Identification of the Effective Crane Hook’s Cross Section

Identification of the Effective Crane Hook’s Cross Section | 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 Identification of the Effective Crane Hook’s Cross Section Md Nazmul Hasan Dipu, Mahbub Hasan Apu, Pritidipto Paul Chowdhury This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3439199/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 31 Mar, 2024 Read the published version in Heliyon → Version 1 posted You are reading this latest preprint version Abstract The crane hook is a widely utilized component in several industries for the purpose of lifting things. The crane hook must possess the capacity to withstand the intended load without encountering any complications, hence ensuring the safety of both personnel and the objects being lifted. The process of analysis is crucial for the effective utilization of a crane hook. The primary aim of this study was to determine the most efficient cross-sectional crane hook among five distinct geometric profiles. This was achieved through the application of finite element analysis using Solidworks software. Subsequently, the identified cross-sectional profile was further examined using the Python programming language, taking into account the classical equation of a curved beam. The five cross-sectional shapes seen in the study were circular, rectangular, trapezoidal, I-shaped, and T-shaped. For the purposes of this investigation, the chosen material for each cross-sectional crane hook model was 34CrMo4 steel. Despite the identical boundary constraints imposed on all the chosen cross-sectional crane hook profiles, it was observed that the trapezoidal cross-sectional crane hook exhibited superior performance compared to the others. The trapezoidal cross-sectional crane hook model exhibited a von Mises stress of 202997600 Pa, with a corresponding factor of safety of 3.202. Further experimentation was conducted using Python to examine the trapezoidal profile. The results indicated that an increased level of parallelism in the inner side of the trapezoidal shape corresponded to a higher factor of safety. Hence, it is advisable to maintain the trapezoidal cross-sectional profile of the crane hook, with due consideration given to maximizing the length of the inner parallel side. The enhancement of design leads to a decrease in the likelihood of failure and the occurrence of undesirable accidents. Crane Hook Finite Element Analysis Simulation Numerical Stress Analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. INTRODUCTION 1.1 Significance of Crane Hook In several industries, cranes are used to move big loads from one location to another [1]. The lifting hook holds significant importance within material handling systems due to the inevitability of unforeseen incidents when the operational reliability of the hook is compromised [2]. Furthermore, crane hooks are highly reliable components commonly employed in industrial environments. The hoisting fixture in question is primarily intended for the purpose of engaging a lifting chain ring or link, as well as the pin of a shackle or cable socket. It is imperative that this fixture complies with the relevant health and safety rules, as specified by many sources [3–7]. The occurrence of an unforeseen malfunction in a crane can result in severe consequences, such as the potential loss of human lives, damage to property, and disruptions in production. Therefore, it is imperative to perform a comprehensive investigation of the underlying causes of these errors with the aim of implementing preventive measures to avoid their recurrence [8]. The problems observed in the production lines may be attributed to several factors such as inadequate design, improper utilization, or maintenance issues [8, 9]. Hence, it is imperative to assess the stress generated by the crane hook in order to mitigate the risk of its potential collapse [7, 10]. 1.2 Literature Review In their study, Kishore et al. ( 2020 ) employed a scanning electron microscope to investigate the micro and macro fractography of a 24 T crane hook. Additionally, stress analysis was conducted through the utilization of analytical calculations and finite element modeling utilizing ABAQUS® 2018 version. According to the findings, the finite element analysis demonstrated a high level of agreement with the analytical results in the failure zone of the trapezoidal cross section. A proposal was made to develop a rigorous standard for visual examination. The operation of cranes should have been prohibited in instances where they exhibit significant tool marks or notches. If deemed required, it was advisable to conduct appropriate polishing. Additionally, it was proposed that the implementation of ultrasonic testing for crane hooks should be carried out during scheduled shutdowns in order to identify the presence of fatigue cracks [8]. In their study, Pavlovi et al. (2018) conducted an analysis and optimization of the geometric properties pertaining to the T-cross section of a crane hook. The computation of maximum stresses at specific locations was performed utilizing the Winkler-Bach theory, where the hook was designed as a curved beam. Both Excel and MATLAB were utilized as software tools. The impact of the geometric constraint on optimization outcomes and cost reductions was evident in the obtained results [11]. The essential sliding angle of the crane hook was investigated by Onur ( 2017 ). The study incorporated multiple analytical approaches, including the finite element analysis method, curved beam theory, and simplified theory, to facilitate a comprehensive comparison of simulation outcomes. The drop in safety factor seen at a sling angle of 51° led to the determination that a sling angle of 51° was crucial [2]. The purpose of Desai and Zeytinoglu's (2016) study was to optimize the cross section of the crane hook by comparing three different profiles: square, circular, and trapezoidal. The study's findings revealed that a trapezoidal cross section of a hook exhibited superior performance in terms of maximum stress when compared to both circular and square cross sections. The Solidworks program was employed as a finite element analysis simulation tool [1]. Uddanwadiker ( 2011 ) conducted a project with the objective of analyzing the stress distribution pattern of the crane hook. This was achieved by the use of the finite element approach, and the obtained results were afterwards validated using the technique of photoelasticity. Two approaches were employed in this study, namely Finite Element Analysis (FEA) and photoelasticity. A finding was made indicating that by extending the region on the inner side of the hook at the point of maximum stress, the level of stress was reduced. From an analytical perspective, it could be observed that the introduction of a 3 mm increase in thickness resulted in a reduction of strains by around 17%. Therefore, the design could be modified by augmenting the thickness of the inner curve, so substantially reducing the likelihood of failure. Furthermore, it was proposed that a forging manufacturing technique be employed to produce crane hooks, since that would enable the crane hook to withstand a significant tensile load compared to the casting production process [7]. In their study, Torres et al. ( 2010 ) conducted an investigation with the aim of determining the factors that contributed to the failure of the crane hook during its operational use. Metallurgical analysis was employed in the investigation of crane hook failures. The failure could be attributed to the development of cracks within the heat-affected zone due to liquification, leading to a brittle fracture. The utilization of the counterfeit crane hook as an indivisible entity was advised [12]. In their study, Gough et al. ( 1934 ) utilized the principles of stress analysis to examine the structural integrity of different cross-sectional designs of crane hooks. A comprehensive explanation is provided on the calculation of bending moment in crane hook loading scenarios, employing the principles of curved beam bending. Furthermore, the utilization of fatigue testing to ascertain the aspect of safety is exemplified. The utilization of photoelasticity has been incorporated alongside the finite element analysis (FEA) technique in the modeling of crane hooks. The photo elastic method entails fabricating an acrylic copy of the object being investigated and subjecting it to identical loading conditions as the authentic component. Fringe patterns can be observed in specific optical configurations, referred to as polariscopes, due to the optical properties inherent in acrylic materials [13]. 1.3 Research Gap In the extant literature, distinct geometrical cross-sections of crane hooks were investigated to find the optimal design. However different designs were investigated under different boundary conditions which made it difficult to compare them precisely and find out the optimal design. Again, multiple conceivable variations of dimensions of a particular shape are possible under same boundary conditions. So, an optimal design should consist of not only an optimal geometrical shape but also an optimal dimension for the particular shape. Furthermore, to facilitate in real life scenario, it is necessary to consider the factor of safety for each sectional profile. But, a limited number of studies were identified that conducted this comprehensive examination of the specific geometric characteristics of a cross-sectional crane hook. 1.4 Objective of This Study The objective of this study is to determine the most efficient cross section for crane hooks among five distinct options using finite element analysis. Additionally, the study aims to conduct a more detailed examination of the selected cross section through iterations based on programming language. 