Question

Please show work

Problem 5: Consider the continuous beam structure shown below. For each node, state the force/moment and displacement/rotation boundary conditions required to properly set-up a solution by the stiffness method. Indicate unknown values with a "u 24 k 125 k-ft 200 k-ft

Answer shown below

Answer 1

The node are considered at, 1, 2, 3: At mode 1: It is deflected vertically and also rotated: Because v = v_1, moment = 200 Theta = Theta_1 Therefore Total Degree of freedom = 2. At node 2: It is only rotated, No vertical deflection Because v = 0, moment = m_2 Theta = Theta_2 Therefore Total Degree of freedom = 1 \r\n At node: It is deflected, and also rotated Because v = 0: moment = -125 Theta = Theta_3 Therefore Total degree of freedom = 1 Therefore DOF = h(v_1, Theta_1, Theta_2 and Theta_3) rightarrow Global co-ordinate: Rightarrow Displacement, [0]: [U] = [K]^-1 [P] [P] = Force vector = [24 200 0 -125] [k] = Global stiffness matrix [U] = [k]^-1 [P] where [U] is Unknown displacement = [v_1 Theta_1 Theta_2 Theta_3] [Because v = vertical translation Because Theta = Rotation Because moments]