Transcription of Strength of Materials and Failure Theories
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Strength of Materials and Failure Theories
1 Strength of Materials and Failure Theories 2010 State of Stress This is a 2D state of stress only the independent stress components are named. A single stress component z can exist on the z-axis and the state of stress is still called 2D and the following equations apply. To relate Failure to this state of stress, three important stress indicators are derived: Principal stress, maximum shear stress, and VonMises stress. Principal stresses: knownorGivenxyyxyx 3222122, If y=0 (common case) then knownorGivenxyxx 3222122, If x = y=0 then 1 = 2 xy. If y= xy = 0, then 1 = x and 2=0. x xy y z 2 Maximum shear stress Only the absolute values are important. 222),,(3223max,313,1max,2112max,23max,13 max,12max, Max If 3=0, the 222223max,13,1max,2112max, The Vom Mises stress: 2)()()(231232221 v When 3=0, the von Mises stress is: 212221 v When only x, and xy are present (as in combined torsion and bending/axial stress or pure torsion), there is no need to calculate the principal stresses, the Von Mises stress is: 223xyxv Note that in pure shear or pure torsion x =0.
1 Strength of Materials and Failure Theories 2010 State of Stress This is a 2D state of stress – only the independent stress components are
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