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Lecture

Normal Stress in Beams: Bending Analysis

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 normal stresses in beams during bending, including the concept of a neutral axis, calculation of normal stresses, and determination of the second moment of area for simple and complex shapes. The lecture progresses from discussing the assumptions made for shear loading to deriving the flexure formula and exploring the second moment of area. Examples are provided to illustrate the calculation of the second moment of area and centroid for different cross-sections, emphasizing the importance of understanding the distribution of stresses in beams.

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Instructor

Georg Fantner

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Related concepts (32)

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.

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.

Stress (mechanics)

In continuum mechanics, stress is a physical quantity that describes forces present during deformation. An object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has units of force per area, such as newtons per square meter (N/m2) or pascal (Pa).

I-beam

I-beam is a generic lay term for a variety of structural members with an or -shaped cross-section. Technical terms for similar items include H-beam (for universal column, UC), w-beam (for "wide flange"), universal beam (UB), rolled steel joist (RSJ), or double-T (especially in Polish, Bulgarian, Spanish, Italian and German). I-beams are typically made of structural steel and serve a wide variety of construction uses. The horizontal elements of the are called flanges, and the vertical element is known as the "web".

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.

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Explores shear stresses and shear flow in beams under nonuniform bending, emphasizing the distribution of shear stresses and shear flow.

Beams under Flexure