Assignment Task
Task
Question 1
(a) A 6 m cantilever is subjected to the loading conditions as shown in Figure Q1(a)
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(i) Apply an appropriate technique to plot the free-body diagram of the cantilever and show clearly all the forces and moments acting on the cantilever.
(ii) Plot the shear force diagram along the length of the cantilever.
(iii) Plot the bending moment diagram along the length of the cantilever.
(b) The cantilever has a rectangular cross-section with a uniform thickness of 2 cm and outer dimensions as shown in Figure Q1(b). Solve for the value of the moment of inertia of the cantilever about the x-x axis which is oriented parallel to the horizontal ground.
(c) The cantilever is fabricated out of 2024-T3 aluminium alloy with properties as shown in Table Q1(c). Verify if the cantilever is airworthy. Explain your answers with appropriate reasons.
Question 2
(a) An engineer was tasked to design a shaft that will be used to drive a helicopter tail rotor. His first design was a hollow shaft with an inner radius of 2 inches and an outer radius of 3 inches. The shaft would be fabricated out of metallic alloy with an ultimate tensile strength of 80 ksi and an ultimate shear strength of 51 ksi.
(i) Calculate the maximum torque that can be transmitted by the hollow shaft. State clearly all the assumptions you have made.
(ii) The engineer then decides to re-design the rotor shaft by melting the hollow shaft and re-fabricate it into a solid shaft of the same length. Assuming that there is no net loss in mass during the re-fabrication process, calculate the maximum torque that can be transmitted by this new solid shaft.
(b) The engineer is exploring the possibility of changing the material of the solid shaft described in Q2(a)(ii) with one that has a higher fatigue resistance property. In your appraisal of the selection of new materials being considered having sufficient structural strength to withstand the rotor loads, discuss FOUR (4) other factors that the engineer need to consider. Explain your answers with appropriate reasons.
Question 3
(a) A 4 m long beam has an inverted C-shaped cross section as shown in Figure Q3(a). X-X and Y-Y are two perpendicular axes that pass through the centroid of the cross-section. Calculate both the 2nd moment of area, Ixx and Iyy.
(b) The 4 m long beam described in Q3(a) is pin-supported at both ends and subjected to a concentrated compressive force P that acts along the horizontal axis through its centroid, as shown in Figure Q3(b). This beam is also supported at its midpoint but it is free to deform along its horizontal axis.
The material properties of the steel beam are:
Modulus of Elasticity = 200 GPa
Ultimate Compressive Strength = 700 MPa
Yield Strength = 525 MPa
(i) Calculate the critical buckling load of the beam.
(ii) By computing the necessary margin(s) of safety, examine if the beam will fail by buckling or compressive rupture when the concentrated compressive force P is 1.0 MN.
Question 4
An antenna panel as shown in Figure Q4(a) is a square-shaped panel with the high-gain SATCOM antenna mounted at its center using four installation screws. The antenna panel is to be mounted on the side of the aircraft fuselage using twenty-two solid rivets.
(a) Describe the aircraft modification procedures you will adopt to mount the above antenna panel onto the side fuselage skin of an aircraft. Illustrate with diagrams where necessary. You may assume that the installation design has sufficient strength to withstand the loading experienced in flight and hence there is no requirement to consider the structural analysis process in this case.
(b) Explain what is a statically determinate structure. List the THREE (3) equations of static equilibrium that defines this structure.
(c) Appraise the similarities and differences between aircraft modification and repairs. Illustrate your answer with relevant examples.
(d) Define a fitting factor. Explain where it is applied and why it is necessary.
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