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

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.