2. ii
Abstract
The purpose of this assignment is to design a truss bridge that could withstand as much
weight as possible. The goal is to build the bridge design to its optimal strength by using the
cheapest building material available. Three designs were though out during the planning
phase and each group member was tasked to calculate a design specification. Thereafter, the
results were compared to identify the best design and thus the building phase begun. It was
decided that Popsicle stick will be utilize due to three major factors namely durability,
availability and being economical.
3. iii
Table of Contents
Abstract………………………………………………………………………………………..ii
Table of Contents……………………………………………………………………………..iii
1.0 Introduction.……………………………………………………………………………….1
2.0 Design Background………………………………………………………………………..2
3.0 Design Proposal…………………………………………………………………………3-7
4.0 Construction Phase………………………………………………………………………8
4.1 Marking Criteria……………………………………………………………...8-10
4.2 Final Bridge Construction…………………………………………………….11-12
5.0 Cost Analysis……………………………………………………………………………13
6.0 Results and Discussion…………………………………………………………………...14
6.1 Results………………………………………………………………………...14-15
6.2 Discussion……………………………………………………………………..…15
7.0 Personal Contribution and Reflection……………………………………………………16
8.0 Conclusions and Future Development…………………………………………………...16
9.0 Appendixes……………………………………………………………………………17-24
10.0 References…………………………………………………………………..………..25
4. 1
1.0 Introduction
As a mechanical engineer, there are four core subjects that we should at least be familiar
with. They are aerodynamic, thermodynamic, mechanical kinematic and lastly, structural
analysis. In structural analysis, it is vital to be able to identify, calculate and determine the
effects of each load on the physical structure and their components. The following
assignment requires student to design a truss bridge that could withstand as much weight as
possible by using the cheapest building material available.
For this assignment, aside from the technical aspect of calculating and building the bridge, it
also portray scenario akin to the real world. In the real world, superior or client will always
demand the best design or results yet restrict and limit budgets to a minimal. An engineer will
then have to find solutions and designs that are cost effective yet meet or even top the
requirement and demands. Engineers are also generalized to have poor reporting writing
skills. Therefore, this assignment aims not only to train our technical skill but our writing
skill while stimulating the working world situation.
5. 2
2.0 Design Background
Dimensions (Based on the assignment criteria)
The bridge will be placed on a flat support which is 30cm apart.
A vertical point load will be placed at the centre of the truss.
The bridge should consist of two identical trusses joined by members so that the two
truss is 10cm apart
Maximum allowable height for the bridge is 25cm.
Figure 2.1
During the planning phase, many design were though up. Since the weight of the bridge is
also part of the marking criteria, three designs were chosen among the many base on their
simplicity and durability. The idea is to have a design that has the least truss therefore
reduces the overall weight of the bridge. More important however, is that the design must not
be too complicated less the building of the bridge could lead to disastrous result. Each
member was entrusted with one design and were tasked to analysis and calculate their
following counterparts. Thereafter, the final results were collated to identify the best truss
design for this assignment.
6. 3
3.0 Design Proposal and Calculations
3 models were considered under the assumptions of,
- Load = 20 Kg
- FLoad = Mass * Gravity
= 20 * 10
= 200 N
Load located at the centre of the bridge
Side View Front View
Each side of the bridge will experience
- Fy = 0
0 = F + F - 200
2F = 200
F = 100 N
The best model was selected by observing the force on each truss and how it is distributed.
Only the best model will be shown below. The other two model calculation can be observed
in the appendix (Model 2) & (Model 3).
200 N
F F
200 N
7. 4
Model 1
Reaction Forces
- MA = 0 (Clockwise as +ve)
0 = 100 * 0.15 – RI * 0.3
RI = 50 N
- My = 0
0 = RA – 100 + RI
0 = RA – 100 + 50
RA = 50 N
Forces in each truss
Joint A
- Fy = 0
0 = 50 – FAB * Sin 72o
FAB = 52.57 N
- Fx = 0
0 = – FAB * Cos 72o + FAC
0 = – 52.57 * Cos 72o + FAC
FAC = 16.25 N
B D F H
CA E G I
100RA RI
72o
15 cm
11 cm
15 cm
72o
FAB
FAC
50 N
8. 5
Joint B
- Fy = 0
0 = FAB * Sin 72o - FBC * Sin 72o
0 = 52.57 * Sin 72o - FBC * Sin 72o
FBC = 52.57 N
- Fx = 0
0 = FAB * Cos 72o + FBC * Cos 72o - FBD
