition to stating that the stresses in the concrete section tend to be high in shear behavior and low in the direction of torsional behavior, the reason for this is that the eccentricity from the shear center is small and causes a small torsional moment whose effect is small compared to the impact of bi-axial shear and bi-axial bending stresses. What confirms this analysis and opinion is that the direction of displacement of the site is in one direction, which is the negative direction of the local axes of the section, and it is without rotation angles. This confirms that the torsional moment is slight, and its frequency in this model is not perceptible. Table 2- Stress at mid-section / Group A Concrete stresses No. S XX S YY S ZZ S XY S YZ S XZ U X U Y UR B1 +0.701 +0.3473 +4.038 +0.316 +0.1504 +0.220 -0.7989 -1.070 -1.392 -1.519 0 B2 +0.755 +0.3145 +4.265 +0.460 +0.0948 +0.162 -0.4245 -0.7302 -0.6703 -1.006 0 B3 +0.948 +0.6104 +4.363 +0.387 +0.0459 +0.157 -0.4909 -0.8442 -0.8685 -1.159 0 Steel rebar stresses 9.3 Group – B When applying a pure torsional moment concentrated in the mid-span of the tilted beam, it is clear that the stresses are distributed harmoniously along the length of the model and in opposite directions in both directions to the right and left of the torsional torque concentrated in an attempt to create distortions on the section in a warping manner. The highest stresses on the rebar are concentrated at the ends of the tilted beam because they are the stabilizer supports that resist the pure torsional moment. This situation is the same as in the case of a standard or tilted beam. The stresses are very close; some are equal, and there are no significant differences. The main reason behind this behavior is the use of pure torsional torque. In this case, the loads do not simulate the practical reality without the effect of shear and bending stresses on the section. Table 3- Stresses at mid-section / Group B Concrete stresses No. SXX SYY SZZ SXY SYZ SXZ UX UY UR B4 +0.7823 +0.454 +1.058 +0.387 +1.257 +2.447 +1.35 -1.414 +1.350 -1.410 +4.928×10 -3 B4-N +0.876 +0.539 +1.075 +0.387 +1.274 +2.261 +1.325 -1.449 +0.5634 -0.5653 +4.727×10 -3 B5 +0.636 +0.441 +0.815 +0.225 +1.265 +1.258 +0.915 -0.923 +0.910 -0.928 +3.059×10 -3 B6 +0.630 +0.446 +0.8338 +0.220 +1.267 +1.260 +0.9148 -0.923 +0.9094 -0.9283 +3.057×10 -3 Steel rebar stresses 9.4 Group – C When the three types of loads - shear, bending, and torsion - are combined, this leads to the actual loading state so that the effect of the forces on each other and the effect of the tilted angle of the beam are observed. The stress in the tensile reinforcement increased to its maximum in the third model, which had the smallest reinforcement area . The stresses on the tilted beam can be explained as complex overlapping stresses based on shear flow and compressive stress in the upper layers and shear flow in the lower layers with the biaxial shear stress and the presence of tensile stresses on the tilted beam acting together at the same time. The critical factor that increases the efficiency of the tilted beam that bears these stresses together compared to standard models is the moment of inertia of the section, which changes with a change in shape or angle of inclination so that the section can withstand a higher degree of bearing. Table 4- Stresses at mid-section / Group C Concrete stresses No. SXX SYY SZZ SXY SYZ SXZ UX UY UR B7 +2.429 +3.129 +1.286 +1.261 +0.264 +0.397 +0.1273 -0.3104 +0.0346 -0.3186 +1.116×10 -3 B8 +2.309 +2.499 +1.237 +1.067 +0.3959 +0.355 +0.1030 -0.2722 +0.0227 -0.2822 +0.958×10 -3 B9 +1.863 +2.486 +1.968 +1.065 +0.3872 +0.358 +0.1100 -0.3126 +0.0182 -0.3219 +1.07×10 -3 B.R.L +0.412 +4.462 +1.399 +1.011 +0.5424 +0.096 +0.9514 -0.2995 +0.1242 -0.0843 1.924×10 -3 Steel rebar stresses When searching and comparing the standard beam model B13 and the tilted beam model B7, it becomes clear that the shear stresses that the tilted beam can bear are higher due to the approximation of the total shear area in the two directions X-Y of the tilted beam, as well as the focus on the fact that the standard beam can bear bending stresses in one direction mainly and is very weak in the second direction. This is clear from the stresses it can bear in both directions, while the tilted beam can bear bending stresses that are close in values. With the stability of the shear flow that causes the torsional moment in both models, it is noted that the standard beam is generally weaker than the tilted beam. 10. Conclusion The ability of the tilted beam to withstand pure torsional moment is not affected if the beam is tilted or without a tilting angle. The reason is that the torsional moment is interpreted as a shear flow in the outer layer of the section, which will not be affected by the tilt of the element. However, suppose the torsional moment is applied with shear forces. In that case, there will be a change in the shear forces with the shear flow due to the torsional moment, which brings us back to the fact that the inclination angle affects the biaxial shear area. Suppose the bending moment is applied to them as the actual case. In that case, compressive stresses will occur in the upper part, which contributes to increasing the strength of the section against the resulting shear stresses and weakness in the section in the lower part, the tension area, which will cause an increase in the stresses on the concrete section. Here, it is clear that reinforcing steel or strengthening the tension area with carbon fiber sheets may be a good step in not increasing the areas of the concrete sections and making the best use of the section properties. Declarations Data Availability Statement (DAS): The data supporting this study's findings are available from [figshare] at [ https://figshare.com/s/dc64631b001e581a748c ]. These data were derived from the ABAQUS program analysis following resources available in the public domain. Any other data related to this study are available from the corresponding author upon reasonable request. All data requests should be directed to [ [email protected] ]. Author Contribution Prof Dr. Saad Khalaf suggested the research subject Hassan Hussein search for the problem Hassan Hussein makes an analysis on the ABAQUS programHassan Hussein and Prof Dr. Saad Khalaf Analyzed, studied, and discussed the results. References Artobolevsky, I. I. (1975). Mechanisms in modern engineering design. Mir Publishers , 1 , 454. Bhasker, R., & Menon, A. (2020). Torsional irregularity indices for the seismic demand assessment of RC moment resisting frame buildings. Structures , 26 , 888–900. Chaisomphob, T., Kritsanawonghong, S., & Hansapinyo, C. (2003). Experimental investigation on rectangular reinforced concrete beam subjected to bi-axial shear and torsion. Songklanakarin Journal of Science and Technology , 25 (1), 41–52. Figueiredo, T. C. S. P., Curosu, I., Gonzáles, G. L. G., Hering, M., de Andrade Silva, F., Curbach, M., & Mechtcherine, V. (2021). Mechanical behavior of strain-hardening cement-based composites (SHCC) subjected to torsional loading and to combined torsional and axial loading. Materials & Design , 198 , 109371. Li, J., Yan, G., Abbud, L. H., Alkhalifah, T., Alturise, F., Khadimallah, M. A., & Marzouki, R. (2023). Predicting the shear strength of concrete beam through ANFIS-GA–PSO hybrid modeling. Advances in Engineering Software , 181 , 103475. Mahdi, M. S., & Mohaisen, S. K. (2021). BEHAVIOR OF STEEL FIBER SELF-COMPACTING CONCRETE HOLLOW DEEP BEAMS UNDER TORQUE. Journal of Engineering and Sustainable Development , 25 (3), 22–33. pt03ch06s01abo04 @ classes.engineering.wustl.edu . (n.d.). https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/pt03ch06s01abo04.html Quadri, A. I., & Fujiyama, C. (2021). Response of reinforced concrete dapped-end beams exhibiting bond deterioration subjected to static and cyclic loading. Journal of Advanced Concrete Technology , 19 (5), 536–554. Shafiq, N., & Akbar, I. (n.d.). A Review of Combined Flexure, Shear & Torsion Strengthening of Reinforced Concrete Beam . Tinini, A., Minelli, F., Belletti, B., & Scolari, M. (2016). Biaxial shear in RC square beams: Experimental, numerical and analytical program. Engineering Structures , 126 , 469–480. van Nimwegen, S. E., & Latteur, P. (2023). A state-of-the-art review of carpentry connections: From traditional designs to emerging trends in wood-wood structural joints. Journal of Building Engineering , 107089. Waryosh, W. A., Mohaisen, S. K., & Yahya, L. M. (2014). Behavior of Rectangular Reinforced Concrete Beams Subjected to Bi-axial Shear Loading. Journal of Engineering and Sustainable Development , 18 (2), 106–121. Yu, J., Luo, L., & Fang, Q. (2020). Structure behavior of reinforced concrete beam-slab assemblies subjected to perimeter middle column removal scenario. Engineering Structures , 208 , 110336. Zhou, J., Chen, Z., Chen, Y., Song, C., Li, J., & Zhong, M. (2022). Torsional behavior of steel reinforced concrete beam with welded studs: Experimental investigation. Journal of Building Engineering , 48 , 103879. Table Table 1 is available in the Supplementary Files section. Plate Plate 1 is available in the Supplementary Files section. Additional Declarations No competing interests reported. Supplementary Files plate1.png Plate - 1 Constraint features Table1.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5347044","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":381685217,"identity":"97032d19-8b0e-4374-bc6f-ea3244021763","order_by":0,"name":"Hassan Hussein Majeed","email":"data:image/png;base64,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","orcid":"","institution":"Mustansiriyah University","correspondingAuthor":true,"prefix":"","firstName":"Hassan","middleName":"Hussein","lastName":"Majeed","suffix":""},{"id":381685218,"identity":"fa253787-011e-49ec-85e0-44c87017c0a9","order_by":1,"name":"Saad Khalaf Mohaisen","email":"","orcid":"","institution":"Mustansiriyah University","correspondingAuthor":false,"prefix":"","firstName":"Saad","middleName":"Khalaf","lastName":"Mohaisen","suffix":""}],"badges":[],"createdAt":"2024-10-28 12:23:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5347044/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5347044/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":69835864,"identity":"14cd5847-340c-4a87-bb33-0aa32db0009c","added_by":"auto","created_at":"2024-11-25 16:14:41","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":47341,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTorsional cracks \u003c/strong\u003e(Shafiq \u0026amp; Akbar, n.d.)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/1b31657d17da3abc09b20dc6.png"},{"id":69835889,"identity":"3d03d6c8-296d-42ac-8fb2-434b7b71a79e","added_by":"auto","created_at":"2024-11-25 16:14:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":100418,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003elongitudinal section of tilted beam – B1\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/5fd60981146d912854158825.png"},{"id":69835853,"identity":"1445230f-7e4a-4b29-9567-b7092c8b81bc","added_by":"auto","created_at":"2024-11-25 16:14:38","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":105216,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003elongitudinal section of tilted beam – B4\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/ca2c50ec8829c410ba512b56.png"},{"id":69835887,"identity":"ed97b951-a21a-4f1c-aa5f-2c1d103acccd","added_by":"auto","created_at":"2024-11-25 16:14:43","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":116750,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;\u003cstrong\u003elongitudinal section of tilted beam – B7\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/8a053e8ce08eb76d878427be.png"},{"id":69835868,"identity":"6e0c2432-0995-48ae-8e1f-1a7cae5ee417","added_by":"auto","created_at":"2024-11-25 16:14:42","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":352211,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eReinforcement stresses B 1-2-3\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/5b6af01d36803ab20828490f.png"},{"id":69835862,"identity":"0d4b2f68-82c2-427d-a1c4-6e200917156d","added_by":"auto","created_at":"2024-11-25 16:14:41","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":358842,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eReinforcement stresses B 4-5-6 - B4-N\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/00a674f1b61b3b6c74b1cf7d.png"},{"id":69836392,"identity":"6c2d00de-a6db-4886-8050-1489c54fe1d6","added_by":"auto","created_at":"2024-11-25 16:22:44","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":461514,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;\u003cstrong\u003eReinforcement stresses B 7-8-9\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/6e4dcdb3b5eca77339f2bc6e.png"},{"id":72808063,"identity":"72e07764-0ada-4c48-b651-536dc00b6504","added_by":"auto","created_at":"2025-01-02 10:47:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2355211,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/4981217c-ed8c-45e9-9ddd-91d54e51ee4b.pdf"},{"id":69835849,"identity":"9a3e0578-8c95-4235-9965-f79b08c8b87e","added_by":"auto","created_at":"2024-11-25 16:14:36","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":120452,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePlate - 1\u003c/strong\u003e \u003cu\u003e\u003cstrong\u003e\u0026nbsp;Constraint features\u003c/strong\u003e\u003c/u\u003e\u003c/p\u003e","description":"","filename":"plate1.png","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/863e45d736696b4aa9ce1a32.png"},{"id":69835891,"identity":"6f443084-b011-42be-b3be-a97d473e5424","added_by":"auto","created_at":"2024-11-25 16:14:44","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":156320,"visible":true,"origin":"","legend":"","description":"","filename":"Table1.docx","url":"https://assets-eu.researchsquare.com/files/rs-5347044/v1/2deb4ba8c266af71a552b8d5.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"The behavior of Tilted RC Beams Under Biaxial Shear and Torsion: A Finite Element Approach","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eTilted reinforced concrete (RC) beams refer to structural elements sloped or slanted in elevation relative to the horizontal plane. These beams are used to achieve architectural requirements, such as providing sloping soffits and creating aesthetically pleasing appearances. The study of tilted RC beams is essential due to the several applications of such structural elements in modern construction. For parallel cases, tilted beams are commonly used to construct ramps in car parks and tilted roof slabs in Amphitheatre construction. (Li et al., 2023)\u003c/p\u003e \u003cp\u003eTilted beams aren\u0026rsquo;t just a design choice but a practical solution. They are used to create modern building spaces, delineate between different internal areas, or create a property, such as a vertical edge to depart a flat roof. Modern structures often use a combination of horizontal and tilted beams, ensuring a continuous and efficiently supported load path from the top of the building to the