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# HW12 - HOMEWORK PROBLEMS Week 12 Due Friday 2 December 1...

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HOMEWORK PROBLEMS Week 12: Due Friday 2 December 1. Figure 1 shows the stresses acting on an element of material. Find the three principal stresses σ 1 , σ 2 , σ 3 and the absolute maximum shear stress τ max . 12 12 8 8 6 6 17 17 all stress components in ksi. Figure 1 2. The principal stresses at a given point are σ 1 = 10 MPa, σ 2 = - 100 MPa. Sketch Mohr’s circle for this state of stress and determine the normal stress on a plane inclined at an angle θ to the principal plane 1. Hence find the range of values of θ for which the normal stress is tensile. 3. A glass wire of 1 mm diameter is tested in tension and found to fracture at a tensile force of 40 N. A similar unbroken wire is used to suspend a mass of 2 kg from the ceiling. The mass is now subjected to a moment T about the vertical axis, causing the wire to be loaded in torsion as well as tension. Find (i) the value of T at which the wire will break and (ii) the angle θ between the fracture surface and the cross-sectional (horizontal) plane.

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