Strain_II - Strain II MECH320-MECHANICS OF MATERIALS...

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1 Strain II MECH320-MECHANICS OF MATERIALS Prepared by: Nasser Eddin Mohamad, Ph.D
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2 Contents Strain at a Point 2D Strain 3D Strain Strain as an Ellipsoid
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3 A general description of strain In this stack we will develop a general characterization of strain in two and three dimensions. As in the case of stress, we will find that to completely describe strain we use tensors.
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4 Finite reference lines Consider a block of material with two reference lines marked on it as shown. Apply Loads As loads are applied to the block, deformation will occur &
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5 General Deformation Let's take a closer look at the deformed reference lines Reference lines distort ! Note that in general the reference lines do not stay straight following deformation. What if we consider very short (i.e. infinitesimal) reference lines?
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6 Infinitesimal Reference Lines Remain Straight As long as we consider vanishingly short reference lines, we can assume that straight segments remain straight following deformation. We will use this fact in the figures and derivations to follow. No matter how large we draw our pictures, though, remember that they are valid in the limit only.
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7 A convention-Infinitesimal Reference lines Here is a picture to help you interpret the figures correctly.
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8 Rigid Body translation Now that we understand how to interpret the reference lines or fibers shown, we can consider how the two fibers displace as the block changes shape. As before, we can describe the total displacement as a combination of rigid body translation &
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9 Rotation + Deformation ... a rigid body rotation. .. ... And deformation. ..
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10 Remove rigid body rotation and translation In order to calculate strain, we must separate the deformations from the rigid body displacement and rotation. So let's remove the rigid body rotation. ...and let s remove the rigid body translation
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11 Deformation only The result is a figure that shows the fibers after loading,
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This note was uploaded on 02/07/2011 for the course MECH 320 taught by Professor D.a during the Spring '09 term at American University of Beirut.

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Strain_II - Strain II MECH320-MECHANICS OF MATERIALS...

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