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 compression 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,
Y
Z
A) Determine the allowable axial load Pallow 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.
2) Tangent Modulus Formula
A steel material is to be used as a compression member. Short column tests resulted in
the following digitized stress strain data. Even thought the data is digitized the original
data is smooth.
Stress, ksi
0
15.8
31.6
35.5
39.5
43.4
47.4
51.3
55.3
59.2
60.0
60.0
Strain, x10-6
0
544
1088
1240
1450
1724
2094
2738
4027
8054
9665
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=125, 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.
a
2t
t
Given that G=200GPa, t=0.75mm. a=16mm and T=200N-m.
A) Is the section 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).
4) A steel T-section is to be used under torsion. The cross section shown below has
dimension bf=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. .
Y
Tx
bf
tf
d
Z
tw
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).