All working out must be shown and reference provided.

1. What are the two matrix methods used for analysis of skeletal structures?

2. Give another name used for the Direct (Matrix) Stiffness Method in structural analysis.

3. Define a statically indeterminate structure. What is meant by the degree of statical indeterminacy?

4. In the Direct (Matrix) Stiffness Method, what governs the size of the problem?

5. Determine the degree of kinematic indeterminacy of the following structure neglecting the axial effects.

6. If the stiffness of the following bar element is known to be AE/L, what is the stiffness matrix "k'' of the element?

7. List two uses of the contragradient law in structural mechanics.

8. Determine the transformation matrix for the following element.

9. If the stiffness of the following spring element is k, write down the stiffness matrix of the element.

10. In the matrix stiffness method, what are the basic unknowns of the problem?

11. State whether the following statement is ‘true' or ‘false'.

"The transformation matrix for a plane truss element is a (2 × 2) matrix and a (3 × 3) matrix for a beam element"

12. Consider the slab-beam bridge shown in following figure:

If the ultimate design load on the bridge beam is found to be 50 kN/m, model the structural system showing all loads.

13. Choose the correct definition for the stiffness matrix from the following.

A. The stiffness matrix of a member is defined as the relationship between the independent forces at the ends of a member and the corresponding relative displacements at the end of the members

B. The stiffness matrix of a member is defined as the relationship between the independent displacements at the ends of a member and the corresponding forces which may not necessarily be independent.

C. The stiffness matrix of a member is defined as the relationship between the independent forces of individual members and material properties of the member.

14. What is the degree of freedom of the following structure (assume members are axially rigid)?

15. Calculate fixed end forces of each member of the above structure (Q15) and show in a sketch.

16. Using the fixed end forces calculated in above Q16, sketch the restraining forces at each joint.

17. If the forces in elements due to displacements of the above structure (Q15) are shown in the following table, calculate the total moments of the elements.

18. Sketch the final bending moment diagram of the structure in Q15 using the above results.

19. Write the stiffness matrix for the following element subjected to torsion. (Length of the element = L, Shear modulus = G, Torsional inertia = J)

20. State the reason why the matrix stiffness method is sometimes identified as the equilibrium method of analysis.

21. Determine the stiffness matrix of the following four spring system. The spring constant k = 200 kN/m

22. Using the direct stiffness method, determine the stiffness matrix for the following spring system.

23. In direct (matrix) stiffness method, what is the main reason to assume that the members of the structure are axially rigid?

24. State a possible disadvantage in excluding axial deformations of members (assuming members to be axially rigid) in structural analysis.

25. In the matrix stiffness method, what is known as the "Transformation matrix"?

Task 1

Model the following structure in the SAP 2000 (or any other) software and generate the Bending Moment Diagram, Shear Force Diagram and Axial Force Diagram from the software. Paste snapshots of each stage.

Please ensure you carry out: Modelling, Enter data, Interpret result, Generate Diagrams

Task 2

Model the following structure in the SAP 2000 (or any other) and generate the Bending Moment Diagram, Shear Force Diagram and Axial Force Diagram from the software. Paste snapshots of each stage.

Task 3

Q1. In following equation, what is symbolized by ‘N*'?

δ_b = c_m/(1- (N^∗/N_omb))

Q2. Write down the equation used to find the Elastic flexural buckling load (N_omb) for braced compressive member.

Q3. Moment Amplification Factor on a Braced Frame An edge column in a building of "simple" construction is of 150UB14 section (EI = 200000 ? 6.66 ? 10⁶), effective length 6m. It has an axial compressive force N * = 100 kN and a uniform bending moment M_m* = 50 kNm calculated by first order analys is. Calculate δ_b and hence the amplified moment that should be used for design.

Q4. If the Member design axial force(N*) is 5000 and Euler elastic buckling load (N_oms) is 60000 in given member, find out the elastic buckling load factor (λ_ms). Length of the member is 4m.

Q5. Draw the shear force diagram for below structure. Results of the moment distribution are also given

Q6. A frame ABC is loaded on AB as shown below figure. Analyse the frame with the help of moment distribution method, and draw the bending moment diagram.