MET 210W – Mohr’s Circle1Mohr’s CircleMET 210WE. EvansStresses in a Plane•Some parts experience normal stresses in two directions These types of problems aretwo directions. These types of problems are called – Plane Stress or– Biaxial StresszCross Section thru BodyTangent and normal to the surface• Force ΔFy→ τzy• Force ΔFx → τzx• ForceΔF→yxConvenient coordinate system• Force z → σz•Make two more cuts in the original body, each perpendicular to the others.
MET 210W – Mohr’s Circle2General State of Stress• Cubic volume element• Characterized by three components on each faceChith• Changes with a different coord. systemRotating the element in any direction changes the state of stress.General State of Stress & StrainσyσxσxτyzτzxτyxτzyτxzτEEEEEEEEEzyxzzyxyzyxxσ+νσ−νσ−=ενσ−σ+νσ−=ενσ−νσ−σ+=εσzσyxyε= strainν= Poisson’s RatioPositive orientations shownFinding Maximum Stress• There are three maximum stresses to beThere are three maximum stresses to be found:– The maximum normal stress, σ= P/A ± Mc/I– The orientation of maximum stress – Mohr’s Circle Tiddtitd– Time dependent maximum stress – endurance strengthPurpose of Mohr’s Circle• Visual tool used to determine the stresses•Visual tool used to determine the stresses that exist at a given pointin relation to the angle of orientationof the stress element.•There are 4 possible variations in Mohr’s Circle depending on the positive directions are defined.
MET 210W – Mohr’s Circle3Sample ProblemA particular pointyσy= -2 ksiSome Part