A 10 m long beam is uniformly distributed loaded (w= 7 kN/m )as shown in Figure 1 (a). The beam is made of two steel plates 209 x 20 mm and a universal beam section Section4 (See Table 1) that are bolted together to form a composite section as shown in Figure (b). The 16 mm diameter bolts are spaced longitudinally every 150 mm. The sectional properties are given in Figure (b) and Table 1. The modulus of elasticity for steel is 200 GPa. a w kN/m a Lm Steel plate Figure (a) Simply supported beam UB Section P Steel plate (b) Section a-a (dimensions not to scale) Figure (b) Section a-a & (c) UB section (c) UB Section A Section X y 1 610UB125 2 610UB113 3 610UB101 4 530UB92.4 5 530UB82 d mm mm 16000 612 229 14500 607 228 13000 602 228 11800 533 209 10500 528 209 br Table 1. Sectional properties UB Section If mm tu mm 19.6 11.9 986 17.3 11.2 875 lyo mm (x100 mm) (x100 mm) 39.3 34.3 14.8 10.6 761 15.6 10.2 13.2 9.6 29.3 554 23.8 477 20.1 a) Determine the bending moment equation (in terms of x, w, and L) at a section located at a distance x from the left support Eldy = M = dx b) Determine the slope equation in the terms of x, w, and L dy dx = EIO = c) Determine the maximum deflection at midspan in the terms of w and L :. El ymax d) Determine the moment of inertia I,, with respect to the centroidal axes. xx = x106 mm e) Determine the maximum deflection of the beam. Ymax = mm (insert "-" sign if the deflection is downward.)