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Non-linear dynamic analysis is becoming more frequent important in structural design and assessing seismic activity of reinforced concrete elements. The overall shape, scale, and geometry of the building determine how it behaves during earthquakes. Progressive collapse is a phenomena that occurs when local deterioration to a key structural member results in entire or partial structural system failure. The approach can be used to investigate reinforced concrete structure behaviour, including force redistribution. In this work, G+10 storey buildings in seismic zone-III are evaluated and compared using Nonlinear two Time history and Pushover approach. Base shear, storey displacements, storey shear, overturning moment, reaction, shear force, bending moment, and time vs acceleration graph are tabulated, and the performance point is calculated using ETABS, which provides information about the structure's overall behavior. [ABSTRACT FROM AUTHOR]

The purpose of this study was to find out the behavior of castellated steel beams under flexural loads only and under the influence of flexural and torsional together as the castellation ratio increases, built-up castellated steel beams are a topic with little published information Moreover, even less research how these beams respond to varying capacity loads (flexure and torsion). The focus of our study is the response of double web castellated built-up steel beams to flexural loads alone and to flexural and torsion loads acting together and how castellation ratios influence them. Built-up double web castellated steel beams' behavior was studied by fabricating and testing six examples. Two symmetric concentrated loads were applied at the third-span points of three castellated steel beams for flexural stress testing. while the other three experienced a flexural and torsional strain simultaneously. The experimental results explained. The shear strength of built- up castellated steel beams decreased as the expansion ratio increased. The percentages of lowering ultimate load at the failure stage decreased when specimens were loaded under torsion and bending moments (11.1% and 26.6%),(16% and 25%) and The mid-span deflection of castellated beams increased as the castellation ratio increased. As well there is a decrease in the stiffness and increase in ductility of the samples when the castellation ratio in the double web increases under the influence of flexural and torsion compared with specimens under flexural only. It has also been observed that the twist angle is influenced by the castellated ratio, it has also been observed that the twist angle is influenced by the castellated ratio. [ABSTRACT FROM AUTHOR]

In this work, to evaluate the behavior of a single pile model under the effect of matric suction, it was embedded in soil with various saturation levels and subjected to a series of two-way lateral cyclic loading tests with different frequencies. By decreasing the water table to three distinct stages, three different suction zones were created in the partially saturated soil. The "soil-water characteristic curve" (SWCC) is the relationship between the gravity water content and matric suction. The pile model used is aluminum of 600 mm in length and 16 mm diameter embedded in (dry, unsaturated and saturated) sandy soil for comparisons. The pile model is under lateral cyclic loading (40N for 40 cycles) of various frequency values (0.05, 0.1 and 0.2 Hz). The study's findings demonstrate that the presence of matric suction greatly affected the pile model's displacement and bending moment. In comparison to saturated circumstances for the same relative density, there was a reduction in bending moments and lateral displacements of 12%, 23%, and 32% for the first, second, and third lowering of the water table, respectively. Additionally, under all saturation conditions, the increase in cyclic lateral loading frequency resulted in a 25% increase in displacement and bending moment. [ABSTRACT FROM AUTHOR]

This study examines the structural performance of different Elevated Storage Reservoirs (ESRs) under static earthquake conditions, focusing on Zone V, a severe earthquake zone, to provide water for human habitation and industry. The study analyses axial forces, bending moments, staging displacement, and horizontal bending moments in columns, beams, and tank walls, revealing significant structural variations among different shapes. This comparative analysis enhances ESR design philosophy for economical, safer, and cost-effective solutions, enhancing resilience in earthquake-prone areas for essential water supply. [ABSTRACT FROM AUTHOR]

The aim of this research is to assess the static responses of prestressed concrete skewed bridges under different types of loads which they were subjected on the bridges structure such as (dead load, post-tensioned load, vehicles load, thermal load, wind load, and loads combination). CSI Bridge Ver.24 was use for Finite element method analysis. Two load cases with three static responses (moment, stress, and deflection) were adopted for each bridge. These load cases were vehicles load case and loads combination case (service loads). There were two types of bridges whichwere selected in this study. These bridges were crossing the expressway of Al-Daura-Yusufiyah which were located in the south of Baghdad City (Capital of Iraq). The results of finite element static analysis explained that the value of positive bending moment, negative bending moment tensile stresses, compression stresses, and vertical deflections were lower than allowable values in ASSHTO LRFD-Bridge requirements of bridges, concluded that the cracks and deflections will not appear within structural members of bridges. The results of damage inspection process showed that there are not any damages which appear on the structural members for U-girder bridge. This study showed that u-girder bridge appeared lower values of vertical deflections than slab bridge. Therefore, it is suitable for construction for high traffic volume. [ABSTRACT FROM AUTHOR]

The importance of retaining wall is when the excavation depth is large from the ground level. It is even more threatening when the water table is present at a shallow depth. Hence a numerical analysis is preferable before commencing the work, to ensure the stability of the wall. A super-structure with 12 floors and 2 levels of the basement is proposed. The basement excavation is done by providing a secant pile as a retaining structure. For the given soil profile, a numerical analysis is performed. The displacement, shear force, bending moment and safety factor is studied. It is observed that the displacement increases with an increase in the depth of excavation due to a reduction in passive pressure and shear force. The depth of maximum bending occurred at a depth of 1.25 times the depth of excavation. The major advantage of doing the analysis is to ensure the safety factor; here the safety factor is well within the safe limit. [ABSTRACT FROM AUTHOR]

It is alarming that an overwhelming 35.46% of unmanaged garbage comprises plastic waste, amounting to 10,129,984 million metric tons. It constitutes approximately 15.6% of the total waste globally. Immediate measures must be taken to curb our plastic consumption and ensure its proper disposal to safeguard our planet. Even though plastic scrap is challenging to recycle, it harms the environment. Instead, using plastic waste as an addition to cement manufacturing becomes a good solution for the construction industry. Concrete's brittle qualities have an impact on the bending moment. Hence, adding fiber is a solution to this problem to improve the mechanical properties of concrete. Polypropylene is a thermoplastic fiber that can be added to strengthen the concrete's ductility and increase its compressive strength and bending moment value. Experimental tests are conducted to achieve this. f'c 25 MPa of compressive strength with a mixed design using polypropylene The compressive strength of the 15 cm x 15 cm x 60 cm fiber beam specimen increases significantly. The average compressive strength of the concrete mixture using PPF 0.7 kg/m3 was increased for fourteen days, reaching 27.93 MPa and 30 MPa for 28 days, respectively. Compared to regular concrete, compressive strength rose from 9.53% to 9.69%. The bending moment is increased, reaching 11231116.95 N.mm at 14 days and 13796629.6 N.mm at 14 days, respectively. Instead, it can reduce the workability of fiber concrete. [ABSTRACT FROM AUTHOR]

