Force Diagram Research Articles

Application of mathematical modeling for calculation of dock structures of the spillway construction of the Krasnodar reservoir

The article deals with modern issues of the application of mathematical modeling taking into account the changing parameters of the reliability of the final resource of the dock structures of the spillway construction of the Krasnodar reservoir. Hydraulic structures of the pressure front of the Krasnodar reservoir are designed and built as structures of the II capital class. Analyzing the performed mathematical modeling, we see that the sections in the wall are “dangerous” at the place where it adjoins the bottom. To perform static calculations, we select a strip with a width of 1 linear meter in the longitudinal direction. Authors apply all types of loads acting on the structure of the strip of the cross-section of the structure and determine the forces in the dangerous sections of the wall and bottom. The main one is the calculation of the structure in the transverse direction. To construct diagrams of bending moments and transverse forces in the bottom plate, with the worst-case scenario of the structure, during mathematical modeling, a model of the dock structures of the spillway construction of the Krasnodar reservoir was built and later various emergency situations under the influence of seismic loads were calculated.

Postcritical Behavior of Nonlocal Strain Gradient Arches: Formulation and Differential Quadrature Solution

Arches are important components in nanostructures and systems. Because of the remarkable strength of nanomaterials, nanoarches are slender, thus enhancing their vulnerability to geometric instability, such as buckling. Although molecular simulations are often employed to analyze nanostructures, their use in routine analysis/design is formidable due to prohibitively exhaustive computation. Equivalent continuum models were developed as alternatives. The buckling and postcritical phenomena of the classical arch also form an important benchmark problem in nonlinear mechanics. This study investigates the buckling and the postcritical behavior of nanoarch subjected to inward pressure using nonlocal (NL), strain gradient (SG) continuum theory. The governing equations are derived in the form of a sixth-order nonlinear integrodifferential equation, unlike the fourth-order for a classical arch. The equation is then solved numerically using a differential quadrature (DQ) with appropriate boundary conditions. An incremental-iterative arc-length continuation is employed for the solution of the resulting algebraic system of equations. The equilibrium paths are traced for the possible instability modes, such as symmetric/antisymmetric bifurcations, snap-through and limit point instability, ascertained with the internal-external force diagrams. A particular instability mode is triggered at a certain threshold/range of the slenderness ratio of the arch, which is significantly influenced by the NL and SG interactions. These interactions not only cause quantitative changes in the instability behavior but also lead to qualitative changes, such as cessation, shift, and conversion of modes, more prominently for SG arches. Similar to classical arches, the prebuckling nonlinearity is shown to be significant.

Study on hybrid fibre reinforced UHPC beams under single and repeated lateral impact loading

This paper investigates the dynamic response of hybrid fibre reinforced ultra-high performance concrete (UHPC) beams against single and repeated low-velocity impact loads. A brief description of the drop weight impact tests on the UHPC beams was presented first followed by the development of the material and structural model in finite element analysis. A plasticity-based concrete material model with validated compressive and tensile strength surface and damage algorithm was adopted for hybrid fibre reinforced UHPC material. Based on the test results, the bond-slip behaviour between steel rebar and UHPC matrix was developed in an empirical form and incorporated in the model. Compared to the model with the bond-slip definition, the model with perfect bonding was found to underestimate the maximum mid-span deflection, which highlighted the necessity of considering the bond-slip behaviour in dynamic analysis where large deflection occurs. The repeated impact tests were performed numerically, and the results were validated with experimental data. A parametric study was then performed to investigate the effect of key parameters, including different impact energy and the same impact energy but different impact numbers. The results indicated when the total energy increased, the repeated impact loads became more hazardous than the single impact load. With the validated model, the dynamic shear force and bending moment distribution diagrams were compared to study the failure mechanism in single and repeated impact loads.

How does student skill on interpreting circular motion situation change in an online physics classroom?

