|Spaghetti Bridge |

Abstract

For this assignment our task was to build as a group a spaghetti bridge with the objective of carrying the most weight as possible using only spaghetti and hot glue, meeting the specifications. The bridges will be loaded until they fall.

After testing to destruction, the bridges loading capacity was 14.4kg, with an initial mas of 0.840kg. This gave a weight to strength ratio of 17.1 putting the group at 4th/8th position in class.

From this it was learned the bridge held 14.4kg which is 140N therefore one Truss held 70N. These calculations helped us understand how our bridge coped with the forces and helped us answer the question of what caused our bridge to fail and where our bridge failed?

Contents
Abstract ii
Introduction 1
Background 2
Analysis 3
Design 5 Methodology 5
Calculations 6 Newton’s laws: 6 Forces on the bridge 6 Stability: 6 Truss analysis 6 Structural stability of Final Bridge: 7 Testing: 7
Simulation: 7
Results: 8 Bridge failure analysis: 8 Spaghetti beams: 8
Conclusion 9
Limitations 10
Recommendations 11
List of References 12
Appendix 14 Spaghetti Bridge Activity Report 14 Group productivity and progress 18 Further Calculations 19

Introduction

For this assignment the aim is to research and construct a spaghetti bridge in a group consisting of six members with the objective of designing a bridge that supports the most load whilst meeting the specifications in the design brief. This will be done through research, calculations and designing prototypes which will lead to a better final product. Once research, calculations and design have been gathered the bridge will be tested in a controlled environment.

Background

Triangles can be the foundation of building a solid structure. Large structures such as bridges are formed by trusses. Trusses are also formed by triangles. Through research the discovery was made that the triangles structure gives them the ability to bear a large load without collapsing. If a triangular structure does collapse it is most likely due to material fatigue and not the structure itself. If you have a triangle set on it’s base and apply a load to at the top it will hold it without collapsing as the force is distributed by the two sides. A truss is a set of triangles sharing sides which makes it even stronger as the triangles also keep their solid properties. The conclusion was made that all sorts of triangles can be used as they are all able to hold a large amount of weight. However, equilateral triangles are the strongest type of triangle as all sides are the same length which means the weight is distributed evenly. With this in mind we used the Equilateral triangles in all of our testing and the final bridge design. (Alexis O. – 2013)
In the final design the type of triangle used in construction was the isosceles as two of the sides would be longer than the third. The design procedure being opted was the bowstring. The bowstring/Whipple design is a very effective way of building a bridge. This is because it disperses the weight along the arch and towards the abutments. However, after testing the spaghetti’s flexibility and strength, it was realised that it would be quite difficult to make the arched shape effectively. The spaghetti would snap if bent too much, therefore failure was foreseen. In an attempt to solve this issue and make the spaghetti stronger it was used more of it to make a thicker strand.
By this slight change it was created a stronger design as each triangle added allowed the weight to be distributed better . The isosceles triangle structure creates the possibility of an increase of triangles in the basic structure. This means the bridges height can be formulated without effecting the width of the bridge design. (Cridlebaugh, 2008).
Unfortunately, this reduced the flexibility of the spaghetti which made it harder to create an Arch in the final and prototype designs. From testing the decision was made to stick with making a simple yet effective design bearing in mind our resources where fairly limited in the start of the project. The final bridges construction is made up of many equilateral triangles which are good as they are able to hold weight better than other forms of triangles such as isosceles and right angled.

Analysis

As there are many variations of the truss, the main focus of this discussion would be the simple types. A truss is a structure made of smaller parts, varying only in length and shape. Truss bridges have been identified as deck, pony and through. These terms are used to describe the placement of the travel surface in relation to the structure (Cridlebaugh, 2008). The truss bridges were one constructed of wooden timers, and later included iron tension members. Over the century, the truss has evolved from the simple design of the king post truss to more advanced combinations of truss. An example of this is the Ikitsuki bridge in the Nagasaki Prefecture of Japan which is a continuous truss bridge with arch shapes incorporated into the design. This bridge has held the record for the longest continuous truss bridge span since it opened in 1991 (Tatsuyuki, F et al. 1999).

[pic]
Figure 1,Wikipedia Cliff320, 2007
[pic]
Figure 2 HistoricBridges.org

Originally designed by Thomas and Caleb Pratt in 1844, the Pratt truss is the most common and has been adapted into many variations. “The basic identifying features are the diagonal web members which form a V-shape. The centre section commonly has crossing diagonal members”(Cridlebaugh, 2008).

