1011SCG – MATHEMATICS 1A

ASSIGNMENT 1 -- 2015 Semester 3

Due week 5

TOTAL 100 MARKS

This is the first of two assignments that you will get in this course. It is worth 5% of your final mark.

THIS ASSIGNMENT IS DUE BY 11 PM ON FRIDAY of WEEK 5 OF SEMESTER. THIS ASSIGNMENT MUST BE SUBMITTED ELECTRONICALLY TO QIBT THROUGH

TURNITIN. MORE INSTRUCTIONS WILL BE GIVEN TO YOU IN CLASS.

Read these instructions carefully

• Extensions must be requested in advance but will only be given in the most unusual situations. Late submissions with no extension will be subject to QIBT’s late penalty policy.

• The presentation of your answers matters a lot – you must explain what you are doing and you must use proper mathematical notation (as used in texts, notes etc). Just writing an answer without working is not enough.

• You must hand in a signed assignment cover page to your Lecturer/Tutor during the first lesson after the assignment.

Guidelines for submitted work

• This is an academic assignment so it must be referenced. Include a Reference list at the end of your assignment. You must cite all the different authors from different sources (books, journals, electronic). Please do not use Wikipedia or other such non--refereed sources.

• Start each new question on a new page.

• Conduct a spell check yourself and ensure you have a critical friend read and comment on your English usage, grammar, punctuation and other technical issues.

• Please use Microsoft Word Equation to express any mathematical formulas needed, and Microsoft Word to write the assignment.

• You may use graphical or drawing software to show your graphs.

• Please use size 12 font for any written work.

• Leave a wide margin on the left for feedback comments from your teachers.

What is plagiarism

Plagiarism is when you submit work that is not yours. Even if you make slight changes in symbols it is still plagiarism. Plagiarism is cheating and is wrong. If it is detected all the people whose answers are extremely similar will get zero marks for the questions involved.

It is a good idea to discuss problems with other people. It is often helpful to work in study groups, but you must write up your answers by yourself and your examples must be unique.

Any similarities identified with TURNITIN will be investigated and penalties will be applied in line with QIBT academic integrity policy. This policy can be found at http://policy.qibt.qld.edu.au/

Marking Criteria – Total 100%

Submitted report – 30%

Work done in class and verified by your tutor – 20% Oral exam – 50%

LEARNING GOALS:

• Calculate the components of a force vector.

• Add two force vectors together.

• Draw a free body diagram.

• Write and solve a force vector equilibrium equation.

• Use the Method of Joints to calculate the internal force in every member in a truss that is statically determinate.

• Mathematically determine which is the weakest member of your bridge.

TASKS:

According to the Bridge Client Brief (Appendix A), you will design a bridge with the given specifications. This assignment consists of producing the mathematical evidence to calculate the strength of the members of one side of this bridge.

Your first task is to investigate bridge designs that you think are appropriate for this task. Bridges are very important structures and whether you are going to pursue a structural engineering career or not, this project will catapult you into the world of engineers. If you have done the 1007ENG Engineering Fundamentals project already, or are doing it this semester, you may use your scaled design as your guide for your calculations. If your are doing this project in the future this assignment will help you with many of the tasks.

Once you have researched the designs, you need to produce a 2--Dimensional space sketch or graph of your own design that meets the specifications given in appendix A. It can be as simple or as elaborate as you like. You may even go as far as using a CAD program (if you know how), or your own hand drawn, neat and tidy, design, which you have scanned and added to your document. However, you need to describe the exact length, height and weight of your bridge (reasonable approximations are acceptable), the number of truss sections and the amount of weight, it needs to support. You can ignore dynamic load (research what this means). The design will be assessed on calculations’ accuracy and not on its appearance, however it must be readable, or it will not count.

Your second task is to calculate (using vectors) the static load, which includes the Net--force on each joint, also known as internal member force. You will need to consider the specifications given carefully and make sure you include the weight of the car and track, as well as the test weight in your calculations. You may assume the car is in the middle of the bridge. Make sure you state clearly the assumptions made for your design. Your final task is to produce a report clearly showing all the tasks mentioned above. This has to be typed as per the instructions given in the guidelines at the start of this document, and submitted to Turnitin.

Method of joints

For this task we can reduce the bridge to a 2--dimensional space. An example of how this method works is shown in the link https://bridgecontest.org/assets/2013/09/la3.pdf

At each joint you must show clearly two equations, one equation for the horizontal balance and one equation for the vertical balance of the forces at play. If your bridge has sections that are statically indeterminate, for simplification purposes these can be ignored, that is, show clearly or highlight in your design which members are statically indeterminate and therefore ignored for the purpose of making the bridge statically determinate.

