Calculate the displacements reactions and internal forces

Question

CVNG4050/5050 Advanced Structural Analysis Mid-Term Exam

Q1. The element shown in the figure has two sections, which have different I and length, but same E. Develop the stiffness matrix (4x4) of the element in terms of the D.O.F's of nodes i and j only. Ignore axial deformation; therefore, consider only vertical deformation (v) and rotation (θ) at each node.

Q2. Analyze the following beam as shown in the figure using the element developed in question 1. Calculate the reactions and draw the shear force and bending moment diagrams. E= 25,000 MPa and I = 10x10⁸mm⁴.

Q3. Calculate the displacements, reactions, and draw the bending moment diagram for the following system. E = 200,000 MPa. I = 100x10⁶ mm⁴.

4. Calculate the displacements, reactions and internal forces for the system shown. For the beams E = 200,000 MPa, I = 500x10⁶ mm⁴, and A = 12x10³ mm². For the truss members A = 8x10³ mm².

Textbook - Matrix Structural Analysis Second Edition by William McGuire, Richard H. Gallagher and Ronald D. Ziemian.