[pic]
Figure 3 Cridlebaugh 2008

An adapted version of the Pratt Truss design is the “camelback” truss by Charles H. Parker. This variation is designed to have a top chord which does not stay parallel with the bottom chord which results in a slight curvature. “This creates a lighter structure without losing strength; there is less dead load at the ends and more strength concentrated in the centre” (Cridlebaugh, 2008)
[pic]
Figure 4 Cridlebaugh 2008

Design

In order to create the bridge it was essential to come up with a design which would be the most suitable to sustain the highest load possible. After some research, it was concluded collectively that to make the spaghetti bridge the spaghettis were shaped in triangles as it would make the bridge more stable, rather than using squares. It was also decided that the triangles would be done in a taller manner.

Methodology

• As a group it was decided that “camelback” Pratt truss design was the most suitable for the final spaghetti bridge.

• Calculations based on the structural stability formula allowed the group to judge whether the “camelback” Pratt truss was a stable design.

• On graph paper, the side view was drawn of our truss bridge design. The span of the bridge was 60 cm, while the height was 20 cm, decreasing from 20cm to 19, 17 14 and 10 cm for each beam, which allowed our bridge to have a curvature. The width of the bridge was 15 cm to allow enough space for the car to be able to pass and to meet the specification of the loading platform.

• Once the drawings were completed dimensions were established to give an estimate of each members.

• After finalising the template on graph paper, the design was transferred on to cardboard as a suitable working surface. From the drawing the lengths of the individual members were established.

• The next step was the actual construction of the bridge. To start of the construction of the bridge, two identical sides were built.

• After completing both sides the platform was built, which was then followed by the supporting structure at the top of the bridge.

• Once each side was completed, it was assembled the left, right and bottom sides of the bridge.

• Before connecting all sides to each other, verify that all sides are according to the template design.

• After finishing gluing all sides to each other and wrapping up all the details it is time to weigh the bridge.

• The final bridge weighed 840grams

• The bridge held 14.41kg.

• The success ratio

Calculations

Newton’s laws:

Newton’s laws needs to be considered for our bridge especially his 3rd law which states that “When Body A exerts a force on Body B, Body B exerts an equal and opposite force on Body A” (Newtons Third Law (2013). This is important when loads are applied onto the bridge for example a car travelling along the deck of our bridge would exert a pressure on the deck and the deck would exert an equal upwards force to keep the care there. We would need to make sure our deck is able to cope with this pressure without breaking. We made sure our deck was able to cope with this force by finding its Centre of Gravity and allowing any load being placed on the bridge to act at that point. Calculating the Centre of Gravity of our deck gave us 0.30 x 0.25m which is where the loading bay was placed. (Tutor Vista (2013)).

Centre of Gravity = [pic]
[pic]
Figure 5

Forces on the bridge

When something pushes down on the beam, the beam bends. Its top edge is pushed together, and its bottom edge is pulled apart.
Forces acting on a bridge • The pull of the earth on every part • The ground pushing up the supports • The resistance of the ground • The weight of the vehicle

Stability:

The formula below was used to calculate the stability of our structure. Stability is important factor of the break; ensuring it would not collapse on itself due to a poor structure and distribution of weight. In this equation it shows the static determinacy and stability of a bridge. The structure can be analysed using equations of equilibrium alone and is statically determinate using the following formula. (Parra M., 2013)

Truss analysis

Structural stability formula
K=2J-R Where: K= The unknown to be solved J= Number of Joints M= Number of members R= 3(numbers of sides of a triangle)
K Results Analysis If M=K : Stable Design If MK : Indeterminate Design

Structural stability of Final Bridge:

Joints = 20
Members = 37
K = 2(20) - 3 = 37
37 = M = K Therefore: the design is stable

Testing:

Simulation:

[pic]

Figure 6 Bridge Design.(2013)

Results:

Bridge failure analysis:

After testing the bridge to destruction the findings are that the actual bridges loading capacity is 14.4kg, with a mass of 0.840kg. This gave us a weight to strength ratio of 17.1 putting our group 4th/8th in or class. Once it was obtained these figures we used them to determine the weight to load ratio as seen below:

From this it was learned the bridge held 14.4kg which is 140N therefore one Truss held 70N. Dividing the 70N by each main beam (7) in the truss lead there to be 1.02kg evenly distributed on each beam which is close to our tested beam of 8 strands which held 1.5kg. Finally we learned the reaction force on both Trusses was 35N. These calculations helped us understand how our bridge coped with the forces.

Spaghetti beams:

Once we had finalised the bridges design, the next step was to test the bridge and have some initial ideas of the bridges beams. We tested the load capacity of 3 strands of spaghetti which on average held 0.682kg; we then used 8 strands of spaghetti which held 1.49kg, over double the original beam. From here we knew that having more strands would increase the maximum load but at a cost of weight.

Conclusion

Overall, as a group taking into account all the limitations and setbacks throughout this assignment the final product went quite well. During this assignment most of the time was spent on collecting data about bridge designs. This helped to formulate an understanding of construction, hence a better design. Through research it was found that triangles are the best shape at distributing weight evenly, and that the Pratt Truss design was the most suitable to meet the requirements for the bridge. Due to time spent in research and a good design, the final test of the spaghetti bridge went better than expected as the weight of the bridge to loading ratio gave 17.14 times its own weight, a better result than the prototype which was 12.06 times the weight of the bridge to loading ratio.