High-school physics has become challenging to many teachers after their classrooms were moved to an online platform. How to teach effectively is concerned when students struggled to grasp the concept learning in the online classroom. Circular motion is the topic that the students could not understand the content well while concentrating on the screen. This work aims to investigate the achievement of using peer instruction to teach the first three steps of circular motion problem solving strategy. These are (i) identify the path of motion and its radius, (ii) draw a free-body diagram, and (iii) find the force components acting on the object. The approach was implemented to an online physics classroom with 12 high-school students. The result was analyzed from pre- and post-test data, and student practices during the teaching. The finding showed that there were more students who could interpret the circular motion situation correctly than at the beginning of the class. The path of motion and the forces acting on the object could be identified, and some students could find the centripetal force correctly. Moreover, their interaction in the class related to the of their understanding of the topic.

Marketing Risk Path Identification of Small and Medium-sized Energy Enterprises Based on ISM-MIMAC

To explore the path identification of marketing risk factors in small and medium-sized energy enterprises, this study extracts 16 factors influencing marketing from 3 aspects of the external environment, internal management and information feedback through literature analysis and expert interviews. In this paper, the interpretative structural model (ISM) is used to construct the multi-level structural diagram of influencing factors and the influencing factors are divided into three layers: direct factors, intermediate factors and fundamental factors. Then the matrix impact of cross multiplication applied to classification (MICMAC) is used to analyze the factors affecting the risk of small and medium-sized energy enterprises, and then the driving force and dependency classification diagram of marketing risk factors is drawn. The results show that the dependence and driving force of financing risk, partners, marketing personnel and other factors are relatively weak, and risk treatment can be prioritized. The factors such as lack of policies, sudden factors and organizational structure have high driving forces, which are the key factors that constitute the marketing risks of energy enterprises, and should be focused on. This study takes the marketing risk factors of small and medium-sized energy enterprises as the research object, and the research results have certain universality, which can provide new solutions for small and medium-sized energy enterprises to face marketing risks.

Analisis Rancangan Rangka Kompor Hemat Energi Berbahan Bakar Air

Analysis of the design of this energy-efficient stove for distributing the results from the HHO (Hydrogen Hydrogen Oxygen) generator and turning this HHO into a fire. The purpose of this analysis is to determine the strength of the stove frame with the maximum load it can accommodate. This stove is made with a design and structure that is larger in scale with new innovations that combine metal materials and concrete materials where the two materials are combined to create a sturdy and strong stove structure, the structure of this stove is innovated from the stove in general. The result of the force diagram shows that the bending stress of the weld seam is smaller than the allowable stress of the material, namely: wb = 8, 03×10-3 180 N/mm2. Therefore the stove is safe to use.

Experimental and numerical study on the impact resistance of ultra-high performance concrete strengthened RC beams

To enhance the impact resistance of built reinforced concrete (RC) members, the effectiveness of using ultra-high performance concrete (UHPC) for strengthening RC structures was investigated in this study. The mechanical properties of UHPC were evaluated by the uniaxial compression, tension and flexural bending tests. Drop weights with hemispherical and wedge-shaped indenter were adopted to impact the beam specimens with and without UHPC strengthening. A total of six beams, including three control RC beams and three UHPC jacketed RC (RC-UHPC) beams, were tested. The beams were prestressed in the axial direction with a 200 kN force. The test results revealed that the UHPC jackets improved the structural impact resistance. With an impact mass of 411 kg and an impact velocity of 4.95 m/s, the maximum and residual deflection of the RC-UHPC specimen decreased by 15.3 % and 21.1 % as compared to the RC control specimen, and the failure mode shifted from diagonal shear failure to flexural failure. To further investigate the dynamic responses of the beams, a detailed finite element model was established and validated with the test results in terms of the impact force, structural deflection and damage profile. The dynamic shear force and bending moment distribution diagrams were numerically derived to examine the failure mechanism of the test specimens. Finally, a parametric study was conducted to evaluate the effect of different impact locations and UHPC jacket length on the impact resistance of strengthened RC beams.