With the continuous development of the city, many new tunnels inevitably pass through the area near the existing tunnel, which may have a greater impact on the existing tunnel. In this paper, the finite element model reflecting the tunnel position is established by using ABAQUS software combined with dynamic simulation analysis method and Python language programming. The influence of the relative position of the new tunnel (L,α) on the deformation of the existing tunnel, the stress of the supporting structure and the ground settlement is studied. The results show that with the increase of relative distance (L), the convergence force, maximum axial force and bending moment of lining decrease gradually. When L is constant, with the increase of α, the convergence of the roof and floor of the existing tunnel increases, and the maximum ground settlement decreases. The maximum axial force and bending moment of the existing tunnel lining increase with the increase of |α|. This paper provides a reference for the rational planning and line selection of the tunnel. [ABSTRACT FROM AUTHOR]

The main ideal of this document is to Analyze and Design of a Multi storey structure applying a Software usually known as STAAD Pro and its cost prediction using a AI technique called Machine Learning. In this we are designing a multi storey building of G+12 which involves load calculations, sesmic load conditions and analysing of building by STAAD pro and also analyzing the building erect for chancing the bending moments, shear forces, deflections and also underpinning details for the structural members of structure(similar as shafts, columns & crossbeams) for developing the provident and sustainable design. For this design process we used Indian standard code books of IS 456-2000, IS 875 (Part 1,2,3,5). AUTOCAD software is used for development of plans and the plan is imported to staad pro and designed. The total height of the building is 39m and the area of the building is around 8000sq.ft consisting of 12 floors. This paper also introduces machine learning (ML) technology to optimize design costs. In our project we used linear regression algorithm. Linear regression relationships are modelled using a linear prediction function that estimates unknown model parameters from data. Data is given in form of datasets that comprises of attributes such as essential building materials and their cost according to the area, so that the future cost is predicted accordingly. The result obtained in trained model and the manual estimation is accurate. In this project we are calculating and comparing the cost of high rise, mid rise and dwarf buildings through machine learning as well as through manual estimation of the building. [ABSTRACT FROM AUTHOR]

In this study a simplified bilinear capacity curve of a frame structure is reconstructed by means of a limit analysis strategy based on the implementation of genetic algorithms. The proposed procedure takes into account the second order effects considering a post-yielding softening branch. In order to consider the progressive damage in the frame, the pre-yielding branch is determined with reference to a linear model where rotational springs are introduced in some critical sections of the frame. The calibration of the stiffness of each rotational spring is performed considering the bending moments at the corresponding section when the first plastic hinge in the frame opens. The results obtained through the proposed simplified strategy are validated with well-established approaches based on nonlinear static analyses, showing the reliability and the computational efficiency of this methodology. [ABSTRACT FROM AUTHOR]

This paper is proposed to numerically study effects of impact angle, impact position, posture, and height of pedestrian on kinematics and injury responses. A finite element human body model was employed to develop vehicle-pedestrian crash simulations. A 50th-percentile adult male (AM50) in standing and walking postures were considered. The human body model was set to impact a passenger car at its corner and at the centre of the bumper with 90° and 45° impact angles. Eight simulations were conducted. Since Asian pedestrians are usually smaller than their American counterpart, this paper also investigated the effect of pedestrian height by scaling down the AM50 model to a typical Asian height and weight. Four additional simulations were conducted. It was found that the impact position at the vehicle front-end affected the head impact location. Impacting at the corner position had high chance of head impacting the A-pillar which led to severe head injury. Impact angles also showed influence on the kinematics and injury response. Knee bending moment for the 45°impact angle was smaller than the 90°impact angle while bone bending was not much different. The 90° impact angle exhibited lower head injury criteria than the 45° impact angle. The results also revealed that different pedestrian postures led to some different kinematics with respect to the head impact location and speed. Pedestrian in walking posture exhibited more severe head and thorax injuries while the standing posture showed higher bending moment of the lower extremities. Finally, the human body model with Asian height exhibited higher risk of head injury than using AM50 data. The results of this study will be useful to vehicle manufacturers in designing a front structure of the vehicle and pedestrian protection systems. [ABSTRACT FROM AUTHOR]

The simulation of the injection molding process of semi-crystalline thermoplastics is widely used and commercially available. Typical use cases for process simulations are melt flow optimization, tool design and finding process parameter sets for the production. In recent years, injection molding simulations also provide the prediction of shrinkage and warpage. These simulations, however, neglect the variations in local mechanical properties caused by inhomogeneous solidification and the resulting locally different spherulites microstructure. In order to account for the locally inhomogeneous solidification and the resulting local microstructure, and hence to improve the precision of the warpage prediction, a multi-scale simulation chain is developed and presented here. The multi-scale simulation chain predicts the shrinkage on the part scale taking into account the mechanical property distribution, which is derived based on the local microstructure using a two-stage numerical homogenization scheme. The numerical homogenization is able to consider the local degree of crystallization, which is noticeable reduced in the surface layers of the component, resulting in a reduction of the mechanical properties. To show the applicability of the multi-scale simulation chain, an experimental validation is presented using injection molded plates with thickness steps. The final warpage is measured using a tactile measurement (Zeiss O-Inspect 442). The bending moment caused by warpage and relative magnitude are compared with the numerical results. [ABSTRACT FROM AUTHOR]

The purpose of this research is to compare the results of utilising the manual approach vs STAAD Pro to assess and design a roof for a circular water tank that is lying on the ground. Two groups were compared using a t-test based on an independent sample. Both groups, 1 (the control) and 2 (the experimental) each have 9 samples total (STAAD Pro). Using G power of 50 and alpha of 0.05, we were able to acquire an accurate sample size of 18. Manual and STAAD Pro were used for the analysis and design. Shear stress, bending moment (BM), and deflection were all tested using an independent t-test, and the results indicated no statistically significant differences between the groups (p-values of 0.25, 0.88, and 0.20, respectively; p>0.05). Since p>0.05, it may be inferred that there are no statistically significant differences between the manual and STAAD pro approaches to design. With less work, STAAD Pro produces outcomes that are on par with those of a solution developed in accordance with the requirements of the IS code. Thus, STAAD Pro is an effective tool for modelling, analysing, and designing lightweight buildings. [ABSTRACT FROM AUTHOR]

