Problem 1 Part A - Three Cable Tower - Forces The first step is to consider the forces acting on the tower. The following assumptions will be made regarding these forces. The maximum wind force acting on the tower will be F = 26 kN. The wind force will be treated as a concentrated force acting at the top of the tower at point A. The force is horizontal to the ground (parallel to the x-y plane) and will coming from a direction defined by angle 0 measured with respect to the positive x-axis. We will only consider wind directions acting between cables AB and AC (0 0 120). See diagram below. The weight of the cables will be neglected. None of the cables are pre-tensioned. This means that if there is no wind force, the tension in the cables will be zero. The tower exerts an upward force on point A. Fw D Three cable design D 120 120420 Fw x TOP VIEW Lets consider the consiquence of the cable not being pre-tensioned. Considering the cables are not pre-tensioned and the wind force will be at angles directed between cables AB and AC, what is the magnitude of the tension in cable AD? Note: Cables can only exert a force while in tension. View Available Hint(s) TAD = Submit vec Part B - Three Cable Tower - Forces ? kN The magnitude of the tensions in cables AB and AC will change as the wind direction 0 varies. In order to find the cables' maximum tensions, we will need to solve for them as a functions of wind direction 0. To do this we begin by finding the components of the wind force in terms of 0. Write the x, y, and z components of the wind force in terms of variables F and e. Write each component separated by a coma. Rememer that the wind force is parallel to the surface of the Earth. Also note that the positve x direction in the top view diagram is pointing down and the positive y in pointing to the right. vec (F2, Fy, F) Submit Request Answer Part C - Three Cable Tower - Forces ? KN Which direction is the force from the tower direted with respect to the coordinate system provided in the tower diagram? O positive z direction O negitive y direction O positive x direction O positive y direction O negigive x direction O negitive z direction Submit Request Answer Part D - Three Cable Tower Geometry - Cable AB Now the cable forces need to be written in component form. This is done by multiplying the magnitude of the cables by unit vectors directed along the cables: FAB FABUAB where AB = FAB TAB D 120 1204 120 TOP VIEW Three cable design A D Given the tower height of h = 36m and the anchor distance of r = 28 m, find the unit vector directed along cable AB. Enter each component separated by commas using three significant figures. View Available Hint(s) AB(i,j,k) Submit vec Part E - Three Cable Tower Geometry - Cable AC Next, the same is done for cable AC. FAC FACAC where == BAC = TAC TAC 120 120 20 Fw TOP VIEW ? h Fw D Three cable design Given the tower height of h = 36m and the anchor distance of r = 28 m, find the unit vector directed along cable AC. Enter each component separated by commas. View Available Hint(s) AC(i,j,k) Submit t vec ? Learning Goal: In this design challenge students will... apply vector and equilibruim concepts to a real world engineering problem. make engineering decisions based on the analysis of a cabling system. graphically present the results of your analysis using MS Exel or other graphing software. Design Scenario: You are part of a team that will design a portable tower. The tower will be used by emergency responce teams for a variety of applications including wireless comunications, weather monotoring, and survelence. Your roll is to design the cable support system. This will include specifying the... the diameter of the steel cable the total length of cable needed estimated cost of the cable The tower will be have a hight of h = 36 m with the cables attached at its top. The cables will be anchored uniformally around the tower at a distance r = 28 m from its base (see diagrams below). In order to choose the cable size, you will need to calculate the tensions they experience under storm-force wind loads. B D Three cable design D 120 1204 120 TOP VIEW Review