Q5. P → X A B. L/4 3L/4 Figure 5 Figure 5 shows a cantilever beam with a hollow circular cross- section, loaded at point

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Q5 P X A B L 4 3l 4 Figure 5 Figure 5 Shows A Cantilever Beam With A Hollow Circular Cross Section Loaded At Point 1 (243.08 KiB) Viewed 60 times

Q5. P → X A B. L/4 3L/4 Figure 5 Figure 5 shows a cantilever beam with a hollow circular cross- section, loaded at point B. (a) In your own words, define Castigliano's theorem and modified Castigliano theorum and explain when you might need to use a 'dummy load. 1 (b) Using the modified form of Castigliano's theorum, find an expression for the deflection of the beam at Point A. Clearly show all your working out. Include a sketch of the beam. (c) If the outer diameter of the beam is 30mm; wall thickness = 2 mm; Young's Modulus, E = 205 GPa; total beam length, L = 1.5 m and load P = 600 N, calculate the following: (i) the second moment of area, I, of the beam (ii) the flexural rigidity of the beam (iii) the vertical deflection of the beam at point A.