Comparative tests of glass and glass-basalt-plastic samples were carried out and quantitative values of the characteristics of strength, rigidity and durability were obtained. The glass and glass-basalt plastic samples differed in their technological manufacturing parameters, namely: filler nomenclature (samples made of glass fiber and samples made of glass-basalt fiber), winding modes (amount of filler to the total volume of content). The diagnostic results showed that the ratio of loads at which the samples have the same durability indicates the advantage of glass-basalt-plastic samples. This characteristic allows us to judge the load-bearing capacity of the sample. The purpose of this work was to determine the ring stiffness, strength and durability under loading conditions similar to the operation of a geophysical probe in an aggressive environment (temperatures up to 150°C, hydrogen sulfide up to 0.1%, hydrochloric acid up to 10%, cyclic dynamic axial loads, bending moment, high external pressure (up to 100 MPa). As a result of studying the loading process, the following results were obtained: the superiority of the strength characteristics of samples made of glass basalt fiber over samples made of glass was confirmed; the sample loading program has been adjusted to minimize the influence of residual deformations on the maximum force value; a hybrid material – glass-basalt plastic – was proposed as an alternative to glass, capable of maintaining load-bearing characteristics in the aggressive operating conditions of a geophysical probe. [ABSTRACT FROM AUTHOR]

There are innumerable methods for solving continuous beams, including the slope and deflection method, the moment distribution method, the flexibility matrix method, and the stiffness matrix method. Each method has its own identity. The final results of all four methods are shear force, bending moment, slope, and deflection. Even if all approaches yield the same result. The issue now is the time duration of those methods. One assessment should take approximately over thirty minutes to complete. Another issue is that the entire analysis will be repeated even if only one parameter is changed. Computer-based analysis is the best solution to all of these problems. Python is a computer programming language that has recently gained popularity due to its syntax simplicity. The code can be executed as soon as it is written in this case. A four-span continuous beam will be analyzed using Python in this paper, and the results will be compared to the conventional stiffness method. Initially, inputs are sent to Python using finite element procedures. The analysis is performed with Numpy, and the results are printed. Numpy is a Python library that is capable of performing all mathematical analysis, particularly on arrays and matrices. The analysis in this paper is carried out using Google colab as a plot form and Numpy as a tool. [ABSTRACT FROM AUTHOR]

This manuscript is about designing a glass wall cleaning machine on the outside of a high-rise building, where the walls are almost entirely glass. Previous cleaner design has many weaknesses than this product. This design includes the calculation of mechanical systems, DC motors, suction pads, construction, and control system circuits. The calculation and experimental data such as the Suction pad can withstand a maximum load of 35kg. From the DC motor test results, the time value is 5000 µs. It takes 5 seconds to rotate the cleaning cloth and move the vacuum foot. The highest deflection value and bending moment value occur when the loading point is in the middle. This product has better work time, power efficiency, and a bigger safety factor. [ABSTRACT FROM AUTHOR]

Research on the compression behavior of concrete has been widely carried out, on the other hand, information about the behavior of concrete in tension was limited. The existing concrete tension tests are the splitting, direct tensile, and rupture tests. These methods provide information on the tensile strength of concrete through concrete tension stiffening tests. This paper aims to elaborate on the experimental study to develop and construct the equation of concrete tensile strength based on the tension stiffening effect mechanism. The basic principle of this newly proposed method was the composite action between steel and concrete. The straight and continuous steel bar was embedded in concrete to ensure no eccentricity that could interfere with research data due to the bending moment. 45 Specimens made from cylinder concrete with 101.6 mm diameter and 450 mm length, steel bar embedded at the center of the section. Three concrete mixes with actual compressive strength of 31.66 MPa, 40.27 MPa, and 46.60 MPa and steel bar diameters of 15.9 mm, 18.7 mm, and 21.7 mm were used as variables. The test was performed by applying an incremental tensile loading at both ends of the steel specimen with a load rate of 5-10 kN/minute to obtain a force-displacement relationship. The curve must be lessened with steel bar response to get the load-displacement of tension concrete, and then by dividing load with concrete area and displacement with the length of both LVDT can be generated stress-strain of tension concrete. This study shows that the tension-stiffening effect is affected by the reinforcement ratio. Where the reinforcement ratio increases, the tension-stiffening decreases. The steel bar to concrete-area ratio higher tends to more cracks. The concrete tensile strength of this research is taken from the stress of the first crack indicates very close to the direct tensile test but slightly higher. [ABSTRACT FROM AUTHOR]

The objectives of this study are to inspect structural member of bridge to identify any damage in these members, to analyze the internal forces in designed and service stage by adopting static analysis, to determine bending moment, vertical shear force, axial force, tensile stress, compression stress, and vertical deflection under effect of dead load, prestressed load, moving load, temperature load, and combination of these loads, to evaluate the structural performance of bridge structure. Bata bridge was selected as case study in this study which was located in Babylon province near center of Hilla city. Ver. 24 is used in the analysis of bridge structure model for static. The inspection process of structural damages for bridge structure show that there are many damages in the old bridge especially in the concrete deck, expansion joints, and abutments structure. The results of analysis showed that the span No. 1 of bridge structure suffers from higher values of positive bending moment, tensile stress, and downward vertical deflection than others spans, and lower values of compression stress and negative bending moment. After improvement of prestressed tendons, the values of vertical deflection of bridge structure were decreased by more than 50% according to values before improvement. In general, the structural performance of old bridge structure need to improve by using some methods of repairing and strengthening to decrease the tensile stress and downward vertical deflection. External prestressing tendons is suitable method in the state of old bridge. [ABSTRACT FROM AUTHOR]

The article conducts an experimental study to investigate the opening effect on the capacity and behavior of built-up steel beams with corrugated webs. Five specimens were fabricated and tested under a two-point load, one of them without openings in its web (control specimens), while the other four specimens had openings at their maximum bending moment zone with various shapes of the same equivalent area (circular, rectangular, square, and rhombus). The results of load-deflection curves for all tested specimens were recorded; also, the distributed of deformation in control beam and around of openings was plotted using Digital Image Technique (DIC). The results show that the presence of an opening in the pure flexural zone of a beam negligible affect the beam's final carrying capacity compared with the control specimen and the difference between them is only in the form of mode failure in the beam. The specimen that contains one opening has more toughness because the load capacity is greater and shows less ductility. From this test, the circular opening is the best type of opening, while the failure shape of rhombus opening is the more dangerous. [ABSTRACT FROM AUTHOR]

