Lecture 13- Structures 3

# Lecture 13- Structures 3 - AOE 2104-Aerospace and Ocean...

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AOE 2104--Aerospace and Ocean Engineering Fall 2010 Virginia Tech October 21 2010 Aircraft Structures 3 Click to edit Master subtitle style AOE 2104 Introduction to Aerospace Engineering Aircraft Structures 3

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AOE 2104--Aerospace and Ocean Engineering Fall 2010 Virginia Tech October 21 2010 Aircraft Structures 3 Imagine a moment placed on a beam: The beam will bend due to this applied moment How can we predict the stresses induced in the material from this? Beam is said to deform in a circular arc with large radius where some “line elements” or “fibers” elongate or contract Using this assumption, a formula can be developed to predict stresses in a cross section – known as Flexure formula! Beam bending
AOE 2104--Aerospace and Ocean Engineering Fall 2010 Virginia Tech October 21 2010 Aircraft Structures 3 Flexure formula y is defined as the distance from the neutral axis to the point of interest in the cross-section – what is the neutral axis ? Some line elements originally parallel to the x-axis, loosely called fibers, are elongated and some are shortened in the deformed beam. Hence one fiber does not change length . It is called the NEUTRAL AXIS Plane cross sections perpendicular to the x-axis in the undeformed beam remain plane and perpendicular to the neutral plane in the deformed beam Beam bending I My = σ

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AOE 2104--Aerospace and Ocean Engineering Fall 2010 Virginia Tech October 21 2010 Aircraft Structures 3 Material is homogenous and isotropic Homogeneous: Uniform composition throughout Isotropic: Material properties have same value measured along axes in all directions Beam is initially straight and the longitudinal filaments bend into circular arcs with a common center of curvature Plane sections remain plane Radius of curvature is large with respect to dimensions of the cross- section Important assumptions made for Flexure Formula
AOE 2104--Aerospace and Ocean Engineering Fall 2010 Virginia Tech October 21 2010 Aircraft Structures 3 Click to edit Master subtitle style A preview of beams bending with end constraint Both point and distributed loads arise on aircraft wings: - Large point loads from engines - Distributed loading from lift distribution, internal structure, fuel Point loads Distributed loads

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## This note was uploaded on 10/02/2011 for the course AERO 1234 at Virginia Tech.

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Lecture 13- Structures 3 - AOE 2104-Aerospace and Ocean...

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