Reference no: EM13831698

Assignment

1-

1.1 Introduction

A truss structure is shown in Fig. 1, with all members made of the same material with the same cross-section. Your task is to calculate the force in each of the members and determine which has the largest (magnitude of) force (and is therefore the one most likely to fail, ignoring effects such as buckling).

Figure 1: Schematic of truss for Question 1. Blue arrows and text represent applied forces; red arrows and text represent reaction forces; and magenta numbers denote member number, as used in Eqs. (1)-(5).

Based on the laws of statics, the following equations can be derived for the forces in each member:

F1 cosa + F2 = -Bx (1)
F1 sina = -By (2)
F1 sina + F3 + F4 sinß = -P (3)
F5 = -F4 cosß (4)
F4 sinß = -Cy . (5)

The values for the reaction forces can be solved from the global statics equations: (5)

Bx = 0 (6)
By + Cy = P (7)
ByL1 = CyL2 . (8)

For your assignment, the following values are to be used: (8)

L1 = 6.1748m (9)
L2 = 8.8276m (10)
H = 3.6355m (11)
P = 2.2981kN. (12)

1.2 Requirements

For this assessment item, you must produce MATLAB code which:

1. Solves the set of simultaneous equations (1)-(5) to determine the unknown forces.

2. Determines which member has the largest magnitude force.

3. Reports to the Command Window which member has the largest magnitude force and the value of the force in that member.

4. Produces a plot that visualises the force in each member. A minimum requirement is to plot the forces; for maximum marks, the truss itself will be plotted with each member coloured so that the colour represents the value of force.

5. Has appropriate comments throughout.

You must also solve the set of simultaneous equations by hand to verify your code; submit this working in a pdf file. Your MATLAB code must test (verify) whether the computed values of forces are the same as calculated by hand.

1.3 Assessment Criteria

Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.

Quality of the code

Quality of header(s) and comments

Quality of calculation of the forces

Quality of reporting

Quality of visualisation

Quality of verification based on hand calculations

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2.1 Introduction

There are some entries in the data for ass1data.xls which are invalid: there are no measurements for a number of times. These blank entries in Excel are imported as NaN into MATLAB. Note that sometimes no measurements are recorded, while at other times some measurements are recorded and others are absent. Your task is to complete Assignment 1 (i.e. report the average power in an undisturbed stream of air for every single time that is listed), so you must provide each hour with an entry for all the variables except for Wind direction. This means you will need to process a total of 4 variables. Look up "nan" in the MATLAB help for assistance in functions pertaining to NaN.

2.2 Requirements

For this assessment item, you must produce MATLAB code which:

1. Identifies which entries are missing.

2. Displays a message in the Command Window showing how many missing entries there are for each of the relevant variables.

3. Uses a range of methods for replacing the missing entries:

(a) sets the missing entry to zero

(b) uses the value from the previous entry

(c) uses the value from the next entry

(d) uses linear interpolation

(e) uses spline interpolation

4. Checks that none of the inserted values is non-physical (i.e. checks that all of the inserted values satisfy the physical properties of speed, temperature and pressure).

5. Displays a message in the Command Window with a brief assessment of how good each method is, whether it is suitable for the task of processing all 4 variables and why. You should also note which method you think is best and, if necessary, add any additional comments to justify that choice.

6. Uses the method that was chosen to be the best to create a complete data set for the 4 variables.

7. Displays a message in the Command Window showing the average power and the maximum power for the entire dataset.

8. Saves the complete dataset for the time and 4 variables to a text file and also a mat-file for future use.

9. Has appropriate comments throughout.

You must also use linear interpolation by hand to replace the second entry of wind speed (replace the known value in the second row of data with an interpolated value); submit this working in a pdf file. Your MATLAB code must test (verify) whether this value is the same as computed by the code for linear interpolation to replace the second entry.

2.3 Assessment Criteria

Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.

Quality of the code

Quality of header(s) and comments

Quality of identifying which are missing entries

Quality of replacing the missing entries with an appropriate value

Quality of checking entries

Quality of discussion

Quality of reporting

Quality of file output

Quality of verification based on hand calculations

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3.1 Introduction

One of the columns in the ass2data.xls report is the speed of the maximum wind gust in the last 10 minutes. It is expected that there is a strong correlation between the average windspeed for the past hour (which is listed as "Wind speed in km/h") and the maximum wind gust. Identify if such a relationship exists and what error exists in this relationship. The file ass2data.xls is identical to ass1data.xls, except every row with a missing entry has been removed (so you don't need to have completed Question 2 to attempt this question).

