Mohrs Circle - Stresses in a Plane Some parts experience normal stresses in two directions directions These types of problems are called Plane Stress or

Mohrs Circle - Stresses in a Plane Some parts experience...

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MET 210W – Mohr’s Circle 1 Mohr’s Circle MET 210W E. Evans Stresses in a Plane Some parts experience normal stresses in two directions These types of problems are two directions. These types of problems are called – Plane Stress or – Biaxial Stress z Cross Section thru Body Tangent and normal to the surface • Force Δ F y → τ zy • Force Δ F x → τ zx • Force Δ F y x Convenient coordinate system • Force z → σ z Make two more cuts in the original body, each perpendicular to the others.
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MET 210W – Mohr’s Circle 2 General State of Stress • Cubic volume element • Characterized by three components on each face Ch ith • Changes with a different coord. system Rotating the element in any direction changes the state of stress. General State of Stress & Strain σ y σ x σ x τ yz τ zx τ yx τ zy τ xz τ E E E E E E E E E z y x z z y x y z y x x σ + νσ νσ = ε νσ σ + νσ = ε νσ νσ σ + = ε σ z σ y xy ε = strain ν = Poisson’s Ratio Positive orientations shown Finding Maximum Stress • There are three maximum stresses to be There are three maximum stresses to be found: – The maximum normal stress, σ = P/A ± Mc/I – The orientation of maximum stress – Mohr’s Circle Ti d d t i t d – Time dependent maximum stress – endurance strength Purpose of Mohr’s Circle • Visual tool used to determine the stresses Visual tool used to determine the stresses that exist at a given point in relation to the angle of orientation of the stress element. There are 4 possible variations in Mohr’s Circle depending on the positive directions are defined.
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MET 210W – Mohr’s Circle 3 Sample Problem A particular point y σ y = -2 ksi Some Part
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