2. METHODS 2.1 Sequence of the Study The research commenced by doing a comprehensive evaluation of existing literature, identifying a gap in the current body of knowledge, and subsequently generating novel ideas. Subsequently, the research aim was established with the purpose of operationalizing the aforementioned hypothesis. Boundary conditions were frequently revised along with necessary assumptions. Subsequently, computer-aided design (CAD) models were created, followed by the execution of a pilot finite element analysis (FEA) simulation. This pilot simulation aimed to check the CAD models as well as assess the selected boundary conditions. Finite element calculations were conducted on five distinct cross-sectional profiles of crane hooks—circular, rectangular, trapezoidal, I-shaped, and T-shaped profiles. Trapezoidal geometric shapes have the highest factor of safety when compared to other shapes. Hence, the trapezoidal profile was subjected to additional analysis using the Python programming language, based on classical equations. This analysis involved testing alternative sizes of trapezoidal profiles, while maintaining a constant trapezoidal height and profile area. Subsequently, the findings and subsequent discourse were formulated in accordance with the analysis conducted. In conclusion, this study has provided a comprehensive analysis of the subject matter. The findings have led to several recommendations for further action. However, it is important to acknowledge the limits of this study, which may have impacted the results. In light of these limitations, future research should be conducted to address these gaps and build upon the current findings. 2.2 Boundary Conditions and Assumptions To accurately compare all five cross-sectional crane hooks, the following assumptions and boundary conditions needed to remain the same for all of those crane hook models: Das et al., ( 2018 ) did a failure analysis of the crane hook by letting 4 tons (40 kN almost) of constant force as well as Onur ( 2018 ) considered 40kN force for crane hook analysis [14, 18]. Similarly, Fetvaci (2006) et al. analyzed a simple crane hook by finite element analysis under consideration of 5 tons (50 kN almost) force [15] and Krishnaveni et al., ( 2015 ) also performed a static analysis of crane hook T section by applying 6 tons (60 kN almost) force [16]. In this study, an external constant downward force of F = 50 kN was considered. In addition, the force acts in real the world between the contact surface of the rope, which goes throughout the crane hook, and the crane hooks inside surface. This contract surface is a minute area. So, force should have to be applied on a small load carrying surfaces during the finite element analysis [17–19]. Therefore, the inside surface of each design crane hook was split into a little portion at the portion where the load was applied. Cross-section areas should be designed in such a way that each one has the same amount of area. A rounded 2827 mm2 area was chosen for all of those cross sections. So, the same amount of cross-sectional area helped to make a logical comparison of all this study’s crane hooks. Having an inside radius of 50mm for all selected crane hooks. Having an outside radius of 110mm for all selected crane hooks. 34CrMo4 is a strength class T of the crane hook [2]. Hence, all the models in the study had the same material, which was 34CrMo4. Because it has better mechanical properties which is suitable for crane hook. The same fine mesh was applied for each model. 2.3 Five Selected Cross Sections For the simulation investigation, five CAD models of various crane hooks were created: circular, rectangular, trapezoidal, I-shaped, and T-shaped. After rounding off, each of those crane hook models had a cross-sectional area of 2827 mm2. Figures 2 a–e depicted the selected cross-sectional areas. Here each of these profiles has 60mm gaps between two faces so that the constant boundary condition can be maintained—the difference between curved beams inside radius 50mm and outside radius 110mm is 60mm. 2.4 Material Selection for this Study If a crack develops in the crane hook, it can cause a fracture of the hook and lead to a serious accident. So, the right material section for a crane hook is important [2]. If too brittle material were chosen, it would fail suddenly during the work when a crack developed. Because in brittle fractures, there is sudden propagation of the crack, and the hook fails suddenly. This type of fracture is very dangerous because it is difficult to detect. So, workers at that time would not have had a moment to move on. So sudden failure should be avoided by not choosing too brittle material. On the other hand, the crack propagates continuously in a ductile fracture, is more easily detectable, and is hence preferred over a brittle fracture [7]. But too much ductile material will not be able to play by the same rule as a crane hook’s activities. So, a material should be chosen that is neither too brittle nor too ductile. Crane hook's minimum yield strength is related to four strength classes (M, P, S, T, V). Strength class-T denotes structural low alloy steel such as 34CrMo4 [2, 20] which was chosen for this study for its high lasting strength and creep strength at high temperatures, good impact toughness at low temperatures, good hardenability, and medium machinability. Table 1 Material properties of 34crmo4 steel. Properties Value Elastic modulus 210000 MPa Poisson ratio 0.28 Mass density 7800 Kg/m 3 Tensile strength 900 MPa Yield strength 650 MPa These properties, shown in Table 1 , have been taken from the Solidworks® materials library. Table 2 Mesh properties. Matrices Value Mesh type Solid mesh Mesh density Fine Mesh parameters Standard mesh Jacobian points 4 points This information shown in Table 2 has been taken from the Solidworks® during this simulation study. 2.5 Tools and Technique Solidworks® 2020 was employed for both the CAD model development and the FEA simulation. And the Python programming language was used to do iterations on the basis of curve-beam equations. Four stress analysis techniques are max von mises stress, max shear stress (tresca), mohr-coulomb stress, and max normal stress. Among those max von mises stress technique is considered the best predictor of actual failure analysis of ductile materials (aluminum, steel, bronze, brass, etc). Another technique namely max shear stress (tresca) is also applicable for ductile materials but its result is less accurate. However, both mohr-coulomb stress and max normal stress are suitable for brittle materials (glass, cast iron, etc). Max normal stress is the least accurate technique among all [17]. Therefore, max von mises stress technique was chose for this study in light of 34CrMo4 material properties. 2.6 Curve Beam Equations for Python Code Curved beams are known to transfer loads more efficiently than straight beams [21]. Crane hooks are one of the mechanical elements that appear in the shape of curve beams, written by Nudehi and Steffen, ( 2021 ) in chapter two of the book entitled Analysis of Machine Elements Using Solidworks® Simulation 2021 [17]. The curved beam’s classical equations [1, 7, 17, 22] are mentioned below which were used to write Python language code. Curved beam stress = ± bending stress ± axial stress. .. .. .. .. .. .. .. .. .. .. (i) Stress at inside, σ i = \(\frac{MCi}{AeRi}\) + \(\frac{F}{A}\) . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . (ii) Stress at outside, σ o = - \(\frac{MCo}{AeRo}\) + \(\frac{F}{A}\) . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . (iii) where, Ri = radius to inside (concave surface) R o = radius to outside (convex surface) = R i + h. .. .. .. .. .. .. .. .. .. .. (iv) h = width of beam cross-section which was height of the trapezoidal in this study = R o - R i . .. .. . (v) S i = inside parallel side length of trapezoidal profile S o = outside parallel side length of trapezoidal profile A = cross-sectional area of beam= \(\frac{1}{2}\) × (S i + S o ) \(\times h\) = 2827 millimeters square constant in the study.. . (vi) R c = radius to centroid of beam = R i + \(\frac{\text{h}{\text{S}}_{\text{i}} + 2{\text{S}}_{\text{o}}}{3{\text{S}}_{\text{i} }+ {\text{S}}_{\text{o}}}\) . .. .. .. .. .. .. .. .. .. .. (vii) R n = radius to the neutral axis = \(\frac{\text{A}}{{\text{S}}_{\text{o} }- {\text{S}}_{\text{i}}+ \frac{\left({\text{S}}_{\text{i}}{\text{R}}_{\text{o} }- {\text{S}}_{\text{o}}{\text{R}}_{\text{i} }\right)}{\text{h}} \times \text{l}\text{n}\left(\frac{{\text{R}}_{\text{o} }}{{\text{R}}_{\text{i} }}\right)}\) . .. .. .. .. .. .. .. (viii) C i = distance from the neutral axis to the inside surface = R n - R i . .. .. .. .. .. .. .. (ix) C o = distance from the neutral axis to the outside surface = R o - R n .. .. .. .. .. .. .. . (x) e = distance between the centroidal axis and neutral axis = R c - R n . .. .. .. .. .. . (xi) F = applied vertical force which was 50000N in the study D h = horizontal distance between the vertical line along which force is applied and the centroidal axis M = bending moment = F × D h . .. .. .. .. .. .. .. .. .. .. .. . (xii) In equation (ii), both first and second terms are positive because both stresses are tensile stresses for this study. On the other hand, in equation (iii), first term is negative as it faces compressive stress, but second term is positive. As it faces tensile stress for this study. The factor of safety’s equation [17] is mentioned below which were also used to write Python language code. Safety factor = \(\frac{strength}{stress}\) . .. .. .. .. .. .. .. .. .. .. .. .. .. (xiii) The flowchart depicted in Fig. 3 shows how the aforementioned equations were implemented in Python codes. Only the trapezoidal shape required the use of this specific set of code and calculations. When compared to other geometric profiles, the trapezoidal cross section offered the highest safety factor. As a result, it became the subject of further research. 