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 crosssectional (horizontal) plane.
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 Fall '07
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 Force, Shear Stress, Shear, Stress, maximum shear stress

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