foundations. This design strategy helps prevent unplanned differential settlements or moving within the structure, reassuring structural engineers and designers. (van Nimwegen \u0026amp; Latteur, 2023)\u003c/p\u003e \u003cp\u003eTilted RC beams, or flanged walls, are commonly found and widely used in buildings. They are under-researched, and their structural behavior under load is complex. Over the past two decades, a few studies have been done on tilted beams in shear or torsional cases; studying tilted RC beams is crucial for several reasons. Torsional behavior evaluation is a complex phenomenon in RC beams, and understanding it is essential for safe and efficient design; traditional analytical approaches struggle to model torsional fracture mechanisms accurately. For structural safety, torsion affects the overall stability and safety of structures. RC beams subjected to torsion may experience shear cracking, diagonal tension, and twisting deformation. (Zhou et al., 2022)\u003c/p\u003e \u003cp\u003eIn structural engineering, the twisting moment of the structural elements is referred to as the torsional moment. When a structural member is subjected to a torque or twisting of one end relative to the other, the member twists or rotates. The resisting force of a structural member to this type of loading is called torsional moment. The torsional moment is one of the three-moment types in the materials' mechanics, including the bending moment and shear force. A torsional moment acts about the longitudinal axis of a structural member. It is also known as \"twisting\" or \"twisting moment\" because it can cause a member's section to twist about its longitudinal axis. The unit of torsional moment is usually expressed in Nm or Newton meters. Understanding the distribution of the torsional moment around the cross-section of a structural member is crucial, as it helps to understand the material's property in torsion. The torsional moment will be generated in the circular cross-section by applying a torque (twisting force) on one of the surfaces. The magnitude of the torsional moment at a specific location is controlled by the distribution of material around the cross-section and the value of torque applied. Unlike bending and axial movement effects, the position of the maximum torsional moment and the distribution pattern of the torsional moment within a structural member cannot be easily predicted, and they are geometry and loading-specific. The torsion calculation is a common step in checking the design of structures. It is also critical for material selection and analyzing the structural stiffness under different loading conditions. Many structural components, such as shafts, transmission poles, and beams, are theoretically designed to resist the torsional moment. (Bhasker \u0026amp; Menon, 2020)\u003c/p\u003e"},{"header":"2. Mechanism of load transfer in tilted beam","content":"\u003cp\u003eThe load transfer mechanism of titled RC beams starts with a certain percentage of applied load from the slab transferred to the beam. This percentage will depend on the magnitude of the vertical loads and the system's stiffness. The rest of the load is directly transferred to the beam. The force transfer from the slab to the beam occurs through the top portion section. When the beam and the slab are cast monolithically, negative moments will develop as the applied load from the slab to the titled beam increases. This will rotate the slab in a downward direction, and as a result, the propped cantilever action will form, and the moment in the beam will start to decrease from mid-span to the ends. Near the support, positive moments will develop due to the negative moments in the slab. According to Sutherland's studies, the magnitude of the end moment will increase with a higher tilt angle. Also, the transfer of slab load to the beam is generally more efficient with a lower tilt angle. This is because a higher tilt angle results in a larger free-body diagram for the slab. When an applied load from the slab reaches the potential of the maximum negative moment, this forms what we call a 'breaking' joyous moment at the ends near the support. From there, the load is directly transferred from the slab to the beam and the moment the beam starts to increase from mid-span to the ends. (Yu et al., 2020)(Quadri \u0026amp; Fujiyama, 2021)\u003c/p\u003e"},{"header":"3. Torsional cracks","content":"\u003cp\u003eTorsional cracks are tensile stress cracks inclined at an angle toward maximum principal stress. They are caused by shear stress exceeding the shear strength of the affected material. Tensile stresses then cause cracks to form at 45\u0026deg; in the direction of the shear force, essentially in a torsional mode. Torsional cracks occur in concrete when combined shear and compressive forces result in tensile stress exceeding the material's tensile strength. This can occur, for example, when a column is subjected to eccentric loading, resulting in the column sliding against its base. Torsional cracks can also occur in welds, often at the interface between the weld and parent material. Indicate a severe loss of material strength, which must be prevented wherever possible. (Figueiredo et al., 2021)\u003c/p\u003e "},{"header":"4. Theoretical of analysis","content":"\u003cp\u003ePrevious research revolved around studying tilted beams at an angle of 45 degrees with an eccentricity of the load applied from the shear center of the concrete section. In these studies, models with a rectangular concrete section were used, with different dimensions for each survey.(Chaisomphob et al., 2003)(Waryosh et al., 2014)\u003c/p\u003e \u003cp\u003eIn the other research, work was done on changing the inclination angle pattern on models with a square concrete section and loading without eccentricity of the load from the shear center to test biaxial shear on the sides, whether equally when using a tilted angle of a 45-degree or unevenly when using other angles.(Tinini et al., 2016)\u003c/p\u003e \u003cp\u003eResearch related to torsion focused on highlighting pure torsion and studying its effects on the behavior of concrete beams. The research was based on static loading on beams using simultaneous biaxial shear, torsional moments, and pure torsion for one group.\u003c/p\u003e"},{"header":"5. program analysis","content":"\u003cp\u003eAs shown before, this research started with the specimen shape of previous research in the first group using a notch to make biaxial shear, biaxial flexural, and torsion, as field tests had been done previously. For pure torsional analysis, in the second group, just a tilted rectangular section with the same span subjected to pure torsional moment at mid-section, at the end proposed and worked on specimens using a lever system to make case simulate real cases to action all load types in the same time to analyze and study the behavior of tilted beam in this case. To conduct a comprehensive study of the analysis aspects, it was decided to adopt various types of analysis on the ABAQUS program, starting with models tilted at an angle of 45˚ degrees using a lever system to analyze specimens in the form of static analysis to study the linear and nonlinear behavior of the properties of the concrete section for the tilted beam section and study the effect of tilted angle on section strength.