Bending Moment Diagram Research Articles

Investigation of BFRP bar reinforced geopolymer concrete filled BFRP tube columns

An experimental investigation was carried out on a novel type of concrete-filled tube column, which used geopolymer concrete and basalt-fibre-reinforced-polymer reinforcing bars and confinement tube. Geopolymer concrete was used in place of ordinary Portland cement concrete to counter the sustainability challenges of conventional cement manufacture. Longitudinal basalt-fibre-reinforced-polymer bars were used to replace steel reinforcement to avoid corrosion, while basalt-fibre-reinforced-polymer tube confinement was used to replace the conventionally used steel helix to enhance strength and ductility. Compressive load–deformation behaviour of 200 mm dia., 800 mm high specimens under concentric, 25 mm eccentric, 50 mm eccentric and four-point bending loads was experimentally investigated. Experimental axial load–bending moment diagrams were then produced. Although geopolymer concrete is normally considered to be more brittle than Portland cement concrete, the test results showed that the specimens with geopolymer concrete were more ductile compared to those with Portland cement concrete. It was also found that increased load eccentricity resulted in ductility enhancement in specimens with both types of concrete with basalt-fibre-reinforced-polymer bars and tubes, while steel-reinforced specimens suffered loss of ductility with increased load eccentricity.

Architectural form finding in arboreal supporting structure optimisation

Sustainable Development Goals have become a key factor in the design in the twenty-first century. The relationship between the architectural and structural systems is becoming a matter of relevance for sustainable design. The search for minimum material consumption can be seen by drawing inspiration from the solutions found in Nature. The high efficiency of natural forms, has become a contribution to research on tree-like structures. The purpose of the research was to identify the main aspects of arboreal supporting structures shaping and optimization at the early state of design. The methodology is to optimize the geometry of dendriforms, based on optimizing the shape of the bending moment diagram and adjusting it to the shape of the final bar structure. The primary conclusion of the studies indicates that the structural and architectural optimization, implemented in an early stage of designing might significantly improve material consumption without substantial changes in architectural appearance.

Mathematical modeling in the problems of the geodesic control of the stressed-formated state of the gas pipelines at above-ground parts

Geodetic methods of monitoring the stress-strain state of gas pipelines in the areas of overhead pipeline crossing involve obtaining discrete data on the deformation of its axis in the form of a set of three coordinates (x, y, z). For their elaboration a mathematical model of the experimental-theoretical method of geodetic control of gas pipelines’ SSS is proposed. The simulation process was performed on the basis of geodetic discrete data, based on which, using the Lagrange interpolation polynomial, the equation of the line of bending of the axis of the gas pipeline was obtained, which allowed to pass further to the bending moments along the entire span. The accuracy of the proposed method has been estimated, which showed that the obtained bending moment diagrams reflect the SSS of gas pipelines with an accuracy of 1.5% in the central part of its span, and with the approach to the peripheral sections the error increases to 6%. It is shown that the obtained expression of the maximum bending moment allows us to form the required number of additional equations for the disclosure of a statically indeterminate system of "gas pipeline-support", taking into account the possibility of fastening on stretch marks. The mathematical model is presented aimed at decomposition of overburden gas pipeline structures, which allows to model the SSS at each of the spans separately within the integral structure.. It is established that additional stretch marks reduce the maximum bending stress by 22%, and in case of loss of one of the stretches of the bearing capacity of the gas pipeline SSS increases by 11.1-14.8% depending on the previous stretch tension. The proposed mathematical model for the processing of discrete data forms the basis of the experimental-theoretical method of geodetic control of the gas pipelines’ SSS, taking into account their structural and technological factors.

Degree of Curve for Bending Moment Diagram Cantilever and Simply Supported Beam Carries an U.V.L

Degree of Curve for Bending Moment Diagram Cantilever and Simply Supported Beam Carries an U.V.L

Heuristic Catenary-based Rule of Thumbs to Find Bending Moment Diagrams

There are numerous nature-inspired curves representing certain structural behaviour being utilised in form-finding process by some famous architects. By closely scrutinising these forms, some interrelated morphological analogies between different structural forms and functions, such as the similarity between free-standing tension-only elements and the shape of bending moment diagram of a beam under the same load condition, can be explored. Most studies in the field of statics principles have only focused on developing numerical and mathematical approaches which are not suitable for practitioners who prefer quick access to the general forms. This paper first gives a brief overview of the most common archi-structural forms through the history of the architecture, and attempts to find the shape of bending moment diagrams through a new simple heuristic method based on drawing an analogy between natural tension-only forms and the diagrams. The purpose of this research is to propose a shortcut to diagram drawing substituting the general time-consuming methods as well as enhance the architects' perception of bending behaviour of a structural element. A holistic approach is utilised, integrating the natural curves, bending moment diagrams and some rule of thumbs used to define the tapered beam or portal frame general shapes. This simple non-computational method can ease the design process. It will also be useful for educational purposes as well as pre-design phase conception including identification of the critical points of bending elements as well as designing tapered beams and portal frames.