Limitations

Although the Spaghetti Bridge went well, due to limitations we weren’t able to grasp from our bridge design, the full potential the bridge could had supported weight.

Limitations such as:

Design Brief

From the rules established in this assignment it didn’t allow us to do a number of things that could have made the bridge more capable of supporting a larger amount of load.

Design Brief constraints:

• The bridge between the two end surfaces needed to be at least 50 cm apart from each other • The edges of the level surface in which the bridge was placed couldn’t be used as support, only the top level surfaces were allowed. • Boiling the spaghetti wasn’t allowed as well, which could have helped our bridge to become stronger. This would have strengthened the bridge in a substantial way, since when you boil the spaghetti and then let it dry, it will become harder to break, and more resistant.

Epoxy Glue

Another limitation which occurred during the creation of the spaghetti bridge was the epoxy glue. Epoxy glue was the best option as it was the best glue to create rigid joints. Also, when using the glue, as it was very quick to dry; we would try to rush gluing the joints, which in chain affected the overall stability and strength of the spaghetti bridge. Other constraints were that the epoxy glue was hard to spread and very time consuming, as it was required to mix the substances and then with a spatula spread between the spaghetti. Budget wise, the epoxy glue was very expensive and only sold in small portions in comparison with the other glues.

PVA Glue

Initially PVA glue seemed like a good idea, however after applying the glue to one side of the bridge we met a setback. Upon looking back, it was an idea which should have been further tested prior to fully coating the final design. The PVA glue completely cracked the bridge, setting us back for quite some time.

Time

Time was one of our biggest limitations. In order to build the spaghetti bridge, time was essential as it is an assignment which is very time consuming and challenging if it’s to be done correctly. As this assignment was a new project in Coventry College, we came across various uncertainties such as lack of equipment and a set brief. Ideally prototype bridges should have been a big part of this assignment as well, but due to time constraint sufficient numbers of tests were not carried out.

Recommendations

Given a chance to do this project again, it would be better to allocate the time better. This would allow more time to carry out more tests and sufficient background knowledge in order to provide a better design and result. Further uncertainties could be avoided such as; PVA Glue, Epoxy Glue and equipment’s. Research should be narrowed down and shouldn’t take too much time on research. Make sure several simulations and calculations are done for the final product as it will be a back up to be certain that the bridge will have a good weight to loading ratio.

List of References

Alexis O., (2010) The science behind triangles, list of references available from
< http://www.reference.com/motif/science/why-is-the-triangle-the-strongest-shape > [28/09/2013]

Wikipedia, the free encyclopedia (2011) The List of References illustrated [online] available from < http://en.wikipedia.org/wiki/Buckling > [30/09/2013]

The history of Bridges (2010) The List of References illustrated [online] available from
< http://www.historicbridges.org/bridges/browser/?bridgebrowser=truss/maple/ > [28/09/2013]

The List of References illustrated (2010) [online] available from [01/10/2013]

Bridge Design.(2013) The List of References illustrated [online] available from the virtual bridge design website.
< http://www.jhu.edu/virtlab/bridge/truss.htm >[28/09/2013]

Cridlebaugh,B.(2012) The List of References illustrated [online] available from Bridge basics.
< http://pghbridges.com/basics.htm > [01/10/2013]

Choochoostuff.com (2012) The List of References illustrated [online] available from numen’s supply
< http://www.choochoostuff.com/BRASS.html > [05/10/2013]
Figure 7:
Wikipedia Cliff320 (2007) The List of References illustrated [online] available from
< http://en.wikipedia.org/wiki/File:Ikitsuki_Bridge_1031230.jpg> [05/10/2013]

Figure 8:
HistoricBridges.org (2003) The List of References illustrated [online] available from
< http://www.historicbridges.org/truss/maple/wibc3.jpg > [05/10/2013]

Tatsuyuki, F., Yasuaki, C. (2008) ‘Civil engineering in engineering Japan’. Japan Society of Civil Engineers Article, Volumes 29 – 31

Parra M. (2013) The List of References illustrated [online] available from
< http://www.slideshare.net/illpa/bridge-1421612 >

Newtons Third Law (2013) The List of References illustrated [online] available from
< http://www.physicsclassroom.com/class/newtlaws/u2l4a.cfm> [01/10/2013]

Bridge Basics (2000-2001) The List of References illustrated [online] available from
< http://www.pbs.org/wgbh/buildingbig/bridge/truss_forces.html >[02/10/2013]

Tutor Vista (2013) The List of References illustrated [online] available from http://formulas.tutorvista.com/physics/center-of-mass-formula.html [02/10/2013]

-----------------------
qwezxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm