05~chapter 05

# 05~chapter 05 - Materials engineering science processing...

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Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

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Standard Solution to Elastic Problems Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon Figure 5.1 Three common modes of loading: (a)– tie with a circular cross-section loaded in tension (b) – beam with rectangular cross- section loaded in bending (c) – shaft of circular cross-section loaded in torsion
Elastic Extension or Compression Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon Relation between load, deflection and stiffness Shape of cross-section does not matter because the stress is uniform across the section

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Elastic Bending of Beams Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon Curvature of initial straight axis……………………… Stress cause by bending moment in a beam with a given Young’s modulus……………… Second moment of inertia……………………………. u: displacement parallel to y-axis M: bending moment y: distance from neutral axis
Cross-sectional Area and Second Moments for Four Shapes Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon Figure 5.2

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Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon Figure 5.3 Stiffness of a beam under transverse loading C 1 is the only value that depends on the distribution of the load
Torsion of Shafts Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon Figure 5.4 τ : shear stress r : radial distance from axis of symmetry K : resistance to twisting (torsional equivalent of I) G : shear modulus T /θ: torsional rigity

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Buckling of Columns and Plates Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon If sufficiently slender, an elastic column or plate, loaded in compression, fails by elastic buckling at a critical load Figure 5.5 Value of n depends on the end constraints of the beam
Vibrating of Beams and Plates Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon Figure 5.6 An undamped system vibrating at its natural frequency can be expressed as the simple problem of a mass, m, attached to a spring of stiffness, k Lowest natural frequency of system Natural frequency based

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## This note was uploaded on 02/15/2012 for the course MASC 310 taught by Professor Nutt during the Fall '08 term at USC.

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05~chapter 05 - Materials engineering science processing...

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