Equilibrium of particles, rigid bodies, frames, trusses, beams, columns; stress and strain analysis of rods, beams, pressure vessels. E MCH 210 E MCH 210 Statics and Strength of Materials (5) This course is a combination of E MCH 211 and E MCH 213. Students taking E MCH 210 may not take E MCH 211 or 213 for credit, or vice versa. Students will learn how forces and moments acting on rigid and deformable bodies affect reactions both inside and outside the bodies. Students will study the external reactions, and their inter-relationships; the discipline of statics (E MCH 211), as well as the associated internal forces and deformations, quantified by their corresponding stresses and strains; the discipline of strength of materials (E MCH 213). The student will be able to analyze and design simple structural components based bon deflection, strength, or stability. Students will be prepared to analyze and design simple structures and take upper division courses in mechanics of materials and structural analysis and design. Students will communicate their analysis through the use of free-body diagrams and logically arranged equations.
Equilibrium of particles and rigid bodies, frames, trusses, beams, columns; stress and strain analysis of rods, beams, pressure vessels. E MCH 210H E MCH 210H Statics and Strength of Materials, Honors (5) This honors course is a combination of E MCH 211 and E MCH 213. Students taking E MCH 210H may not take E MCH 211 and 213 for credit, or vice versa. The same general topics are covered as in E MCH 210, but in a more advanced fashion and with more advanced applications. Students will learn how forces and moments acting on rigid and deformable bodies affect reactions both inside and outside the bodies. Students will study the external reactions, and their inter-relationships - the discipline of statics (E MCH 211), as well as the associated internal forces and deformations, quantified by their corresponding stresses and strains - the discipline of strength of materials (E MCH 213). The student will be able to analyze and design simple structural components based on deflection, strength, or stability. Students will be prepared to analyze and design simple structures and take upper division courses in mechanics of materials and structural analysis and design. Students will communicate their analysis through the use of free-body diagrams and logically arranged equations.
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Equilibrium of coplanar force systems; analysis of frames and trusses; noncoplanar force systems; friction; centroids and moments of inertia. E MCH 211 E MCH 211 Statics (3) Engineering Mechanics is the engineering science that relates forces and moments to the motion (displacement, velocity, acceleration) of bodies. The understanding of the concepts of force, moment, and motion is essential to design efficient engineering components ranging from a bridge to a wing strut to a robot arm to the mother board of a computer. Statics (E MCH 211) is the foundational course for both Dynamics (E MCH 212), which is the study of motion and the forces causing motion, and Strength of Materials (E MCH 213), which is the study of deformation and strength design of solids. Statics will provide students with the tools and guidance to master the use of equilibrium equations and Free Body Diagrams (FBD's) and to solve real engineering problems. Students should leave this class with the ability to logically approach a variety of static engineering problems, to translate a physical situation into an analytic model, and to use various mathematical tools to determine desired information. Course topics include: introduction and vectors, problem solving, force vectors, particle equilibrium, moments/couples, equivalent systems, distributed loads/FBDs, rigid body equilibrium, trusses, frames and machines, 3-D equilibrium, friction, centroids and center of gravity, and moments of inertia.
Axial stress and strain; torsion; stresses in beams; elastic curves and deflection of beams; combined stress; columns. E MCH 213 E MCH 213 Strength of Materials (3) In this elementary course on the strength of materials the response of some simple structural components is analyzed in a consistent manner using i) equilibrium equations, ii) material law equations, and iii) the geometry of deformation. The components analyzed include rods subjected to axial loading, shafts loaded in torsion, slender beams in bending, thin-walled pressure vessels, slender columns susceptible to buckling, as well as some more complex structures and loads where stress transformations are used to determine principal stresses and the maximum shear stress. The free body diagram is indispensable in each of these applications for relating the applied loads to the internal forces and moments and plotting internal force diagrams. Material behavior is restricted to be that of materials in the linear elastic range. A description of the geometry of deformation is necessary to determine internal forces and moments in statically indeterminate problems. The underlying mathematics are boundary value problems where governing differential equations are solved subject to known boundary conditions. Students will be able to:a) Identify kinematic modes of deformation (axial, bending, torsional, buckling and two dimensional) and associated stress states on infinitesimal elements and sketch stress distribution over cross sections b) Analyze determinate and indeterminate problems to determine fundamental stress states associated with kinematic modes of deformation c) Apply strength of materials equations (and formulas) to the solution of engineering and design problems d) Recognize and extract fundamental modes in combined loading and do the appropriate stress analysis e) Extract material properties (modulus of elasticity, yield stress, Poisson's ratio) from data and apply these in the solution of problems f) Calculate the geometric properties (moments of inertia, centroids, etc) of structural elements and apply these in the solution of problems.which will enable them to solve real engineering problems.
