Notes: Before preparing your assignment for submission, please refer to the assignment preparation guidelines given at the end of this sheet and the marking rubric/scheme posted in the Study Desk. The Textbook for this course is “Structural Analysis” by R C Hibbeler, 9th edition in SI Units. This assignment is worth 20% to your overall grade, i.e. 200 marks.

**Q1. Statically indeterminate beam analysis. (30 marks)**

a) Calculate the BMs at all the joints of the beam shown in problem 11.7 (p. 491) using the slope deflection method. (14 marks)

b) Calculate the BMs at all the joints of the same beam shown in problem 11.7 (p. 491) using the moment distribution method. (14 marks)

c) Compare the values of BMs obtained using the two methods a) and b) and comment.

(2 marks)

**Q2. Statically determinate or indeterminate truss analysis by the stiffness method. (50 marks)**

a) Determine the stiffness matrix of the whole truss given in problems 14.9 and 14.10 (p. 583). Indicate the degrees-of freedom in all the stiffness matrices. (18 marks)

b) Calculate all the nodal displacements and all the member forces for the truss.

(16 marks)

c) Repeat the problem using the Strand7 finite element software package. Show the truss model with loadings and boundary conditions. Submit a hard copy from Strand7 showing the nodal displacements and member forces (highlight these in the hard copy). (10 marks)

d) Present a table showing the comparisons of member forces from the stiffness method (manual calculations) and Strand7 analysis. Comment on the comparisons of the values between the two. (3 marks)

e) Is this truss statically determinate? Explain with reasoning. (3 marks)

**Q3. Statically determinate or indeterminate beam analysis by the stiffness method (45 marks)**

a) Determine the global stiffness matrix of the beam of problem 15.10 (p. 603). Indicate the degrees-of freedom in all the stiffness matrices. (10 marks)

b) Determine the rotation at node 2 of the beam and reactions at the supports. Show all calculations. (20 marks)

c) Solve the problem using the Strand7. Show the model with all the nodes and element numbers and boundary conditions. Display the deflected shape and BMD. (10 marks)

d) Show a table comparing the stiffness method (manual calculations) calculations of the rotation at node 2 and all the reactions with those of Strand7 results. Comment on the comparisons of the values between the two. (2 marks)

e) If the support at node 2 settles by 20 mm, what change will happen in the stiffness equation KD=Q.

University of Southern Queensland

**Q4. Statically determinate or indeterminate frame analysis by the stiffness method (45 marks)**

a) Determine the stiffness matrix of the frame of problems 16.5 and 16.6 (p. 619). Indicate

the degrees-of freedom in all the stiffness matrices. (10 marks)

b) Determine all the displacement components at node 2 and all the reactions including

the reactions at node 2. Show all calculations. (18 marks)

c) Draw the BMD of the frame on the compression side showing all the salient values.

Show all calculations. (5 marks)

d) Repeat the problem using the Strand7. Show the model with all the nodes and element

numbers and boundary conditions. Submit a hard copy from Strand7 showing the all

the reactions (highlight these in the hard copy). Display the bending moment diagram

for the frame. (10 marks)

e) Compare the BMD from Strand7 with the theoretical one and also compare the

respective values of maximum BM. Comment on the comparisons of the values

between the two. (2 marks)

**Q5. 2D modelling using the Strand7 (30 marks)**

a) A 4 m x 4 m plate (in the xy plane) with 6 mm thickness, is fixed at all the edges and is

loaded by pressure loading of 1 kN/m2 in the downward (-z) direction. The plate is

made of steel (E = 200 GPa, density = 7850 kg/m3). Refer the example in Sec 9.9 of

studybook.

i. Show the plate model with the loading and boundary conditions. Use Quad8

element with 4 x 4 mesh for the full plate. (6 marks)

ii. Using Quad8 element and 4 x 4 mesh for the full plate determine the maximum

deflection of the plate in the downward (-z) direction. Where is the location of

maximum deflection? (4 marks)

b) Starting from 2 x 2 mesh, show a convergence plot for the maximum deflection of the

plate described in part a). Hint: increase the mesh size from 2 x 2 to 4 x 4 etc. and then

plot the deflection with respect to the mesh size and comment on your finding.

(5 marks)

c) If the boundary conditions of the plate is changed to simply supported from fixed as

was in part a) keeping every other parameters as same, will the deflection increase or

decrease in this case and explain why do you expect it to happen? (5 marks)

d) Plane stress problems are a class of 2D problems. Draw the figures of all the elements

that can be used for modelling plane stress problems in Strand7. State how many

degrees-of-freedom each node has and show this for any one element. (10 marks)

Assignment Preparation Guidelines

The following is an outline of the format for Assignment Submissions in this subject:

- Print your name in the upper right hand corner.
- Follow a logical sequence in obtaining your solution. Show all calculation details. A marker must be able to check your work, quickly and accurately.
- Draw all necessary sketches, figures and free body diagrams. Do not write “refer to assignment sheet or text book’’ for figures.
- Define all variables used in the calculations.
- Use appropriate units.
- Show final answers clearly. Use a box around or two forward slashes or double underlines to show your answer. If appropriate provide a clearly labeled summary table for each question.
- Do not show final answers to large number of significant places. Three significant places will be appropriate in most cases.
- For Strand7 results/plots, present them with white background instead of black.
- Ensure that in the scanned Strand7 plots, the values are readable, otherwise marks will be deducted.

A penalty may be applied for “poor overall appearance” if students have not adhered to the above listed guidelines (see marking scheme for details).