Advanced Mechanics of Materials
Exam No. 1
Answer all problems in a neat and orderly fashion. Present the solutions in a
manner. For full credit, clearly show the answers to each question.
All work is to be done without consultation with others
Any questions regarding the exam can be made to Dr. Caccese only.
I agree to this criteria ________
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.
n chord of a small steel truss consists of two L5 × 3 × 1/2 steel angles arranged
with long legs back
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
the allowable axial load Pall
ow that may be supported by this
compression chord. Use the AISC equations
for buckling of steel compression
and assume E = 29,000 ksi and the yield strength Y = 36 ksi.
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
Even thought the data is digitized the original
data is smooth.
Draw a graph of the stress vs. strain and
stress vs. tangent modulus
methods used in formulating the stress vs. tangent modulus
Draw a graph of the critical buckling stress vs. KL/r using the tangent modulus
for ths material
Determine the critical slenderness ratio that governs the behavior between elastic and
Given a member with a KL/r = 35
, determine the critical buckling
stresss using the tangent modulus formula.
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
mm and T=20
Is the sect
ion a valid thin walled section?
Determine the torsion constant, J
) Determine the angle of twist per unit length theta,
) Determine the maximum shear
) 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
section is to be used under
orsion. The cross section shown below has
in, d=10in, tw=0.5 in
. It is subjected to
a torque at the
centerline of Tx
= 1,500 in
and the member is simply supported with respect to
St. Venent torsion constant
each leg of the section
due to the
Explain how the warping restraint effects the stresses and deformation of the section
(no calculations required).