Your third task, once you have predicted the strength of each member, is to identify from your calculations which is the weakest member of your bridge or where is your bridge most likely to break first, again how this is done can be found in this document https://bridgecontest.org/assets/2013/09/la3.pdf

SOME EXTRA HELP

Physical Forces & Bridge Design

The work of a bridge is to support itself and its load against the pull of gravity (stress). Stress on a material usually results in strain or a change in the material's shape. There are two types of stress: compression and tension. In a bridge, stress is also caused by the pull of gravity. The amount of stress is determined by the weight of the bridge plus its load.

Compression – A member bearing weight is under compression.

Tension – A member being pulled is under tension.

SOME USEFUL LINKS AND RESOURCES

https://bridgecontest.org/resources/file--folder--bridges/ look for Learning Activity #3 https://www.youtube.com/watch?v=nNrdzAz_NFM

https://www.youtube.com/watch?v=56eTM36Z9--A

APPENDIX A

Spaghetti Bridge Client Brief

QIBT -- 1007ENG Engineering Fundamentals Lab

1. Requirement

Construct the lightest spaghetti bridge that will meet the performance criteria of supporting a moving car carrying a load of 3.5 kg while also meeting design specifications.

2. Specification

The test rig schematic shows the arrangement that will be used to test your bridge. The roadway/“Track” is made of aluminium, weighing 0.9kg and is hinged in 5 places across the bridge and at each end. The “Car” (which also weighs 0.9kg) will be allowed to run down the small hill on the left and across the bridge. The bridge must be not less than 648mm long (at the bottom) and be able to support the road 102 mm above the base of the bridge. Theroad/“Track”is 80mm wide.

To assess the maximum load capabilities of the bridge, the load carried by the car will be increased incrementally up to a maximum of 3.5 kg or until the bridge fails. To win this competition you must build the lightest bridge that can support a moving car carrying a load of

3.5 kg.

3. Materials

This project will use THIN dry spaghetti as the ONLY construction material, along with suitable glue. The choice of glue or glues is entirely up to the team.

4. Bridge Design Criteria:

For your bridge to be successful, it MUST fit into the “test rig” and meet the design specifications and performance criteria respectively:

The bridge MUST

1. be not less than 648mm long (at the bottom)

2. be 102mm high (from bottom supports to top)

3. be no more than 80 mm wide (for track to sit upon)

4. weigh less than 180 grams

5. rest on two end supports only

6. be constructed from THIN cylindrical dry spaghetti, joined with a suitable glue Test Rig Schematic

ASSIGNMENT 1 -- 2015 Semester 3

Due week 5

TOTAL 100 MARKS

This is the first of two assignments that you will get in this course. It is worth 5% of your final mark.

THIS ASSIGNMENT IS DUE BY 11 PM ON FRIDAY of WEEK 5 OF SEMESTER. THIS ASSIGNMENT MUST BE SUBMITTED ELECTRONICALLY TO QIBT THROUGH

TURNITIN. MORE INSTRUCTIONS WILL BE GIVEN TO YOU IN CLASS.

Read these instructions carefully

• Extensions must be requested in advance but will only be given in the most unusual situations. Late submissions with no extension will be subject to QIBT’s late penalty policy.

• The presentation of your answers matters a lot – you must explain what you are doing and you must use proper mathematical notation (as used in texts, notes etc). Just writing an answer without working is not enough.

• You must hand in a signed assignment cover page to your Lecturer/Tutor during the first lesson after the assignment.

Guidelines for submitted work

• This is an academic assignment so it must be referenced. Include a Reference list at the end of your assignment. You must cite all the different authors from different sources (books, journals, electronic). Please do not use Wikipedia or other such non--refereed sources.

• Start each new question on a new page.

• Conduct a spell check yourself and ensure you have a critical friend read and comment on your English usage, grammar, punctuation and other technical issues.

• Please use Microsoft Word Equation to express any mathematical formulas needed, and Microsoft Word to write the assignment.

• You may use graphical or drawing software to show your graphs.

• Please use size 12 font for any written work.

• Leave a wide margin on the left for feedback comments from your teachers.

What is plagiarism

Plagiarism is when you submit work that is not yours. Even if you make slight changes in symbols it is still plagiarism. Plagiarism is cheating and is wrong. If it is detected all the people whose answers are extremely similar will get zero marks for the questions involved.

It is a good idea to discuss problems with other people. It is often helpful to work in study groups, but you must write up your answers by yourself and your examples must be unique.

Any similarities identified with TURNITIN will be investigated and penalties will be applied in line with QIBT academic integrity policy. This policy can be found at http://policy.qibt.qld.edu.au/

Marking Criteria – Total 100%

Submitted report – 30%

Work done in class and verified by your tutor – 20% Oral exam – 50%

LEARNING GOALS:

• Calculate the components of a force vector.

• Add two force vectors together.

• Draw a free body diagram.