3. RESULTS AND DISCUSSIONS 3.1 Finite Element Analysis The finite element analysis simulation results of maximum von Mises stress (Max von Mises stress is considered the predictor of actual failure of ductile materials and provides a good indication of true factor of safety [17]) for five distinct geometrical cross sections of the crane hook are shown in Figs. 4 a–e; these cross sections were circular, rectangular, trapezoidal, I-shaped, and T-shaped profiles. The maximum magnitude of von Mises stresses on circular, rectangular, trapezoidal, I-shaped, and T-shaped profiles was found to be 282979584 Pa, 215177440 Pa, 202997600 Pa, 237289264 Pa, and 218187936 Pa, respectively. Among those, the trapezoidal profile had the lowest maximal von Mises stress. The simulation results also indicated the factor of safety—defined as the ratio of ultimate stress to working stress: it shows the component’s excess strength over the needed strength to carry that load [17, 23–25]—of the five cross-sectional crane hook profiles shown in Figs. 4 f–j. The factor of safety of circular, rectangular, trapezoidal, I-shaped, and T-shaped profiles was determined to be 2.297, 3.021, 3.202, 2.739, and 2.979 (rounded off to thousandths). The trapezoidal profile had the highest safety factor of all. Table 3 Simulation results summary of all five selected cross-sections. Cross section Von Mises stress Factor of safety Circular 282979584 Pa 2.297 Rectangular 215177440 Pa 3.021 Trapezoidal 202997600 Pa 3.202 I-shaped 237289264 Pa 2.739 T-shaped 218187936 Pa 2.979 3.2 Programming Language Based Iterations Albeit it was found from the FEA that the trapezoidal cross section was the best one of all, several trapezoidal shapes were possible under same boundary conditions of 2827 square millimeters and a height of two parallel sides of 60mm. So, more investigation was needed. The Python iteration for the several trapezoidal profiles was done in light of the Python code mentioned in Appendix-A while maintaining the same boundary conditions. These results were put in Table 4 . Table 4 Python iterations based on classical curve beam equations Iterations Inside parallel side (mm) Outside parallel side (mm) Parallel distance (mm) Area (mm squares) Maximum stress (Pa) Factor of safety 1 4.23 90 60 2827 428633840 1.516 2 14.23 80 60 2827 333411400 1.950 3 24.23 70 60 2827 276101551 2.354 4 34.23 60 60 2827 238540557 2.725 5 44.23 50 60 2827 212795880 3.055 6 54.23 40 60 2827 194958839 3.334 7 64.23 30 60 2827 183037694 3.551 8 74.23 20 60 2827 176169175 3.690 9 84.23 10 60 2827 174414640 3.727 It needs to be mentioned that the results of finite element analysis and classical equation-based analysis are different even when the same input values are given. In addition, Onur ( 2018 ) also showed that FEA result and curved beam theory-based result of maximum stress were different [18]. But, as Nudehi, S. S., and Steffen, J. R. (2021) wrote in chapter two of the book Analysis of Machine Elements Using Solidworks Simulation 2021, the finite element analysis method gives a more accurate solution than that of the classical method does [17]. Thus, albeit iteration 4 had the same boundary conditions in both methods, —finite element analysis and the classical method—the results were different. The deliberation of using the Python tool and classical equations on the earlier obtained trapezoidal profile by FEA was to do many iterations to find a pattern on how the trapezoidal profile was germane to the factor of safety: so, finding a pattern was the top priority. Table 4 shows that the factor of safety gradually increased when the outside parallel side of the trapezoidal profile was subjected to a decrease: both variables were inversely proportional to each other. Therefore, the less the outside parallel side of the trapezoidal profile, the greater the factor of safety it gives, while boundary conditions were the same. It is shown in Figs. 6 a–i. 4. CONCLUSIONS 4.1 Summery of the Study Based on the analysis and findings, it is found that a crane hook with a trapezoidal cross-sectional shape offers the utmost degree of safety depicted in Figs. 5 a–e. Although all of these cross-sectional crane hooks share the same boundary conditions, it is evident that the trapezoidal cross-sectional crane hook exhibits superior performance compared to the other designs in light of factor of safety. The trapezoidal cross-sectional hook experiences the lowest level of stress when subjected to an external load. The utilization of a trapezoidal cross section in the construction of the crane hook is a favorable option due to its ability to enhance the factor of safety and mitigate the likelihood of accidents. It is more appreciated to keep the inside parallel side length of the trapezoidal profile as long as possible. Because it improves the profile of the design in light of safety. Figures 6 a-i express this idea where Fig. 5 a represents the profile of iteration-1 in Table 4 . Similarly, Figs. 6 b-i indicate the profiles of iterations of 2–9 respectively. 4.2 Recommendations for practical implementation Design a crane hook with a trapezoidal cross-sectional profile in order to improve safety. Keep the outside parallel side as small as possible to make better cross section. It can be inferred from Fig. 6 i that a trapezoidal profile whose outside parallel side is near zero becomes a triangular profile, which is the best one. 4.3 Limitations and Future Works The study did not take into account the presence of a fillet radius. However, it is important to note that in practice, the removal of sharp edges is necessary to ensure the comfort of the rope or chain that passes through the crane hook. In future research, it might be prudent to investigate incorporating a rational fillet radius. Declarations Declaration of Competing Interest The authors declare that they have no competing interests. Credit authorship contribution statement All authors contributed to the study. The order of authors listed in the manuscript has been approved by all of us. The individual contributions of the authors are given herewith: manuscript writing, idea generation, research method development, tool selection, 3D CAD models development, performed simulation analysis, and Python coding: [Md Nazmul Hasan Dipu]; manuscript writing, 2D drawings, line drawings, and flowchart making: [Mahbub Hasan Apu]; manuscript writing and critically revised the whole work: [Pritidipto Paul Chowdhury]. All authors have read and approved the manuscript. Data availability The CAD models can be given upon request. Funding The authors did not receive any founding or support from any organization or institution. Acknowledgements Not applicable in this section. References Desai, N., & Zeytinoglu, N. (2016). Design and Optimization of the Geometric Properties of a Crane Hook. World Journal of Engineering and Technology, 04(03), 391–397. https://doi.org/10.4236/wjet.2016.43038 Onur, Y. A. (2017, December 11). Investigation of the effect of the sling angle and size on the reliability of lifting hooks. SIMULATION, 94(10), 931–942. https://doi.org/10.1177/0037549717744646 American Society of Mechanical Engineers. (2005). Overhead and Gantry Cranes: Top Running Bridge, Single or Multiple Girder, Top Running Trolley Hoist (ASME B30.2). American Society of Mechanical Engineers. (2006). 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Soil Investigation and Pile Design. Onshore Structural Design Calculations , 345–385. https://doi.org/10.1016/b978-0-08-101944-3.00008-5 Elishakoff, I. (2005, January). Stochasticity and safety factors: Part 1. Random actual stress and deterministic yield stress. Chaos, Solitons & Fractals , 23 (1), 321–331. https://doi.org/10.1016/j.chaos.2004.04.028 Additional Declarations No competing interests reported. Supplementary Files APPENDIX.docx Cite Share Download PDF Status: Published Journal Publication published 31 Mar, 2024 Read the published version in Heliyon → 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. 