AE 5339
HOMEWORK SET NO.8
Due April 11, 2017
1. (a) The moments of inertia of the tapered and constant area segments of the
cantilever beam shown in the following Fig. 1 are given by I1 = (c1x+c2)-1 and I2
respectively. Determine the deflection of the bea
ME 5339
HOMEWORK SET NO. 7
Due April 4, 2017
Two problems will be graded for 15 pts each and 5 pts will be given the ungraded
problems if reasonable efforts were conducted. (35 points)
Problem 7-1
An aluminum cylinder (Ea=70GPa, Ya=414MPA and a=0.33) with
Chapter 9
Column Buckling
MAE4301/ME5339 Spring 2017
Department of Mechanical & Aerospace Engineering
Chapter 9
1
OUTLINE
9.1 Critical Compression Load.
(Concept of buckling)
9.2 Column with Pin-Ended Support.
9.3 Effect of End Conditions in Column Buckli
AE5339/MAE4301/ME5339
Supplementary Notes: Set 7 (chapter 8)
Problem SN7-1
Using Castiglianos method, determine the horizontal deflection of Point B in the figure.
All members have a cross-sectional area A; members 1, 2, 4 and 5 are of length L, and membe
AE5339/MAE4301/ME5339
Supplementary Notes: Set 8 (chapter 9)
Problem SN8-1
Problem SN8-2
A steel column with a cross-section of 12 cm x 16 cm is 4 m in height and its fixed at its base. The
column is braced against buckling in its weak direction only by a
Chapter 11
Fracture Mechanics Analysis in
Structural Design
MAE4301/ME5339 Spring 2017
Department of Mechanical & Aerospace Engineering
Chapter 11
1
OUTLINE
11.1 Background.
11.2 Fracture Process.
11.3 Fundamental Fracture Modes.
11.4 Stress Field in a Cr
ME 5339
HOMEWORK SET NO. 9
Due Apr. 13, 2017
(Two problems will be graded.) Each one will be graded for 15 points.
Problem 9-1
A simply supported beam of flexural rigidity, EIb is propped up at its center by a
column of flexural rigidity, EIc (see the fig
MAE4301/ME 5339
SUPPLEMENTARY NOTE SET NO. 9
(For Chapter 10)
Problem SN9-1
The endurance limit of a steel member is 12 MPa and the tensile strength is 385
MPa. What is the fatigue strength corresponding to a life of 70,000 cycles?
Problem SN9-2
Estimate
MAE4301/ME 5339
HOMEWORK SET NO. 10
Two problems selected for grade will be counted for 15 points each and the rest of the
two will be counted for 5 points each if the reasonable efforts are performed. (40pts)
Due Apr. 20, 2017
Problem 10.1
A steel has an
Problem 1 2 /(7L
Mark T for truth and F for false in the following statements and correct the statement if
false. (40 pts)
a) A circular bar with the longitudinal axis of x and the side and up axes of y and z ,
respectively is under torsion, T pointing to
Review for the Mid-Term Exam
AE5340/MAE4301/ME 5339/ Spring 2008
Department of Mechanical & Aerospace Engineering
Chapter Mid-Term Review-60
Mid-Term Exam
Date: March 13 (Thursday), 2008 Total Scores: 180 points
Part I: Comprehension: 80 pts
Part 2: Compu
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AE5339/MAE4301/ME5339
Supplementary Notes: Set No. 2
Problem SN2-1
A round bar is composed of tree segments of the same material (see figure below). The
diameter is d for the length BC and DE and nd for the length CD where n is the ratio of
the two diamet
AE5339/MAE4301/ME5339
Supplementary Notes: Set No. 4
Problem SN4-1
A round shaft of diameter 1.5 in. loaded by a bending moment M=5000lb-in. and a
torque T=8000 lb-in, and an axial tensile force, N= 6000 lbs. If the material is ductile
with a yield streng
AE/ME5339
Supplementary Notes: Set 3
Problem SN3-1
Show that the Airy stress function given below is the solution of the semi-infinite elastic
medium acted upon by a uniform pressure q on one side of the origin.
p
[
y
=C ( x 2+ y 2) tan1 xy
x
]
y
x
Note:
AE5339/MAE4301/ME5339
Supplementary Notes SET NO.1
Problem SN1-1
A stress state at a point P is given as below.
10 3 5
3 1 2 x10 3 Psi
5 2 4
Consider a plane through the point M characterized by the directional cosines:
l
3
2
m
2
4
n
2
4
a) Find the no
ME5339/MAE4301-004
Structural Aspects of Design
(Spring semester 2017)
This course provides analytical methods of structural analysis and failure theories that are used in
design analysis. The course also provides analytical methods for fatigue life asses
Table of Airy Stress Function, to
x
Order
2
3
4
5
4=0 gives
Order
2
y 2
y
2
x 2
x
2
xy
x
y
1
a2 x 2
2
0
a2
0
b2 xy
0
0
-b2
1
c2 y 2
2
c2
0
0
0
a3 x
0
0
b3 y
-b3 x
c3x
0
-c3 y
d3 y
0
0
0
a4 x2
0
0
b4 xy
c4 x2
c4 y2
-2c4 xy
d4 xy
0
e4 y2
0
0
0
a5 x3
AE5339/MAE4301/ME5339
Supplementary Notes SET NO.5
Problem SN5-1
A cantilever beam made of aluminum alloy has a Z section of uniform thickness for
which I y
8
2 3
th , I z th 3 , and I yz th 3 . Determine the maximum bending
3
3
stress in the beam subjec
Problem 1.1
A state of stress at a point in a structural part is given as
3 4 0
4 9 0 MPa
0
0 5
An octahedral element is shown below. Find the normal and shear stresses on the plane
ABC for the state of stress given above.
z
A
Note: 0A=0B=0C=5 cm.
0
y
AE5339/MAE4301/ME5339
SOLUTIONS
HOMEWORK SET NO.3
Due February 19, 2015
Problems 1&2 are graded (22 total points)
Write your course number and section number clearly on the first page.
Solution:
First find the stresses from the given Airy stress function.
AE5339/MAE4301/ME5339
HOMEWORK SET NO.4
Due February 27, 2017
Both problems will be graded. (20 points)
Problem 4.1
The internal loadings at a section of the beam consist of an axial force of 500 N, a shear
force of 800 N, and two moment components of 30
AE5339/MAE4301/ME5339
HOMEWORK SET NO.2
Problem 2.1
A 50-mm-square plate is subjected to the stresses shown in Fig. 1. What deformation is
expected by diagonal BD? Express the solution in terms of E, for = 0.3 using two
approaches
(a) Determine the compon
AE5339/MAE4301/ME5339
HOMEWORK SET NO. 5
Due March 2 (Thursday) , 2017
(2 problems will be graded.) (24pts)
Problem 5.1
The beam cross-section is shown in the following figure. The centroid of the cross-section
is located at (y0, z0)= (-t, 7t) as sketched