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Problem Solution Homework #3
3.1
Solution:
1. Saint-Venant: as the shaft twists the plane, cross-sections are warped but the
projections on the x-y plane rotate as a rigid body, then,
(3.1.1)
: warping function
: angle of twist per unit leng

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Problem Solution Homework #2
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2.1 Solution:
a. Deformed shape
b. Strain components
c. Volume Change
, since
2.2 Solution:
Finding rigid body rotation by taking the average rotation of two adjacent sides.
If the deformation is small enough,

Problem Solution Homework #6
7.1
Solution:
From equilibrium, axial forces of the bars can be easily determined as
Only the compressed bar 13 may suffer buckling when the weight W increases. Since
bar 13 is connected with pin at both ends, its buckling l

Problem Solution Homework #6
6.1
Solution:
The stress-strain relation can be expressed as
Where average stress is
Dilatation for small strain,
Bulk modulus,
For the state of plane stress, we have
The strain energy density associated with the volume dila

Problem Solution Homework #5
5.1
Solution:
Assume: Transverse shear force acts through the shear center, no torsional effect exists.
Loss of material at the cut is negligible, centroid of the cross-sectional area is obviously
at the center.
Shear flow c

Problem Solution Homework #4
4.1
Solution:
Vertical distances between the centroid and the origin
Moments of Inertia
Assume h
where
Stress
Maximum positive stress
Maximum negative stress
Hence, the absolute maximum stress is
Neutral axis is located alon

Problem Solution Homework #1
1.1 The beam of a rectangular thin-walled section (t is very small) is designed to carry both bending
moment M and torque T. If the total wall contour length L = 2(a+b) is fixed, find the optimum b/a
ratio to achieve the mos