Force Diagram Research Articles

ПОСТРОЕНИЕ УПРУГОЙ ЛИНИИ БАЛКИ И ОПРЕДЕЛЕНИЕ ВЕЛИЧИНЫ И НАПРАВЛЕНИЯ ГЛАВНЫХ НАПРЯЖЕНИЙ В СЕЧЕНИИ БАЛКИ

The paper uses the data from diagrams of I-beam transverse forces and bending moments to calculate the values and directions of primary stresses at three points of the beam cross-section – on the neutral axis, above and below it. To calculate the values of primary stresses, the graphic analytical method with the construction of Mohr's circles is used. Further, the article presents an algorithm for constructing a beam deflection line and calculating cross-section deflections. To determine deflections, the universal beam deflection line equation is used. After determining the largest deflection value, conclusion is made that the hardness condition of a steel I-beam is met.

Development and Validation of the Force Diagrams Representation Test

Experts and students frequently use force diagrams as a physics representation to understand the force concept. This study aims to develop and validate a force diagram representation test that physics teachers in senior high schools can use. Research and development is implemented in this study by following some steps: analyze, define, design, implement, and evaluate. The 225 senior high school students in Pontianak are involved in this study, from the pilot study to the testing on a large scale. Data analysis includes measuring content validity, reliability index, and parameters of the test using the Rasch model. The test consists of 25 items in a multiple-choice format that cover three contexts: horizontal plane, inclined plane, and hanging object, and covers three situations, including the object being at rest, moving with constant velocity, and moving with constant acceleration. The results show that the content validity test obtained a score of 0.95 for the very good category, and the readability index results obtained a score of 7.42, which means it is easily understood by high school students. Rasch analysis shows that a unidimensional percentage is 30.5%, which means the test is able to measure one ability, and item reliability is 0.98. All items fit the Rasch model and had varying item difficulties. This study indicates that the force diagram representation test (FDRT) can be used by teachers as one of the instruments to measure students’ understanding of force.

Critical Thinking Skills in Rotational Dynamics: Learning Physics With and Without Free-body Diagrams

This quasi-experimental study investigates the impact of using free-body diagrams on the critical thinking skills of students studying rotational dynamics at MAN 1 Sungai Penuh. The study involved 140 eleventh-grade students, divided into an experimental group and a control group, each consisting of 70 students. The experimental group received instruction using free-body diagrams, while the control group followed traditional teaching methods. Critical thinking skills were assessed using a test comprising five essay questions, each representing different aspects of critical thinking: likelihood and uncertainty analysis, problem solving and decision making, reasoning, hypothesis testing, and argument analysis. Descriptive statistics and independent samples t-tests were employed to analyze the data. The results revealed that the experimental group outperformed the control group in all aspects of critical thinking skills, with statistically significant differences and strong effect sizes. Specifically, the experimental group showed notable improvements in argument analysis, reasoning, and hypothesis testing. The findings suggest that the use of free-body diagrams significantly enhances students' critical thinking skills in the context of rotational dynamics. This study underscores the importance of incorporating visual learning aids in physics education to foster deeper understanding and improve analytical skills. The results have important implications for teaching practices, advocating for the integration of free-body diagrams to develop students' higher-order thinking skills effectively

Обоснование перспективной схемы кривошипного гидромотора для гидропривода опорно-поворотного устройства манипулятора лесовозного автопоезда

The task of increasing the efficiency of hydraulic manipulators with traditional column turning mechanisms installed on logging road trains can be solved by installing column turning mechanisms with crank hydraulic motors from hydraulic cylinders. Variants of the arrangement of hydraulic cylinders in a crank hydraulic motor were studied graph analytically by determining tangential and radial forces acting on the rotary column of the hydraulic manipulator. At first, calculations were performed based on static methods to evaluate the effect of forces on the rods of hydraulic cylinders in the working positions of the column rotation mechanism. After that, using the COMPASS computer-aided design system, circular diagrams of tangential and radial forces of the considered options for the arrangement of hydraulic cylinders in a crank hydraulic motor were constructed. Further, in the Microsoft Excel program, graphs of changes in tangential forces acting on the rotary column of the hydraulic manipulator were plotted. Schemes with five and six hydraulic cylinders have the best option of influencing the bearings in which the column is rotated. The ranges of radial forces for them ranged, respectively, from 3.32 to 22.07 kN and from 11.175 to 11.297 kN, and tangential forces – from 257.893 to 285.274 kN, and from 300.471 to 354.059 kN, which can be used in the design of new drive designs for turning columns of hydraulic manipulators. For the practical implementation of the proposed design of the crank hydraulic motor, it is planned to make a rational choice of the location of the hydraulic cylinders of the crank hydraulic motor on the frame of the logging road train on the basis of simulation modeling.

