Stress Distribution in Cantilever Beams with Different Hole Shapes: A Numerical Analysis

Currently, cast steel beams are used extensively due to their many structural applications and serviceable performance due to the distinctive and significant properties they have, such as light weight, high strength, and the ability to withstand various weather conditions and temperatures. Along with other crucial qualities, it has rather modest economic costs. The fabrication of 'cellular' beams, which are lighter deeper sections, from structural sections. These sections are made by rewarding hot rolled steel sections that have been sliced into deeper beams with a sequence of circular holes. The pieces can be made into quite big holes through which services can travel, and they are structurally sound. Cellular girders are better suited for use in practical applications as long-span secondary beams than girders without slots because the shear capacity of a beam is frequently significantly reduced by slots. The openings where shear stresses are very high can be strengthened by filling them in or using horizontal stiffeners, allowing them to be created for use as primary members. Utilizing fabricated sections, a distinct design for cellular beams allows for the selection of the flange widths, web thickness, and depth to best match the applied loads and opening dimensions. Fabricated cellular beams are more effective for heavily loaded primary beams because the web thickness may be easily increased [1-3].

Numerous researchers have proposed various techniques in various studies to investigate the magnitude of stresses and deflections in curved beams under various loading situations [4-6]. While many research studies took into account bending and stretching simultaneously, for instance [7, 8]. Ghuku and Saha [9] in this article by merging the bending and stretching loading states, a curved beam with a geometric cutout in the shape of a circular hole was modeled for the primary LS. In the study [10], polished beams adopt a tapered shape and have circular openings on their surface. These openings have various diameters. The findings of this study indicate that the ideal diameters and opening spaces for each of the span lengths in order to achieve the lowest pressure and displacement are different. In the studies [11-14], beams were the subject, and cantilevering beams were created by giving the beam a tapered shape. Results from these studies show that the tapered shape is very ideal for cantilever beams because the internal bending and shearing force of the supports, which creates the specific load, is concentrated only in the region close to the support because the cantilever beam is fixed by only one support. In the study [15], a novel kind of cell bundle with sinusoidal apertures was investigated and contrasted with conventional circular apertures. Three beams with various opening sizes were chosen. In order to determine the final values of the force, this study first set out to identify the patterns that result in the failure of these beams. The experimental findings provided valuable qualitative and quantitative data that can be used to better understand and predict the behavior of the cellular bundles that contain the sinusoidal openings. The numerical model that was created and tested performed well in predicting the experiment's outcomes. Additionally, it may be used as a tool to produce complementary results in order to build an analytical model. Nowadays, cellular beams are used extensively in steel construction, and in actual field applications, they are the most widely used long-span system. Whereas this new variety of these cell bundles demonstrated a mechanical behavior with regard to bending resistance that is almost identical to that of openings with open rectangular shapes [16]. It is much harder to identify the critical regions surrounding circular openings than those that are rectangular or hexagonal, where it appears that the corners are the critical regions [17]. Numerous studies, in particular the study [18], presented significant findings through a study based on finite element technology, which was used to develop a new and ideal method for reliable design in order to confirm the capacity of these cell bundles with circular openings to withstand various stresses in addition to bending resistance. In the study [19], the influence of hole diameter with hole place on the lateral torsion behavior of cantilever beams was investigated. Imperforated sample and perforated sample were two different sets of samples used in this study. Based on the findings, it was determined that the diameter of the hole and its place have an impact on the lateral bending behavior, particularly for short beams. Seven different web opening shapes circle, square, pentagonal, and hexagonal were utilized in this article. using the finite element technique to build models [20]. The results demonstrate that displacements and different stresses are significantly influenced by the type and shape of openings on the surface of the sill. In the study [21], the ANSYS program was used to perform static and dynamic analyses of the cast steel beam section in order to compare the deflection, stress distribution, and shear stress. The outcomes under a consistent light load are significant.