Study on the bending moment diagram of straight and inclined pile groups in saturated sands with different thicknesses

Study on the bending moment diagram of straight and inclined pile groups in saturated sands with different thicknesses

Programming for solving plane rigid frame based on MATLAB

Based on the idea of the matrix displacement method, this paper designs a program which can be used to solve the internal force of the continuous beam and rigid frame with MATLAB. It mainly demonstrates how to design a program to realize the matrix displacement method with MATLAB. In addition, some techniques are included in order to realize the correspondence between the manual calculation and the computer calculation, such as “Using lambda to locate”, “Crossing out rows and columns” and visual design. Therefore, based on the structural mechanics, combined with the principle of matrix displacement method, this paper shows the whole process from inputting the information of the rigid frame to solving the internal force of the rigid frame to outputting the bending moment diagram using MATLAB as the programming tool.

BeamBending: a teaching aid for 1-D shear force and bending moment diagrams

BeamBending: a teaching aid for 1-D shear force and bending moment diagrams

Design and Analysis of State Transport Utility Vehicle-Bus

Passenger transport is an inseparable ingredient of public transport system for developing and developed nations. In present work design and analysis of state transport utility vehicle ~ bus is carried out. Present paper focuses on the design enhancements in structural features of sub and superstructure without any alterations on the chassis provided by OEMs. Limiting dimensions of bus as prescribed by automotive industry standard and central motor vehicle rules are the design constraints accounted in the present work. This work was commenced with the thorough study of sub and superstructure configurations, seat locations, passenger load patterns, locations of doors, windows and emergency exits and other relevant bus attributes. Hand calculations for evaluation gross section modulus of chassis and cross member combination are presented. Usage of shear force and bending moment diagrams to evaluate the stress and deflection for the proposed load patterns is made before proceeding for finite element analysis. Finite element modelling and analysis of the sub and super structure combination is carried using shell elements with the presumption that chassis of the bus is rigid. Roll-over analysis of bus for the present configuration is presented.

Numerical fundamentals and interactive computer graphics system for the nonlinear analysis of planar frames

Abstract Recent scientific and computational advances have facilitated the analysis of slender structural systems subject to instability. With the employment of more sophisticated numerical tools and algorithms, it is possible to accurately determine the critical points (limit and bifurcation loads) as well as the post-critical behavior of the structural system. In the computational context, efficient data structures are needed to enable code and graphic interface expansion for the generation of models and visualization of the results obtained. Thus, an interactive object-orientated graphic computational system is presented herein. It has been developed using MATLAB/GUI, with pre-processing, analysis and post-processing capacities for planar structural frames. The nonlinear finite element developed and implemented for the structure modeling is formulated considering second order effects. Therefore, with the computational tool presented, the geometric nonlinear effects and stability of the structural system can be directly addressed, and the visualization of the numerical results are accessed through interactive controls that permit data inclusion and analysis verification. The engineer-designer can see the structural model discretization, the equilibrium path, its deformation configuration, the force and bending moment diagrams at the moment that he runs the program and in each load step. It is also possible to export the images, videos or tables of the obtained numerical results. The example presented demonstrates the capacity of the developed graphic computational system.

Engineering representations guide student problem‐solving in statics

AbstractBackgroundEngineering students inconsistently apply equilibrium when solving problems in statics, but few studies have explored why. Visual cognition studies suggest that features of the visual representations we use to teach students influence what domain knowledge they use to solve problems. However, few studies have explored how visual representations influence what problem‐solving strategies and domain knowledge students of different levels of expertise use when solving problems that require them to create and coordinate multiple representations.Purpose/HypothesisThis study addressed the following research question: How do students with different levels of expertise coordinate their problem‐solving strategies, problem‐solving heuristics, and representation features when sketching their shear force and bending moment diagrams?Design/MethodWe conducted think‐aloud interviews while students sketched shear force and bending moment diagrams. These interviews were subsequently analyzed using the constant comparative method to examine the effect of representations on students' problem‐solving approaches.ResultsThree themes emerged from the data: Students used heuristics that are based on perceptually salient features to sketch their shear force and bending moment diagrams; students across levels of expertise rely on the object translation heuristic rather than equilibrium problem‐solving schema to sketch and reason through their shear force and bending moment diagrams, and domain knowledge aids students' ability to resolve conflicting heuristics. Our findings suggest that students primarily rely on heuristics triggered by representation features they notice.ConclusionsStudents engaged with shear force and bending moment diagrams not as a way to describe systems that are not accelerating but as a series of representations that “should go to zero” or arrows that make things “not zero.”