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Dipu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYDCCwyDCAMarAGJm5gYStBw4A9LCSEDLAWTOwTYQSUAL33HeYxIMBXfkGPjPGH/+OK82mr8dqOVHxTacWiQP86VJMBg8M2aQyDGTOLjteO6Mw4wNjD1nbuPUYnCYxwyo5XBigwSPGcPBbcdyG4BamBnbCGupbwA67MPBOcdy5xOrJYGBIcdA4mBDTe4GQlqAfkm2SDB4ZtgmkVYmcebYgdyNQC0H8fmF7/zZgzc+/Lkjz89/ePOHipq63HnnDx988KMCtxYGBh4GhgRg7LBBeOCYRY0srFqQ1NThVzwKRsEoGAUjEgAAJJ1a0sKt0wkAAAAASUVORK5CYII=","orcid":"","institution":"Shahjalal University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Md","middleName":"Nazmul Hasan","lastName":"Dipu","suffix":""},{"id":292163392,"identity":"6aa65f5a-6e0b-49e4-8838-d75d72f0e4c5","order_by":1,"name":"Mahbub Hasan Apu","email":"","orcid":"","institution":"Sylhet Engineering College","correspondingAuthor":false,"prefix":"","firstName":"Mahbub","middleName":"Hasan","lastName":"Apu","suffix":""},{"id":292163393,"identity":"691f3bfd-7e04-4741-9992-fc1ebe131b41","order_by":2,"name":"Pritidipto Paul Chowdhury","email":"","orcid":"","institution":"Shahjalal University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Pritidipto","middleName":"Paul","lastName":"Chowdhury","suffix":""}],"badges":[],"createdAt":"2023-10-12 21:59:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3439199/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3439199/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1016/j.heliyon.2024.e29918","type":"published","date":"2024-04-01T00:36:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":54891422,"identity":"cd38d0bf-aacd-4fca-8a15-36a51d5ed98b","added_by":"auto","created_at":"2024-04-18 07:44:48","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":126741,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFlowchart of the methodology of this study.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3439199/v1/6297a8edd4a0512c6910ae94.jpg"},{"id":54891423,"identity":"a032f6fe-e727-424c-97c5-3910730c82bc","added_by":"auto","created_at":"2024-04-18 07:44:48","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":20121,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDimension of cross-sectional profiles of the crane hooks.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-3439199/v1/483775a1cf1e8815ab72dedb.png"},{"id":54891425,"identity":"b8381b47-53b8-46b1-9413-85096a05a55a","added_by":"auto","created_at":"2024-04-18 07:44:48","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":76118,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePython code executing flowchart\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3439199/v1/d8d75f9c960cc97de3305d19.jpg"},{"id":54891428,"identity":"15443225-95ce-4d57-b5f3-4bc3f0009b2e","added_by":"auto","created_at":"2024-04-18 07:44:48","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":756798,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSimulation results of von mises stress and factor of safety for five different cross sectional crane hooks.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-3439199/v1/0cde8f0c8083dbbfd654068c.png"},{"id":54891906,"identity":"7a37895f-2300-43ba-ad09-687bec3d2f5b","added_by":"auto","created_at":"2024-04-18 07:52:48","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":91464,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of different standard geometrical profiles based on factor of safety.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3439199/v1/d93b8f0e1b471817e208a03e.jpeg"},{"id":54891427,"identity":"7bf6a072-eda2-4de0-924b-fa32e6c742a5","added_by":"auto","created_at":"2024-04-18 07:44:48","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":96535,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProfile shape improvement from left to right.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3439199/v1/bc2239fd59f3741972d0f40c.jpeg"},{"id":55693825,"identity":"4aa55dc3-c1d4-45c7-a3d7-2f7ff3c4877e","added_by":"auto","created_at":"2024-05-02 00:36:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1338758,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3439199/v1/62593107-6fc6-403f-ac7f-cd2693192423.pdf"},{"id":54891905,"identity":"11920763-adb2-4c06-8b91-c044fbc1201a","added_by":"auto","created_at":"2024-04-18 07:52:48","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":27204,"visible":true,"origin":"","legend":"","description":"","filename":"APPENDIX.docx","url":"https://assets-eu.researchsquare.com/files/rs-3439199/v1/c772fc90269787b5a34d70aa.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Identification of the Effective Crane Hook’s Cross Section","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1 Significance of Crane Hook\u003c/h2\u003e \u003cp\u003eIn several industries, cranes are used to move big loads from one location to another [1]. The lifting hook holds significant importance within material handling systems due to the inevitability of unforeseen incidents when the operational reliability of the hook is compromised [2]. Furthermore, crane hooks are highly reliable components commonly employed in industrial environments. The hoisting fixture in question is primarily intended for the purpose of engaging a lifting chain ring or link, as well as the pin of a shackle or cable socket. It is imperative that this fixture complies with the relevant health and safety rules, as specified by many sources [3\u0026ndash;7]. The occurrence of an unforeseen malfunction in a crane can result in severe consequences, such as the potential loss of human lives, damage to property, and disruptions in production. Therefore, it is imperative to perform a comprehensive investigation of the underlying causes of these errors with the aim of implementing preventive measures to avoid their recurrence [8]. The problems observed in the production lines may be attributed to several factors such as inadequate design, improper utilization, or maintenance issues [8, 9]. Hence, it is imperative to assess the stress generated by the crane hook in order to mitigate the risk of its potential collapse [7, 10].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e1.2 Literature Review\u003c/h2\u003e \u003cp\u003eIn their study, Kishore et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) employed a scanning electron microscope to investigate the micro and macro fractography of a 24 T crane hook. Additionally, stress analysis was conducted through the utilization of analytical calculations and finite element modeling utilizing ABAQUS\u0026reg; 2018 version. According to the findings, the finite element analysis demonstrated a high level of agreement with the analytical results in the failure zone of the trapezoidal cross section. A proposal was made to develop a rigorous standard for visual examination. The operation of cranes should have been prohibited in instances where they exhibit significant tool marks or notches. If deemed required, it was advisable to conduct appropriate polishing. Additionally, it was proposed that the implementation of ultrasonic testing for crane hooks should be carried out during scheduled shutdowns in order to identify the presence of fatigue cracks [8].\u003c/p\u003e \u003cp\u003eIn their study, Pavlovi et al. (2018) conducted an analysis and optimization of the geometric properties pertaining to the T-cross section of a crane hook. The computation of maximum stresses at specific locations was performed utilizing the Winkler-Bach theory, where the hook was designed as a curved beam. Both Excel and MATLAB were utilized as software tools. The impact of the geometric constraint on optimization outcomes and cost reductions was evident in the obtained results [11].\u003c/p\u003e \u003cp\u003eThe essential sliding angle of the crane hook was investigated by Onur (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The study incorporated multiple analytical approaches, including the finite element analysis method, curved beam theory, and simplified theory, to facilitate a comprehensive comparison of simulation outcomes. The drop in safety factor seen at a sling angle of 51\u0026deg; led to the determination that a sling angle of 51\u0026deg; was crucial [2].\u003c/p\u003e \u003cp\u003eThe purpose of Desai and Zeytinoglu's (2016) study was to optimize the cross section of the crane hook by comparing three different profiles: square, circular, and trapezoidal. The study's findings revealed that a trapezoidal cross section of a hook exhibited superior performance in terms of maximum stress when compared to both circular and square cross sections. The Solidworks program was employed as a finite element analysis simulation tool [1].\u003c/p\u003e \u003cp\u003eUddanwadiker (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) conducted a project with the objective of analyzing the stress distribution pattern of the crane hook. This was achieved by the use of the finite element approach, and the obtained results were afterwards validated using the technique of photoelasticity. Two approaches were employed in this study, namely Finite Element Analysis (FEA) and photoelasticity. A finding was made indicating that by extending the region on the inner side of the hook at the point of maximum stress, the level of stress was reduced. From an analytical perspective, it could be observed that the introduction of a 3 mm increase in thickness resulted in a reduction of strains by around 17%. Therefore, the design could be modified by augmenting the thickness of the inner curve, so substantially reducing the likelihood of failure. Furthermore, it was proposed that a forging manufacturing technique be employed to produce crane hooks, since that would enable the crane hook to withstand a significant tensile load compared to the casting production process [7].