MEE 455

Advanced Mechanics of Materials
Exam No. 1
Fall
2011
Name __________________
________
______
Instructions:
1.
Answer all problems in a neat and orderly fashion. Present the solutions in a
professional
manner. For full credit, clearly show the answers to each question.
2.
All work is to be done without consultation with others
(no exceptions)
.
Any questions regarding the exam can be made to Dr. Caccese only.
I agree to this criteria ________
___________________________ (signature/date)
3. Submit your solution no later than 11:00 am on Monday Nov. 21. The solution
should either brought to class of placed in my mailbox in the ME office.
TAKE HOME
1
)
Column Behavior
A compressio
n chord of a small steel truss consists of two L5 × 3 × 1/2 steel angles arranged
with long legs back

to

back as shown in the Figure below. The angles are separated at
intervals by spacer blocks that are 0.375 in. thick. If the effective length is
KL =
12
ft,
A)
Determine
the allowable axial load Pall
ow that may be supported by this
compression chord. Use the AISC equations
for buckling of steel compression
members
and assume E = 29,000 ksi and the yield strength Y = 36 ksi.
B)
Determine the spacer block thickness where the moment of inertia about the Y
and Z axes are the same.
Z
Y
2) Tangent Modulus Formula
A steel material is to be used as a compression member. Short column tests resulted in
the following
digitized
stress strai
n data.
Even thought the data is digitized the original
data is smooth.
Stress, ksi
Strain
, x10

6
0
0
15.8
544
31.6
1088
35.5
1240
39.5
1450
43.4
1724
47.4
2094
51.3
2738
55.3
4027
59.2
8054
60.0
9665
60.0
16108
A)
Draw a graph of the stress vs. strain and
a
stress vs. tangent modulus
curves. State
methods used in formulating the stress vs. tangent modulus
curve
.
B)
Draw a graph of the critical buckling stress vs. KL/r using the tangent modulus
formula
for ths material
.
C)
Determine the critical slenderness ratio that governs the behavior between elastic and
inelastic.
.
D)
Given a member with a KL/r = 35
and KL/R=1
25
, determine the critical buckling
stresss using the tangent modulus formula.
3) Torsion
A three cell shape is subjected to a torsional moment, T. Each cell is in the form of a
regular hexagon with dimension a as shown.
The thickness of the perimeter walls is t and
the thickness of the adjoining cells (the 2 webs) is 2t typical.
Given that G=
200GPa, t=0.75mm. a=1
6
mm and T=20
0N

m.
A)
Is the sect
ion a valid thin walled section?
B)
Determine the torsion constant, J
C
) Determine the angle of twist per unit length theta,
D
) Determine the maximum shear
stress.
E
) If the 2 web walls have a slit in them determine the torsion constant, J and compare to
that found in part A).
a
t
2t
4) A steel
T

section is to be used under
t
orsion. The cross section shown below has
dimension b
f=6
in,
tf=0.6
in, d=10in, tw=0.5 in
. It is subjected to
a torque at the
centerline of Tx
= 1,500 in

lb
and the member is simply supported with respect to
torsion.
.
A)
Determine the
St. Venent torsion constant
J.
B)
Determine the
maximum
Sr. Venant
shear
stress
on
each leg of the section
due to the
twisting moment.
.
C)
Explain how the warping restraint effects the stresses and deformation of the section
(no calculations required).
Tx
Z
Y
d
b
f
tf
tw
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