Quiz-08-Summer10 - positive abscissa and 0 to 80 kPa on the...

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Quiz #8 (Due by 2400 hours Friday, 30 July 2010) This is a take-home quiz. Accepting a take-home quiz means that you pledge to yourself to be honest and do the quiz alone. The grade is highly dependent on the quality of your drawing, and the clarity of your calculations (in Math Type found in WORD). When finished, transmit to me your WORD file plus your AutoCAD file via e-mail. Problem Statement: A direct shear test is run on a medium dense sandy silt, with the normal stress σ n = 65 kPa, and K o = 0.5. At failure, the normal stress is still 65 kPa and the shear stress is 41 kPa. Find: 1) Draw the Mohr circles for initial conditions “i” and failure conditions “f”. 2) Find the principal stresses at failure; 3) Find the orientation of the failure plane. Perform your calculations in both SI and US units. Helping Notes: 1) Prepare a grid-ruled background with faint grey, with a scale of 0 to 150 kPa on the
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Unformatted text preview: positive abscissa, and 0 to 80 kPa on the positive ordinate. Hint: see my Mohr-02 in “300 Solved Problems” notes; 2) Draw the first Mohr circle “i” on the grid-ruled background. Notice that since, and K o = 0.5, if the normal stress σ n = σ 1 = 65 kPa, then σ 3 = 32.5 kPa; 3) The failure point “ F ” shows the result of holding the same normal stress, but adding a shear stress of 41 kPa. Now, you can prove that the angle of internal friction φ = 32º. 4) Since the failure circle passes through “F”, find the center of that circle. See if you get a coordinate of 91 kPa, 0. Now find the maximum and minimum principal stresses for the failure circle (these should be 139 and 43 kPa respectively). Check your results with the figure shown on the next page. 5) Would an assumption that the failure plane is horizontal be a good one? Why?...
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Quiz-08-Summer10 - positive abscissa and 0 to 80 kPa on the...

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