Using steel jackets around reinforced concrete columns is a widespread technique for static and seismic retrofitting applications. The dimensionless interaction diagrams for reinforced concrete columns strengthened with steel angles are not attempted yet. Thus, this paper presents the formulation of dimensionless interaction diagrams for reinforced concrete columns strengthened with steel angles and strips. The axial loads and uniaxial bending moments are calculated using the plastic stress distribution method, and then the dimensionless interaction diagrams are generated. These diagrams enable analysis (estimation of the column load carrying capacity) and design (required amount of steel reinforcement) of such columns. Numerous examples are given to explain the Use of the new proposed diagrams. These examples have shown that the new proposed charts are straightforward in structural analysis and design applications. [ABSTRACT FROM AUTHOR]

In this paper comparison of shear force and bending moment of T beam deck slab having longitudinal girder and cross girder is done using courbon's method (manual analysis) and grillage model (using staad pro). Construction stage wise grillage model is prepared in staad pro. Bridge having carriage widths of 7.5 m have two types of live load as per IRC 6 i.e. Class 70R (W) and Class A-2 lanes. Static check of grillage model is compared with manual calculation having 0% difference. For dead load, shear force and bending moment of girder difference using manual calculation and grillage model comes out to be 0.64% and 2%. In manual calculation the reaction factor of an individual girder is calculated using courbon's method and multiplied with maximum bending moment. In live load calculation, for Class 70R (W), difference in bending moment for girder A, girder B and girder C comes out to be 26.45%, 4.78% and 28.66% but total moment difference is 0.05% while for Class A-2 lanes), difference in bending moment for girder A, girder B and girder C comes out to be 21.57%, 9.92% and 16.53% but total moment difference is 0.7%. So, from the result it can be seen that the total design moment of the girder comes out to be nearer using both the method while the girder wise difference in bending moment is found to be higher for outer girder and lower for inner girder. [ABSTRACT FROM AUTHOR]

Members of open double-symmetrical cross-sections are widely used in steel structures. In many cases their webs are subjected to transverse compression resulting from the effect of adjacent members or from the concentrated transverse loads. Resistance of the member web to transverse compression is affected by number of aspects, e.g. structural solution of the joint (welded or bolted with end plate), possible longitudinal normal stress in the member caused by axial load or bending moment, interaction with shear or effect of local buckling of the web. The paper focuses on specific problem of resistance of the web to transverse compression resulting from transverse load applied close to the unstiffened end of the member. The investigation of the resistance of the web to transverse compression is performed using advanced geometrically and materially nonlinear numerical analysis for various distances of the transverse load from the unstiffened end. The influence of this distance on transverse compression resistance is quantified. Rolled and welded cross-sections of various web slenderness are investigated. The results are, where possible, compared with results obtained from available design standards. [ABSTRACT FROM AUTHOR]

The article presents a method for calculating reinforced concrete floors using an approximation in the form of a cross-rod system. It is shown that the appearance of cracks in the concrete changes the bending and torsional stiffness of the floor elements. However, almost all software solutions for structural analysis account only for the change in the bending stiffness of the rod elements, as a result of the formation of cracks. The torsional stiffness, on the other hand, remains the same and does not change during the iterative calculations. As a result of this lack of consideration, the forces in complex statically indeterminate systems are obtained with errors. To eliminate this drawback, it is proposed to account for the change in the torsional stiffness of the rods as a result of cracking. Formulas are provided to account for the change in bending and torsional stiffnesses, due to the formation of cracks, as part of the iterative calculations of floors and cross-rod systems. It is shown that after calculating the cross-rod system, it is easy to account for the forces in a solid slab. The formulas for the transition from the bending and torsion of the rod system, to the bending and torsion of a solid slab are provided. A method for determining the reactions in the supports of the elements that are used in the calculation of rod systems, by the displacements method is provided, taking into account the variable stiffness along the length of each element. This, as a result, increases the accuracy of the forces being determined. Using a reinforced concrete cross-rod system with plan dimensions of 6000x6000 mm, as an example, it is shown that when the change in the torsional stiffness of the rods, due to the formation of cracks is accounted for, the torsional moments in the rods can vary by more than 260%, compared to the calculation without taking into account the change in torsional stiffness. Bending moments differ up to 20%. These results show that when designing statically indeterminate reinforced concrete systems, it is important to account for the variation in the torsional stiffness of the elements, as a result of concrete cracking. [ABSTRACT FROM AUTHOR]

The drawing method of diagrams "bending moment – curvature" that describe the cross-section stress-strain state of the reinforced concrete elements with consideration of an axial force is proposed in the article. Diagrams "bending moment – curvature" at different values of an axial force are shown. It is seen from the diagrams that compressive axial force increases the crack resistance of the cross-section but leads to the brittle destruction. The maximum bearing capacity of the cross-section is reached with application of the reduced axial force αN=0,4. Results of the reinforced concrete frame analysis with the usage of diagrams "bending moment – curvature" drawn with and without consideration of axial forces are compared with the results of the experimental research. Mistake does not exceed 1-2%. [ABSTRACT FROM AUTHOR]

The application of the numerical analytical method of boundary elements for solving problems of flat bending stability of thin-walled rod systems under any arbitrary combination of transverse loads is presented. The basic cases when the bending moment is zero and when it is constant are considered. A solution is also constructed for the case when clean bending takes place only in some part of the rod. In the considered cases the rod is hinged at the ends, which does not influence in any way the generality of the solution because of peculiarities of NA BEM; the difference will be only in expressions of constants of integration and fundamental functions of this or that problem. Numerical realization of the developed algorithm is shown on the example of an I-beam cross-section rod. The value of the minimum critical moment calculated in the paper is exactly equal to its value determined by S. P. Timoshenko's formula It is pointed out that this approach allows us to obtain the solutions of the complex problems of the theory of stability of thin-walled rods when restrictions on boundary conditions are removed, different transverse loadings and any structure of rod systems including frames and uncut beams can be taken into account. With an arbitrary law of bending moment change, it is proposed to replace this arbitrary law by a stepwise dependence, i.e., a system with distributed parameters is replaced by a set of systems with constant parameters. [ABSTRACT FROM AUTHOR]

