MEE 455 - Advanced Mechanics of Materials Exam No. 1 Fall 2011

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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