Department of Mechanical Engineering, National Cheng-Kung University
Advanced Mechanics of Materials
Homework #1
Issued: Monday Feb. 23, 2009
Due: Monday, March. 09, 2009
10 Points each, total 80 points
1.6. The following describes the stress distribution in a body (in megapascals):
 x  x 2  2 y,  y  xy  y 2 z,  xy   xy2  1
 yz  0,
 xz  xz  2 x 2 y,  z  x 2  z 2
Determine the body force distribution required for equilibrium and the
magnitude of its resultant at the point x = －10mm, y = 30mm, z = 60mm.
1.15. A thin skewed plate is subjected to a uniform distribution of stress along its sides
as shown in Fig. P1.15. Calculate (a) the stresses x, y, xy, and (b) the principal
stresses and their orientations.
1.26. A structural member is subjected to a set of forces and moments. Each
separately produces the stress conditions at a point shown in Fig. P1.26.
Determine the principal stresses and their orientations at the point under the
effect of combined loading.
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Department of Mechanical Engineering, National Cheng-Kung University
Advanced Mechanics of Materials
1.35. For a given state of stress at a point in a frame, certain stress components are
known for each of the two orientations shown in Fig. P1.35. Using Mohr’s circle,
determine the following stress components: (a) xy, and (b)x’y’, and y’.
1.45. At a specified point in a member, the state of stress with respect to a Cartesian
coordinate system is given by
12 6 9 
 6 10 3  MPa


 9 3 14
Calculate the magnitude and direction of the maximum principal stress.
1.47. The stresses (in megapascals) with respect to an x, y, z coordinate system are
described by
 x  x 2  y,
 z  x  6 y  z
 y  y 2  5,
 xy   xz   yz  0
At point (3, 1, 5), determine (a) the stress components with respect to x’, y’, z’ if
1
3
1
3
l1  1, m2  , n2 
, n3  , m3  
2
2
2
2
and (b) the stress components with respect
l1  2
to
x”,
y”,
z”
if
5 , m1  1 5 , and n3  1. Show that the quantities given by Eq.(1.29)
are invariant under the transformations (a) and (b).
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Department of Mechanical Engineering, National Cheng-Kung University
Advanced Mechanics of Materials
1.53. The state of stress at a point in a member relative to an x, y, z coordinate system
is
 20 10  10
 10 30 0  MPa


 10 0 50 
Determine the normal stress  and the shearing stress  on the surface
intersecting the point and parallel to the plane: 2x+y－3z=9.
1.58. The state of stress at a point in a member relative to an x, y, z coordinate system
is given by
 100 0  80
 0
20
0  MPa

  80 0
20 
Calculate (a) the principal stresses by expansion of the characteristic stress
determinant; (b) the octahedral stresses and the maximum shearing stress.
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