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eGroup - A\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eUse a tilted rectangular beam with a notch that carries a point static load with three types of reinforcements:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSpecimen-1 (B1)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePrimary reinforcements 8 bar \u0026Oslash; 20 mm\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003estirrups \u0026Oslash; 12 mm @ 100 mm C/C\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eGroup - B\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eUse a tilted rectangular beam without a notch and use pure torsional moment on the longitudinal section of the beam with the same three types of reinforcements\u003cspan dir=\"RTL\"\u003e: -\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSpecimen-4 (B4)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePrimary reinforcements 8 bar \u0026Oslash; 20 mm\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003estirrups \u0026Oslash; 12 mm @ 100 mm C/C\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eGroup - C\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eUse a tilted rectangular beam angle of 45˚ degrees (b 200 mm \u0026amp; h 500 mm) with a cantilever (b 200mm \u0026amp; h 200 mm) carry point load that causes shear \u0026amp; torsional stresses on a tilted beam longitudinal section with the same three types of reinforcements: -\u003c/p\u003e\n\u003cul style=\"list-style-type: circle;\"\u003e\n \u003cli\u003eCantilever reinforcement \u0026nbsp;\u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003ePrimary reinforcements 4 bar \u0026Oslash; 20 mm \u0026nbsp;\u003c/p\u003e\n\u003cp\u003estirrups \u0026Oslash; 12 mm @ 80 mm C/C\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSpecimen-7 (B7) \u0026nbsp;\u0026nbsp;\u003c/strong\u003ePrimary reinforcements 8 bar \u0026Oslash; 20 mm \u0026nbsp;\u003c/p\u003e\n\u003cp\u003estirrups \u0026Oslash; 12 mm @ 100 mm C/C\u003c/p\u003e"},{"header":"6. ACI limitation design","content":"\u003cp\u003eThe models are designed according to the requirements of the ACI code by calculating the ultimate torsional moment and checking the shear and flexural design to avoid failure under shear force or bending moments so that the models can be tested and analyzed in the ABAQUS program. Started calculation for torsion with the minimum spacing between bars and maximum reinforcement area (\u003cb\u003eS\u003c/b\u003e\u003csub\u003e\u003cb\u003emin\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e= 300 \u0026ndash; d/4 \u0026ndash; d/2\u003c/b\u003e) and from this ultimate torsional moment can calculate the load needed to be subjected to the lever arm to make torsion action plus the by axial shear and flexural.\u003c/p\u003e \u003cp\u003ed\u0026thinsp;=\u0026thinsp;460 / S\u003csub\u003emin\u003c/sub\u003e = 300\u0026ndash;460/4\u0026ndash;460/2 / S\u003csub\u003emin\u003c/sub\u003e = 300\u0026ndash;115 \u0026ndash; 230\u003c/p\u003e \u003cp\u003eso for over-designed in shear, use S = (100\u0026ndash;200 \u0026ndash; 300)\u003c/p\u003e"},{"header":"7. Program Analysis Criteria","content":"\u003cp\u003eThe analysis criteria are divided into several introductory paragraphs, starting from the criteria of the materials used for the sections until reaching the final analysis, which will be presented in detail below. These criteria were fixed according to the static to create the best analysis conditions and be as close as possible to resembling objective reality\u0026mdash;the actual loading conditions of the static analysis. This static load is direct. The nonlinear properties of concrete were defined to try to study its behavior well in the theoretical analysis and the extent of its impact on the behavior of structural elements.\u0026nbsp;\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eMaterial criteria\u0026nbsp;\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe analysis criteria for the materials were chosen based on the material properties from the actual sites in the construction work, as also explained in the practical analysis chapter, without any reduction or safety factors to reach the maximum limits of the material. Because the first step in the research was based on theoretical analysis, the concrete properties were taken from a ready file of the program library uploaded on public sites. These properties were fixed in all the models used in the theoretical static analysis to study the behavior of the tilted beam, as well as to try to study the nonlinear behavior of concrete in these structural elements. All material properties are shown in Appendix C\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eStep criteria\u0026nbsp;\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe step used: type static, Riks with the maximum number of \u003cstrong\u003eincrements 20\u003c/strong\u003e and used equation solver \u0026ndash; matrix storage \u003cstrong\u003eunsymmetric\u003c/strong\u003e. Made convert severe discontinuity iteration \u003cstrong\u003e(on)\u003c/strong\u003e and extrapolation of the previous state as the start of each increment was \u003cstrong\u003e(parabolic)\u003c/strong\u003e not linear.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eInteraction criteria \u0026nbsp;\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eUsed embedded interaction between concrete section and rebar reinforcement\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eMesh criteria \u0026nbsp;\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eFor the static analysis, the mesh used for concrete 25 mm was \u003cstrong\u003eTet\u003c/strong\u003e shape, and the geometric order was Quadratic. For bars, reinforcement mesh is used at 50 mm with standard type and linear geometric order with family type truss to ensure the reinforcement is just tension and compression.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eBoundary conditions criteria\u0026nbsp;\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eFixed-end faces prevent displacement and rotations at the end to simulate the actual cases of tilted beams in concrete structures with continuous or linked ends in frame structures. The load was divided into several types. For static analysis, 50 KN was used at the end of the lever arm or on the notch, which acts as a 60 KN/m pure torsional moment.\u003c/p\u003e"},{"header":"8. The general behavior of static analysis used in ABAQUS","content":"\u003cp\u003eThe load acted on the cantilever beam, and that point load transferred to the support of the cantilever, which is the tilted beam as a load with a transverse torsional moment at mid-section where the cantilever is linked with the tilted beam as the lever system. \u0026ldquo;\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eThe lever system is one of the mechanical systems found in nature whose operation requires the presence of a solid physical body, i.e., the lever, capable of rotating around an axis or a fixed fulcrum, and is affected by force (effort) and resistance, and both the line of action of the effort and the line of action are far apart. Resistance is a perpendicular distance from the axis of rotation, where this distance is known as the arm.