Stress and Strain Exam Prep
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Stress and Strain Exam Prep
Sample questions with model answers
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1.4. Determine the principal stresses for the following stress tensor: $\begin{pmatrix} 24 & 3 & 6 \\ 3 & 32 & -5 \\ 6 & -5 & 12 \end{pmatrix}$
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Calculate eigenvalues of the stress tensor.
The full exam-length answer is in the app.
1.6. Calculate the magnitude and orientation of the principal strains from the following strain rosette measurements measured at a point on the free surface of a solid body: $\epsilon_0 = 0.0002$, $\epsilon_{45} = -0.0001$, $\epsilon_{90} = 0.0003$
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Apply strain transformation equations to find principal strains.
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1.5. Given the following 2D stress state: $\sigma_1 = 60$ MPa and $\tau_{max} = 20$ MPa. On the supplied graph paper: (a) Draw the Mohr's circle for this stress state. (b) Graphically determine the normal stresses given a shear stress of -16.7 MPa. (c) Determine the angle of the plane of this stress state. Show this angle on the diagram.
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Use Mohr's circle construction and trigonometric relations.
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2.3. Sketch the strain-softening curves for the material shown above as a function of plastic strain for the cohesion, friction angle and dilation angle.
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Draw curves showing reduction in cohesion and friction angle with plastic strain.
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