Chapter10

# Chapter10 - Mechanics Materials 1 Mechanics Chapter 10...

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FAMU-FSU College of Engineering Department of Mechanical Engineering Chapter 10 Chapter 10 Axial Loading Axial Loading

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Saint Saint - - Venant Venant s Principle s Principle • This principle states that : “ the actual distribution of the load over the surface of its application will not affect the distribution of stress or strain on sections of the body which are at an appreciable distance (relative to the dimensions) away from the load”. • Any convenient statically equivalent loading may therefore be substituted for the actual load distribution, provided that the stress analysis in the region of the load is not required.
The concentrated load produces a highly nonuniform stress distribution and large local stresses near the load. However, the stress smoothes out to a nearly uniform distribution This smoothing out of the stress distribution is an illustration of Saint- Venant’s principle. He observed that near loads, high localized stresses may occur, but away from the load at a distance equal to the width or depth of the member, the localized effect disappears and the value of the stress can be determined from an elementary formula such as A P = σ

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Saint Saint - - Venant Venant s Principle s Principle • The St- Venant’s principle is important because it applies to almost every other type of member and load as well. • It allow us to develop simple relationships between loads and stresses and loads and deformations. • The determination of the local effect of loads is then considered as as separate problem usually by experiment or the theory of elasticity.
Elastic Deformation of an Elastic Deformation of an Axially Loaded Member Axially Loaded Member The stress in the element mn The strain in the same element is Using Hooks law, since the material is assumed to deform elastically δ is called the deformation, elongation, or flexibility AE PL E L L E E L A P = = = = = = σ δ ε A P = L = AE PL =

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Deformation of Deformation of Nonuniform Nonuniform Axially Loaded Member Axially Loaded Member • For a bar consisting of several prismatic parts having different axial forces, dimensions , or materials , the total elongation is given as δ can be positive if resultant force are tension, or negative when force is negative memebr the of area sectional Cross : A member the of Modulus s Young' : E member the of Length : L member at the force axial Resultant : P parts of number Total : n bar with the of parts various for the index numbering the : i i i i i = = n i i i i i A E L P 1 δ
Deformation of Nonuniform Nonuniform Axially Loaded Member Axially Loaded Member • When the axial force or the cross sectional area varies continuously along the axis of the bar, then we integrate to find the elongation; P(x): axial force at a section located a distance x from one end. A(x) : cross sectional area of the bar as a

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## This note was uploaded on 12/11/2011 for the course EML 3011 taught by Professor Schwarz during the Spring '09 term at FSU.

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Chapter10 - Mechanics Materials 1 Mechanics Chapter 10...

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