Event structure, force dynamics and verb semantics

This article presents a cognitive model of event structure that can be used to explain several features of the semantics of verbs. The model consists of four basic components: agent, patient, force vector and result vector. Each component is described in terms of the theory of conceptual spaces. The force vector is the cause of the result vector. Unlike other event models both the cause and the effect are included in the representation of a single event.The model is used for two central topics. Firstly, to provide a force dynamic representation of causation. Secondly, to give a unified analysis of Aktionsart in terms of different forms of vectors, using force diagrams that are extensions of those used by Croft and others. It is then shown that the event model can be used to derive a variety of semantic features of verbs. In particular, I analyze manner-result complementarity, the ambiguity of the passive participle, and the role of goals (telicity).

Schema coaching techniques part 2: Schema case conceptualisation and psychoeducation

The role of the coaching psychologist is fundamentally that of facilitator of change, however when clients are stuck and troubled it can be helpful to use appropriate psychotherapeutic techniques. This should only be done after the coach has suitable training and after addressing the relevant ethical issues. This paper is the second in a series on the techniques of schema coaching and it explores schema case conceptualisation and schema psychoeducation. These are the first two techniques set out in the octagon model of schema coaching. Case conceptualisation is an important starting point in schema coaching as it generates the rationale and framework, underpinned by evidence, used to understand the client’s issues and to plan future coaching. Case conceptualisation has the following phases, generating the initial understanding based on the presenting issues, the psychosocial assessment including understanding of the social context, physical health, history, mental state, risks and strengths, the understanding of the origins of the presenting issues, the development of need statements and finally the formulation of goals. Case conceptualisation also includes the analysis and mapping of modes or mood states seen in the initial coaching sessions. The mode map is a simple diagram of the dynamic forces operating between the child, inner critic and healthy adult modes. By contrast, psychoeducation is the phase that provides information and support so that the client can better understand and cope with their Early Maladaptive Schema (EMS). Psychoeducation helps the client to understand the nature of basic human needs, how these can be met or thwarted, and how a range of life patterns develop. It helps the client to clarify their EMS that are at the heart of their presenting issues and to understand how these arose, how they impact their lives and how they can be treated.

Motion of an active bent rod with an articulating hinge: exploring mechanical and chemical modes of swimming

Swimming at the microscale typically involves two modes of motion: mechanical propulsion and propulsion due to field interactions. During mechanical propulsion, particles swim by reconfiguring their geometry. When propelled by field interactions, body forces such as phoretic interactions drive mobility. In this work, we employ slender-body theory to explore how a bent rod actuator propels due to a mechanical mode of swimming via hinge articulations and due to a chemical mode of swimming via diffusiophoretic interactions with a solute field. Although previous theoretical studies have examined mechanical and chemical modes of swimming in isolation, the simultaneous investigation of both modes has remained unexplored. For the mechanical mode of swimming, our calculations, both numerical and analytical, recover Purcell’s scallop theorem and show that the bent rod actuator experiences zero net displacement during reciprocal motion. Additionally, we calculate the trajectories traced by a bent rod actuator under a non-reciprocal hinge articulation, revealing that these trajectories are influenced by the amplitude of the hinge articulation, geometric asymmetry, and the angular velocity distribution between the two arms of the bent rod actuator. We provide intuitive explanations for these effects using free-body diagrams. Furthermore, we explore the motion induced by simultaneous hinge articulations and self-diffusiophoresis. We observe that hinge articulations can modify the effective phoretic forces and torques acting on the bent rod actuator, either supporting or impeding propulsion. Additionally, during self-diffusiophoretic propulsion, reciprocal hinge articulations no longer result in zero net displacement. In summary, our findings chart a new direction for designing micron-sized objects that harness both mechanical and chemical modes of propulsion synchronously, offering a mechanism to enact control over trajectories.

