Chapter8

Chapter8 - Mechanics & Materials 1 Mechanics &...

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Unformatted text preview: Mechanics & Materials 1 Mechanics & Materials 1 FAMU-FSU College of Engineering Department of Mechanical Engineering Chapter 8 Chapter 8 Stress and Strain Stress and Strain Stress Stress • An imaginary plane is perceived to separate the structure into two distinct portions. • One portion is selected as the free body diagram • This selected portion is subjected to two types of forces: – external forces and couples that are applied directly to it – distributed system of forces exerted on it by the portion that was named. Stress Stress – The distributed force system that acts on the cutting plane represents the molecular forces that material particles an either side of the imaginary cutting plane exert on each other. – The exact distribution of those molecular forces on the exposed plane of the free body diagram is unknown Stress: Equilibrium Stress: Equilibrium • Replace distributed force system by an equivalent force- couple system ∑ = + i F R ∑ ∑ = + × + i i i G F r M •F i , G i → concentrated forces and couples applied directly to the surface Stress Stress • To connect the components R x , R y , R z and M x , M y , and M z with actual force we need the concept of stress. • Stress- force per unit area • ∆ a x- increment of area perpendicular to the x-axis • ∆ R- increment of force R acts on ∆ a x • Note nomenclature: first subscript refers to direction of normal to plane; second subscript refers to direction of force stress shear a R stress shear a R stress normal a R xz x z a xy x y a xx x x a x x x lim lim lim ⇒ = ∆ ∆ ⇒ = ∆ ∆ ⇒ = ∆ ∆ → ∆ → ∆ → ∆ τ τ σ Stresses: Normal and Shear Stresses: Normal and Shear Stress Dimensions Stress Dimensions • The stress component σ x that is perpendicular to the imaginary plane is called normal stress • Normal Stress either: – tensile : pulls the cutting plane ( σ : +ve ) – compressive : pushes the cutting plane ( σ : -ve ) • F u → force normal to the area element ∆ A A F u a ∆ ∆ = → ∆ lim σ Normal Stress Normal Stress Shear Stress Shear Stress • Stress component parallel to imaginary plane • F → tangential force A F A ∆ ∆ = → ∆ lim τ Average Normal Stress in an Axially Laded Member Average Normal Stress in an Axially Laded Member • Normal Force acts on any cutting plane producing a normal stress (either tension or compression) that is uniform over the area of the cutting plane assuming: 1. Force acts at the centroid of the area 2. Material deforms uniformly Axial Loading...
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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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Chapter8 - Mechanics & Materials 1 Mechanics &...

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