Redo Exercise 4.17 for the case where the vertical loading is 50 MPa in tension and the

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Redo Exercise 4.17 for the case where the vertical loading is 50 MPa in tension and the horizontal loading is 50 MPa in compression.

Data from exercise 4.17

Using cylindrical coordinates, we wish to determine and compare the uniaxial stress strain response of both an unconfined and confined isotropic homogeneous elastic cylindrical sample as shown. For both cases we will assume that the shear stresses and strains will vanish. For the unconfined sample, the stresses σr = σθ = 0, while for the confined sample, the strains er = eθ= 0. Using Hooke’s law in cylindrical coordinates (A.8), show that the uniaxial response for the unconfined case is given by the expected relation σz = Eez, while the corresponding relation for the confined situation is σz = E∗ ez, where E = [(1 – / (1 + v) (1–2v)]. Finally make a plot of E/E versus n over the range 0≤v≤0.5 and discuss the results.

of = 0 g = 0 0  z (Unconfined) 0  (Confined) e = e = 0

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