An I-beam cantilever with one end supported is used to carry a distributed load of P N/mm where it is resisted by moment and shear stress as shown in Figure 2. The length (1) of the cantilever beam is I mm. (i) (ii) Task X P Figure 2 dv T, dx K,GS 10 mm 80 mm 10 mm. The general equation of deflection due by bending moment is: dV M dx EI 60 mm 5 mm Where E (200000N/mm) is the elastic modulus and I is the second moment of area. I must be calculated with respect to the centroidal axis perpendicular to the applied loading. The general equation of deflection created by shear force is: Where G (76920N/mm2) is the elastic shear modulus, S is the total cross-section area and Ky is the ratio between the web area and the total cross-section area. Note: The horizontal elements are flanges, while the vertical elements are the webs 1. Develop the analytical solution to determine the deflection along the beam. 2. Develop MATLAB/octave programs for all approximation methods (RK2-Midpoint, RK2- Ralston and RK4) to estimate the deflection (vi) behaviour along the beam. a. Plot the deflection (v) curves (deflection Vs Length) for all approximation methods together with the analytical solution (Question 1). Please use suitable step size that able to generate at least 20 segments. b. Discuss on the accuracy of the approximation methods as well as the computational effort (accuracy vs computational effort). What would be the suitable approximation method to be used in your opinion? Justify your reasons. 3. By using the suitable approximation method (based on your opinion in Question 2b), What would be the deflection behaviour if the I-Beam is replaced by the T-, H- and Z-beam as shown in the Figure 2 that have same cross-sectional area? a. Plot the deflection (v) curves (deflection Vs Length) for all beams. Compare and discuss the results with the I-Beam. 10 mm Based on your results, which shapes of the beam would you recommend to be used in any general structural designs? Justify your reasons. 100 mm 60 mm Sample program Delta x = 1 x (m) 0 50 100 150 10 mm 1 Actual Solution aaa.aaaa a 10 mm 5 mm 100 mm 10 mm Numerica Solution bbb.bbbb 60 mm Approximate Error (%) X.XXXXX 60 mm 5mm True Error (%) X.XXXXX 5.mm 10 mm 105 mm 60 mm