Module Learning Outcomes :
1. Apply force vectors in the analysis of the system of forces acting on a particle in static mechanics.
2. Use knowledge of system of forces and material properties in the analysis and design of structures.
3. Solve kinematic and kinetic problems involving uniform motion.
4. Describe fluid properties, their measurement and relevance to fluid flow.
5. Apply engineering and thermodynamic principles and equations to transport phenomena involving heat transfer.
CASE STUDY A
Assuming the role of a trainee on the verge of undertaking a structural integrity engineer position, you were presented with two technical problems involving beams (structural components). The first one is associated with the cantilever beam shown in figure 1a, subjected to a bending moment on its free-end (the magnitude of the force applied is negligible compared to the moment caused). The second one is associated with a similar cantilever beam, but, this time, subjected to a uniformly distributed load varying from 0 to 4 kN/m; as shown in figure 1.b, and with length.
1. Your task is to analyse and deduce the output values for the following:
a. Determine the reaction forces/moments (if at all present) for the supports of both beams.
b. Write the expressions for the internal shear force and bending moment for both beams.
c. Draw the shear force and bending moment diagrams
d. Identify the position and magnitude of the maximum shear force and bending moment values, stating clearly their units.
2. Part of the role you are intending to assume consists in interpreting a physical situation, so as to describe it and model it properly. In order to show your understanding of different loading configurations and their causes, EXPLAIN what type of load is expected on the wing spar (main beam) of an aircraft wing, due to the elements highlighted in figure 2, and QUALITATIVELY draw a sketch of the imposed loads. The cross-section of the spar is wider at the connection with the fuselage and approximately constant at mid span. State your assumptions.
CASE STUDY B
1. The mechanism constituted by a crank and a sliding piston is used in many applications in engineering, and is found in a multitude of configurations. One of such is the offset slider-mechanism shown in figure 3 below, whose crank rotates at a constant angular velocity of 300 rpm (counter clockwise). Determine the equations that describe the position of the slider (the output mechanism, identified by point B), its velocity and acceleration. For one revolution of the crank, plot the position, velocity and acceleration of the slider as a function of time,which should be expressed in seconds.
You should use Excel (or MATLAB; or, yet, any similar) to implement the calculations for position, velocity and acceleration of the slider for each time increment.
• Use 200 time increments from 0 to the final time interval (which should be calculated).
• Determine the crank angular displacement (θ) for each time increment.As initial conditions, make θ = 0 rad when t = 0 s.
• Write the expressions for position, velocity and acceleration in the assignment document (Word file).
• Once the work in Excel is done, copy the plots and the table of data to the assignment document (Word file).
CASE STUDY C
1. You are an engineer employed as a consultant for a shipyard recently installed in the coastal areas of the UK. A rectangular barge, with 450 kN of weight, was suspected to have been built with the wrong dimensions,but is already in a water tank, which renders direct measurements impracticable. You notice, though, that the barge floats with the base of its hull 1.5 m below the water line. Based on this, determine:
i. The area of the barge; if the original plans stated 35 m 2 , were the suspicions correct?? Draw a free-body diagram for the situation.
ii. The maximum weight of cargo the barge can carry, if it can float no more than 2.0 m below the level of the water.
iii. Imagine that, instead of floating with the base of the hull 1.5 m below the surface of the water, the barge is kept afloat on the surface of the water. Moreover, the length of the barge is three times its width. What would have to be the mass of the barge for this situation to be physically possible??
Consider: temperature of the water: 20ºC; 998 kg/m 3
2. You might have heard about an Internet challenge known as “the bottle challenge”, in which a bottle, having approximately 1/3 of its volume filled with water, is thrown in air to describe a full loop and must fall upright on a surface (a table, for example). Regarding the physical events that take place in this challenge, answer the following:
a. Differently than when the bottle is completely empty or when it is completely full, it is possible to make it fall upright on a surface, in a stable manner. Why?? Is there any similarity between this system and the lab experiment you carried out with a pontoon??
b. Since the loop trajectory of the bottle is a full rotation around its cap, draw a free-body diagram of the bottle at the most critical point of its motion and derive an expression for the minimum velocity with which a bottle of length L needs to be thrown, so that it falls steady and upright on the surface of the table.
c. Considering the energy aspects, EXPLAIN why the bottle filled up to approximately 1/3 of its volume does not bounce back, once it hits a hard surface, while the empty bottle and the full bottle do bounce.
HINT: take into consideration the properties of the fluids, as well as the physical events and forms of energy involved in the landing of the bottle.
CASE STUDY D
As a newly employed graduate trainee Engineer with BAE Systems, the head of Engineering has instructed your departmental mentor to assign you to the new cooling system for a laser scanner to be tested under cold air conditions. The air chamber where the laser scanner is located needs to be maintained at 0ºC. The internal coefficient of convection heat transfer was determined to be . The lateral surfaces of the chamber are 35 mm thick, and made of a composite fabricated with expanded polystyrene foam and a plate of carbon fibre, with a coefficient of thermal conductivity of 0.021 W/(mK). The top surface of the chamber is made of the same material, but is 40 mm thick, and the bottom surface is well insulated. The temperature of the room housing the chamber is kept constant at 25ºC by an independent cooling system, and the coefficient of external convective heat transfer was estimated to be . The internal dimensions of the chamber were provided as 250 mm (length), 170 mm (width) and 152 mm (height). You are asked to provide the following parameters:
a. The total thermal resistance of the air chamber against heat transfer from the ambient (room).
b. The amount of heat transferred from the room to the chamber.
c. If the cooling system for the laser in the chamber is capable of converting 40% of its electric power in useful mechanical energy, and it is supplied with 2.52 W, calculate the amount of heat the cooling system injects in the chamber and the total thermal load (which is the sum of this parameter with the parameter calculated in b).
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