Pushover Analaysis of Irregular Tall RCC Structures

The paper is based on the study of the Response of Irregular Plan Tall RCC structures by Pushover Analysis in order to find the Base Shear, Pushover Curve, Performance limit, Shear force Diagrams, Bending Moment of the structure. Nonlinear Static Analysis, is also called as “pushover analysis”, and is also regarded as the most widely used analysis method for estimation of performance of Irregular tall RCC structures. Most of the significant Seismic Codes which proposes methods for seismic analysis of new or existing tall RCC Structures have been originally defined for simple regular structures. Therefore the analysis of the seismic response of irregular Tall RCC Structures is difficult due to nonlinear and inelastic response of the structures and more difficult than that of regular structures. Most of the codes (IS 1893 (Part 1) 2016[1], ATC-40 1996[2], EC8-1 2004[3]) uses the concept of “regularity”, taking into account distribution of mass, stiffness and strength in the structures, both in plan and in elevation. But real structures seldom act in accordance with these regularity requirements, resulting in a narrowly dependable application of the basic non-linear static analysis. For the study we are considering two G+19 storey T shaped and U shaped irregular tall framed RCC structures having height of 68 meters each and storey height of 3.3 meters. Pushover Analysis is carried out using shear walls at different locations in the structure. The objective of this study is to finds out which irregular plan tall structure is the most efficacious in resisting lateral loads. The software used for modelling and analysis is ETABS 2017.

Meclib: Dynamic and Interactive Figures in STACK Questions Made Easy

Abstract—Making and interpretation of drawings and schematics is an important skill to be developed in engineering education. The question type STACK in the Moodle learning management system combined with the interactive graphics library JSXGraph has a great potential for implementation of e-learning resources addressing these skills in formative and summative settings. The authoring process of such materials is complex due to multiple markup and programming languages like HTML, LaTeX, Maxima and JavaScript (JS) being involved. The Meclib concept mitigates this complexity and allows for efficient bulk production of material with consistent appearance and user experience. The core of Meclib is a set of pre-defined JSXGraph-based objects with an interface to Maxima, such that no problem specific JS code is required at all. The present paper outlines the basic ideas of the implementation and demonstrates the approach for some typical examples of different complexity. The focus is on applications in engineering mechanics, starting from static illustrations up to an editor for free body diagrams, with rich adaptive formative feedback.

A new approach for the computation of design shear force in reinforced concrete walls subjected to seismic loads

SummaryThis paper investigates the dynamic shear amplification in reinforced concrete shear walls designed according to the seismic provisions of the current Turkish Building Earthquake Code (TBEC‐2018). Shear walls with a high ductility level and different aspect ratios are examined to evaluate the design shear force calculated by using the dynamic amplification factor (βv) and overstrength factor (D) defined in TBEC‐2018. For this purpose, response spectrum analyses (RSAs) are first carried out on two‐dimensional cantilever shear walls with heights of 30, 45, and 60 m and with lengths of 1.5, 3, and 4.5 m in the plan. Then, a total of 198 nonlinear time history analyses (NLTHAs) are performed with real and simulated ground motions matched to the elastic design spectrum defined in TBEC‐2018. The comparison of the design shear forces obtained from RSA and the shear demands obtained from NLTHA along the heights of the walls reveals that the design shear forces calculated according to TBEC‐2018 may underestimate the actual shear demands from studied ground motions. Moreover, the applicability of the updates proposed to TBEC‐2018 for the design shear force and shear force diagram along the wall height in reinforced concrete shear wall‐frame systems to cantilever shear walls is also examined.

Design and Dynamic Analysis of a 2 Dual Axes Solar Tracking Mechanism

This paper describes the implementation of general multibody system dynamics on sun tracker mechanism. In this study, a dual axes solar tracking mechanism designed within the scope of a project to obtain an efficient electrical energy from solar rays is examined. Dynamic and kinematic calculations of the moving and joint places in the mechanism were made. This study is important as the use of an efficient solar tracker is very useful in military, industrial and residential areas. Free Body Diagrams of all the elements or limbs that make up the sun tracker mechanism have been drawn. Thus, dynamic and kinematic values at elements points were calculated. The proposed dynamics model of the mechanism offers an accurate and fast method to analyze the dynamics of the mechanism knowing that there is no suchwork available for sun tracker. Also, 3D tracker elements were drawn and planned in Solid Work program. The simulation gives a clear idea about energy parameters for different link lengths of the mechanism over a linear displacement.