EMCH 302H is a required course for engineering science students. This course presents the fundamental principles of classical thermostatics, thermodynamics, and heat transfer with relevant engineering applications. The students are expected to develop skills necessary to apply these principles to common engineering problems involving properties of matter, energy, non-reacting mixtures, and energy transport. The classical thermostatics and thermodynamics instruction will typically take 9 weeks. Control volume analysis techniques are introduced for closed and open systems undergoing both quasi-static and dynamic processes. The techniques are applied to analyze common power and refrigeration cycles, including gas and vapor systems. Diffusion in fluid and solid mixtures will also be considered. Special attention will be devoted to the notions of Helmholtz and Gibbs free energies as well as enthalpy. Use and significance of these concepts constitutive theories of gas, fluid, and solid materials systems will be discussed. The heat transfer component of the course will typically take 4 weeks. Instruction on heat transfer, will cover the three classical modes of heat transfer: conduction, convection, and radiation. Heat exchangers and heat transfer from extended surfaces are presented at a very basic level. Two weeks will be devoted to an introduction to statistical thermodynamic concepts in which a thermodynamic system is viewed as an ensemble whose state can be characterized in phase space. Enough background will be provided to compare and contrast the classical and statistical notions of entropy.
The Carleton Laboratory has a rich history of supporting the New York engineering community with specialty testing services. We have served industry in a wide variety of problems, ranging from high-strength manhole covers to full-scale shoring system tests, as well as fatigue testing of suspension bridge wires and monotonic and cyclical concrete mansonry block test courses.
The Carleton Laboratory transcends disciplines as the largest fully integrated and shared teaching, research, and testing center at Columbia University. Firstly, we provide a rich teaching environment for undergraduate and graduate students in Civil Engineering and Engineering Mechanics and related fields. The Carleton Lab's vast portfolio of research and testing equipment is available to students and researchers across the University. Our goal is to generate new knowledge that provides actionable solutions to the problems of the present and the future. We also offer testing services to outside academic, industry, and government clients to support innovation and respond to urgent challenges in the built environment. Welcome!
Structural failure (fracture) is a problem in biomechanics. Its solution resides, in part, in identifying the material and structural properties of bone that determine its mechanical resistance to structural failure. Bones must be stiff so that they do not bend when loaded, otherwise movement against gravity would not be possible. However, bones must also be flexible, otherwise their ability to absorb energy by elastic and plastic deformation will decrease and the energy imparted will be dissipated only by microdamage or complete fracture. Thus, failure may occur if bones deform too much (exceeding their peak strain) or too little (exceeding their peak stress). Phylogeny and ontogeny make bone "just right" for the functions it is predicted to perform, but the genetic material was not warned about the increased longevity the female enjoys after ovarian failure. Age-related and menopause-related abnormalities in bone remodeling produce loss of the material and structural properties that no longer keep bone "just right". High remodeling reduces the mineral content of bone tissue resulting in loss of stiffness (resistance to shortening in compression and lengthening in tension when loaded). Sex hormone deficiency increases the volume of bone resorbed and reduces the volume of bone formed in each BMU. Solutions to the biomechanic problem will emerge provided that the material and structural properties of bone that determine its strength are measured and studied. Drugs are available to reduce remodeling rate so that there is more time for completion of secondary mineralization to restore bone stiffness. If remodeling is suppressed too much the production of microdamage may increase as homogeneous and highly mineralized bone is less resistant to microdamage progression while reduced remodeling targeted to microdamage may result in microdamage accumulation. Drugs are available to reduce osteoclastic bone resorption and increase osteoblastic bone formation, which together will restore bone balance in the BMU and so prevent further loss of bone mass, prevent thinning and loss of trabeculae, thinning of cortices, and progression of porosity. These approaches prevent the progression of fragility but will not restore bone architecture. Even if a positive BMU balance is achieved, drugs that reduce remodeling are unlikely to reverse the structure damage. Slow remodeling means there are too few remodeling foci depositing their small net positive bone volume to progressively thicken cortices or trabeculae. Agents that are anabolic, that increase bone formation on the periosteal and endosteal surfaces are needed to restore the structure of bone. Other articles in this volume address this challenge. We do not understand the proportional contributions made by differences in bone size, cortical thickness, trabecular number, thickness, connectivity, tissue mineral content, microdamage burden, osteocyte density, porosity, to differences in spine and hip fracture rates within a sex, between sexes, between races, or between treatment, and control arms in clinical trials. The challenge for the future is to measure these specific materials and structural determinants of bone strength. Whether a combination of these material and structural properties will more accurately identify women likely to sustain fractures, or improve approaches to drug therapy is unknown. The quest to eliminate fragility fractures is a distant horizon seen through a glass darkly at this time. 0852c4b9a8
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