civil engineering

CASE STUDY A Part 1 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 L=6 m. Figure 1 – Generic cantilever beam (a); beam under distributed load (b). Your task is to analyse and deduce the output values for the following: Determine the reaction forces/moments (if at all present) for the supports of both beams. Write the expressions for the internal shear force – V(x) – and bending moment – M(x) – for both beams. Draw the shear force and bending moment diagrams (suggestion: use Excel or similar software). Identify the position and magnitude of the maximum shear force and bending moment values, stating clearly their units. 20 marks 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. ≤200 words 10 marks Note: You are required to use your own words. Figure 2 – Wing spar and some elements. 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). Figure 3 – Offset slider-crank mechanism. 35 marks