Hydrodynamic modelling of a multi-body wave energy converter using the Moving Frame Method

Significant wave energy conversion may be achieved with multiple floats with several modes of motion combining constructively to generate power. With the M4 system, power take off is at hinges to absorb resulting pitch motions. Complexity increases with number of floats and conventional vectorial multi-body dynamics may be conveniently replaced by the recently formulated moving frame method based on the calculus of variations to avoid free-body diagrams and joint reaction forces. Furthermore by utilising group theory to gather spatial rotations and angular velocities in a common structure, the obtained notation is general and straight-forward to apply for single and multi-body systems. This paper lays the foundations for incorporating hydrodynamic forces into the moving frame method. The method is applied to 3, 6 and 8 float cases in regular and irregular waves with results compared to the vectorial method and experimental measurements, showing close agreement. It is suggested that this is a more natural and general approach for complex multi-body, multi-hinge hydrodynamics systems.

On designing plane-faced funicular gridshells

Concepts from isotropic geometry, Timoshenko’s shell theory, Airy stress functions and Maxwell’s reciprocal diagrams are combined in the design of plane-faced funicular gridshells. The notions of self-Airy and mixed-Airy gridshells are introduced, with an emphasis on self-tied gridshells. This paper extends the work of J.C. Maxwell for 2D pin-jointed trusses to 2.5D gridshells with the addition of a new reciprocal figure called the slope diagram. The form, force and slope diagrams are combined by a mixed area calculation to produce another new figure called the Maxwell-Mondrian diagram. A powerful new design process leveraging the relationship between the gridshell geometry and the Airy stress function is presented.

Ensemble Force Spectroscopy of a G-Quadruplex Cluster on a Single-Molecule Platform.

Single-molecule methods offer high sensitivities with precisions superior to bulk assays. However, these methods are low in throughput and cannot repetitively interrogate the same cluster of molecular units. In this work, we investigate a tandem array of G-quadruplexes on a single-molecule DNA template with a throughput of at least two orders of magnitude higher than single-molecule force spectroscopy. During mechanical unfolding by optical tweezers, the array of G-quadruplexes experiences identical force, temperature, and ionic conditions, which not only reduce environmental noise but also render unfolding transitions indistinguishable among individual G-quadruplexes. The resultant ensemble behaviors are analyzed by scanning force diagrams, which reveals accurate F1/2 values, where 50% of G-quadruplexes are unfolded. Independent of the number of G-quadruplexes (n > 15) contained in a cluster, F1/2 can effectively evaluate G-quadruplex ligands in a new method called differential scanning forcemetry. When the same G-quadruplex cluster is subject to a series of constant forces in force-jump experiments, unfolding rate constants of G-quadruplexes can be effectively evaluated as a function of force. The high precision demonstrated in all of these measurements reflects the power of repetitive sampling on the same cluster of single-molecule entities under identical conditions. Since biomolecules such as DNA, RNA, and proteins can be conveniently incorporated in a tandem array, we anticipate that this ensemble assay on single-molecule entities (EASE) provides a generic means of ensemble force spectroscopy to amalgamate the accuracy of ensemble measurements with the precision of single-molecule methods.

Understanding Students’ Free-Body Diagrams Using the Metarepresentations Survey for Physics

Study purpose. The Metarepresentations Survey for Physics (MSP) was developed to assess students’ metarepresentational knowledge during physics problem solving. Materials and methods. The survey was given to 288 introductory-level college physics students. Psychometric properties of the instrument, including construct validity, were evaluated by confirmatory factor analysis and Rasch analysis. Results. We also examined students’ beliefs about the use of free-body diagrams, as well as thoroughly examined the link between students’ problem solving success and free-body diagrams. Conclusions. We recommend the use of the MSP for physics instructors and science education researchers who want to evaluate students’ free-body diagrams. Additionally, we suggest the subject of physics can be replaced with chemistry, genetics, or another science to assess metarepresentations in other domains.

Finite Element Method for Analysis of Off-Center Connected Continuous Beams

The study of the structural elements goes through the premise of their centric support and centric connection. In reality, it is common to see elements with different cross-sections connected by offset axes, for example to align some of their edges, or those that are supported with off-center supports. Such inter-element eccentricities and off-center supports leads to a change in the stress-strain state from the traditional ones known from the available literature and university textbooks. In previous publications with participation of the author, exact nonlinear and approximate analytic solutions of similar problems for beams under various loading, support and connection conditions have already been published. The finite element method provides an approximate approach for computer analysis. In this paper, results obtained through a computer program created in the MATLAB, based on a finite element accounting for eccentricity in connection and off-centering of support, are demonstrated. The results shows values in the diagrams of internal forces differing by up to 15-30% compared to the classical theory of centric connection and centric supporting.

