Realization of the stiffness matrix of statically indeterminate trusses and 20 bar sensitivity penalty method using Mathcad

This paper examines the stiffness matrix of two-dimensional statically indeterminate truss structures.  Using Mathcad, a stiffness matrix analysis of a truss problem is completed as a template for other sorts of problems.  This allows learners to understand the stiffness matrix theory and rapidly acquire the basic concepts of analysis theory.  As is shown in the example, the transformation of the matrix is apparent and the overall structure of the stiffness matrix can be easily constructed.  Unknown reactions and member forces caused by unknown displacement were calculated as well.  In addition, the problem of the 20 bar boundary condition sensitivity penalty method explained in the example 2 for structure analysis.  Although this process is difficult to acquire due to complex procedures, it is beneficial for students because they can check for errors using Mathcad. Keywords: truss, stiffness matrix, Mathcad, penalty method, structure analysis  &nbsp

Dynamic analysis of the vehicle-structure interaction: a direct and efficient computer implementation

The simulation of the dynamic behavior of a structure subjected to sets of moving loads originated by vehicles whose structural behavior is also considered corresponds to a task not efficiently addressed by standard finite element packages. The capability of solving this type of problems has been introduced in the FEMIX 4.0 computational code by means of an integrated formulation, which includes equilibrium and compatibility equations, with unknowns that consist on displacements and interaction forces. Each system of linear equations is efficiently solved by considering the characteristics of each submatrix of the coefficient matrix

Program of Research in Aeronautics

A prospectus of the educational and research opportunities available at the Joint Institute for Advancement of Flight Sciences, operated at NASA Langley Research Center in conjunction with George Washington University's School of Engineering and Applied Sciences is presented. Requirements of admission to various degree programs are given as well as the course offerings in the areas of acoustics, aeronautics, environmental modelling, materials science, and structures and dynamics. Research facilities for each field of study are described. Presentations and publications (including dissertations and theses) generated by each program are listed as well as faculty members visting scientists and engineers

Mixed Approaches to Handle Limitations and Execute Mutation in the Genetic Algorithm for Truss Size, Shape and Topology Optimization

A high-performance genetic algorithm for the optimal synthesis of trusses in discrete search spaces is developed. The main feature of the proposed computational procedure is the possibility of obtaining effective solutions without the violation of any constraint. In general, a varying of cross-sectional areas of bars, coordinates of nodes and topology system is provided. A group of individuals in the population can be accepted for further consideration only if all specified limitations have been fulfilled. Penalties that significantly change an objective function are introduced for other individuals. This mechanism of handling limitations provides for correction of inaccuracies that can introduce penalty functions for satisfying the problem conditions. Both a random change to the entire set of admissible values and a random choice of values among adjacent elements in this set can be performed during the mutation stage. Standard test examples for benchmark mathematical functions and trusses show high efficiency of the considered iterative procedure in terms of solution accuracy

Improving the safety of steel bridges through more accurate and affordable modeling of connections

This thesis develops an improved and affordable method to model the connections of steel truss bridges with a view of improving their design, analysis and safety. The issue came to the fore when the I35-W Bridge in Minnesota collapsed on August1, 2007 [NTSB, 2008]. After many Finite Element Analyses, the National Transportation Safety Board (NTSB) found the buckling of an under-designed gusset plate to be the main cause of the disaster. After this tragedy, the Federal Highway Administration (FHWA) focused its attention on all the 465 steel deck truss bridges present in the National Bridge Inventory [NTSB, 2008], and provided guidelines to bridge owners to verify the safety of these kind of bridges. The present work focuses on the means to assess the structural safety for these particular types of steel truss bridges, and proposes a method for the correct and efficient modeling of the connections. It starts with the basic question: “how safe is it to consider all the connections in these types of bridges as rigid joints?” The work is organized in three parts: • the first gives an overview of the problem of the structural safety of complex structure such as bridges, and proposes the use of the sub-structuring method, [Przemieniecki, 1968], [Bontempi and Arangio, 2008]; • the second part reviews the relevant literature, standards and codes. Both the Eurocodes and the American codes are missing a way to assess the stiffness and strength of gusset plate connections. This work aims at filling the gap between advanced computing methods that can be brought to bear on a failure investigation, and the rigid connections, linear beam analysis typical of routine design, [AASHTO, 1994], [Astaneh, 2010], [Ballio and Mazzolani, 2005], [Crosti and Duthinh, 2010], [Chambers and Ernst, 2005], [EN 1993-1-8, 2003]; • in the third part, the proposed method is applied to the I-35W Bridge. The I-35W is classified as a Fracture Critical Truss Bridge, meaning that the failure of one major element would cause the collapse of the whole structure. The method makes use of the detailed finite element models of the NTSB and FHWA to find the strength and stiffness of the joint in question and replace it with five spring elements. The method provides accuracy and substantial computational savings for repeated load cases, particularly if many joints in the structure are similar, [NTSB, 2008], [FHWA, 2009]. The goal of the thesis then is to develop accurate but computationally affordable connection models to improve global analysis and thus allow bridge owners to predict the effects of joint deterioration, design deficiencies and to guide the requirements for structural monitoring.