\u003c/p\u003e \u003cp\u003eIn their study, Torres et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) conducted an investigation with the aim of determining the factors that contributed to the failure of the crane hook during its operational use. Metallurgical analysis was employed in the investigation of crane hook failures. The failure could be attributed to the development of cracks within the heat-affected zone due to liquification, leading to a brittle fracture. The utilization of the counterfeit crane hook as an indivisible entity was advised [12].\u003c/p\u003e \u003cp\u003eIn their study, Gough et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1934\u003c/span\u003e) utilized the principles of stress analysis to examine the structural integrity of different cross-sectional designs of crane hooks. A comprehensive explanation is provided on the calculation of bending moment in crane hook loading scenarios, employing the principles of curved beam bending. Furthermore, the utilization of fatigue testing to ascertain the aspect of safety is exemplified. The utilization of photoelasticity has been incorporated alongside the finite element analysis (FEA) technique in the modeling of crane hooks. The photo elastic method entails fabricating an acrylic copy of the object being investigated and subjecting it to identical loading conditions as the authentic component. Fringe patterns can be observed in specific optical configurations, referred to as polariscopes, due to the optical properties inherent in acrylic materials [13].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e1.3 Research Gap\u003c/h2\u003e \u003cp\u003eIn the extant literature, distinct geometrical cross-sections of crane hooks were investigated to find the optimal design. However different designs were investigated under different boundary conditions which made it difficult to compare them precisely and find out the optimal design. Again, multiple conceivable variations of dimensions of a particular shape are possible under same boundary conditions. So, an optimal design should consist of not only an optimal geometrical shape but also an optimal dimension for the particular shape. Furthermore, to facilitate in real life scenario, it is necessary to consider the factor of safety for each sectional profile. But, a limited number of studies were identified that conducted this comprehensive examination of the specific geometric characteristics of a cross-sectional crane hook.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e1.4 Objective of This Study\u003c/h2\u003e \u003cp\u003eThe objective of this study is to determine the most efficient cross section for crane hooks among five distinct options using finite element analysis. Additionally, the study aims to conduct a more detailed examination of the selected cross section through iterations based on programming language.\u003c/p\u003e \u003c/div\u003e"},{"header":"2. METHODS","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n\u003ch2\u003e2.1 Sequence of the Study\u003c/h2\u003e\n\u003cp\u003eThe research commenced by doing a comprehensive evaluation of existing literature, identifying a gap in the current body of knowledge, and subsequently generating novel ideas. Subsequently, the research aim was established with the purpose of operationalizing the aforementioned hypothesis. Boundary conditions were frequently revised along with necessary assumptions. Subsequently, computer-aided design (CAD) models were created, followed by the execution of a pilot finite element analysis (FEA) simulation. This pilot simulation aimed to check the CAD models as well as assess the selected boundary conditions. Finite element calculations were conducted on five distinct cross-sectional profiles of crane hooks\u0026mdash;circular, rectangular, trapezoidal, I-shaped, and T-shaped profiles. Trapezoidal geometric shapes have the highest factor of safety when compared to other shapes. Hence, the trapezoidal profile was subjected to additional analysis using the Python programming language, based on classical equations. This analysis involved testing alternative sizes of trapezoidal profiles, while maintaining a constant trapezoidal height and profile area. Subsequently, the findings and subsequent discourse were formulated in accordance with the analysis conducted. In conclusion, this study has provided a comprehensive analysis of the subject matter. The findings have led to several recommendations for further action. However, it is important to acknowledge the limits of this study, which may have impacted the results. In light of these limitations, future research should be conducted to address these gaps and build upon the current findings.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003e2.2 Boundary Conditions and Assumptions\u003c/h2\u003e\n\u003cp\u003eTo accurately compare all five cross-sectional crane hooks, the following assumptions and boundary conditions needed to remain the same for all of those crane hook models:\u003c/p\u003e\n\u003col style=\"list-style-type: lower-alpha;\"\u003e\n\u003cli\u003e\n\u003cp\u003eDas et al., (\u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e) did a failure analysis of the crane hook by letting 4 tons (40 kN almost) of constant force as well as Onur (\u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e) considered 40kN force for crane hook analysis [14, 18]. Similarly, Fetvaci (2006) et al. analyzed a simple crane hook by finite element analysis under consideration of 5 tons (50 kN almost) force [15] and Krishnaveni et al., (\u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e) also performed a static analysis of crane hook T section by applying 6 tons (60 kN almost) force [16]. In this study, an external constant downward force of F\u0026thinsp;=\u0026thinsp;50 kN was considered.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eIn addition, the force acts in real the world between the contact surface of the rope, which goes throughout the crane hook, and the crane hooks inside surface. This contract surface is a minute area. So, force should have to be applied on a small load carrying surfaces during the finite element analysis [17\u0026ndash;19]. Therefore, the inside surface of each design crane hook was split into a little portion at the portion where the load was applied.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eCross-section areas should be designed in such a way that each one has the same amount of area. A rounded 2827 mm2 area was chosen for all of those cross sections. So, the same amount of cross-sectional area helped to make a logical comparison of all this study\u0026rsquo;s crane hooks.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eHaving an inside radius of 50mm for all selected crane hooks.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eHaving an outside radius of 110mm for all selected crane hooks.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e34CrMo4 is a strength class T of the crane hook [2]. Hence, all the models in the study had the same material, which was 34CrMo4. Because it has better mechanical properties which is suitable for crane hook.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eThe same fine mesh was applied for each model.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n\u003ch2\u003e2.3 Five Selected Cross Sections\u003c/h2\u003e\n\u003cp\u003eFor the simulation investigation, five CAD models of various crane hooks were created: circular, rectangular, trapezoidal, I-shaped, and T-shaped. After rounding off, each of those crane hook models had a cross-sectional area of 2827 mm2. Figures\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea\u0026ndash;e depicted the selected cross-sectional areas. Here each of these profiles has 60mm gaps between two faces so that the constant boundary condition can be maintained\u0026mdash;the difference between curved beams inside radius 50mm and outside radius 110mm is 60mm.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n\u003ch2\u003e2.4 Material Selection for this Study\u003c/h2\u003e\n\u003cp\u003eIf a crack develops in the crane hook, it can cause a fracture of the hook and lead to a serious accident. So, the right material section for a crane hook is important [2]. If too brittle material were chosen, it would fail suddenly during the work when a crack developed. Because in brittle fractures, there is sudden propagation of the crack, and the hook fails suddenly. This type of fracture is very dangerous because it is difficult to detect. So, workers at that time would not have had a moment to move on. So sudden failure should be avoided by not choosing too brittle material. On the other hand, the crack propagates continuously in a ductile fracture, is more easily detectable, and is hence preferred over a brittle fracture [7]. But too much ductile material will not be able to play by the same rule as a crane hook\u0026rsquo;s activities. So, a material should be chosen that is neither too brittle nor too ductile. Crane hook's minimum yield strength is related to four strength classes (M, P, S, T, V). Strength class-T denotes structural low alloy steel such as 34CrMo4 [2, 20] which was chosen for this study for its high lasting strength and creep strength at high temperatures, good impact toughness at low temperatures, good hardenability, and medium machinability.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eMaterial properties of 34crmo4 steel.