\u003c/span\u003e (Artobolevsky, 1975)\u0026rdquo;. These combined loads simulate real cases that can affect the tilted beam. This behavior helped make analysis more accessible and took us to known points that calculate displacement and rotation. Perhaps the most common case in structural designs and the most complex models used in this research is when using a cantilever plate supported by an inclined beam that produces a continuous torsional moment along the entire span, and more equations are needed to solve this situation. In addition, ensure that the cantilever beam does not fail before the tilted beam uses a rigid beam (over-designed beam in flexure, shear, and torsion), so ensure no losses approximately when the static load acts on the system and make can three types of cracks (flexural, shear and torsional cracks) when the beam high reinforced for flexural and shear that help to be just torsional crack clear appearance in the field test. At laboratory and program analysis, the foremost parameters to be measured were load displacement at the cantilever, angle of twist at the mid-section, and displacement of the mid-section.\u003c/p\u003e"},{"header":"9. Results","content":"\u003cp\u003eWhen the results of both theoretical and practical analysis are delved into in-depth, it becomes clear that the method proposed in this research (creating a cantilever beam on the inclined beam to be examined to solve the torsional loads) is more effective than the methods in previous research if what is required is to produce loads that mimic the objective reality in the structures. Structural (biaxial bending and biaxial shear loads in addition to torsional moment): This impression was evident in both theoretical analysis and practical testing.\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eThe purpose of this method is to avoid any imperfections that appeared in previous research made in the same laboratory, whether in the \u0026ldquo;Bi-axial shear capacity of the tilted solid reinforced concrete beam subject to point loading.\u0026rdquo;(Waryosh et al., 2014)\u003cstrong\u003e\u0026rdquo;\u003c/strong\u003e or \u003cstrong\u003e\u0026ldquo;Behavior of steel fiber self-compacting concrete hollo deep beams under torque.\u003c/strong\u003e(Mahdi \u0026amp; Mohaisen, 2021)\u003cstrong\u003e\u0026rdquo;\u0026nbsp;\u003c/strong\u003eTherefore, one of the main points that was focused on in this research is making the ends of the tilted beams completely fixed, whether in the theoretical program ABAQUS or in the practical test. The second point was how to apply the load to make torsional action and make a rigid cantilever to ensure it did not fail before the tilted beam. Searched on when applying point load at the end caused (shear action, bending moment, and high torsional moment) that simulate the actual case, whether in previous research on torsion used frame at end applied only torsional moment and that not simulate real cases.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e9.1 Overall program ABAQUS Static Analysis Results.\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe result shown in the tables for concrete was a maximum range of stresses at the mid-section of the tilted beam and figures for steel rebar stresses, which can be compared in each group of specimens and between groups. This clear and concise presentation of the results keeps the audience interested in the findings. Before presenting the results, clarifying what they mean and their significance in\u0026nbsp;structural design and analysis is necessary\u003cspan dir=\"RTL\"\u003e.\u003c/span\u003e The results were divided into the stresses of the concrete section at the applied load point (the mid-section of the tilted beam), representing the stresses in the three-dimensional axis, and the three-dimensional plans. This facilitates the comparison of each model\u0026apos;s effect and behavior. The steel reinforcement stresses were presented in the figures to clarify the stress distribution at all bars. These practical implications of the results provide valuable insights for future structural designs and analyses. It was decided to display the tilted beam\u0026apos;s displacement and angle of rotation for each node. The highest individual displacement for each node is represented by the angle, which also means the node\u0026apos;s rotation angle. The significance of these results in the context of structural design and analysis cannot be overstated, as they provide a solid foundation for future research and practical applications.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e9.2 Group \u0026ndash; A\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFrom a first glance at the analysis results with the same loading, as expected, whenever the reinforcement area is reduced, the stresses on the remaining reinforcement increase, and it is noted that the highest stresses in the reinforcement are in the direction of tension-resisting the bending moment. In addition to stating that the stresses in the concrete section tend to be high in shear behavior and low in the direction of torsional behavior, the reason for this is that the eccentricity from the shear center is small and causes a small torsional moment whose effect is small compared to the impact of bi-axial shear and bi-axial bending stresses. What confirms this analysis and opinion is that the direction of displacement of the site is in one direction, which is the negative direction of the local axes of the section, and it is without rotation angles. This confirms that the torsional moment is slight, and its frequency in this model is not perceptible.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2- Stress at mid-section / Group A\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp; \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConcrete stresses\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"602\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 6.96517%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eNo.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eS\u003csub\u003eXX\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.1111%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eS\u003csub\u003eYY\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1161%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eS\u003csub\u003eZZ\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eS\u003csub\u003eXY\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.1111%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eS\u003csub\u003eYZ\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eS\u003csub\u003eXZ\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.9403%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eU\u003csub\u003eX\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1161%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eU\u003csub\u003eY\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.2869%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eUR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 6.96517%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eB1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.701\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.1111%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.3473\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1161%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+4.038\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.316\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.1111%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.1504\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.220\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.9403%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.7989\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-1.070\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1161%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e-1.392\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-1.519\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.2869%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 