Leak-before-Break (LBB)-Based Safety Verification of Reverse Cyclic Loading for 316L Stainless Steel: A Study Using Flat ESG Specimens

The leak-before-break design concept is based on J-R curves, which are obtained by J-R tests on various types of specimens and are known to be dependent on the cyclic load history. The J-R curves of standard specimens suggested by the American Society for Testing Materials are determined based on quasi-static tensile loading. However, seismic loading induces a reverse cyclic loading that alternately applies a tensile and a compressive load to nuclear plant piping. Therefore, it is very important to obtain the fracture toughness characteristics under reverse cyclic loading for the integrity estimation of nuclear plant piping. The objective of this paper is to study the effects of reverse cyclic loading on the fracture toughness characteristics of SA312 TP316L stainless steel, which is a nuclear plant piping material. J-R tests on a flat, equivalent stress gradient specimen with varying incremental displacement were carried out. The test results were reviewed by comparing the J-R test results under quasi-static loading. In addition, the safety margin of the nuclear plant piping was evaluated using a crack driving force diagram method. For the SA312 TP316L stainless steel, the results showed that the J-R curves were decreased with a decrease in the incremental displacement. When the incremental displacement was set to 0.25 mm, the unstable crack growth point value was about 73.0% of those for the quasi-static loading conditions.

An active learning approach to teach distributed forces using augmented reality with guided inquiry

AbstractMastering the concept of distributed forces is vital for students who are pursuing a major involving engineering mechanics. Misconceptions related to distributed forces that are typically acquired in introductory Physics courses should be corrected to increase student success in subsequent mechanics coursework. The goal of this study was to develop and assess a guided instructional activity using augmented reality (AR) technology to improve undergraduate engineering students' understanding of distributed forces. The AR app was accompanied by a complementary activity to guide and challenge students to model objects as beams with progressively increasing difficulty. The AR tool allowed students to (a) model a tabletop as a beam with multiple distributed forces, (b) visualize the free body diagram, and (c) compute the external support reactions. To assess the effectiveness of the activity, 43 students were allocated to control and treatment groups using an experimental nonequivalent groups preactivity/postactivity test design. Of the 43 students, 35 participated in their respective activity. Students in the control group collaborated on traditional problem‐solving, while those in the treatment group engaged in a guided activity using AR. Students' knowledge of distributed forces was measured using their scores on a 10‐item test instrument. Analysis of covariance was utilized to analyze postactivity test scores by controlling for the preactivity test scores. The treatment group demonstrated a significantly greater improvement in postactivity test scores than that of the control group. The measured effect size was 0.13, indicating that 13% of the total variance in the postactivity test scores can be attributed to the activity. Though the effect size was small, the results suggest that a guided AR activity can be more effective in improving student learning outcomes than traditional problem‐solving.

Study of dependence of lubrication layer thickness in a plain thrust bearing of a sealed pump with a magnetic clutch on area of the working wheel equalizing holes

BACKGROUND: Nowadays, using sealed pumps for transferring various liquids is widespread. Increasing the service life and operation reliability of sealed pumps with a magnetic clutch is a relevant technical task.
 AIM: Search for relatively simple ways of increasing the service life and operation reliability of sealed pumps with a magnetic clutch, in particular, study of influence of area of the working wheel equalizing holes on lubrication layer thickness in a thrust bearing.
 METHODS: In the mathematical model, the diagram of forces acting at a rotor of a centrifugal pump with hydrostatic bearings operating with the transferred liquid was analyzed and the equilibrium equation was obtained. The influence of such centrifugal pump geometric parameters as area of the working wheel equalizing holes on lubrication layer thickness in a thrust hydrostatic bearing was taken into account in the calculation.
 RESULTS: In the paper’s conclusion, there is dependency graph of lubrication layer thickness in a thrust bearing on area of the working wheel equalizing holes. As it is shown in the graph, the axial force is quite sensible to area of an equalizing hole of a centrifugal pump working wheel.
 CONCLUSION: The practical value of the study lies in the formulated influence of area of the working wheel equalizing holes on lubrication layer thickness in a thrust bearing of a centrifugal pump, given in the paper’s conclusion.

Online physics tutorial using problem-solving worksheet: A case study with preservice science teachers

The research-designed worksheets have been shown in our previous study. They could help engage students during lectures and tutorials. However, it was implemented only in face-to-face teaching. This study aimed to investigate if the worksheet can also help engage students as well as facilitate effective teaching in an online tutorial class. The basic concept of force and motion, particularly a free-body diagram, was applied. The worksheet was structured into three task boxes: 1) interpreting a situation, 2) identifying variables, and 3) drawing the diagram. The approach was trialed with 30 preservice science teachers. In the tutorial, the lecture was reduced to the minimum and the discussion based on the activity in the worksheet was encouraged between students and between students and teacher. Open-ended questions were used as pre- and post-tests to examine students’ understanding. A video clip investigated the interaction during the classroom. The results from the SOLO levels showed that most student difficulties found in the pre-test were reduced. Prior to the tutorial, some students could not identify the forces on an object correctly. After the tutorial, their understanding improved. The normalized gain was in the high-level judging from the post-test. The students’ reflections also revealed positive feedback.