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eProperties\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eValue\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eElastic modulus\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e210000 MPa\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003ePoisson ratio\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.28\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMass density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7800 Kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTensile strength\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e900 MPa\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eYield strength\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e650 MPa\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThese properties, shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, have been taken from the Solidworks\u0026reg; materials library.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eMesh properties.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eMatrices\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eValue\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMesh type\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eSolid mesh\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMesh density\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eFine\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eMesh parameters\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eStandard mesh\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eJacobian points\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4 points\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThis information shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e has been taken from the Solidworks\u0026reg; during this simulation study.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003e2.5 Tools and Technique\u003c/h2\u003e\n\u003cp\u003eSolidworks\u0026reg; 2020 was employed for both the CAD model development and the FEA simulation. And the Python programming language was used to do iterations on the basis of curve-beam equations.\u003c/p\u003e\n\u003cp\u003eFour stress analysis techniques are max von mises stress, max shear stress (tresca), mohr-coulomb stress, and max normal stress. Among those max von mises stress technique is considered the best predictor of actual failure analysis of ductile materials (aluminum, steel, bronze, brass, etc). Another technique namely max shear stress (tresca) is also applicable for ductile materials but its result is less accurate. However, both mohr-coulomb stress and max normal stress are suitable for brittle materials (glass, cast iron, etc). Max normal stress is the least accurate technique among all [17]. Therefore, max von mises stress technique was chose for this study in light of 34CrMo4 material properties.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n\u003ch2\u003e2.6 Curve Beam Equations for Python Code\u003c/h2\u003e\n\u003cp\u003eCurved beams are known to transfer loads more efficiently than straight beams [21]. Crane hooks are one of the mechanical elements that appear in the shape of curve beams, written by Nudehi and Steffen, (\u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e) in chapter two of the book entitled Analysis of Machine Elements Using Solidworks\u0026reg; Simulation 2021 [17]. The curved beam\u0026rsquo;s classical equations [1, 7, 17, 22] are mentioned below which were used to write Python language code.\u003c/p\u003e\n\u003cp\u003eCurved beam stress\u0026thinsp;=\u0026thinsp;\u0026plusmn;\u0026thinsp;bending stress\u0026thinsp;\u0026plusmn;\u0026thinsp;axial stress. .. .. .. .. .. .. .. .. .. .. (i)\u003c/p\u003e\n\u003cp\u003eStress at inside,\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n\u003cp\u003e\u0026sigma;\u003csub\u003ei\u003c/sub\u003e =\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{MCi}{AeRi}\\)\u003c/span\u003e\u003c/span\u003e + \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{F}{A}\\)\u003c/span\u003e\u003c/span\u003e. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . (ii)\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eStress at outside,\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n\u003cp\u003e\u0026sigma;\u003csub\u003eo\u003c/sub\u003e = - \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{MCo}{AeRo}\\)\u003c/span\u003e\u003c/span\u003e +\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{F}{A}\\)\u003c/span\u003e\u003c/span\u003e. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . (iii)\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere,\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n\u003cp\u003eRi\u0026thinsp;=\u0026thinsp;radius to inside (concave surface)\u003c/p\u003e\n\u003cp\u003eR\u003csub\u003eo\u003c/sub\u003e = radius to outside (convex surface)\u0026thinsp;=\u0026thinsp;R\u003csub\u003ei\u003c/sub\u003e + h. .. .. .. .. .. .. .. .. .. .. (iv)\u003c/p\u003e\n\u003cp\u003eh\u0026thinsp;=\u0026thinsp;width of beam cross-section which was height of the trapezoidal in this study\u0026thinsp;=\u0026thinsp;R\u003csub\u003eo\u003c/sub\u003e - R\u003csub\u003ei\u003c/sub\u003e. .. .. . (v)\u003c/p\u003e\n\u003cp\u003eS\u003csub\u003ei\u003c/sub\u003e = inside parallel side length of trapezoidal profile\u003c/p\u003e\n\u003cp\u003eS\u003csub\u003eo\u003c/sub\u003e = outside parallel side length of trapezoidal profile\u003c/p\u003e\n\u003cp\u003eA\u0026thinsp;=\u0026thinsp;cross-sectional area of beam= \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{1}{2}\\)\u003c/span\u003e\u003c/span\u003e \u0026times; (S\u003csub\u003ei\u003c/sub\u003e + S\u003csub\u003eo\u003c/sub\u003e) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times h\\)\u003c/span\u003e\u003c/span\u003e = 2827 millimeters square constant in the study.. . (vi)\u003c/p\u003e\n\u003cp\u003eR\u003csub\u003ec\u003c/sub\u003e = radius to centroid of beam\u0026thinsp;=\u0026thinsp;R\u003csub\u003ei\u003c/sub\u003e +\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{\\text{h}{\\text{S}}_{\\text{i}} + 2{\\text{S}}_{\\text{o}}}{3{\\text{S}}_{\\text{i} }+ {\\text{S}}_{\\text{o}}}\\)\u003c/span\u003e\u003c/span\u003e. .. .. .. .. .. .. .. .. .. .. (vii)\u003c/p\u003e\n\u003cp\u003eR\u003csub\u003en\u003c/sub\u003e = radius to the neutral axis =\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{\\text{A}}{{\\text{S}}_{\\text{o} }- {\\text{S}}_{\\text{i}}+ \\frac{\\left({\\text{S}}_{\\text{i}}{\\text{R}}_{\\text{o} }- {\\text{S}}_{\\text{o}}{\\text{R}}_{\\text{i} }\\right)}{\\text{h}} \\times \\text{l}\\text{n}\\left(\\frac{{\\text{R}}_{\\text{o} }}{{\\text{R}}_{\\text{i} }}\\right)}\\)\u003c/span\u003e\u003c/span\u003e. .. .. .. .. .. .. .. (viii)\u003c/p\u003e\n\u003cp\u003eC\u003csub\u003ei\u003c/sub\u003e = distance from the neutral axis to the inside surface\u0026thinsp;=\u0026thinsp;R\u003csub\u003en\u003c/sub\u003e - R\u003csub\u003ei\u003c/sub\u003e. .. .. .. .. .. .. .. (ix)\u003c/p\u003e\n\u003cp\u003eC\u003csub\u003eo\u003c/sub\u003e= distance from the neutral axis to the outside surface\u0026thinsp;=\u0026thinsp;R\u003csub\u003eo\u003c/sub\u003e - R\u003csub\u003en\u003c/sub\u003e.. .. .. .. .. .. .. . (x)\u003c/p\u003e\n\u003cp\u003ee\u0026thinsp;=\u0026thinsp;distance between the centroidal axis and neutral axis\u0026thinsp;=\u0026thinsp;R\u003csub\u003ec\u003c/sub\u003e - R\u003csub\u003en\u003c/sub\u003e. .. .. .. .. .. . (xi)\u003c/p\u003e\n\u003cp\u003eF\u0026thinsp;=\u0026thinsp;applied vertical force which was 50000N in the study\u003c/p\u003e\n\u003cp\u003eD\u003csub\u003eh\u003c/sub\u003e = horizontal distance between the vertical line along which force is applied and the centroidal axis\u003c/p\u003e\n\u003cp\u003eM\u0026thinsp;=\u0026thinsp;bending moment\u0026thinsp;=\u0026thinsp;F \u0026times; D\u003csub\u003eh\u003c/sub\u003e. .. .. .. .. .. .. .. .. .. .. .. . (xii)\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eIn equation (ii), both first and second terms are positive because both stresses are tensile stresses for this study. On the other hand, in equation (iii), first term is negative as it faces compressive stress, but second term is positive. As it faces tensile stress for this study.\u003c/p\u003e\n\u003cp\u003eThe factor of safety\u0026rsquo;s equation [17] is mentioned below which were also used to write Python language code.\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n\u003cp\u003eSafety factor = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{strength}{stress}\\)\u003c/span\u003e\u003c/span\u003e. .. .. .. .. .. .. .. .. .. .. .. .. .. (xiii)\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eThe flowchart depicted in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows how the aforementioned equations were implemented in Python codes. Only the trapezoidal shape required the use of this specific set of code and calculations. When compared to other geometric profiles, the trapezoidal cross section offered the highest safety factor. As a result, it became the subject of further research.