Recent research has looked into the possibility of using FRP composites, such as CFRP sheets that are externally bonded pile, to strengthen RC beams with large longitudinal holes [22]. CFRP strips that are cemented to the surface area [23]. Many studies have compared the use of conventional and modern composite materials, which are used in many fields, including aviation, construction, industry, and other fields, in order to obtain an engineering structure that is distinguished by light weight and has the same resistance to stresses and strains that appear on it as a result of carrying different loads. These studies made mention of these subjects [24-30].

Seven Beams models will be created in the current work, the first model without holes and the other sixth models having holes of different shapes (square, triangular, circular, hexagonal, and rectangular). The ANSYS program will be used to solve it using the finite element technique. Along with the weight of the beam itself, a combined load of bending load and additional load in the form of torque will be imposed. The results will be compared to the displacements, stresses, and strains that occur in the five models, with the first model without holes, after loading. The models with holes all have the same weight, making it possible to select the model with the best efficiency among the five when compared to the first model without holes.

The following topics will be continued in the article: Models shapes and dimension, Materials selected, Results and discussion, Path results. Conclusions, Recommendations and future studies, and References.

Table 1. Mechanical characteristics of the models [31-33]

The results of loading the seven models with various loads and of analysing the finite element technique results using the ANSYS program allow us to draw the following conclusions.

(1) To create a safe design, every engineer creating a mechanical design for a component must understand when to use the von mises stress ($\sigma_{ {von }}$) and keep its value less than the yield strength ($\sigma_{y}$) of that material. Using this theory, we note that the yield stress ($\sigma_{y}$) with a value of (370MPa) was equal to the phonon von Mises stress ($\sigma_{ {von }}$) for the first and third models. Using this theory, it was found that the third model (with rectangular openings) was superior to the rest of the models when compared to the first model because its value was the same in both models (370MPa).

(2) According to the maximum shear stress theory, a material will start to fail or give way to failure if its maximum shear stress is equal to or greater than its yield stress value in the uniaxial tensile test. When this theory is applied to the results, we can see that the shear stress values of the seven models were lower than the metal's shear stress yield, which was (370MPa). The second model, with a value of (62.7MPa), was the best one.

(3) The values of the other six models show an increase of varying percentages when compared to the value of the deflection in the first model. This is evident when comparing the values of the first model with the remaining models. These results show that, based on the deflection, the second model is the best and the fifth model is the worst.

(4) The seventh model is the best of all the models, according to the results of the highest values of stress intensity in the seven models. The value of stress intensity was the lowest among the seven models, reaching (261MPa), while the highest value of stress intensity was in the first model, with a value of (294MPa).

(5) The principal stress limit theory is based on the idea that inelastic behavior or failure is controlled by the normal stress limit. The maximum principal stresses ($\sigma_1, \sigma_2$) of the design criterion may not be greater than the working stress ($\sigma_{y}$) of the material. Without fail, this condition must be met ($\sigma_1, \sigma_2 \leq \sigma_y$). From the results obtained for the highest principal stresses values ($\sigma_1, \sigma_2$) for the seven models, and compared with the metal yield stress value ($\sigma_{y}$) to achieve the safety condition ($\sigma_1, \sigma_2 \leq \sigma_y$). It can be seen that this condition is met only by the second, third, seventh and seventh models.

(6) Another conclusion is that all models function safely under maximum strain energy theory, where the value of the principle normal stresses ($\sigma_1, \sigma_2$), were ($\sigma_{M-1}=56 \mathrm{MPa}$, $\sigma_{M-2}=19 \mathrm{MPa}$, $\sigma_{M-3}=111 \mathrm{MPa}$, $\sigma_{M-4}=119 \mathrm{MPa}$, $\sigma_{M-5}=49 \mathrm{MPa}$, $\sigma_{M-6}=89 \mathrm{MPa}$, $\sigma_{M-7}=119 \mathrm{MPa}$), and fulfilling the condition of this theory $\left(\sigma_1^2+{\sigma_2}^2-2 \mu \sigma_1 \sigma_2\leq{\sigma_y}^2\right)$ and this suggests that the seventh and seventh models are the two best models, according to this theory.