Towards Homological Methods in Graphic Statics

Recent developments in applied algebraic topology can simplify and extend results in graphic statics – the analysis of equilibrium forces, dual diagrams, and more. The techniques introduced here are inspired by recent developments in cellular cosheaves and their homology. While the general theory has a few technical prerequisites (including homology and exact sequences), an elementary introduction based on little more than linear algebra is possible. A few classical results, such as Maxwell's Rule and 2D graphic statics duality, are quickly derived from core ideas in algebraic topology. Contributions include: (1) a reformulation of statics and planar graphic statics in terms of cosheaves and their homology; (2) a new proof of Maxwell's Rule in arbitrary dimensions using Euler characteristic; and (3) derivation of a novel relationship between mechanisms of the form diagram and obstructions to the generation of force diagrams. This last contribution presages deeper results beyond planar graphic statics.

An Investigation of Stability, Controllability and Observability of a Three Degree of Freedom Translational Mechanical System using State Space Approach

State-space modelling approach which is essentially time-domain developed in the late 1960s is a new approach to the analysis and design of complex control systems. Several researches have carried out modelling and analysis of mechanical systems with a number of degrees of freedom of movement using state space approach among which is the work of Sivak and Darina (2012) who modelled a system with two degrees of freedom. In this paper, therefore, we provide an extension of the work of Sivak and Darina to model and analyse a three degree of freedom translational mechanical system using state-space approach. The system was first presented in equivalent free body diagrams, then Newton's second law of motion was used to derive its equations of motion. The State-space formulation in the controllable canonical form obtained from the time-domain differential equations is adopted and the Laplace transform method was used in the analysis to determine the poles (natural frequencies) of the system using two numerical examples in MATLAB software. The software was also used to determine the controllability and observability matrices of the system. The stability, controllability and observability of the system were then discussed from the poles, controllability matrix and observability matrix respectively. Tables of numerical values and line graphs were used to present the results obtained from the analysis. Finally, in these results, the system was found to be stable, controllable and observable suggesting that a state feedback ( pole placement ) control design for the system is possible.

An integrated e-learning approach for teaching statics to undergraduate engineering students

Free body diagrams are a pictorial representation of a body with forces acting on it. Developing the skill to draw and interpret free body diagrams is imperative in an engineering curriculum as it helps students visualize and comprehend the problem. Engineering students tend to have difficulty using free body diagrams due to a lack of spatial understanding, especially when dealing with three-dimensional static problems. Students are often required to draw free body diagram on paper as part of their problem solutions. While this approach is adequate, it still does not allow students to interact with and develop a deeper understanding of free body diagrams. Educational tools developed to build on the understanding of free body diagrams are either limited to a two-dimensional space or does not provide students a comprehensive platform to completely solve a static problem. In this paper, the authors propose a digital platform that allows students to solve both two and three-dimensional free body diagrams for unknown forces. The platform incorporates Merrill’s Principles of Learning and a clear workflow diagram to assist students in better understanding free body diagrams. The proposed solution also presents an improved feedback system to improve the learning experience of students. Furthermore, the proposed solution addresses the needs of instructors by providing them the means to analyze their students’ performance at different stages of the problems.

Analysis of the Trajectory of Free-throws

This research paper delves into the intricate realm of free-throw shooting in basketball, combining advanced dataanalytics and artificial intelligence to dissect the trajectory of human-generated free-throws and induce the theoretically“perfect shot” by AI. This study aims to introduce the sport of basketball, provide valuable insights into the science ofbasketball shooting, and ultimately contribute to developing the skill of free-throw shooting. I used a real-life exampleof a free-throw shot to achieve this goal. Using the model, I molded a horizontal and vertical distance-time graph onthe coordinate plane to estimate the velocity at each second. By utilizing some physics kinematics, I was able to drawa free-body diagram of the basketball in motion and analyze the possible factors affecting its trajectory. Finally, as allmy research points toward the same goal, I hope to mathematically optimize the perfect trajectory to maximize thelikelihood of a perfect shot by an AI.

