ASSIGNMENT 9: T6
From Equation 23.5 from Megson, for Cell I
1
d
q1 34i 340 q2 34i
dz I 2 AG
i
(1)
For Cell II
1
d
q1 34i q2 23 34i 45 52 q3 52
dz II 2 A2G
(2)
For Cell III
1
d
q2 25 q3 12 25 56 61
dz III 2 A3G
(3)
Where,
ds
t
So
12 56 0.5

ASSIGNMENT 10: (21)
The thickness is set to 1 mm. The I-Beam is symmetric about two axes, so the moment
of inertia about those axes can be calculated easily.
This is all done using a MATLAB script for the optimization; the formulas used for this
optimizat

ASSIGNMENT 7: S1
To calculate the location along the beam height where failure occurs I wrote a MATLAB
script, this can be found at the end of the assignment.
Below all the relevant equations I used to write the script
Failure occurs at the maximum Von mi

ASSIGNMENT 9: T6
From Equation 23.5 from Megson, for Cell I
(1)
For Cell II
(2)
For Cell III
(3)
Where,
So
(4)
Substituting (4) into (1), (2) & (3) gives
(5)
(6)
(7)
Also
(8)
By equating (5), (6) & (7) and substitute those in (8) the shear flows are deter

ASSIGNMENT 8: T1
(1)
(2)
Using the relation:
and
And redefining the axis, rotate it 45 degrees clockwise we get
(3)
This means only shear stress is present. Since With t equal to 1 mm, it follows that
(4)
and
(5)
with,
(6)
Now we can use,
(7)
It follows t

ASSIGNMENT 6: B13
This is a statically indeterminate structure. So the normal equilibrium approach does not
work! Use the energy method.
The first step is to choose the redundant member.
Taking DB as the redundant member we assume that it sustains a tensi

ASSIGNMENT 5: B11
Apply the two boundary conditions. w=0 at 0 and at L1+L2
w A0 A1 x A2 x 2
(1)
From the first boundary conditions, it follows that:
0 A0
(2)
And from the second boundary condition, it follows that:
0 A1 ( L1 L2) A2 ( L1 L2)2 A1 A2 ( L1 L2

ASSIGNMENT 7: S1
To calculate the location along the beam height where failure occurs I wrote a
MATLAB script, this can be found at the end of the assignment.
Below all the relevant equations I used to write the script
Failure occurs at the maximum Von mi

ASSIGMENT 4: B1
To determine when the beam fails, we consider 3 cases:
1. Yielding by compression
2. Yielding by tension
3. Column buckling
Start with 1. and 2.
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ASSIGNMENT 6: B13
This is a statically indeterminate structure. So the normal equilibrium approach does
not work! Use the energy method.
The first step is to choose the redundant member.
Taking DB as the redundant member we assume that it sustains a tensi

ASSIGNMENT 5: B11
Apply the two boundary conditions. w=0 at 0 and at L1+L2
(1)
From the first boundary conditions, it follows that:
(2)
And from the second boundary condition, it follows that:
(3)
So,
(4)
(5)
And,
(6)
The energy in the beam is given by:
(

ASSIGNMENT 1: (2)
Start with the formula for compression to calculate the thickness t,
z
My
I
(1)
Not using the thin-walled approximation gives:
z
4
MR0
4
( R0 R14 )
(2)
Rewriting Equation (2) to find the inner radius lead to:
4
( R0 R14 )
MR0
4
R14 R0

ASSIGMENT 4: B1
To determine when the beam fails, we consider 3 cases:
1. Yielding by compression
2. Yielding by tension
3. Column buckling
Start with 1. and 2.
(1)
(2)
(3)
It follows that for compression
(4)
and for tension
(5)
So to calculate the compre

ASSINGMENT 3: (5)
Start with:
x
0 3.5 y
0
x y
y
(1)
So,
7
3.5 y y 2 f ( x)
y
4
(2)
And
y
y
0 3.5 x
0
x
x
7
3.5 x x 2 f ( y )
x
4
(3)
(4)
Obviously , so
72
7
y f ( x) x 2 f ( y )
4
4
(5)
It can easily been seen that:
7
f ( x) x 2
4
(6)
&
f ( y)
7

