Engineering Question
BEng Aircraft Maintenance – Batch: March 2024 Engineering Science 2 – EA210MED Assignment 1 – Solid Mechanics SCENARIO: You have recently joined the maintenance department of First Flight Company as a trainee engineer. Your direct manager requested you to complete specific tasks to test your knowledge. Part of your report entails that you provide a sound explanation of the theory and calculate specific parameters in terms of the mechanics of materials. TASK 1 – Mechanics of Materials Mechanics of materials provide us with valuable information regarding the behaviour of solid bodies under the influence of loads. You are required to define and explain the following concepts that relate to mechanics of materials. Use equations and diagrams to supplement your answer: a) Strain and how to measure it experimentally b) Young’s Modulus of Elasticity c) The Stress resulting from different types of loading such as Tension/Compression, Shear, Bending and Torsion 1 TASK 2 – Stress & Strain Your next task is to find the following required values a) Axial Loads are applied at indicated locations on a bronze bar fastened between a steel and an aluminum bar as shown in the below diagram. What should be the highest value of P that will: a. Limit the total elongation to 3 mm b. Limit the stress in the steel to 140 MPa c. Limit the stress in the aluminum to 80 MPa d. Limit the stress in the bronze to 120 MPa The assembly is assumed to be suitably braced so buckling will not occur. Consider Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa. b) The below diagram represents: a. A 2.5 m diameter driving wheel at 80°C b. A steel tire (90 mm wide and 12 mm thick) that just fits over the wheel at 25°C The temperature difference will make the steel tire shrunk onto the wheel. If the deformation of the wheel caused by the pressure of the tire is neglected and the assembly cools to 25°C.; Find the thermal strain of the tire and the contact pressure between the tire and wheel. Consider α = 13 μm/(m·°C) and E = 250 GPa. 2 TASK 3 – Beams & Theory of Bending Aircraft beam structures can be represented using free-body diagrams in order to carry out certain calculations of the loads exerted on them. a) Define Centroid, Neutral Axis and second moment of Area. Explain the Parallel Axis Theorem and its applications b) For the shape below find the second moment of area about the axis AA a) Using the shear diagram in the below graph a. b. c. d. e. Construct the bending moment diagram Construct the load diagram Provide the values at each change of Load points Provide the values at each point of Zero Shear Given that the section modulus of the beam is 3250 cmᶾ, determine the allowable bending stress, while ignoring the weight of the beam. 3 b) The below diagram represents a steel bandsaw plate wrapped around a pulley (R=160mm). The dimensions of the plate are: width = 20 mm and thickness = 2 mm. a. Calculate the maximum flexural stress developed in the bandsaw b. Find the minimum diameter pulley if the flexural stress is limited to 200 MPa Consider E = 180 GPa. TASK 4 – Torsion Drive shafts and drive couplings are all subjected to twisting and torsional loads. An important use of shafts is to transmit power between parallel planes, as in aircraft engines or helicopter rotors. a) Explain the Engineer’s Theory of Torsion and state the assumptions made in this theory b) A steel propeller shaft is to transmit 5.5 MW at 180 rpm without exceeding a shearing stress of 60 MPa or twisting through more than 1° in a length of 25 diameters. Calculate the proper diameter if G = 83 GPa. c) A solid shaft with built-in ends is subject to a torque T as shown in below figure. a. Prove that the resisting torques at the walls are T1 = Tb/L and T2 = Ta/L. b. How would these values be changed if the shaft were hollow? 4 d) The below diagram represents 2 shafts, one is hollow, and one is solid. The hollow is made of bronze with D = 7 mm and d = 5mm. the solid shaft goes inside the hollow one with diameter equal to the inner diameter of the hollow shaft (d=5mm). both shafts are rigidly fastened together at their ends. a. Calculate the torque that can be applied to the composite shaft while limiting the shear stresses in the bronze to 55 MPa and in the steel to 83 MPa Consider G = 40 GPa for the bronze and G = 83 GPa for the steel TASK 5 – Dynamics The laws of motion define the relationship between forces and how they act on certain bodies that result in uniformly accelerated motion. Since the wing can be regarded as a static structure, we will look into the more dynamic components and systems on the aircraft. a) Define and explain the following concepts that relate Newton’s Law of motion. Use diagrams to support your answer. i. ii. Moment of Inertia and its calculation Radius of Gyration and its calculation b) A Large train accelerates from rest slowly. The angular acceleration of the wheels is 0.25 rad/s2 and the radius is 0.35 m. The wheels complete 200 revolutions (assume no slippage): a Calculate how far the train has moved down the track b Find the final angular velocity of the wheels and the linear velocity of the train c) Two boxes are pulled by a force F as shown in below figure. If the friction assumed to be zero and the box X has an acceleration of 4m/s2, Calculate the acceleration of the box Y. 5 d) While stopping at the side of the road, a police car spots a speeding motorist travelling at 160 km/h. An immediate chase start, with the police car accelerating at a constant 2.5 m/s2. i. ii. iii. Find the time required for the police car to intercept the speeder Calculate the distance travelled by the police car before the interception What was the velocity of the police car at the interception e) The time taken for an object to move from A to D along the red path in 30 minutes and 50 seconds. i. ii. Calculate the average speed of the object in m/s Calculate the average velocity of the object in m/s END 6
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