Buckling resistance of steel H-section beam–columns: In-plane buckling resistance

Buckling resistance predictions resulting from flexural and flexural–torsional buckling of double tee section members subjected to compression and bending are considered. A novel analytical model is developed for establishing design criteria based on decomposition of the member buckling behaviour into in-plane and out-of-plane resistance. The former is based on second-order bending relationships of load effects of structural members with in-plane equivalent imperfections, while the latter is based on the stability theory of thin-walled open sections. First part of this study presents an analytical formulation of the in-plane buckling resistance of beam–columns. In this regard, further decomposition is postulated for the in-plane first-order bending moment diagram that results in the loading state to be the superposition of two components. The first component is related to symmetrical loading and the second to antisymmetric loading. To consider the second-order effects, prebuckling displacements generated by the abovementioned loading components are amplified with regard to the inversion of the residuum of the buckling force utilisation ratio in order to obtain approximate values of second-order displacements and internal moments. As a result, the in-plane interaction curve, expressed in dimensionless coordinates, that describes the beam–column in-plane flexural buckling resistance without considering lateral–torsional buckling effects, is obtained. The results of nonlinear finite element simulations are used for the verification of the developed analytical formulation. It is concluded that this proposal yields less conservative predictions than those based on the interaction relationships of clause 6.3.3 of Eurocode 3, Part 1–1.

Interaction diagram based method for fire resistance design of eccentrically loaded concrete-filled steel tubular columns

Previous investigations have highlighted that the current design method in Annex H of EN 1994-1-2 for the calculation of fire resistance of slender concrete-filled steel tubular (CFST) columns was unsafe, which led to the appointment of a Project Team (SC4.T4) by the European Committee for Standardization (CEN) to develop a new Annex H in EN1994-1-2 to replace the existing one. This paper presents the outcome of the Project Team, a new simplified fire design method for CFST columns, focusing in particular on eccentrically loaded columns for which there had been no systematic research. An extensive parametric study consisting of 5046 analysis cases has been carried out, covering all the practical ranges of application of CFST columns. The method accounts for minor and major axis eccentricities with large eccentricities up to e/D = 1. Different bending moment diagrams, ranging from single curvature to double curve bending, were considered. The proposed new design method is in line with the cold design method in EN1994-1-1 and achieves the criteria of acceptance for safe and accurate design of structures in fire which were set by the CEN/TC250 Horizontal Group Fire.

Analysis For Force And Deformation Of The Pile And Wall Interaction Based On Three Methods

This paper adopts: 1. Li Zheng deep foundation software; 2. Equivalent Beam Method; 3. Midas GTS NX. As to the study of pile-wall interaction structure, how to distribute the horizontal load based on the three methods. The results of comparative analysis show that there are consistency in the distribution discipline and trend of bending moment diagram and shear diagram obtained by the three methods. The piles in row bear most of the horizontal earth pressure and the basement exterior wall can reduce the thickness. In addition, the technology has a wonderful engineering economy and can provide reference for future engineering applications.

Parametric study on austenitic stainless steel beam-columns with hollow sections under fire

This research work presents a parametric numerical study on the resistance at elevated temperatures of stainless steel members, subjected to combined bending and axial compression. Previous studies have shown the need for the development of further research works aiming at better predicting the fire behaviour of stainless steel beam-columns. However they have only considered beam-columns composed of stocky I sections. Hence, this paper focuses on austenitic stainless steel (European grade 1.4301 also known as 304) beam-columns composed of square hollow sections (SHS) and circular hollow sections (CHS), considering different cross-sections classes (1 to 4), according to Eurocode 3 (EC3) classification.The numerical analyses were performed using the finite element program SAFIR, with material and geometric non-linear analysis considering imperfections. The influence of the following parameters was evaluated: bending moment diagram shape, cross-section slenderness considering the local buckling occurrence on the thin-walled sections, and member slenderness for the global instability due to flexural buckling.Comparisons between the obtained numerical results and the interaction curves of Eurocode 3 are presented. The results show that specific design approach should be developed for these stainless steel members under fire situation, taking into account the above mentioned parameters.