3.2 Requirements

For this assessment item, you must produce MATLAB code which:

1. Determines what type of curve-fit is appropriate for each set of data.

2. Demonstrates that the chosen curve-fit is the best both graphically and numerically.

3. Plots both sets of data and the chosen curve-fit on a single graph.

4. Displays a message in the Command Window stating which type of curve-fit was chosen, stating the parameters of the curve-fit and the result of the numerical test of the curve-fit.

5. Has appropriate comments throughout.

3.3 Assessment Criteria

Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.

Quality of the code

Quality of header(s) and comments

Quality of determination of appropriate curve-fit

Quality of plots (e.g. axis labels, titles)

Quality of reporting of curve-fit

4

4.1 Introduction

It is suspected that the Air Temperature and the Mean sea level pressure in the ass2data.xls report each have a normal distribution. You should perform some analysis to determine whether this is the case. The file ass2data.xls is identical to ass1data.xls, except every row with a missing entry has been removed (so you don't need to have completed Question 2 to attempt this question).

Assuming that the temperature and pressure can be considered to be normal distributions, what distribution do you think the density should have? Compare the mean of the actual distribution of density to the theoretical value (based on the means of pressure and temperature). Comment on whether the theoretical value is close to the actual value and discuss why it is similar/different. Note that you cannot simply compute a theoretical standard deviation for the density.

4.2 Requirements

For this assessment item, you must produce MATLAB code which:

1. Calculates the mean and standard deviation for each of temperature and pressure and reports the values to the Command Window.

2. Produces appropriate graphs or calculations to verify whether the temperature and pressure can be modelled by a normal distribution and discusses the outcome by reporting to the Command Window.

3. Calculates the mean for the density based on the data for density (actual value) and the means of pressure and temperature (theoretical value). Reports the actual and theoretical values to the Command Window and discusses whether these are close.

4. Has appropriate comments throughout.

You must also calculate by hand the mean and standard deviation for the first 5 values of temperature; submit this working in a pdf file. Your MATLAB code must test (verify) whether these values are the same as computed by the code for the first 5 values.

4.3 Assessment Criteria

Your code will be assessed using the following scheme. Note that you are marked based on how well you perform for each category, so the correct answer determined in a basic way will receive half marks and the correct answer determined using an excellent method/code will receive full marks.

Quality of the code 5 marks

Quality of header(s) and comments 5 marks

Quality of calculation and reporting of temperature, pressure mean, std 30 marks

Quality of assessment of whether either temperature or pressure satisfy normal distribution 20 marks

Quality of calculations of mean density and comparison 20 marks

Quality of verification based on hand calculations 5 marks

5

You are to write a brief report (about 100 words, excluding any code), which includes:

1. A description of an instance during the writing of your code for this assignment where there was a problem (e.g. a bug, an error, an unexpected result) or the most challenging aspect to overcome.

2. What steps you took to overcome the problem or challenge (including any code you wrote to test the problem/challenge).

3. The code before you resolved the problem or challenge, highlighting the line(s) of code where the problem or challenge occurred.

4. The code after you resolved the problem/overcame the challenge.

The problem report will be assessed using the following scheme:

Description

Excellent description of a difficult problem and effective solution 5

Good description of a moderate problem and useful solution 4

Reasonable description of a genuine problem with a pragmatic solution 3

Poor description or Problem is not very challenging or Solution is not effective/efficient 2

Problem is trivial or Solution is poor 1

No report or description does not include a genuine problem 0

Submission

Submit your code, with the "ass1data.xls" and "ass2data.xls" files that are provided to you ( or an equivalent conversion to xlsx), by the due date to the StudyDesk. Submit your problem report as a pdf file that contains selectable text (your assignment will not be marked if the pdf file does not satisfy this requirement). Note that:

• only code appearing in *.m files will be marked.

• You may need to convert the ass1data.xls and ass2data.xls files to another format ( e.g. ass1data.xlsx) to import properly into MATLAB. In that case, you must submit the files that you actually import using your code.

• You do not need to rename your files when uploading: the system automatically segregates different students' submissions.

• Uploading your files:

- You can submit your code with the Excel files in a *.zip file (do not archive in another file format such as rar or 7 z ).

- Your problem report and all other pdf files must be separate files that aren't archived.

- For any file that is not *.pdf or *.m, Turnitin will produce an error message stating that you have to "consult your system administrator". This is normal behaviour and means that you have successfully uploaded that file.

• You will NOT receive any confirmation of receipt. If you can see that the files have uploaded, then you have successfully submitted your assignment. There is no need to click a "send for marking" button, but you will have to click a button confirming that the submission is your own work.