Assignment3-solution

# Assignment3-solution - Calculate the maximum shear stress...

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1. Calculate the maximum shear stress for two cases: (a) 4 xx yy zz xy MPa MPa 1 σ σσ τ === = (b) same as case a, except that 0 zz = . Why is the maximum shear stress larger in case b? The three principal stresses for case a) are 123 5, 4, 3 MPa = == so the maximum shear stress is max 1 3 1 1 2 MPa τσ =− = . For case b) the principal stresses are 3, 0 , so the maximum shear stress is max 1 3 1 2.5 2 MPa = . The reason for the smaller shear stress in Case a) is that it is much closer to hydrostatic pressure where there are no shear stresses at all. Problem 2.8 A state of hydrostatic stress is given by the following: [] = 0 0 0 0 0 0 0 0 0 Show that on any surface the force (or stress vector) is always perpendicular to the surface and that the magnitude of the stress vector is equal to 0 . Solution: Lets write stress vector t in terms of [ ] given on any plane k j i n z y x n n n + + = () k j i z y x z y x z y x n n n n n n t t t + + = = 0 0 0 0 0 0 0 0 0 0 . We can rewrite this in vector form as n t 0 = . That is stress vector on any given plane is a vector of magnitude 0 and has the same direction with the normal vector of the plane (perpendicular to the plane).

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Assignment3-solution - Calculate the maximum shear stress...

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