Question

please help! I need help finding and solving equations of equilibrium to find the max tension in the cables and the angle that results in the maximum tension, I also have pictures below of the work I have so far all I really need is equations for the 4 cable part and that's it but I put the whole assignment so you could see thanks!

Tower Support System Challenge Challenge Scenario: Due to weather conditions, a major communication tower n the Rio Grande Valley has failed and needs replaced. As a result, the Texas Department of Information Resources (DIR) has launched a project that includes the design of a new portable communication tower to temporarily replace the main tower. The emergency tower consists of a fixed tower of height 35 m (about 115 ft) supported by cables at the top. The cables will be uniformly anchored a distance of 20 m from the tower base as illustrated in the following diagrams As an engineer, your challenge is to design a cable support system for this portable communication tower. As a part of the design, you need to determine the nominal cable diameter such that the cables can withstand storm force wind loads. You also want to minimize the cost of the system. There are two cable configurations that you can choose from consisting ofeither 3 or 4 cables. 3-Cable System: 120° 120 1 +x 0 HX +z Side view of tower Top view of tower 4-Cable System ty 90° I+x +Z +Z Side view of tower Top view of tower Generate Ideas: You are requested to brain storm ideas about how you will solve this challenge. a) Write down clear complete ideas (sentences) your understanding of the challenge. In other words, summarize the goal and requirements of the project. b) Without solving the challenge, indicate information you think will be required to solve the challenge, the science or engineering concepts needed, and the steps that might be required to determine a solution. c) From which direction do you think the wind force will produce the largest cable load in each of the cable systems? Indicate the direction with respect to the angle 0 shown in the diagrams. Explain your reasoning. d) Write down a list of questions you have about the challenge. Tower Support System Challenge System Gcomctry: Before a force analysis can be conducted on the system, you need to work out the geometry of the system using the provided coordinate system. You will do so as follows: 1. Locate the coordinates, (x.y.z), of the cables anchor points using the information ovided on the tower diagrams 3 Cable System Anchor Point Coordinates x.ν.z 4 Cable System Anchor Point Coordinates 2. Use the coordinate of the system to define the position vectors that point from the top of the tower to each anchor point, Use the position vectors to determine the unit vectors that define the orientation of each cable in space pointing Irom the top of the tower to each anchor point. 3. Position and Unit vectors for the 3 Cable System: Cable AB; Cable AC Cable AD Position and Unit vectors for the 4 cable system: Cable AB: Cable AC: Cable AD: Cable AE: Tower Support System Challenge Wind direction analysis: As the wind direction changes the loads on the cables with change also. The first task in designing the support systems is to determine the direction of the wind force that will produce the maximum load in a single given cable. To do this, we will set the distance of the cables, R, to a fixed distance. Keeping R fixed, you will calculate the tensions in the cables in terms of the wind direction angle, 0, relative to the coordinate system as shown in the diagram below. This should be done for both the 3 and 4 cable system The following will be included in the reporting of your analysis. All work must be shown and neatly presented 1. Sketch a clear Free Body Diagram of the system at point A with all forces labeled an unknown variable developed in the previous section 2, write the wind force Fw in component form with the wind direction angle, θ, as 3. Write the tensions and tower force in component form using the unit vectors 4. Develop equilibrium equations for the system. 5. Solve and clearly express the magnitude of the cable loads in terms of the unknown variable, 9, the wind direction angle. 6. Determine the wind direction angle at which the tensions in cables are the largest from the equations developed in 4. This can be done by plotting the tensions as a function of the wind direction angle Microsoft Excel or any other graphing program of your choosing.(Also, you can analytically calculate the wind direction by finding the maximum of the functions developed in 4 using differential calculus.) 7. Once the maximum tension is determined, find the maximum force the tower will experience. This is need in the design of the tower itself. This is done by plotting the tower force as a function of wind angle. The maximum tower force does not necessarily occur at the same wind angle as the maximum tension 120 120 +X 0 +Z Side view of tower Top view of tower ay cCafé Iced Coffee Da 闷 2 McCafe 2. EST. 1993 McCafe EST. 1993 25 McCafé Hot Coffee Satisfying coffee made with 100% t-ces sel Arabica beans. CaS VR $ PRİNTEO ON RECYCLED PAPER S0% Post-Consumer Content Analysis Based on the calculations, the (Blank) Cable system is the safest and most cost-effective design that can be used. The maximum tension recorded was approximately (Blank Tension)kN as opposed to (Blank Tension)kN. The tension was measured while the wind angle for Ta was 30-degree meanwhile T was at 0 degrees. TABLE TITLE: SystemMax. Tension Wind angle Max. Tower Cable size Total cable Total cable kN 58.1 Force (kN) (mm) length (m 120.93 cost (USD) 3-cable 4-cable 30 1189.95 Conclusions Based on your analysis in the previous section, clearly state which cabling system you recommend and why. Make sure to state how cable size, cost, maximum tensions, and the tower force were used to make your decision.

Answer 1

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