Question 2 A steel beam member with a hinge connection (pinned) at x = 0 and x = / has the following properties: length 1 = 5 m, cross-sectional area A = 50 cm, I = 1.2(107) mm, p = 7850 kg/m and E 200 GPa. = a. Derive the beam's response when the point force shown in Figure 2 is applied at its mid span. Plot the response at the mid span and at x = = 1 m for t = 0 to 0.5s. Are the responses different? In what way? How many modes are needed to capture the motion of the beam? f(t), kN 4 3 2 1 0 -1 -5 0 5 LO W4 t = O~ass Fo D = 3KN t, s Figure 2. b. Derive the beam's steady state response when subject to harmonic excitation over half of its span (see Figure 3) where Fo beam for t = 0 to 0.5s. = 480 N/m. Plot the response at the mid span of the Fosin (50t) Pined-Pined 1/4 K Figure 3. Left end k 1/4 w(ost) = wxx (0,+1=0 Right end. w(4+) =Wxx (4+1=0