This paper considers the application of the limit equilibrium method to the calculation of a double hinged circular arch loaded with a uniformly distributed vertical load. It is assumed that the arch has a rectangular cross-section made of a homogeneous elastic plastic material with different tensile and compressive yield strengths. The peculiarity of the limit state calculation is that the section works elastically until the transition to a plastic state of the entire section. If the action of the longitudinal force is not taken into account, in the limiting state a classical plastic joint is formed in the cross-section, which allows unlimited rotation relative to each other of the sections located infinitely close to the plastic joint. If the bending moment and the longitudinal force are taken into account simultaneously in the limit state, the possibility of unlimited rotation and unlimited linear displacement of the sections located infinitely close to the origin of the plasticity arises. In order to calculate the limit load for an arch, it is first necessary to obtain a dependence describing the strength area of the cross-section. This dependence relates the ultimate moment and ultimate longitudinal force for the section and is often referred to as the yield stress condition. In this paper the yield stress conditions for rectangular sections of arches with constant and variable stiffness are presented. Using yield conditions of the section and equations of balance of the arch it is possible to construct and solve an optimization problem for finding the minimum load which satisfies both equilibrium and yield equations. Thus, the target function of the problem is the value of ultimate load and the design variable is the coordinate of section which goes into the plastic stage. This problem was solved by means of spreadsheets. Also non-linear calculations of arches with constant and variable stiffness were performed in PC Lira-SAPR. Comparison of the calculation results showed their satisfactory convergence. [ABSTRACT FROM AUTHOR]

Hollowcore slabs are commonly used for floor and roofs of residential and commercial buildings. Extensive research has been done on precast structures, but only limited studies have been done on the cast-in-place diaphragm's tie-beams modeling aspects. This article presents a methodology of modeling precast concrete floor rigid diaphragm made of hollowcore slabs with the cast-in-place tie beams and evaluating its accuracy. two types of model were designed:1. whole rigid slab supported on two opposite sides only (one-way slab); 2. discrete slabs with parallel cast-in-place diaphragm struts. Designed load is q=1 t/m2, for in-plane rigidity analysis the lateral force P=1 t is considered. The study slab thickness is 120 mm. The concrete class concrete B25 (Eb = 30 MPa – tangent modulus of elasticity of concrete B25; E = 18.5 MPa – secant modulus of elasticity). The analyses were conducted using the LIRA-SAPR software package. The modeling process is illustrated in detail. The diagrams of bending moments and deflections are presented, comparison between the two models was done. Both methods give correct results, reflecting the actual structural action of the precast concrete hollowcore floor. [ABSTRACT FROM AUTHOR]

Bridge construction design on this design used a prestressed PCI concrete I-Girder. The span of bridge was 40 m which is consist of 3 spans with total length for 120 m. The calculation of the analysis for the structure depends on the structural type. For this design, the bridge was assumed to be indeterminate static which the bridge reactions are more than 3. The internal forces of I-Girder consist of shear forces and bending moment which can be get by simulate the bridges loading that related to the bridge structure. The software for designing the bridge structures and obtained the internal forces value are using SAP 2000 software and manual calculation method. The internal forces data was obtained by calculating the girder structure using manual calculation and analyze using SAP2000 software and be compared by the values. The internal forces is taken at 20 m, 30 m, and 40 m span of girder to be compared the difference value of manual calculation and software analysis using regression line. [ABSTRACT FROM AUTHOR]

Properly designed stiffening walls should reduce displacements (eccentricities) and safe transfer of horizontal shear forces to the foundation. The load may be caused by the action of wind on structures or the uneven subsidence of the ground. Although the stiffening elements ensure the geometric constancy of entire buildings, there is still no clear-cut regulation allowing the distribution of loads between the individual stiffening parts. In the literature, it is most often recommended to determine the values of shear forces and bending moments in proportion to the structure's stiffness - however, there are no clear guidelines for its determination. The total stiffness method (presented by the authors at the WMCAUS 2021 conference) estimates the stiffness of solid stiffening walls and walls with openings. The wall stiffness is calculated as the reciprocal of the total wall displacement under the action of a horizontal load. The equivalent stiffness is the sum of the stiffnesses of the masonry fragments. The necessity to divide the wall into components is most often due to the presence of window or door openings. There are horizontal lintel strips and vertical stiffening fragments in the plane of each wall. The shear wall can be calculated in two static schemes - fixed on both sides or cantilever. In calculations, the height of the vertical wall fragments is most often taken as the total height of the pillar based on the building geometry. Such an assumption would be valid only in the linear-elastic range of the building's behaviour. However, the cracking stresses in the masonry structure account for about 30% of the value of failure stresses. Cracks and damage to the wall, which may appear even at low stresses, cause a rapid decrease in the structure's stiffness. Experimental studies confirm that cracks and damages increase width before the building is destroyed under a horizontal load and cover an increasingly more extensive wall area. The actual height of the vertical pillars, and thus the total stiffness of the shear wall, is different than in the calculations that do not take into account the effect of the reduced stiffness. The paper proposes an experimental determination of the height of vertical inter-hole pillars in the stage before cracking the central part of the wall. Based on the author's research on a single walls and small building (low rise) with an uncomplicated shape, the actual height of the vertical fragments of the stiffening walls was analyzed. The test walls and building consisted of autoclaved aerated concrete (AAC) masonry units. The analyzes were devoted to monotonically loaded masonry structures. A hydraulic actuator applied the horizontal load at the level of the slab. The reduction of the height of vertical piers assumed in the calculations was based on the analysis of the walls cracking morphology and patterns. [ABSTRACT FROM AUTHOR]

In the present paper a program THINWALLRES is explained to obtain the elastic and plastic resistance of thin walled HVH sections under many combinations of the internal forces: axial force N, shear forces Vz and Vy, bending moments My and Mz, bimoment B, warping torsional moment Tw (= Mxw) and Saint Venant torsional moment Tt (= Mxs). The program THINWALLRES can at the moment solve various HVH-sections (H – Horizontal upper flange, V – Vertical web, H – Horizontal bottom flange), i.e. I-sections and H-sections that can be monosymmetrical, channel sections and Z-sections. The background of the theory is briefly explained. The results provided by the program are the elastic normal stresses, shear stresses and von Mises stresses due to any combinations of eight internal forces. The plastic stress distribution under given internal forces, plastic factor and up to ten different interaction diagrams combinations may be obtained with THINWALLRES. The results in the form of diagrams are helpful in the safe and economic design of metal (steel and aluminium) thinwalled members of the Classes 1, 2 and 3. [ABSTRACT FROM AUTHOR]