A Mathematical Model to Evaluate the Impact of Yoga Poses on Body

Daily Yoga activities are part of a ten-posture series with linked relaxation and aerobic exercise, resulting in a balancing of flexibility and extensions. Because this series is often repeated and advocated by several yoga professionals, structural modeling to justify its purported health advantages is needed. Older is recommended to do more workouts to maintain activity, given the increasing pressures in societal, economical, and health issues as a result of the elderly society. They are, regrettably, unable to do so due to a variety of physical and psychological obstacles. The whole body form changes significantly as people get older, and sag. One of the most important variables in regaining their drive and comfort throughout social activities might be the layout of their apparel. The impact of athletics on older is investigated in this study. Depending on rigid body movements and free-body diagrams, a numerical model is built for each position in the yoga exercises. The idea of static equilibrium is used to calculate the forces and moments that different joints experience. The model given in this study was developed under a variety of assumptions. But what is discovered in practice is that the knees carry the maximum joint action while the ankle and wrist are discovered to play a major part in transferring the ground response forces throughout yoga. Thus, it would imply that the model is a good tool for forecasting the forces and durations that happen not just during the yoga positions but also during other situations.

Tolerance analysis by static analogy: numerical and experimental results

Industrial requirements to design high quality products in shorter and shorter times impose the use of numerical models to estimate the geometrical deviations of these products, which are assemblies, starting from the geometrical deviations of their components. Numerical models may support this estimation activity, thus reducing the time to market and the design costs. The free-body model is an interesting numerical method to translate the tolerance chain into a static problem solved by algebraic or graphical procedures by using the free-body diagrams of force analysis. This work presents a free-body model that is able to deal with dimensional and geometrical tolerances that involve translations of the features to which the tolerances are applied. Moreover, it validates the free-body model for tolerance analysis of rigid parts by defining and solving a case study through numerical and experimental activities. The present work uses a case study to demonstrate the effectiveness of the free-body model by underlining that the experimental results obtained are very close to those from the numerical model.

Конечно-элементное моделирование состояния металлических конструкций каркасного здания

For the considered groups of structures - metal trusses, beams, columns, landings and marches of a multi-storey frame building, a continuous visual and detailed instrumental examination was performed. For load-bearing structures, verification calculations of their bearing capacity were performed. Based on a comparison of the defects identified during the inspection and the results of verification calculations, an assessment of the technical condition was made for individual structures, for each group of structural elements, as well as for the building as a whole. For structures with defects and damage, recommendations are given for their restoration and repair. Additional damages and defects were recorded, the appearance of which is associated at the object under study due to a forced break in the production of construction work. The results of surveys and calculations showed that the technical condition of landings and marches can be considered generally efficient. The results of the verification calculation showed that the technical condition of the metal columns as a whole can be considered efficient. The results of the verification calculation on the computer of metal truss structures are presented in the form of a mosaic and diagrams of internal forces. When performing verification calculations, the finite element method was applied.

Predicting the Response of RC Beam from a Drop-Weight Using Gene Expression Programming.

For structures and load-bearing beams under extreme impact loading, the prediction of the transmitted peak impact force is the most challenging task. Available numerical and soft computing-based methods for finding peak impact force are not very accurate. Therefore, a simple and user-friendly predictive model is constructed from a database containing 126 impact force experiments of the simply supported RC beams. The proposed model is developed using gene expression programming (GEP) that includes the effect of the impact velocity and the impactor weight. Also identified are other influencing factors that have been overlooked in the existing soft computing models, such as concrete compressive strength, the shear span to depth ratio, and the tensile reinforcement quantity and strength. This allows the proposed model to overcome several inconsistencies and difficulties residing in the existing models. A statistical study has been conducted to examine the adequacy of the proposed model compared to existing models. Additionally, a numerical confirmation of the empirical model of the peak impact force is obtained by reference to 3D finite element simulation in ABAQUS. Finally, the proposed model is employed to predict the dynamic shear force and bending moment diagrams, thus rendering it ideal for practical application.