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A 13 m long beam is uniformly distributed loaded (w= 20 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 Section 4 (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 1111111 a Lm Figure (a) Simply supported beam Steel plate UB Section y. (c) UB Section UU P Steel plate (b) Section a-a (dimensions not to scale)
Section X 1 2 3 4 5 610UB125 610UB113 610UB101 530UB92.4 530UB82 Table 1. Sectional properties UB Section A d bf tr y mm mm mm mm 16000 612 229 19.6 14500 607 228 17.3 13000 602 228 14.8 11800 533 209 15.6 10500 528 209 13.2 tw mm 11.9 11.2 10.6 10.2 9.6 Ixe (x108 mm) 986 875 761 554 477 lyo (x108 mm) 39.3 34.3 29.3 23.8 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 dạy ΕΙ = M= dx²
b b) Determine the slope equation in the terms of x, w, and L dy ΕΙ dx = ΕΙΘ = c) Determine the maximum deflection at midspan in the terms of w and L :. El Ymar = утах
d) Determine the moment of inertia I, with respect to the centroidal axes. 1 = x10 mm e) Determine the maximum deflection of the beam. Уmax mm (insert "-" sign if the deflection is downward.)