Create design in your way

EGEN 203 Final Allen

It is getting close to summer which for me brings a desire to play in water and hopefully a chance to build something outside. Rope swings are generally a terribly unsafe and exhilarating way to combine building something and playing in water. For our final project we will be adding some engineering experience to the summer activity of rope swing construction. Not all water bodies are lucky enough to be surrounded by cliffs, or even trees. For this scenario we will imagine that we are spending a couple weeks on Fort Peck Lake and want a rope swing. At our camp there are no trees, nothing to anchor a swing to, but we did bring a bunch of scraps from a construction site. Notably we have three 16’ long 2x6 pieces of lumber, numerous 8’ long 2x4s and a lot of nails. Our goal is to design a fun and safe rope swing tower.

EGEN 203 Final Allen

The tower must be constructed of 2x4 pieces of lumber, joined by nails which act as pins, so our tower takes the form of a truss. Each 8’ 2x4 can transmit 600 lbs of tensile or compressive load and each 2x6 can transmit 1000 lbs of axial load at 8’ long and 300 lbs at 16’ long. To keep things relatively simple you can model one truss and assume that your tower is made of two trusses, each of which takes half the load (like a railroad bridge). You do not need to consider how the two trusses are joined. Your truss must be able to safely transmit the load of the jumper during the maximum swing load without tipping. You must determine the reactions at the ground to determine if counter weight is needed and where you will place the weight to keep the tower from tipping. Your counter weight is limited to four 50-lb sandbags. You may assume that the tower itself weighs nothing and that it rests on the ground without attachment. To remain statically determinant, you can only have two contact points with the ground. To be safe the connection of the rope to the tower must extend at least 10’ over the water so that the water is deep enough for people to not hit the bottom of the lake after they land. The long 2x6 wood members can be nailed together in multiple configurations to form a single 16’ long beam that attaches to your truss. For instance you can nail two boards together to make a single beam that is 3” thick and 5.5” high, or create an “I” beam. You can only attach the beam at 2 joints in the truss. You must make a beam shear an moment diagram for your swing beam. The maximum moment in your beam is limited by the stress in the wood and can be determined by the equation:

𝑀𝑎𝑥 𝑀𝑜𝑚𝑒𝑛𝑡 = 400 -𝑙𝑏𝑠 𝑖𝑛!2 3𝐼"

5

𝑦

Where: 400 lb/in2 is the max stress in the wood, 𝐼" = moment of inertia about the centroidal z- axis, and y is the longest distance from the centroidal axis to the top or bottom of your beam cross section. You must also determine the load that the structure will likely be subjected to. This load will drive your beam and truss deign. The rope swing should be designed such that my Uncle who is 280 lbs can use it safely. To calculate the velocity of an object at the bottom of the arc of the rope swing you may use the calculation:

𝑣 = 82𝑔∆ℎ Where: v = velocity in ft per second, g = 32.2 ft/s2, and ∆h = change in height from the jump point to the bottom of the swing. Assume that max load occurs when the swinger is at the bottom of the swing rotation when the rope must transmit the load of the jumper and any forces generated by tangential velocity of the swinger around the center of the swing.

EGEN 203 Final Allen

For your project you may work individually or in pairs. Your design submittal is expected to include: (5%) A system wide FDB. (20%) An analysis of external forces. (20%) A truss analysis with the force in each member calculated under the swing load. (20%) A beam shear and moment diagram for your swing arm beam. (20%) An analysis of the cross-section of your swing arm beam that calculates the centroid and the moment of inertia about the centroid of your beam cross-section. (15%) Design originality, creativity, buildability, and clarity of communication. This final project is worth 20% of your final grade. Each pair, or if you work alone, individual must submit work that is original. I hope you can have some fun with the design component, but do not spend too much time on it. There is no “correct” solution. You will be assessed based on your analysis of whatever system you design. The more complicated the truss, the more difficult the project. Communication of your process is key. Please ensure that you have addressed each components of the project and I encourage questions and discussion in the General Channel on Teams.