Evaluation of Strength Reduction Factor for Concentrically Braced Frames Based on Nonlinear Single Degree-of-Freedom Systems

Strength Reduction Factor (R-Factor), often referred to as Response Modification Factor, is commonly used in the design of lateral force resisting systems under seismic loading. R-Factors allow for a reduction in design base shear demands, leading to more economical designs. The reduction of strength is remedied with ductile behavior in members of proper detailing. Modern seismic codes and provisions recommend R-Factors for many types of lateral force resisting systems. However these factors are independent of the system fundamental frequency and many other important system properties, resulting in factors that may result in an unfavorable seismic response. To evaluate the validity of prescribed R-Factors an extensive analytical parameter study was conducted using a FEM single degree-of-freedom Concentrically Braced Frame (CBF) under incremental dynamic analysis over a suite of ground motions. Parameters of the study include brace slenderness, fundamental frequency, increment resolution, FEM mesh refinement, effects of leaning columns, and effects of low-cycle fatigue. Results suggest that R-Factor can vary drastically for CBF systems with differing properties

24th National Timber Bridge Design Competition

For the 2016 Senior Design project, our team elected to design and construct a short-span pedestrian bridge for the 24th National Timber Bridge Design Competition. The competition was sponsored by the Southwest Mississippi RC&D council (SMRCD) of the Forest Products Society in association with the American Society of Civil Engineers. There were a number of different design and testing requirements to abide by, including both competition regulations as well as AASHTO guidelines pertaining to the construction of pedestrian bridges. [1] A great deal of diligence was taken to assure that our team performed well in the competition; every rule and regulation was carefully considered and designed to. [5] Throughout the course of this project our team was exposed to many aspects of a structural engineering project: an iterative design process, procurement coordination, and construction. The bridge performed really well during testing, deflecting a mere 7.58m, which was only about 73% of the allowed deflection of 0.42”. This performance, along with other bridge characteristics, lead to the team placing 1st nationally in the competition. Furthermore, in order to contribute to the development of our surrounding community, we worked extensively with the Santa Clara County Parks to arrange a donation. Our hopes are to one-day encounter our finished product in a local park

Computer assisted teaching of steel design

A method for use in creating a university level course is presented. The specifics of each of the steps is given in general terms to allow its application to as many different topics as possible. This method is then specifically applied in the formation of a fundamental steel design course using the American Institute of Steel Construction Specification. The reasoning utilized in each phase of development is documented. A lecture style presentation complemented by a series of student oriented computer programs was chosen for use. The details of the course material in outline form is given along with the computer programs written for an IBM 2741 terminal --Abstract, page iii

An active engagement pedagogy for introductory solid mechanics

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2002.Includes bibliographical references (p. 387-393).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Introductory Solid Mechanics has historically been taught using the traditional methods of blackboard instruction. In the Mechanical Engineering Department, we have undertaken an initiative to comprehensively transform the pedagogy of 2.001 (Mechanics and Materials I), an undergraduate course in Solid Mechanics. This transformation represents a radical shift in the teaching paradigm, one which is best described as an active engagement model. Through discovery-based and cooperative learning, it is hoped that students will develop conceptual understanding of the course material, that students will become comfortable working in teams, that student retention of course material will improve, that students will be able to engage in independent learning, and that student satisfaction will improve. There are several components to this new pedagogy: physical desktop experiments, Web-enabled learning modules, a portable computing initiative, a new classroom, and a change in the lecture format. This thesis will describe all of these, but will focus on the development of the Web modules, the synthesis of these elements in developing the new pedagogy, and preliminary assessment of the project. The thesis is dually intended as a presentation of original research and as a working document for others who may wish to undertake a project of similar scope.Jaspal Singh Sandhu.S.M

Symmetry in Modeling and Analysis of Dynamic Systems

Real-world systems exhibit complex behavior, therefore novel mathematical approaches or modifications of classical ones have to be employed to precisely predict, monitor, and control complicated chaotic and stochastic processes. One of the most basic concepts that has to be taken into account while conducting research in all natural sciences is symmetry, and it is usually used to refer to an object that is invariant under some transformations including translation, reflection, rotation or scaling.The following Special Issue is dedicated to investigations of the concept of dynamical symmetry in the modelling and analysis of dynamic features occurring in various branches of science like physics, chemistry, biology, and engineering, with special emphasis on research based on the mathematical models of nonlinear partial and ordinary differential equations. Addressed topics cover theories developed and employed under the concept of invariance of the global/local behavior of the points of spacetime, including temporal/spatiotemporal symmetries