Deliverables (individual submission required):
 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 yaxis and the distance “x” on the xaxis. 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?
 Based on your calculations, recommend a tower base width for the tower you will build.
 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?
 Calculation of Internal Forces in Tower Legs (Square Tower) and Selection of Base Tower
Width
Tower Construction Requirements:
Tower Height  24 in. 
Tower Width, W_{TOP}  2 in. square 
Tower Width Base, W_{BASE}  2 in. (minimum)
8 in. (maximum) 
Braces  As necessary for stability of tower legs 
Materials  As provided in reference section 
Connections  Pushpins 
Tower to Base Connection  Pushpins 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:
Solve for F_{2} using Eq. 1 and for F_{1} using Eq. 2. Remember that for a four leg tower, the calculated forces F_{1} and F_{2} are divided by two (two tower legs on the left and two on the right of the tower).
Eq. 1. _{2}
Eq. 2. ∑ _{ }= 0 = _{2 }− + _{1}
Use Excel to calculate F_{1} and F_{2} 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 F_{1} 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.

Format your calculations to appear in a Table in Excel as follows:
Table 1 – Tower geometries and associated tower leg forces.
Tower
Base Width (in.) 
Distance from top of the tower, x (in.)  W, Tower
Width at “x” (in.) 
F_{1 }(lbs)  F_{2 }(lbs)  Compression
/ Tension Force in Left Tower Legs, T = F_{1}/2 
Compression Force in
Right Tower Legs, C = F_{2}/ 2 
2  0 (top)  
6  
12  
18  
24 (base)  
4  0 (top)  
6  
12  
18  
24 (base)  
6  0 (top)  
6  
12  
18  
24 (base)  
8  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 yaxis and the distance “x” on the xaxis. 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:
 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, L_{b}, for axial loads of 1 lb to 10 lb in 1 lb increments. Tabulate and graph the results.
Eq. 3. _{ }^{}^{2}
Table 2 – Maximum permissible unbraced lengths, L_{b}, to prevent buckling.
Compression Force in Tower Leg (lbs)  Maximum Permissible Unbraced Length, L_{b} (in.) 
1  
2  
3  
4  
5  
6  
7  
8  
9  
10 
Now consider the calculated unbraced lengths, L_{b}, when designing your tower bracing. For your selected base width and the corresponding compressive loads (from Part A), what should be L_{b} at the bottom part of the tower? How about in the middle section? And how about towards the top of the tower?