Lecture

Beam Bending: Deflection and Applications in Nanotechnology

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In course

ME-231(b): Structural mechanics for SV

This course aims to provide a concise understanding of how materials and structures react to loads. It covers the basics of stress and strain in multi dimensions, deformation and failure criteria. The course is tailored to problems students from life scien ...

Description

This lecture covers the theory of beam deflection, focusing on applications in nanotechnology. Topics include solving beam deflection through integration and superposition, AFM as a versatile tool for nanoscale biology, and the use of AFM cantilever beams for precise measurements. The instructor explains the governing differential equations for beam bending and the concept of statically indeterminate beam deflection. Examples are provided to illustrate the calculation of deflection, shear forces, bending moments, and slopes in statically indeterminate systems.

Instructor

Georg Fantner

Official source

Ontological neighbourhood

Civil engineering

Structural engineering: Topics in structural engineering

Related concepts (26)

Bending moment

In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam. The diagram shows a beam which is simply supported (free to rotate and therefore lacking bending moments) at both ends; the ends can only react to the shear loads. Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads.

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.

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.

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.

Nanotechnology

Nanotechnology, often shortened to nanotech, is the use of matter on atomic, molecular, and supramolecular scales for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal of precisely manipulating atoms and molecules for fabrication of macroscale products, also now referred to as molecular nanotechnology. A more generalized description of nanotechnology was subsequently established by the National Nanotechnology Initiative, which defined nanotechnology as the manipulation of matter with at least one dimension sized from 1 to 100 nanometers (nm).

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