Attempting Escape

Abstract The artwork of sculptor, draftsperson, and installation artist Michael Richards (1963 – 2001) challenges prevalent assumptions about the physical properties, and therefore the aesthetic application, of suspension in Black cultural production. As an African American of Jamaican and Costa Rican descent, Richards grappled with questions of citizenship, racism, and freedom, frequently using motifs of flight and gravity. Although Richards created his work before his untimely death in the September 11 attacks on the World Trade Center, his piece titled Tar and Feather nevertheless anticipates the possibilities, and important limitations, of suspension as a theoretical framework. When placed in conversation with the theoretical discourse that now exists surrounding suspension, Richards's material sculptures and archival sketches posthumously anticipate the limits of conventional strategies for Black possibility. This paper argues that Tar and Feather illustrates the asymptotic imbrication of blackness and freedom, which renders the plot as both a diagram of forces and an abstract aesthetic geography from which to create.

Study of the Influence of the Longitudinal Slipping of a Package of Suspended Bars on Stress Diagrams and on its Deformations

Abstract To calculate the bending deformations of a package of elastic beams suspended by means of tie rods, a calculation algorithm using the step function Φ (x-a) from the professional MATHCAD calculation program was used. The step function Φ (x-a) allowed the writing of the analytical relations of the internal shear and bending forces in the beam subjected to bending and the drawing of the corresponding diagrams. Also, the calculation algorithm allowed the writing of the analytical relations of the deformations of the bar (arrows and rotations) with the help of the loading function Ψ (x), respectively its derivative Ψ d(x). The numerical simulation presented in this work allowed the study of the influence of longitudinal sliding on the internal shear and bending force and deformation diagrams for two presumptive connection situations of package beams that were expressed by the degree of preventing sliding (δ =50% and δ =100%), which is defined as the ratio between the moment of inertia of the hexagonal section comprising the n beams as a unitary whole and the one calculated as the sum of the moments of inertia of the sections of the n beams

RELACJA FORMY I KONSTRUKCJI W MOSTACH PYLONOWYCH SANTIAGO CALATRAVY

One of the most common bridge solutions is suspended structures, among which the work of Santiago Calatrava stands out. The article analyzes the realized asymmetric pylon bridges designed by the architect, with cables on diagonal supports. The research aims to evaluate the pylons in terms of the relationship between the obtained architectural form and the proportions of the diagrams of the main forces. Compliance of the obtained forms with intuitive methods of preliminary design of the structure by architects was examined. The article can be a starting material for interdisciplinary research on optimizing the amount of material.

Algebraic 3D Graphic Statics with Edge and Vertex Constraints: A Comprehensive Approach to Extend the Solution Space for Polyhedral Form-Finding

Built upon a previous algebraic framework for polyhedron-based 3D Graphic Statics (3DGS) that can numerically solve for a variety of dual diagrams given an input force or form diagram, this paper introduces an improved algebraic formulation that integrates edge lengths and vertex location constraints for better control over the results. Those constraints are realized by additional edge and vertex constraint equations to previously established closing equations. The entire system of equations can be solved using the Moore–Penrose inverse (MPI) method, and each solution represents a set of compatible edge lengths for the dual diagram to be constructed. The whole solution space of the equation system provides a wide range of dual diagrams, including forms with both tensile and compressive members, which can be easily explored and was not possible using iterative methods or previous algebraic formulations. This improved formulation has been computationally implemented and released as part of a plug-in software program within the environment of Rhino3D® and Grasshopper3D®, enriching the structural form-finding toolset for designers, engineers, researchers, and educators. The tool’s performance and accuracy are demonstrated through a series of comparative studies with iterative methods. Various case studies are also presented to showcase the application of this method.

Evaluation of Newton's Law Learning

The Force Concept Inventory is a test to determine the level of conceptual knowledge of students about mechanical physics and to evaluate the effectiveness of different teaching strategies on the conceptual component of learning. The test was applied with the purpose of knowing the level of conceptualization of the students who study the subject of Physics in a basic and medium educational institution. The results of the pre-test gave to know the students' level of conceptualization and offered information for the elaboration of workshops based on real physical situations to elaborate force diagrams. The results of the post-test allowed estimating Hake's learning gain and showed evidence about the students' conceptual evolution and information to develop future teaching activities about Newton's laws