The analysis of the influence of random initial imperfections on the static resistance of a hot-rolled steel beam with IPE cross-section is presented in the article. The resistance of the investigated IPE beam is exposed to the effects of lateral-torsional buckling resulting from the bending moment acting about its major principal axis. The resistance of the hot-rolled steel beam is studied using global sensitivity analysis. Initial geometrical and material imperfections are considered as random variables in the determination of the variability of the resistance. The SHELL finite elements and geometrical and material non-linear computational methods of the ANSYS software are used for the evaluation of the resistance. Sensitivity analysis is used to examine the influence of initial imperfections and residual stresses on the resistance (model output). The variance of the model output is evaluated using the Latin Hypercube Sampling method. The sensitivity order of the imperfections based on their influence on the resistance is then determined in the presented case study. [ABSTRACT FROM AUTHOR]

The analysis of flexural behavior of RC beam is accomplished by using Graphical User Interface (GUI) developed in software called MATLAB.MATLAB is algorithmic software that will be used to simulate the problem statement using an algorithm. MATLAB is a high-performance numerical computation and visualisation software package. Shear force diagrams and bending moment diagrams are more necessary to analyse beam because they serve as the foundation for studying beams developed stresses and deflections. MATLAB is a powerful and flexible tool for computational and graphic analysis that can be used as convenient software for beam analysis by generating shear force diagrams and bending moment diagrams for any type of beam based on loading and support conditions. In this current study, Graphical User Interface (GUI) in MATLAB has been built to generate and assess SF diagram and BM diagram for simply supported beam packed with point load and uniformly distributed load. This study is also concerned with conducting non-linear finite element analysis on reinforced concrete beam by developing MATLAB code to find stress distribution, damage behavior and load displacement response. The GUI in MATLAB code is used to develop a quick and efficient method of analysing the reinforced concrete beam. [ABSTRACT FROM AUTHOR]

The problem of plane strain pure bending of a plate made of a linearly elastic–perfectly plastic material with a through-the-thickness gradient of strength properties and tension-compression asymmetry is considered. The gradient of strength properties was produced by accelerated one-sided cooling of the plates made of A32 ship steel from the austenitic temperatures. The purpose of the present work was to analyze the effect of various approximations of the strength gradient on the accuracy of determining the critical bending moment corresponding to the complete yielding of the sheets. [ABSTRACT FROM AUTHOR]

The performance of any multi-storey building hinges on the arrangement of the structural entities. Recently some static and dynamic Linear Analysis and Non-linear Analysis of the building framed structure has been carried out. The most significant characteristics are the Size, shape and geometrical arrangement of the multi-storey frame on which the structural configuration rests. This paper examines those arrangements that have been functional for the dynamic analysis of Steel-Concrete Hybrid and irregular structures. The study, brief out multi-storey composite structures and irregular structures analyzed for seismic loadings considered for many different software's like STAAD-PRO, ETABS, SAP, LS-DYNA, etc. for altered seismic regions across the world. Also, this study describes a study of multiple types of analysis like collapse simulation analysis, pushover analysis, structural performance analysis using finite element-based software. This study covers several different types of anomalies for the responses due to dynamic vibrational loadings and Blast loadings. The relative variables examined, include; bending moments, base-shear, storey drifts, storey-shear, shearing load, Torsional-moment for Beam, column and foundation at different directions. [ABSTRACT FROM AUTHOR]

The paper deals with dynamic response of cylindrical steel reinforced concrete tank subjected to earthquake loading. When a tank containing liquid vibrates, the fluid filling exerts additional hydrodynamic pressure together with hydrostatic pressure on solid domain of the tank. Dynamic analysis of a liquid–filled tank can be done using the concept of generalized single – degree – of freedom (SDOF) systems representing impulsive and convective modes of vibration of the tank – liquid system. The dynamic response of cylindrical tank subjected to earthquake loading are total base shears, total bending moment and total overturning moment. [ABSTRACT FROM AUTHOR]

The paper studies pure bending of a strip (beam) containing through crack which is perpendicular to its axis and asymmetrical about the one. One of the crack tips is in the compressive stress zone and crack faces are in smooth contact near it. The other one is in the tensile stress zone and there is a striplike plastic zone on the crack prolongation line near this tip. The solution is reduced to linear conjunction problems using methods of complex analysis and complex potentials. The length of crack faces contact zone, the length of crack tip plastic zone and crack tip opening displacement are evaluated. Their analytical solution is found. The system of transcendental equations for calculating the length of crack tip plastic zone and parameter, that characterized the length of crack closure zone are established. Formula for calculating the crack tip opening in noncontact tip and dependencies for the stress tensor components on the line, where the crack located are wrote. Numerical analysis of crack tip opening in her noncontacting tip and the length of crack tip plastic zone from reduced external load and location of crack center relative to the axis of the strip (beam) is done. The parameter, that characterized the length of crack closure zone doesn't depend from external load is find numerically and a simple formula for its determination is given. The critical value of the bending moment of fracture of the beam (strip) with the contact crack is estimated based on the δк-model of fracture of crack bodies. [ABSTRACT FROM AUTHOR]

The use of shotcrete in tunnels is common. Durability is one of its most essential qualities. Application speed, cost-effectiveness, and socioeconomic considerations are all important factors to consider. The space here between façade of the trench and the shotcrete lining, the velocity of excavation, and other factors must be noted in the tunnel that has already been excavated. The ideal shotCrete thickness for these models was determined using axial force and bending moment interaction plots for different short depths. The findings of this inquiry, and also the method used, may be applied to the design of mining canal supports and civil engineering tunnels of various sorts. [ABSTRACT FROM AUTHOR]

The paper provides a detailed analysis of the work under load structures of clamp scaffolds and systematizes the features of considering loads and impacts when performing strength calculations. The article analyzes the stress-strain state of free-standing forests. An algorithm for calculating free-standing forests is proposed, considering the features of structural schemes of blocks that are not specified in the normative literature. Based on the results of the analysis of data from a series of numerical experiments, constructive measures are proposed to ensure the load-bearing capacity, rigidity and stability against overturning of spatial blocks of free-standing forests, which will allow installing blocks with a height-to-size ratio exceeding 3,5:1 in open areas (outside buildings and structures) without attachment to existing structures. Considering the eccentric connection of scaffolding elements leads to a complex deformation of columns (oblique eccentric compression), i.e. to increase in the resulting bending moments up to 100%. Using of diaphragms in the design of free-standing clamp scaffolds blocks reduces the displacements of the block nodes by up to 16% in comparison with blocks without a diaphragm Another feature of scaffolds is that they are used for not only classic buildings and structures and for the maintenance and repair of various space stations and aircrafts. [ABSTRACT FROM AUTHOR]

