Jan 14 class notes

Jan 14 class notes - Normal strain A prismatic bar will...

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Normal strain A prismatic bar will change in length when under a uniaxial tensile force…and • Definition of elongation per unit length or strain ( ε ) (epsilon) • If bar is in tension, strain is tensile strain ( taken as Positive) and if the bar is in compression the strain is compressive strain (Negative). Fig 1-2: Prismatic bar in tension. δ (delta). obviously it will become longer in tension and shorter in compression… • Strain is the ratio of two lengths, it is a dimensionless quantity (i.e. no units!!) . It is also sometimes expressed as percent, such as 0.07%.
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Limitations High localized stresses are produced around the holes ! Stress concentrations: high localised stress. Example: The loads P are transmitted to the bar by pins that pass through the holes FIG. 1-3 Steel Eye bar subjected to tensile loads P Is only valid if the stress is uniformly distributed over the cross-section of the bar. This condition is realized if the axial force P acts through the centroid of the cross-section. When the load p does not act through centroid, the bar will be bending. We assume the axial forces are applied at centroid unless it is stated otherwise. Stress distribution around the hole: quite complex. Towards the middle of the bar: the stress distribution gradually approach uniform. Sigma
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Line of action of the axial forces for a uniform stress distribution We assumed the normal stress was distributed uniformly over the cross-section. In order to have uniform tension or compression in a prismatic bar, the axial force must act through the centroid of the cross-sectional area . FIG. 1-4 Uniform stress distribution in a prismatic bar: (a) axial forces P, and (b) cross section of the bar Point proof: Point proof: page 11 page 11 -12 12 *In geometry, the centroid or bary center of an object X in n -dimensional space is the intersection of all hyperplanes that divide X into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of X . *The geometric centroid of a physical object coincides with its center of mass if the object has uniform density , or if the object's shape and density have a symmetry which fully determines the centroid. These conditions are sufficient but not necessary. Position of Centroid: determined by Density and Geometry
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function properly requires that we understand the mechanical behaviour of the materials being used. 1.3
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This note was uploaded on 04/03/2009 for the course MAE 243 taught by Professor Liu during the Spring '08 term at WVU.

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Jan 14 class notes - Normal strain A prismatic bar will...

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