Assignment Tasks:
Question 1: Draw the free body diagrams for:
a. Solar Panel
b. Antenna
c. Support Arms
d. Pole
Question 2: Calculate the total resultant forces of the three drag load distributions, Ds, Do and 04, taking x as the distance along the surface on which the distributed load acts. (Keeping in mind the direction in which those forces are acting). Also calculate down-lift on the panel, Ls.
Question 3: Calculate the internal forces and moments acting on the connection between the solar panel and its support arm, and the antenna and its support arm, assuming that the support arms are attached to the panel and antenna at their mid-points (as drawn in Figure 3), and the resultant forces calculated in Task 1. act at the Centre of Pressure (in this case, the centroid of the depicted drag distributions).
Question 4: Assuming that the support arms are perfectly rigid, transfer the support loads and weights of the components to the pole and define the functions for the internal shear force and bending moment loads on the pole as a function of the distance y above the ground. Thus, draw the shear force and bending moment diagrams for the pole with respect to vertical position y, taking the ground as y = 0. A combination of the method of sections and the graphical method is recommended.
Question 5: Based on the diagrams you have created; determine the locations and magnitudes of the maximum positive and maximum negative (minimum) internal shear and bending loads within the pole. Call these points P (maximum positive shear), Q (maximum negative shear), R (maximum positive bending) and S (maximum negative bending). Sketch the pole and locate (draw in) these points in their respective locations, with vertical co-ordinates.
Question 6: Determine the relevant cross-sectional area A, the moment of inertia I and the polar moment of area J of the pole.
Question 7: Calculate the average shear stress at points P and Q. This will logically give you the maximum internal shear stresses. Given that τallow = 172MPa, do the maximum internal shear stresses exceed the allowable shear stress? What are the implications of this?
Question 8: Calculate the maximum normal stress due to bending ('bending stress') at point R and S. Still given that σallow = 420MPa in both tension and compression, do the normal stresses at these points exceed the allowable normal stress, and is that in tension or compression? What are the implications of this?
Question 9: The payload management team for the program mention to your group that they are having issues with total payload weight and thus ask you if you can find a way to make the antenna assembly lighter and more geometrically efficient. Three potential methods were proposed, based on the modification of the pole as everything else is too standardised already. Discuss the benefits of each approach arid, given your allowable stresses and previously calculated maximum loads, determine which of the following methods would be best if the design change is required, based on changing cross sections and their effect on I alone (these new shapes only apply for this question):
a. A tubular pole design with inner radius r, and outer radius ro
b. An I-beam design
c. A pole of step-changing diameter, starting with a greater diameter at the bottom
Question 10: Another team has approached you with a request for future-proofing the antenna assembly: They would like to attach another antenna to the pole to act as a signal repeater for a potential third colony. However, this antenna would need to be mounted at 90° clockwise around the axis of the pole, relative to the other one (when looking from above, it would essentially come out of the page towards you in Figure 2) and halfway up the pole (height 112), at point E. It experiences the same drag load in terms of direction and magnitude as the first one, and thus creates a torsional moment about the pole. Calculate the ang!e of twist between the baseplate and the longitudinal location on the pole at which the new antenna is mounted and determine the maximum shear stress in the pole due to the torsion moment at that point.
Question 11: Determine the stress state at outer surface of points P and R, as well as the principal stresses at these points and their respective orientations. Do this without and including the torque load.
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