• Write and solve a force vector equilibrium equation.

• Use the Method of Joints to calculate the internal force in every member in a truss that is statically determinate.

• Mathematically determine which is the weakest member of your bridge.

TASKS:

According to the Bridge Client Brief (Appendix A), you will design a bridge with the given specifications. This assignment consists of producing the mathematical evidence to calculate the strength of the members of one side of this bridge.

Your first task is to investigate bridge designs that you think are appropriate for this task. Bridges are very important structures and whether you are going to pursue a structural engineering career or not, this project will catapult you into the world of engineers. If you have done the 1007ENG Engineering Fundamentals project already, or are doing it this semester, you may use your scaled design as your guide for your calculations. If your are doing this project in the future this assignment will help you with many of the tasks.

Once you have researched the designs, you need to produce a 2--Dimensional space sketch or graph of your own design that meets the specifications given in appendix A. It can be as simple or as elaborate as you like. You may even go as far as using a CAD program (if you know how), or your own hand drawn, neat and tidy, design, which you have scanned and added to your document. However, you need to describe the exact length, height and weight of your bridge (reasonable approximations are acceptable), the number of truss sections and the amount of weight, it needs to support. You can ignore dynamic load (research what this means). The design will be assessed on calculations’ accuracy and not on its appearance, however it must be readable, or it will not count.

Your second task is to calculate (using vectors) the static load, which includes the Net--force on each joint, also known as internal member force. You will need to consider the specifications given carefully and make sure you include the weight of the car and track, as well as the test weight in your calculations. You may assume the car is in the middle of the bridge. Make sure you state clearly the assumptions made for your design. Your final task is to produce a report clearly showing all the tasks mentioned above. This has to be typed as per the instructions given in the guidelines at the start of this document, and submitted to Turnitin.

Method of joints

For this task we can reduce the bridge to a 2--dimensional space. An example of how this method works is shown in the link https://bridgecontest.org/assets/2013/09/la3.pdf

At each joint you must show clearly two equations, one equation for the horizontal balance and one equation for the vertical balance of the forces at play. If your bridge has sections that are statically indeterminate, for simplification purposes these can be ignored, that is, show clearly or highlight in your design which members are statically indeterminate and therefore ignored for the purpose of making the bridge statically determinate.

Your third task, once you have predicted the strength of each member, is to identify from your calculations which is the weakest member of your bridge or where is your bridge most likely to break first, again how this is done can be found in this document https://bridgecontest.org/assets/2013/09/la3.pdf

SOME EXTRA HELP

Physical Forces & Bridge Design

The work of a bridge is to support itself and its load against the pull of gravity (stress). Stress on a material usually results in strain or a change in the material's shape. There are two types of stress: compression and tension. In a bridge, stress is also caused by the pull of gravity. The amount of stress is determined by the weight of the bridge plus its load.

Compression – A member bearing weight is under compression.

Tension – A member being pulled is under tension.

SOME USEFUL LINKS AND RESOURCES

https://bridgecontest.org/resources/file--folder--bridges/ look for Learning Activity #3 https://www.youtube.com/watch?v=nNrdzAz_NFM

https://www.youtube.com/watch?v=56eTM36Z9--A

APPENDIX A

Spaghetti Bridge Client Brief

QIBT -- 1007ENG Engineering Fundamentals Lab

1. Requirement

Construct the lightest spaghetti bridge that will meet the performance criteria of supporting a moving car carrying a load of 3.5 kg while also meeting design specifications.

2. Specification

The test rig schematic shows the arrangement that will be used to test your bridge. The roadway/“Track” is made of aluminium, weighing 0.9kg and is hinged in 5 places across the bridge and at each end. The “Car” (which also weighs 0.9kg) will be allowed to run down the small hill on the left and across the bridge. The bridge must be not less than 648mm long (at the bottom) and be able to support the road 102 mm above the base of the bridge. Theroad/“Track”is 80mm wide.

To assess the maximum load capabilities of the bridge, the load carried by the car will be increased incrementally up to a maximum of 3.5 kg or until the bridge fails. To win this competition you must build the lightest bridge that can support a moving car carrying a load of

3.5 kg.

3. Materials

This project will use THIN dry spaghetti as the ONLY construction material, along with suitable glue. The choice of glue or glues is entirely up to the team.

4. Bridge Design Criteria:

For your bridge to be successful, it MUST fit into the “test rig” and meet the design specifications and performance criteria respectively:

The bridge MUST

1. be not less than 648mm long (at the bottom)

2. be 102mm high (from bottom supports to top)

3. be no more than 80 mm wide (for track to sit upon)

4. weigh less than 180 grams

5. rest on two end supports only

6. be constructed from THIN cylindrical dry spaghetti, joined with a suitable glue Test Rig Schematic

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