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Lecture# Beam Bending III and Buckling

Description

This lecture covers advanced topics in beam bending, including the relationship between beam deformation and stress, stress integration, and bending stiffness. It also delves into the concept of buckling, which leads to instability in mechanical systems. The instructor provides examples of cantilever beams with concentrated loads and explains the consequences of the sign convention used in beam analysis. The lecture emphasizes the importance of understanding the behavior of beams under different loading conditions and the significance of superposition in analyzing beam deflection.

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In course

Instructor

ME-104: Introduction to structural mechanics

The student will acquire the basis for the analysis of static structures and deformation of simple structural elements. The focus is given to problem-solving skills in the context of engineering desig

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Beam (structure)

A beam is a structural element that primarily resists loads applied laterally to the beam's axis (an element designed to carry primarily axial load would be a strut or column). Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beams, that in turn induce internal stresses, strains and deflections of the beam.

Bending

In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. When the length is considerably longer than the width and the thickness, the element is called a beam.

Deflection (engineering)

In structural engineering, deflection is the degree to which a part of a structural element is displaced under a load (because it deforms). It may refer to an angle or a distance. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations.

AMD

Advanced Micro Devices, Inc., commonly abbreviated as AMD, is an American multinational semiconductor company based in Santa Clara, California, that develops computer processors and related technologies for business and consumer markets. The company was founded in 1969 by Jerry Sanders and a group of other technology professionals. AMD's early products were primarily memory chips and other components for computers. The company later expanded into the microprocessor market, competing with Intel, its main rival in the industry.

Buckling

In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column.