Design of Wood Tower to Support Wind Turbine
project_hw2_tower_design_fall16.pdf
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Widener University
ENGR 111 – Projects
Project – HW2: Design of Wood Tower to Support Wind Turbine
Due on Wed. Oct.12th
This is a substantial assignment for double credit – 200 points
Deliverables (individual submission required):
1. Tower Leg Forces: Submit a hard copy of Table 1 (shown below) and a graph of the
compression force in the right tower leg, C, vs. x for each of the four tower base widths (four
curves). Plot the compression force on the y-axis and the distance “x” on the x-axis. You
can plot all four curves on a single graph with a legend (better) or create four separate
graphs (acceptable). Answer the discussion question: What happens to the tower leg force
as the tower base width is increased?
2. Based on your calculations, recommend a tower base width for the tower you will build.
3. Tower Leg Bracing: Submit a hard copy of Table 2 (shown below) and a graph of the
maximum permissible unbraced lengths Lb (in.) as a function of compressive load C (lbf) in a
tower leg. Answer the discussion questions: How does Lb vary with C? For the tower base
width you recommended and the corresponding compressive loads, what should be Lb at
the bottom part of the tower? How about in the middle section? Towards the top?
A. Calculation of Internal Forces in Tower Legs (Square Tower) and Selection of Base Tower
Width
Tower Construction Requirements:
Tower Height
Tower Width, WTOP
Tower Width Base, WBASE
Braces
Materials
Connections
Tower to Base Connection
24 in.
2 in. square
2 in. (minimum)
8 in. (maximum)
As necessary for stability of
tower legs
As provided in reference
section
Push-pins
Push-pins and angle brackets
Use static equilibrium equations from your reference section to calculate the maximum tension
and compression forces in the tower legs. Calculate the forces in the legs at the tower base and
at the ¼, ½ , and ¾ points along the height of the tower. Use Excel to perform these calculations
for five tower geometries: a tower top width of 2 in. square with a base width of 2 in., 3 in., 4
in., 5 in., and 6 in.
From the static equilibrium equations of the tower:
Q = 6 N (1.35 lbs)
H = 10 N
(2.25 lbs)
Top of tower
x
Arbitrary point, x, from
top of tower
A
W
F1
F2
Solve for F2 using Eq. 1 and for F1 using Eq. 2. Remember that for a four leg tower, the calculated forces
F1 and F2 are divided by two (two tower legs on the left and two on the right of the tower).
2
Eq. 1.
∑ = 0 = +
Eq. 2.
∑ = 0 = 2 − + 1
− 2
Use Excel to calculate F1 and F2 values for tower sections located x = 6 in., 12 in., 18 in., and 24 in. from
the top of the tower. Note that the distance between the tower legs, W, will change based on the
tower’s base width as shown below.
NOTE: A negative sign for Force F1 indicates that the force in the leg is in tension and the direction of
the force vector on the figure is downward instead of upward as shown.
Tower base width ≠ tower
top width
x
Tower base width =
tower top width = 2 in.
Calculate width of the
tower at the ¼ points.
W = 2 in. (constant)
W
Ex. For a 6 in. wide base,
x = 0 in.,
W = 2 in.
x = 6 in.,
W = 3 in.
x = 12 in.,
W = 4 in.
x = 18 in.,
W = 5 in.
x = 24 in.,
W = 6 in.
Format your calculations to appear in a Table in Excel as follows:
Tower
Base
Width
(in.)
2
4
6
8
Table 1 – Tower geometries and associated tower leg forces.
Compression Compression
Distance from W, Tower
/ Tension
Force in
top of the
Width at
F1 (lbs)
F2 (lbs)
Force in Left Right Tower
tower, x (in.)
“x” (in.)
Tower Legs,
Legs,
T = F1/2
C = F2/ 2
0 (top)
6
12
18
24 (base)
0 (top)
6
12
18
24 (base)
0 (top)
6
12
18
24 (base)
0 (top)
6
12
18
24 (base)
Graph the compression force in the right tower leg, C, vs. x for each of the four tower base
widths (four curves). Plot the compression force on the y-axis and the distance “x” on the x-axis.
You can plot all four curves on a single graph with a legend (better) or create four separate
graphs (acceptable). What happens to the compression force in the tower leg as the tower base
width is increased?
Based on your calculations, choose a tower base width. Note that while wider bases will reduce
the overall tension and compression forces in the tower legs, they require more material and
longer members.
Tower Base Width:
B. Calculation of Unbraced Lengths (Bracing Points) for Tower Legs
The Reference section discusses various modes of tower failure: due to exceeding tensile
strength, compressive strength and shear strength of the balsa wood, and due to buckling.
Here we are going to assume that the tower legs are strong enough to withstand the loading for
all failure modes except buckling. The goal of this part is to estimate the separation distance
between so called bracing, which will protect the tower legs from buckling. See Reference
section for more detail.
Instructions:
Use the Euler buckling equation with a factor of safety = 3 to calculate the maximum
permissible unbraced lengths, Lb, for axial loads of 1 lb to 10 lb in 1 lb increments. Tabulate and
graph the results.
Eq. 3.
= √
2
3
Table 2 – Maximum permissible unbraced lengths, Lb, to prevent buckling.
Compression Force in
Maximum Permissible
Tower Leg (lbs)
Unbraced Length, Lb (in.)
1
2
3
4
5
6
7
8
9
10
Now consider the calculated unbraced lengths, Lb, when designing your tower bracing. For your
selected base width and the corresponding compressive loads (from Part A), what should be Lb
at the bottom part of the tower? How about in the middle section? And how about towards
the top of the tower?
…
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