Piles in offshore structures are vulnerable to lateral loads induced by high wind effects in coastal regions in addition to axial loads from the dead weight of the structure itself. Earthquakes are another source of lateral loads on piles in structures like bridges, dams, and high-to moderate-rise buildings. This study addresses the effect of soil properties around the pile on the structural design criteria (bending moments, shear forces, displacements, and lateral earth pressure) in the piles under combined effect of axial and lateral loads. Two soil types were considered in this study; clay and sand with different stiffnesses for each. The study revealed that the maximum bending moment and maximum shear force induced within the pile sections increases as the soil stiffness increases for both of sand and clay soils. The study revealed that piles embedded in clayey soils exhibits an average higher buckling capacity than in sandy soils. The buckling load in clayey soil surpassed that of the sandy soil by a factor of 20. The study has also incorporated determination of the buckling loads for piles embedded in clayey and sandy soils. [ABSTRACT FROM AUTHOR]

In a composite steel beam, the reinforced concrete slab adds to increased ultimate strength of the composite section when bending and torsion forces are combined Six non-composite and composite reinforced concrete slabs with (rolling section) castellated steel beams were employed in this study. Three non-composite steel beams and three composite beams with RC slabs and varied degrees of castellation (λ) were isolated from the specimens at 0%, 25%, and 50% respectively. The specimens were put through their tests under the impact of bending and torsion forces. This study documents and discusses the overall behavior and reaction of the tested specimens. The ultimate strength, load at cracking, failure mechanism, and load/deflection relationship at midspan of each tested steel beam were all measured. The concrete slab contributes to raising ultimate load by (4.26) % for (λ=0 percent), (9.21) % for (λ=25 percent), and (15.45) % for (λ=50 percent) according to the experimental data. The influence of castellated ratio on composite and non-composite steel beam girder behavior is noticed, with the non-composite section with solid steel beam (λ=0%) having a higher ultimate load than the other sections. The composite solid beams (λ=0%) have a higher ultimate load than the composite section with castellated steel beam. [ABSTRACT FROM AUTHOR]

In recent years, the increasing size of merchant ships demands more precise calculations of global ship hull strength. Hence, accurate prediction of the wave-induced loads more significantly the vertical bending moment in violent seas has become inevitable for structural strength design. To develop an accurate prediction method, more detailed wave-induced local pressure distribution on the whole wetted surface of the ship hull needs to be calculated to obtain the integrated value of the vertical bending moment. For that purpose, some ship hull models are used in this study i.e. slender and blunt Wigley, and bulk carrier models. The 3-D linear frequency domain potential flow method is used to compute the wave-induced pressure and motions of a ship with forward speed in waves. We confirm the promising results of the integrated value of vertical bending moment in comparison with the real ships of bulk carrier model either from experiments and computation methods. In conclusion, this program is fast and reliable to compute the global ship hull strength at a preliminary design stage. [ABSTRACT FROM AUTHOR]

The effect of Soil-Structure Interaction (SSI) on the structural response of circular footing is studied. Linear behavior of soil is considered in the study. Initially, a building frame is analyzed using STAAD Pro. and a circular footing for the central column is designed manually. The circular footing is modeled as a 2-D (or) area element and FEM analysis is carried out using ANSYSl. Four-noded isoparametric element with six DOF at each node, is adopted for discretizing the circular footing model. The greater bending moment at the face of the column was observed in comparison to the conventional design. The SSI is induced by assigning modulus of subgrade of soil as elastic foundation stiffness which resembles Winkler's foundation model. Due to the effect of SSI, it is observed that the maximum bending moment of the circular footing at the face of the column is decreased and hence resulting in the requirement of the lesser area of main reinforcement. Therefore, SSI leads to the economical design of circular footing. Further reduction in bending moment and main reinforcement area is noticed for the square footing of equivalent area. [ABSTRACT FROM AUTHOR]

The aim of this research work is to study the most important parameters that affect the loading capacity and behavior of elliptical ring reinforced concrete beams with (L) section. Twenty specimens were modelled using ETABS Software to study the effect of changing the length of the major axis (while keeping the ratio of the major to minor axis equal to 0.64), width, height, thickness, and loading type. The maximum values of negative bending and torsional moments in addition to midspan deflection increase by 1.24-8.24%, 1.33-11.43%, and 32.5-131%, respectively when the major axis of beam increases by 20-60%. Whereas, major axis increase leads to decrease the maximum positive bending moments and load capacity by 5.91-4.45% and 26.5-52.9%, respectively. That happens due to the extending of span length that happened because of major axis increase. When the beam height increases by 25-75%, the maximum positive and negative bending moments (M+ve) and (M-ve), torsional moments and load capacity increase by 33.92-102.4%, 33.92-100%, 29.84-89.74% and 38.8-116.6%, respectively. While this increase in height leads to maximum deflection decrease by 5-8.4%. That happens because the beam sectional area increases due to increasing beam height. M+ve and M-ve, load capacity and midspan deflection decrease by 0.33-7.9%, 1.61-1.1%, 4-20%, and 11-30%, respectively when beam width increases by 46.6-140%. While this increase in width leads to torsional moment to increase by 2.15-0.87%. The sectional area of beam increases because of width increase, i.e., additional strength capacity. When thickness of beam increases by 100-500%, M+ve, M-ve, load capacity and maximum deflection decrease by 4.25-18.8%, 2.3-16.2%, 7.4-37% and 19.8-67%, respectively, whereas the torsional moments increase by 1.42-0.12%. Finally, torsional moments increase by 0.68-1.49 %, respectively due to testing through partial or full uniform load by 20-100% length of span. [ABSTRACT FROM AUTHOR]

The current work presents a study on strength and behavior of reinforced concrete T-section elliptical ring deep beams through the finite element technique. The parameters that were taken into consideration are diagonal axis (major axis) with the same major axis to minor axis ratio, height, flange thickness, web thickness, and compressive strength of concrete. It is found that the maximum values of positive bending moment (Mmax+ve), maximum negative bending moments (Mmax-ve), maximum torsional moments (Mmaxtor) and deflection increase by about 0.12-0.77%, 1.86-4.9%, 1.9-3.77% and 22.7-77.9%, respectively when the beam diagonal axis increases by 16-50%. Mmax+ve, Mmax-ve, Mmaxtor and load capacity increase by about 68.43-135.3%, 71.13-142%, 61.89-123.8%and 71-142%, respectively when the beam height increases by 50-100%. While the increase in height leads to decrease in the maximum deflection by about 4.62-5.33%. Mmax+ve, Mmax-ve, load capacity and max deflection decrease by about 0.38-4.04%, 1.135-6.25%, 1.51-6.06%, 13.5-30.9%, respectively when the flange thickness increases by 100-200%. While the increase in flange thickness leads to increase in the Mmaxtor by about 0.57-0.42%. Mmax+ve, Mmax-ve, Mmaxtor, load capacity and max deflection increase by about 210.4-446.8%, 156.63-374.9%, 216.5-494%, 215.4-469.2% and 82.4-129.8%, respectively, when concrete web thickness increases by 50-100%. Mmax+ve, Mmax-ve, Mmaxtor, load capacity and max deflection increase by about 15.69-42.49%, 15.78-41.62%,15.81-41.7%, 16.92-44.61% and -0.37-0.37%, respectively, when concrete compressive strength increases by 33.33-100%. [ABSTRACT FROM AUTHOR]