6.96517%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eB2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.755\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.1111%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.3145\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1161%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+4.265\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.460\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.1111%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.0948\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.162\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.9403%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.4245\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.7302\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1161%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.6703\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-1.006\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.2869%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 6.96517%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eB3\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.948\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.1111%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.6104\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1161%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+4.363\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.387\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.1111%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.0459\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.78441%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.157\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.9403%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.4909\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.8442\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1161%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.8685\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-1.159\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.2869%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eSteel rebar stresses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e9.3 Group \u0026ndash; B\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eWhen applying a pure torsional moment concentrated in the mid-span of the tilted beam, it is clear that the stresses are distributed harmoniously along the length of the model and in opposite directions in both directions to the right and left of the torsional torque concentrated in an attempt to create distortions on the section in a warping manner. The highest stresses on the rebar are concentrated at the ends of the tilted beam because they are the stabilizer supports that resist the pure torsional moment. This situation is the same as in the case of a standard or tilted beam. The stresses are very close; some are equal, and there are no significant differences. The main reason behind this behavior is the use of pure torsional torque. In this case, the loads do not simulate the practical reality without the effect of shear and bending stresses on the section.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3- Stresses at mid-section / Group B\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConcrete stresses\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"645\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 5.89147%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eNo.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSXX\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSYY\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSZZ\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSXY\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSYZ\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSXZ\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eUX\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eUY\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.2093%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eUR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 5.89147%;\"\u003e\n \u003cp\u003eB4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.7823\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.454\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.058\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.387\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.257\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+2.447\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.35\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-1.414\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.350\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-1.410\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.2093%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+4.928\u0026times;10\u003csup\u003e-3\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 5.89147%;\"\u003e\n \u003cp\u003eB4-N\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.876\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.539\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.075\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.387\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.274\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+2.261\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.325\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-1.449\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.5634\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.5653\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.2093%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+4.727\u0026times;10\u003csup\u003e-3\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 5.89147%;\"\u003e\n \u003cp\u003eB5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.636\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.441\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.815\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.225\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.265\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.258\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.915\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.923\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.910\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.928\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.2093%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+3.059\u0026times;10\u003csup\u003e-3\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 5.89147%;\"\u003e\n \u003cp\u003eB6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.630\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.446\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.8338\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.220\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.267\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.99225%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.260\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.9148\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.923\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2326%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.9094\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.9283\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.2093%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+3.057\u0026times;10\u003csup\u003e-3\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eSteel rebar stresses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e9.4 Group \u0026ndash;\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eC\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eWhen the three types of loads - shear, bending, and torsion - are combined, this leads to the actual loading state so that the effect of the forces on each other and the effect of the tilted angle of the beam are observed. The stress in the tensile reinforcement increased to its maximum in the third model, which had the smallest reinforcement area\u003cspan dir=\"RTL\"\u003e.