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. RESULTS AND DISCUSSIONS","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003e3.1 Finite Element Analysis\u003c/h2\u003e\n\u003cp\u003eThe finite element analysis simulation results of maximum von Mises stress (Max von Mises stress is considered the predictor of actual failure of ductile materials and provides a good indication of true factor of safety [17]) for five distinct geometrical cross sections of the crane hook are shown in Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea\u0026ndash;e; these cross sections were circular, rectangular, trapezoidal, I-shaped, and T-shaped profiles. The maximum magnitude of von Mises stresses on circular, rectangular, trapezoidal, I-shaped, and T-shaped profiles was found to be 282979584 Pa, 215177440 Pa, 202997600 Pa, 237289264 Pa, and 218187936 Pa, respectively. Among those, the trapezoidal profile had the lowest maximal von Mises stress.\u003c/p\u003e\n\u003cp\u003eThe simulation results also indicated the factor of safety\u0026mdash;defined as the ratio of ultimate stress to working stress: it shows the component\u0026rsquo;s excess strength over the needed strength to carry that load [17, 23\u0026ndash;25]\u0026mdash;of the five cross-sectional crane hook profiles shown in Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ef\u0026ndash;j. The factor of safety of circular, rectangular, trapezoidal, I-shaped, and T-shaped profiles was determined to be 2.297, 3.021, 3.202, 2.739, and 2.979 (rounded off to thousandths). The trapezoidal profile had the highest safety factor of all.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab3\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eSimulation results summary of all five selected cross-sections.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eCross section\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eVon Mises stress\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eFactor of safety\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eCircular\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e282979584 Pa\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.297\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRectangular\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e215177440 Pa\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.021\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eTrapezoidal\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e202997600 Pa\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3.202\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eI-shaped\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e237289264 Pa\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.739\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eT-shaped\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e218187936 Pa\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2.979\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n\u003ch2\u003e3.2 Programming Language Based Iterations\u003c/h2\u003e\n\u003cp\u003eAlbeit it was found from the FEA that the trapezoidal cross section was the best one of all, several trapezoidal shapes were possible under same boundary conditions of 2827 square millimeters and a height of two parallel sides of 60mm. So, more investigation was needed. The Python iteration for the several trapezoidal profiles was done in light of the Python code mentioned in Appendix-A while maintaining the same boundary conditions. These results were put in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab4\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003ePython iterations based on classical curve beam equations\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eIterations\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eInside parallel side\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eOutside parallel side\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eParallel distance\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eArea\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(mm squares)\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eMaximum stress\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(Pa)\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eFactor of safety\u003c/em\u003e\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e90\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e428633840\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.516\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e14.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e333411400\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.950\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e24.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e70\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e276101551\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.354\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e34.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e238540557\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2.725\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e44.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e50\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e212795880\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.055\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e54.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e194958839\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.334\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e64.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e183037694\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.551\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e74.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e176169175\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.690\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e84.23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e60\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2827\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e174414640\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3.727\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eIt needs to be mentioned that the results of finite element analysis and classical equation-based analysis are different even when the same input values are given. In addition, Onur (\u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e) also showed that FEA result and curved beam theory-based result of maximum stress were different [18]. But, as Nudehi, S. S., and Steffen, J. R. (2021) wrote in chapter two of the book Analysis of Machine Elements Using Solidworks Simulation 2021, the finite element analysis method gives a more accurate solution than that of the classical method does [17]. Thus, albeit iteration 4 had the same boundary conditions in both methods, \u0026mdash;finite element analysis and the classical method\u0026mdash;the results were different.\u003c/p\u003e\n\u003cp\u003eThe deliberation of using the Python tool and classical equations on the earlier obtained trapezoidal profile by FEA was to do many iterations to find a pattern on how the trapezoidal profile was germane to the factor of safety: so, finding a pattern was the top priority. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e shows that the factor of safety gradually increased when the outside parallel side of the trapezoidal profile was subjected to a decrease: both variables were inversely proportional to each other. Therefore, the less the outside parallel side of the trapezoidal profile, the greater the factor of safety it gives, while boundary conditions were the same. It is shown in Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea\u0026ndash;i.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. CONCLUSIONS","content":"\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1 Summery of the Study\u003c/h2\u003e\n\u003cp\u003eBased on the analysis and findings, it is found that a crane hook with a trapezoidal cross-sectional shape offers the utmost degree of safety depicted in Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea\u0026ndash;e. Although all of these cross-sectional crane hooks share the same boundary conditions, it is evident that the trapezoidal cross-sectional crane hook exhibits superior performance compared to the other designs in light of factor of safety. The trapezoidal cross-sectional hook experiences the lowest level of stress when subjected to an external load. The utilization of a trapezoidal cross section in the construction of the crane hook is a favorable option due to its ability to enhance the factor of safety and mitigate the likelihood of accidents.\u003c/p\u003e\n\u003cp\u003eIt is more appreciated to keep the inside parallel side length of the trapezoidal profile as long as possible. Because it improves the profile of the design in light of safety. Figures\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea-i express this idea where Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea represents the profile of iteration-1 in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. Similarly, Figs.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003eb-i indicate the profiles of iterations of 2\u0026ndash;9 respectively.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\n\u003ch2\u003e4.2 Recommendations for practical implementation\u003c/h2\u003e\n\u003col style=\"list-style-type: lower-alpha;\"\u003e\n\u003cli\u003e\n\u003cp\u003eDesign a crane hook with a trapezoidal cross-sectional profile in order to improve safety.