Vertical space expansion is common amid rapid development and limited space in dense urban areas, which causes the widespread use of high-rise buildings and underground spaces. A contiguous pile wall (CPW) is an alternative reinforcement to overcome the complexity of underground structures excavation due to space limitations. This reinforcement is easy to implement and relatively does not disturb the surrounding environment. This study discusses a parametric analysis of basement excavation with contiguous pile wall (CPW) reinforcement using finite element (FE). The parametric analysis focuses on comparing the effect of variations in excavation depth (He) and the ratio of excavation dimensions (L/B) on lateral displacement (Ux) and bending moment (Mx) behavior of CPW reinforcement in 3-D and 2-D conditions. Analysis was performed on a 3-D model using Rocscience RS3 and 2-D with RS2. The model is determined as a square excavation on dry silty clay soil. The diameter of the pile (d) used is 0.80 m, with the spacing between the piles set at 1.00 m. The wall penetration (D) is adjusted based on the variations of the excavation depth (He). The results show that the depth (He) and dimension ratio (L/B) of the excavation had a significant effect on the lateral displacement (Ux) and bending moment (Mx) of the pile. Increasing the depth of excavation (He) tends to increase the lateral displacement (Ux) and bending moment (Mx) of the pile, although the wall penetration (D) also increases. Simplification of the deep excavation model under 2-D conditions due to analysis limitations tends to give overestimated values of lateral displacement (Ux) and bending moment (Mx) compared to 3-D analysis based on variations in depth (He) and dimension ratio (L/B) of excavation, although the behavior of the 3-D excavation model with dimension ratio (L/B ≥ 4) is close to the behavior of the 2-D plane strain model. [ABSTRACT FROM AUTHOR]

Bar elements pretensioned by unbonded steel reinforcement placed in narrow ducts are considered in this paper. Such elements find one of their main applications in the field of post-tensioned reinforced concrete. One of the main features of the post-tensioned concrete beams is an interaction between pretensioned strand and rest of the construction body which appears like a distributed balancing load. Increasing of the beam deflection leads to tensioning force change in its strands. This affects to the balancing load that in turn differs the subsequent deflection increasing. Analysis of influence of changing balancing load to equilibrium of cross sections of simply supported post-tensioned reinforced concrete beam has been made in the proposed article by methods of applied mechanics of materials. It is shown that increasing deflection of the beam and corresponding growth of balancing load are compensated by bending moment caused by eccentrical compression of the beam. [ABSTRACT FROM AUTHOR]

In this paper, the application of light gauge steel to composite plate structures was studied experimentally. The light gauge steel section was intended to replace reinforcing bars on the reinforced concrete structures. Observations were conducted for 6 specimens. They were 3 specimens of conventional reinforced concrete structures and the other 3 specimens of composite light gauge steel and concrete ones. All of the specimens had a typical dimension of 300 mm width with 3 variations of the section depths: 80, 100, and 120 mm. The specimens were positioned on the simple supports with a 2000 mm effective span length. Two-point loads loading scheme was subjected to the specimen. The load increased monotonically until the ultimate condition was obtained. The delayed first crack was found on the composite specimens, while on the reinforced concrete, it occurred at the earlier stage of loading. Different types of ultimate conditions were found: compression failure on the uppermost fiber of composite specimen, crack on the pure bending moment and shear spans. As expected, the ultimate load increased linearly as the plate depth increased. Effect of different cross-sectional areas and material's grade between reinforcing bars and the light gauge steel section was considered to obtain equivalent the ultimate load from two different types of the specimens. [ABSTRACT FROM AUTHOR]

In view of the active development of computer-aided computing technologies with software tools for a wide range of engineering tasks, it becomes urgent to choose reasonable and proven methods of calculation that take into account the specific nature of the structure, and comparisons of results. The article considers the features and results of the calculation of the sheet piled quay wall (anchored bulkhead with one level of land tie), obtained using two commonly used specialised programs (CAD Hydrotechnika and PLAXIS 2D) as well as graphically using the example of the refurbished wharf. The main parameters analysed were maximum bending moments and force in the anchor traction. The analysis of the results showed that there was a significant variation in the values of the main parameters, which indicated that more research was needed to identify the reasons for the discrepancy and, if necessary, to correct the calculation methods and algorithms and to verify them. [ABSTRACT FROM AUTHOR]

The article considers the issues of calculating beams on an elastic base consisting of an upper Winkler layer that allows structural deformations and a lower layer that represents an elastic half-plane. To determine the deformations of the lower layer, the Vlasov-Kantorovich variational method was used. A special case of using the first term in the decomposition of the function of vertical displacements of points of the lower layer is considered. The change of vertical displacements along the thickness of the layer is analyzed. The beam calculation is constructed in the form of the method of initial parameters. The expression for the deflection function of the beam is obtained and its calculation for the action of the concentrated force is performed. The value of the bending moment in the middle of the beam is analyzed depending on its rigidity and the parameters of the base. It was found that he values of the moments in the calculation of the beam on the elastic half-plane are higher than in the calculation using the proposed combined model. The approximate variational Vlasov-Kantorovich method allows us to construct various computational schemes of the elastic base. The proposed combined model of the elastic base has great computational flexibility and allows to obtain solutions in a wide range of internal forces in the beam. [ABSTRACT FROM AUTHOR]

The article is devoted to the lateral-torsional buckling of elastic beams loaded with a potential moment. Such problems were previously investigated in a linearized formulation. The prebuckling deformations of the beam is not considered in this setting. We use the nonlinear geometrically exact beam theory and an exact non-linear solution in our article. The exact spatial stability functional and stability equations are obtained by the variation calculus. The exact value of a critical moment for the cantilever beam was obtained. [ABSTRACT FROM AUTHOR]