\u003c/span\u003e The stresses on the tilted beam can be explained as complex overlapping stresses based on shear flow and compressive stress in the upper layers and shear flow in the lower layers with the biaxial shear stress and the presence of tensile stresses on the tilted beam acting together at the same time. The critical factor that increases the efficiency of the tilted beam that bears these stresses together compared to standard models is the moment of inertia of the section, which changes with a change in shape or angle of inclination so that the section can withstand a higher degree of bearing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 4- Stresses at mid-section / Group C\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp; \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConcrete stresses \u0026emsp;\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"614\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 8.14332%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eNo.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSXX\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSYY\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSZZ\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSXY\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSYZ\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSXZ\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eUX\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eUY\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.4723%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eUR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 8.14332%;\"\u003e\n \u003cp\u003eB7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+2.429\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+3.129\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.286\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.261\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.264\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.397\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.1273\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.3104\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.0346\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.3186\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.4723%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.116\u0026times;10\u003csup\u003e-3\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 8.14332%;\"\u003e\n \u003cp\u003eB8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+2.309\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+2.499\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.237\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.067\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.3959\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.355\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.1030\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.2722\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.0227\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.2822\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.4723%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.958\u0026times;10\u003csup\u003e-3\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 8.14332%;\"\u003e\n \u003cp\u003eB9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.863\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+2.486\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.968\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.065\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.3872\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.358\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.1100\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.3126\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.0182\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.3219\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.4723%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.07\u0026times;10\u003csup\u003e-3\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 8.14332%;\"\u003e\n \u003cp\u003eB.R.L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.412\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+4.462\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.399\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+1.011\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.5424\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.12052%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.096\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.9514\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.2995\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 10.2606%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e+0.1242\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e-0.0843\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.4723%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.924\u0026times;10\u003csup\u003e-3\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eSteel rebar stresses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWhen searching and comparing the standard beam model B13 and the tilted beam model B7, it becomes clear that the shear stresses that the tilted beam can bear are higher due to the approximation of the total shear area in the two directions X-Y of the tilted beam, as well as the focus on the fact that the standard beam can bear bending stresses in one direction mainly and is very weak in the second direction. This is clear from the stresses it can bear in both directions, while the tilted beam can bear bending stresses that are close in values. With the stability of the shear flow that causes the torsional moment in both models, it is noted that the standard beam is generally weaker than the tilted beam.\u003c/p\u003e"},{"header":"10. Conclusion","content":"\u003cp\u003eThe ability of the tilted beam to withstand pure torsional moment is not affected if the beam is tilted or without a tilting angle. The reason is that the torsional moment is interpreted as a shear flow in the outer layer of the section, which will not be affected by the tilt of the element. However, suppose the torsional moment is applied with shear forces. In that case, there will be a change in the shear forces with the shear flow due to the torsional moment, which brings us back to the fact that the inclination angle affects the biaxial shear area. Suppose the bending moment is applied to them as the actual case. In that case, compressive stresses will occur in the upper part, which contributes to increasing the strength of the section against the resulting shear stresses and weakness in the section in the lower part, the tension area, which will cause an increase in the stresses on the concrete section. Here, it is clear that reinforcing steel or strengthening the tension area with carbon fiber sheets may be a good step in not increasing the areas of the concrete sections and making the best use of the section properties.