ASSIGNMENT 1: (2)
Start with the formula for compression to calculate the thickness t,
(1)
Not using the thin-walled approximation gives:
(2)
Rewriting Equation (2) to find the inner radius lead to:
(3)
(4)
(5)
For tension:
Now the inner radius and outer

ASSINGMENT 3: (5)
Start with:
(1)
So,
(2)
And
(3)
(4)
Obviously , so
(5)
It can easily been seen that:
(6)
&
(7)
So we can write:
(8)
Now we fill in the location:
(9)
Now we want we find the shear strain, so we use:
(10)
Now we can use:
(11)
The final ans

Yannick Janssen 1356747: 1-4, 1-29, 2-16 & 2-23
Problem 2-23
The weight of the strut is given by:
Where:
= density of material
A = cross sectional area
L = length of the strut
So, the minimum weight of the beams is dependent of its length L and the cross

Yannick Janssen 1356747 3.3 & 3.20
Problem 3.3
Given torsion T on a beam. Compute the maximum shear stress in the following profile:
Each of the three members of the cross-section (the two flanges and the vertical web) will have
the same rate of twist. Th

Problem 3.3
Given torsion T on a beam. Compute the maximum shear stress in the following profile:
What value should t2 have to get a uniform Margin of Safety throughout the profile?

Problem 2-23
To approach this problem I did the following:
1. Set up an equation to determine the radius for the critical buckeling load. This is
dependent on the position of the strut and de maximum moment that is allowed for the
floor.
2. The length of

(1) The skin of a satellite is equipped with three sensors that measure stress in the x, y,
and A directions as shown below. The A sensor has been giving all kinds of problems
and a fix has been developed but nobody is 100% sure the fix works. Management

Yannick Janssen 1356747 Problem 3.3 & 3.20
Problem 3.20
Look at the rectangular cross-section below:
a=10 cm
t1=1 mm
t2=1.2 mm
t3=0.7 mm
Calculate what t4 should be such that the torsional rigidity J is equal to 2.510-6m4.
The rate of twist of a cell is g

Yannick Janssen 1356747: 1-4, 1-29, 2-16 & 2-23
PROBLEM 1-4
The equilibrium equations without body forces are:
(1)
(2)
It is given in the assignment that:
(3)
So:
(4)
(5)
It follows that:
(6)
And
(7)
Apply the condition given in the assignment that:
(8)
A

Yannick Janssen 1356747: 1-4, 1-29, 2-16 & 2-23
Problem 2-16
Left shows the initial situation and right shows the situation after load R is applied.
The forces in point C must satisfy equilibrium.
Since the applied load R at joint C in the figure above is

Yannick Janssen 1356747: 1-4, 1-29, 2-16 & 2-23
Problem 1-29
The free body diagram of a circular ring that is loaded in the vertical plane of symmetry is
shown below.
Due to symmetry it is convenient to make a cut in the middle of the circle, perpendicula

Yannick Sebastian Janssen 1356747 4-20, 4-51, 6-1, 6-4
6-4
A beam, with the profile shown below, is loaded under a bending moment M at the tip. The tip
rotation is measured to be 3o. The beam length is L=0.8m, the shear modulus is 79.5 GPa and
the Poisson

Yannick Sebastian Janssen 1356747 4-20, 4-51, 6-1, 6-4
4-51
Determine b such that the two vertical shear flows are equal and in the opposite direction. You
must consider the cross-section shown below and you may not use the following equation:
The total f

Yannick Sebastian Janssen 1356747 4-20, 4-51, 6-1, 6-4
4-20
(a) Determine the shear flows in the following cross-section without using the equation:
n
n
I xx S x I xy S y s
I yy S y I xy S x s
qs =
t D xds + Br xr
t D yds + Br yr + qso
2
I xx I yy I xy