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eKeep the outside parallel side as small as possible to make better cross section. It can be inferred from Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ei that a trapezoidal profile whose outside parallel side is near zero becomes a triangular profile, which is the best one.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\n\u003ch2\u003e4.3 Limitations and Future Works\u003c/h2\u003e\n\u003cp\u003eThe study did not take into account the presence of a fillet radius. However, it is important to note that in practice, the removal of sharp edges is necessary to ensure the comfort of the rope or chain that passes through the crane hook. In future research, it might be prudent to investigate incorporating a rational fillet radius.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDeclaration of Competing Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCredit authorship contribution statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors contributed to the study. The order of authors listed in the manuscript has been approved by all of us. The individual contributions of the authors are given herewith: manuscript writing, idea generation, research method development, tool selection, 3D CAD models development, performed simulation analysis, and Python coding: [Md Nazmul Hasan Dipu]; manuscript writing, 2D drawings, line drawings, and flowchart making: [Mahbub Hasan Apu]; manuscript writing and critically revised the whole work: [Pritidipto Paul Chowdhury]. All authors have read and approved the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe CAD models can be given upon request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors did not receive any founding or support from any organization or institution.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable in this section.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDesai, N., \u0026amp; Zeytinoglu, N. (2016). Design and Optimization of the Geometric Properties of a Crane Hook. World Journal of Engineering and Technology, 04(03), 391\u0026ndash;397. https://doi.org/10.4236/wjet.2016.43038\u003c/li\u003e\n\u003cli\u003eOnur, Y. A. (2017, December 11). Investigation of the effect of the sling angle and size on the reliability of lifting hooks. SIMULATION, 94(10), 931\u0026ndash;942. https://doi.org/10.1177/0037549717744646\u003c/li\u003e\n\u003cli\u003eAmerican Society of Mechanical Engineers. (2005). \u003cem\u003eOverhead and Gantry Cranes: Top Running Bridge, Single or Multiple Girder, Top Running Trolley Hoist\u003c/em\u003e (ASME B30.2).\u003c/li\u003e\n\u003cli\u003eAmerican Society of Mechanical Engineers. (2006). \u003cem\u003eSlings Safety Standard for Cableways, Cranes, Derricks, Hoists, Hooks, Jacks and Slings \u003c/em\u003e(ASME Standard B30.9)\u003c/li\u003e\n\u003cli\u003eAmerican Society of Mechanical Engineers. (2009). \u003cem\u003eHooks Safety Standard for Cableways, Cranes, Derricks, Hoists, Hooks, Jacks and Slings \u003c/em\u003e(ASME Standard B30.10).\u003c/li\u003e\n\u003cli\u003eDepartment of Labour of New Zealand. (2009). \u003cem\u003eApproved Code of Practice for Cranes Approval of Amendment: 3rd Edition \u003c/em\u003e(2009-go10104).\u003c/li\u003e\n\u003cli\u003eUddanwadiker, R. (2011). 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The Miller Park crane accident. \u003cem\u003eEngineering Failure Analysis\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(6), 942\u0026ndash;961. https://doi.org/10.1016/j.engfailanal.2006.12.002\u003c/li\u003e\n\u003cli\u003ePavlović, G., Savković, M., Zdravković, N., Marković, G., \u0026amp; Stanojković, J. (2018). Analysis and optimization of T-cross section of crane hook considered as a curved beam. IMK-14 - Istrazivanje I Razvoj, 24(2), 51\u0026ndash;58. https://doi.org/10.5937/imk1802051p\u003c/li\u003e\n\u003cli\u003eTorres, Y., Gallardo, J., Dom\u0026iacute;nguez, J., \u0026amp; Jim\u0026eacute;nez E, F. (2010, January). Brittle fracture of a crane hook. Engineering Failure Analysis, 17(1), 38\u0026ndash;47. https://doi.org/10.1016/j.engfailanal.2008.11.011 \u003c/li\u003e\n\u003cli\u003eGough, H. J., Cox, H. L., \u0026amp; Sopwith, D. G. (1934, June). Design of Crane Hooks and Other Components of Lifting Gear. Proceedings of the Institution of Mechanical Engineers, 128(1), 253\u0026ndash;360. https://doi.org/10.1243/pime_proc_1934_128_014_02\u003c/li\u003e\n\u003cli\u003eDas, S., Mukhopadhyay, G., \u0026amp; Bhattacharyya, S. (2018). Failure analysis of a 40 ton crane hook at a Hot Strip Mill. MATEC Web of Conferences, 165, 10006. https://doi.org/10.1051/matecconf/201816510006 \u003c/li\u003e\n\u003cli\u003eFetvacı, M.C., Gerdemeli, İ., Erdil, A.B. (2006). Finite Element Modelling and Static Stress Analysis of Simple Hooks. \u003cem\u003eTMT 2006 Conference\u003c/em\u003e, Spain, 797\u0026ndash;800.\u003c/li\u003e\n\u003cli\u003eKrishnaveni, M., Reddy, M., \u0026amp; Roy, M. R. (2015, July 25). Static Analysis of Crane Hook with T-Section Using Ansys. \u003cem\u003eInternational Journal of Engineering Trends and Technology, 25\u003c/em\u003e(1), 53\u0026ndash;58. https://doi.org/10.14445/22315381/ijett-v25p209 \u003c/li\u003e\n\u003cli\u003eNudehi, S. S., and Steffen, J. R. 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Finite element analysis on curved beams of various sections. 2013 International Conference on Energy Efficient Technologies for Sustainability. https://doi.org/10.1109/iceets.2013.6533377 \u003c/li\u003e\n\u003cli\u003eBudynas, R.G. and Nisbett, J.K. (2015). Shigley\u0026apos;s Mechanical Engineering Design. McGraw-Hill Education.\u003c/li\u003e\n\u003cli\u003eKoerner, R. (2007). The design principles of geosynthetics. Geosynthetics in Civil Engineering, 3\u0026ndash;18. https://doi.org/10.1533/9781845692490.1.3\u003c/li\u003e\n\u003cli\u003eEl-Reedy, M. A. (2017). Soil Investigation and Pile Design. \u003cem\u003eOnshore Structural Design Calculations\u003c/em\u003e, 345\u0026ndash;385. https://doi.org/10.1016/b978-0-08-101944-3.00008-5\u003c/li\u003e\n\u003cli\u003eElishakoff, I. (2005, January). Stochasticity and safety factors: Part 1. Random actual stress and deterministic yield stress. \u003cem\u003eChaos, Solitons \u0026amp; Fractals\u003c/em\u003e, \u003cem\u003e23\u003c/em\u003e(1), 321\u0026ndash;331. https://doi.org/10.1016/j.chaos.2004.04.028\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"Crane Hook, Finite Element Analysis, Simulation, Numerical Stress Analysis","lastPublishedDoi":"10.21203/rs.3.rs-3439199/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3439199/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe crane hook is a widely utilized component in several industries for the purpose of lifting things. The crane hook must possess the capacity to withstand the intended load without encountering any complications, hence ensuring the safety of both personnel and the objects being lifted. The process of analysis is crucial for the effective utilization of a crane hook. The primary aim of this study was to determine the most efficient cross-sectional crane hook among five distinct geometric profiles. This was achieved through the application of finite element analysis using Solidworks software. Subsequently, the identified cross-sectional profile was further examined using the Python programming language, taking into account the classical equation of a curved beam. The five cross-sectional shapes seen in the study were circular, rectangular, trapezoidal, I-shaped, and T-shaped. For the purposes of this investigation, the chosen material for each cross-sectional crane hook model was 34CrMo4 steel. Despite the identical boundary constraints imposed on all the chosen cross-sectional crane hook profiles, it was observed that the trapezoidal cross-sectional crane hook exhibited superior performance compared to the others. The trapezoidal cross-sectional crane hook model exhibited a von Mises stress of 202997600 Pa, with a corresponding factor of safety of 3.202. Further experimentation was conducted using Python to examine the trapezoidal profile. The results indicated that an increased level of parallelism in the inner side of the trapezoidal shape corresponded to a higher factor of safety. Hence, it is advisable to maintain the trapezoidal cross-sectional profile of the crane hook, with due consideration given to maximizing the length of the inner parallel side. The enhancement of design leads to a decrease in the likelihood of failure and the occurrence of undesirable accidents.\u003c/p\u003e","manuscriptTitle":"Identification of the Effective Crane Hook’s Cross Section","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-18 07:44:44","doi":"10.21203/rs.3.rs-3439199/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":"99a8db1c-5e8c-4f8c-9cae-c4b7eb8bc38f","owner":[],"postedDate":"April 18th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-05-01T00:36:05+00:00","versionOfRecord":{"articleIdentity":"rs-3439199","link":"https://doi.org/10.1016/j.heliyon.2024.e29918","journal":{"identity":"heliyon","isVorOnly":true,"title":"Heliyon"},"publishedOn":"2024-04-01 00:36:05","publishedOnDateReadable":"April 1st, 2024"},"versionCreatedAt":"2024-04-18 07:44:44","video":"","vorDoi":"10.1016/j.heliyon.2024.e29918","vorDoiUrl":"https://doi.org/10.1016/j.heliyon.2024.e29918","workflowStages":[]},"version":"v1","identity":"rs-3439199","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3439199","identity":"rs-3439199","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}