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData Availability Statement (DAS):\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe data supporting this study\u0026apos;s findings are available from [figshare] at [\u003cu\u003ehttps://figshare.com/s/dc64631b001e581a748c\u003c/u\u003e]. These data were derived from the ABAQUS program analysis following resources available in the public domain.\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAny other data related to this study are available from the corresponding author upon reasonable request. All data requests should be directed to [\u003cu\[email protected]\u003c/u\u003e].\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eProf Dr. Saad Khalaf suggested the research subject Hassan Hussein search for the problem Hassan Hussein makes an analysis on the ABAQUS programHassan Hussein and Prof Dr. Saad Khalaf Analyzed, studied, and discussed the results.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eArtobolevsky, I. I. (1975). Mechanisms in modern engineering design. \u003cem\u003eMir Publishers\u003c/em\u003e, \u003cem\u003e1\u003c/em\u003e, 454.\u003c/li\u003e\n \u003cli\u003eBhasker, R., \u0026amp; Menon, A. (2020). Torsional irregularity indices for the seismic demand assessment of RC moment resisting frame buildings. \u003cem\u003eStructures\u003c/em\u003e, \u003cem\u003e26\u003c/em\u003e, 888\u0026ndash;900.\u003c/li\u003e\n \u003cli\u003eChaisomphob, T., Kritsanawonghong, S., \u0026amp; Hansapinyo, C. (2003). Experimental investigation on rectangular reinforced concrete beam subjected to bi-axial shear and torsion. \u003cem\u003eSongklanakarin Journal of Science and Technology\u003c/em\u003e, \u003cem\u003e25\u003c/em\u003e(1), 41\u0026ndash;52.\u003c/li\u003e\n \u003cli\u003eFigueiredo, T. C. S. P., Curosu, I., Gonz\u0026aacute;les, G. L. G., Hering, M., de Andrade Silva, F., Curbach, M., \u0026amp; Mechtcherine, V. (2021). Mechanical behavior of strain-hardening cement-based composites (SHCC) subjected to torsional loading and to combined torsional and axial loading. \u003cem\u003eMaterials \u0026amp; Design\u003c/em\u003e, \u003cem\u003e198\u003c/em\u003e, 109371.\u003c/li\u003e\n \u003cli\u003eLi, J., Yan, G., Abbud, L. H., Alkhalifah, T., Alturise, F., Khadimallah, M. A., \u0026amp; Marzouki, R. (2023). Predicting the shear strength of concrete beam through ANFIS-GA\u0026ndash;PSO hybrid modeling. \u003cem\u003eAdvances in Engineering Software\u003c/em\u003e, \u003cem\u003e181\u003c/em\u003e, 103475.\u003c/li\u003e\n \u003cli\u003eMahdi, M. S., \u0026amp; Mohaisen, S. K. (2021). BEHAVIOR OF STEEL FIBER SELF-COMPACTING CONCRETE HOLLOW DEEP BEAMS UNDER TORQUE. \u003cem\u003eJournal of Engineering and Sustainable Development\u003c/em\u003e, \u003cem\u003e25\u003c/em\u003e(3), 22\u0026ndash;33.\u003c/li\u003e\n \u003cli\u003e\u003cem\u003ept03ch06s01abo04 @ classes.engineering.wustl.edu\u003c/em\u003e. (n.d.). https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/pt03ch06s01abo04.html\u003c/li\u003e\n \u003cli\u003eQuadri, A. I., \u0026amp; Fujiyama, C. (2021). Response of reinforced concrete dapped-end beams exhibiting bond deterioration subjected to static and cyclic loading. \u003cem\u003eJournal of Advanced Concrete Technology\u003c/em\u003e, \u003cem\u003e19\u003c/em\u003e(5), 536\u0026ndash;554.\u003c/li\u003e\n \u003cli\u003eShafiq, N., \u0026amp; Akbar, I. (n.d.). \u003cem\u003eA Review of Combined Flexure, Shear \u0026amp; Torsion Strengthening of Reinforced Concrete Beam\u003c/em\u003e.\u003c/li\u003e\n \u003cli\u003eTinini, A., Minelli, F., Belletti, B., \u0026amp; Scolari, M. (2016). Biaxial shear in RC square beams: Experimental, numerical and analytical program. \u003cem\u003eEngineering Structures\u003c/em\u003e, \u003cem\u003e126\u003c/em\u003e, 469\u0026ndash;480.\u003c/li\u003e\n \u003cli\u003evan Nimwegen, S. E., \u0026amp; Latteur, P. (2023). A state-of-the-art review of carpentry connections: From traditional designs to emerging trends in wood-wood structural joints. \u003cem\u003eJournal of Building Engineering\u003c/em\u003e, 107089.\u003c/li\u003e\n \u003cli\u003eWaryosh, W. A., Mohaisen, S. K., \u0026amp; Yahya, L. M. (2014). Behavior of Rectangular Reinforced Concrete Beams Subjected to Bi-axial Shear Loading. \u003cem\u003eJournal of Engineering and Sustainable Development\u003c/em\u003e, \u003cem\u003e18\u003c/em\u003e(2), 106\u0026ndash;121.\u003c/li\u003e\n \u003cli\u003eYu, J., Luo, L., \u0026amp; Fang, Q. (2020). Structure behavior of reinforced concrete beam-slab assemblies subjected to perimeter middle column removal scenario. \u003cem\u003eEngineering Structures\u003c/em\u003e, \u003cem\u003e208\u003c/em\u003e, 110336.\u003c/li\u003e\n \u003cli\u003eZhou, J., Chen, Z., Chen, Y., Song, C., Li, J., \u0026amp; Zhong, M. (2022). Torsional behavior of steel reinforced concrete beam with welded studs: Experimental investigation. \u003cem\u003eJournal of Building Engineering\u003c/em\u003e, \u003cem\u003e48\u003c/em\u003e, 103879.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table","content":"\u003cp\u003eTable 1 is available in the Supplementary Files section.\u003c/p\u003e"},{"header":"Plate","content":"\u003cp\u003ePlate 1 is available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Tilted beam, tilting angle, torsional moment, biaxial shear, finite element analysis","lastPublishedDoi":"10.21203/rs.3.rs-5347044/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5347044/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn recent years, there has been an urgent need to find unconventional solutions to meet the architectural requirements in designs to produce larger spaces using relatively small or proportionate sections that do not negatively affect the aesthetic appearance of the design. From this standpoint, research and study were conducted on inclined beams and the difference between them and regular beams, studying their behavior and capacity and whether the American ACI code specifications apply to them or require a unique code. This research is based on analyzing the behavior of beams under the influence of biaxial shear forces and torsional moments by designing three groups of models to compare them with regular beam models and compare their behavior and the amount of their resistance to loads. Three methods of analysis were used to apply a load; the first method was to apply biaxial shear force, which had eccentricity from the shear center on a notch at the mid-section of the tilted beam to cause biaxial shear and torsion on the longitudinal span. The second method applied pure torsion on the mid-span of the tilted beam, and the third method used a lever system at the mid-span of the tilted beam to cause biaxial shear and torsion. The results of the analysis help to understand the behavior of tilted beams under torsion and the differences between them and the standard beams.\u003c/p\u003e","manuscriptTitle":"The behavior of Tilted RC Beams Under Biaxial Shear and Torsion: A Finite Element Approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-25 16:07:18","doi":"10.21203/rs.3.rs-5347044/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"215e9ae9-4913-4b74-83b5-3b4b92043171","owner":[],"postedDate":"November 25th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-01-02T10:39:06+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-25 16:07:18","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5347044","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5347044","identity":"rs-5347044","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}