two dimensional and 3d loading
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loading, bi axial bendingTRANSCRIPT
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ICBT CAMPUS-MTHND in Engineering
Module : Mechanical PrinciplesLecturer : Mihiran GalagedaraBatch: ME_03; AU_01; MT_01Copies : 65Date : 02/04/2013Session : 01 0f 15
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Two- and three-Dimensional
LoadingBy: Mihiran GalagedaraB.Sc. Eng (Hons)UOM, AMIESL
Faculty of Engineering and Construction, ICBT Campus-MT,Sri Lanka.
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DefinitionsIsotropic MaterialsMaterials are considered to be isotropic if the properties are not dependent on the direction.
- Mass and density- Modulus of Elasticity- Poisson's Ratio- Yield strength etc.
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Orthotropic Materials• In this type of material, the elastic
constant have different values in the x, y and z directions so the results obtained in a test depend upon the direction in which the specimen was cut from the bulk material.
• This applies to materials with grain structures such as wood or rolled materials
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Orthotropic Materials
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Non Isotropic Materials• In this type of material, the elastic
constants are unpredictable and the results from any two tests are never the same.• This applies to materials such as glass
and other ceramics
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Two Dimensional Loading
• All the examples considered so far in this chapter have dealt with slender members subjected to axial loads.• i.e., to forces directed along a single
axis.
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Two Dimensional Loading contd…
• A two-dimensional stress system is one in which all the stresses lie within one plane such as the X-Y plane.
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Two Dimensional Loading contd…
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Two Dimensional Loading contd…
• The total strain in the X direction will therefore be given by:
• and the total strain in the Y direction will be:
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Two Dimensional Loading contd…
• If any stress is, in fact, compressive its value must be substituted in the above equations together with a negative sign following the normal sign convention.
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Quiz1. A material has stress of 2 MPa in the
x direction and 3 MPa in the y direction. Given the elastic constants E = 205 GPa and v = 0.27,calculate the strains in both directions.
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Quiz2. A material has stresses of -2 Mpa in
the x direction and 3 Mpa in the y direction. Given the Elastic constant E = 205 Gpa and v = 0.27, calculate the strains in both directions
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Three Dimensional Loading
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Three Dimensional Loading
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Three Dimensional Loading
• For an element subjected to multi-axial loading, the normal strain components resulting from the stress components may be determined from the principle of superposition. This requires:
1) Strain is linearly related to stress2) Deformations are small
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Three Dimensional Loading
EEE
EEE
EEE
zyxz
zyxy
zyxx
• With these restrictions:
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Three Dimensional Loading
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Quiz3. The steel block shown is subjected to a
uniform pressure on all its faces. Knowing that the change in length of edge AB is -1.2 × 10-3 in., determine
a. The change in length of the other two edges,b. The pressure p applied to the faces of the
block. Assume E = 29 × 106 psi and v = 0.29.
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References1. Hearn E.J, (2000), Mechanics of Materials, ISBN
0 7506 3265 82. Nash.W, Potter M.C, (2011), Strength of
Materials, ISBN: 978-0-07-163507-33. Johnston R, De Wolf J,(2000) Statics and
Mechanics of Materials, McGraw-Hill , ISBN 978-0-07-338015-5