Stiffness Matrix Question

Q.1 The structure ABCDEF shown in Figure Q1 has pin joint supports at A, D, E and F. Member BC has an off-set discrete vertical force of 20 KN as shown. Member AB carries a uniformly distributed vertical load of 3 kN/m acting along its length. All members have the relative flexural rigidities as indicated where El is 1x10 kNm? The solution should involve reference to DATASHEET Q1 as appropriate. i) Using the Displacement (Stiffness) method of matrix analysis and considering flexural deformation only, determine the stiffness matrix [K] for the structure. [7) ii) Determine the load vector (P) for the applied loading. [4] iii) Determine the displacements at B and C. iv) Determine Mac, McB and the Free, Reactive, and Combined Bending Moment Diagrams (BMD) for the beam element BC. [10] 6 m EI 4 m 20KN 3kN/m 3 m B 2EI Pin-joint EI EI | 4 m 4 m Figure Q1 Q.1 The structure ABCDEF shown in Figure Q1 has pin joint supports at A, D, E and F. Member BC has an off-set discrete vertical force of 20 KN as shown. Member AB carries a uniformly distributed vertical load of 3 kN/m acting along its length. All members have the relative flexural rigidities as indicated where El is 1x10 kNm? The solution should involve reference to DATASHEET Q1 as appropriate. i) Using the Displacement (Stiffness) method of matrix analysis and considering flexural deformation only, determine the stiffness matrix [K] for the structure. [7) ii) Determine the load vector (P) for the applied loading. [4] iii) Determine the displacements at B and C. iv) Determine Mac, McB and the Free, Reactive, and Combined Bending Moment Diagrams (BMD) for the beam element BC. [10] 6 m EI 4 m 20KN 3kN/m 3 m B 2EI Pin-joint EI EI | 4 m 4 m Figure Q1