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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