Oscillations of a statically indeterminate system with a finite number of degrees of freedom (the experience with the application of mathematical packages in the technical university course of mechanics)

Symbolic mathematics packages give the opportunity to execute the difficult symbolic transformations with use of computer, abandoning graphic methods. The resilient weightless beam fixed by resilient links and carrying two concentrated masses is considered. Instead of building the bending moment diagram and the later use of Vereshchagin's method for disclosure of static indeterminacy, the equation of distribution of the bending and single moments along the beam length is written, and Mohr's integral is calculated.

Study on Bearing Capacity of Prestressed Pipe Pile Foundation Under Horizontal Load

Background and Objective:Prestressed high strength concrete pipe pile (PHC) shows brittle fracture when subjected to more than its own bearing capacity. Therefore, the non-prestressed steel bar is added to the PHC pipe pile, that is, the mixed reinforced pipe pile (PRC). The mechanical behavior of PRC group piles and PHC group piles under horizontal force is studied, and the bending moment diagram and displacement diagram of the pile body are compared so as to find the weak parts.Material and Method:In this paper, Φ600 pipe piles are chosen, and the PRC pipe piles are made of non prestressed steel bars of the same number as the prestressing steel bars, and the two steel bars are spaced apart. Referring to a specific project of Binhai New Area, the geological parameters are used, and the force analysis of group piles under horizontal force is carried out by using the ANSYS software.Results:ANSYS simulation results show that, under the horizontal loading, when the number of piles in group piles is different, the locations of maximum bending moments are different. Increasing the number of the PRC pipe pile with non prestressed reinforcement can effectively reduce the maximum bending moment of the pile body.Conclusion:Under horizontal load, with the increase of pile number and the pile cap aggrandizement, the position of maximum moment of pile body is shifted from 5-8 times diameter of pile to the top of pile. When the pile number reaches a certain amount, the maximum bending moment will appear at the joint between the pile cap and the pile body. At the same time, increasing the non prestressed steel bar does not influence the bending moment, and the reinforcement of the pile cap and the pile top should be strengthened.

Spatial distribution of Winkler spring stiffness for rectangular mat foundation analysis

Structural design of mat foundations of buildings is often done by performing static analysis of a slab resting on vertical uncoupled Winkler springs. It is already well established that the simplifying assumption of a uniform modulus of subgrade reaction throughout the mat foundation leads to inaccurate results that significantly underestimate the bending moments in the mat. This paper examines the spatial variation of the Winkler spring stiffness constants that is necessary for the mat-on-springs analysis to produce the same slab deflections and bending moment diagrams as finite element analysis that treats the soil as continuum. For this purpose, three-dimensional parametric analyses of slabs resting on elastic soil are performed using the finite element method for various values of soil elastic properties, slab geometrical characteristics and column load configurations. The finite element analysis results were used for back-calculating analytically the equivalent Winkler spring constants at each node of the mat. Based on the numerical results, equations describing the spatial distribution of spring stiffness are proposed. The performance of the proposed equations is compared against existing spring stiffness spatial distribution approaches used in practice.

Behavior of Steel Welded Tapered Beam-column

Steel structural elements with variable cross-section, made of welded plates, are largely used in the construction industry for both beams and columns in accordance with the stress and stiffness demand in the structure. These types of elements are mainly used for the design of single storey frames with pitched roof rafters and pinned column base. Rafters and columns can be designed as tapered members made of steel welded plates, respecting the bending moment diagrams for gravitational load combination. This paper deals with experimental tests performed on tapered beam-columns elements, subjected to both bending moment and compressive axial force together with analytical investigation.

Theory and software introduction of bending moment diagram for calculation and analysis of suspension bridge

This paper reveals the corresponding relationship between the geometric shape of the cable and the bending moment diagram of the simply supported beam under the vertical load of the suspension bridge cable, which can be called the bending moment diagram theory in terms of the elastic theory, deflection theory and finite displacement theory of the suspension bridge structure analysis and calculation. Because the bending moment diagram of simply supported beam is convenient, intuitive and clear in concept, it can greatly simplify the structural analysis and calculation of suspension bridge, and is an accurate analytical solution. The cable shape calculation software of suspension bridge is compiled according to the bending moment diagram theory, which can calculate the empty cable shape and the completed bridge shape under the action of suspender force, and introduces the software function and use method.