0 = 52.57 * Cos 72o + 52.57 * Cos 72o - FBD
FBD = 32.5 N
Joint C
- Fy = 0
0 = FBC * Sin 72o - FCD * Sin 72o
0 = 52.57 * Sin 72o – FCD * Sin 72o
FCD = 52.57 N
- Fx = 0
0 = - FAC - FBC * Cos 72o – FCD * Cos 72o + FCE
0 = - 16.25 - 52.57 * Cos 72o – 52.57* Cos 72o + FCE
FCE = 48.75 N
Joint D
- Fy = 0
0 = FCD * Sin 72o – FDE * Sin 72o
0 = 52.57 * Sin 72o – FDE * Sin 72o
FDE = 52.57 N
- Fx = 0
0 = FBD + FCD * Cos 72o + FDE * Cos 72o – FDF
0 = 32.5 + 52.57 * Cos 72o + 52.57 * Cos 72o – FDF
FDF = 65 N
Joint E
- Fy = 0
0 = FDE * Sin 72o + FEF * Sin 72o – 100
0 = 52.57 * Sin 72o + FEF * Sin 72o – 100
FEF = 52.57 N
72o 72o
FAB
FBD
FBC
72o 72o
FAC FCE
FBC FCD
72o 72o
FCD
FBD
FDE
FDF
72o 72o
FCE FEG
FDE FEF
100 N
9. 6
- Fx = 0
0 = - FCE – FDE * Cos 72o + FEF * Cos 72o + FEG
0 = - 48.75 - 52.57 * Cos 72o + 52.57* Cos 72o + FEG
FEG = 48.75 N
Joint F
- Fy = 0
0 = - FEF * Sin 72o + FFG * Sin 72o
0 = - 52.57 * Sin 72o + FFG * Sin 72o
FFG = 52.57 N
- Fx = 0
0 = FDF – FEF * Cos 72o – FFG * Cos 72o – FFH
0 = 65 - 52.57 * Cos 72o - 52.57* Cos 72o – FFH
FFH = 32.5 N
Joint G
- Fy = 0
0 = - FFG * Sin 72o + FGH * Sin 72o
0 = - 52.57 * Sin 72o + FGH * Sin 72o
FGH = 52.57 N
- Fx = 0
0 = - FEG + FFG * Cos 72o + FGH * Cos 72o + FGI
0 = - 48.75 + 52.57 * Cos 72o + 52.57 * Cos 72o + FGI
FGI = 16.25 N
Joint H
- Fy = 0
0 = - FGH * Sin 72o + FHI * Sin 72o
0 = - 52.57 * Sin 72o + FHI * Sin 72o
FHI = 52.57 N
- Fx = 0
0 = FFH – FGH * Cos 72o – FHI * Cos 72o
0 = 32.5 - 52.57 * Cos 72o - FHI * Cos 72o
FHI = 52.57 N
72o 72o
FEF
FDF
FFG
FFH
72o 72o
FEG FGI
FFG FGH
72o
FGH
FFH
FHI
10. 7
Overall forces of the trusses
Model Maximum Forces Minimum Forces
1 65 N 16.25 N
2 54.95 N 22.79 N < 2 Truss without force >
3 67.58 N 45.46 N < 5 Truss without force >
Table 3.1
As it can be observed, the forces in model 1 are distributed rather evenly and the overall
forces in each truss are much lower compared to the other models. In model 2 and 3, the
trusses located at the center of the bridge experience no forces therefore do not share the load
properly. It is concluded that in model 2, the trusses at the side would receive additional
stresses and most likely cave in when the external force is applied at the middle of the bridge.
As for model 3, it could be observed that each truss endure the highest amount of forces as
compare to the other models therefore is deem to be a inferior model despite having the
forces distributed rather evenly as well. Since model 1 seems to have an edge over the other
two models, it was the obvious choice to pick.
CA E G I
B D F H
16.25 N
32.5 N
16.25 N48.75 N48.75 N
65 N 32.5 N
52.57 N
52.57 N
11. 8
4.0 Construction Phase
The marking criteria of the bridge for this assignment can be found in the sections below. The
bridge will be constructed according to these criteria.
4.1 Marking criteria
Bridge is within specified dimensions
Bridge load reading is among the highest
Bridge cost reading is among the lowest
Bridge weight reading is among the lightest
Bridge load to weight ratio is among the highest
To date, there are four types of common construction materials in building a bridge. They are
namely stone, timber, steel and concrete. Below are tables on the pros and cons of these four
materials and their suitability in regards to this assignment [1].
Materials Ductile Durable Costs Weight Availability
Stone No Yes Partial Heavy Hard
Timber Partial Yes Cheap Light Easy
Steel Yes Yes Expensive Heavy Hard
Concrete Partial Yes Partial Heavy Hard
Table 4.1
12. 9
Ultimate tensile strength (UTS) & Young’s Modulus
Ultimate tensile strength (UTS), often shortened to tensile strength (TS) or ultimate
strength, is the maximum stress that a material can withstand while being stretched or pulled
before failing or breaking. The material with higher value of tensile strength will give the
bride a better chance to survive under critical conditions such as high velocity of wind and
earthquakes. The material with higher tensile strength will allow the bridge to swing in
critical conditions instead of fracture and broken into pieces [2] [6].
Young's modulus, also known as the tensile modulus or elastic modulus, is a measure of
the stiffness of materials. It is defined as the ratio of the stress along an axis over
the strain along that axis. The Young's modulus enables the calculation of the change in the
dimension of a bar made of an isotropic elastic material under tensile or compressive loads.
For instance, it predicts how much a material sample extends under tension or shortens under
compression. Young's modulus is used in order to predict the deflection that will occur in
a statically determinate beam when a load is applied at a point in between the beam's
supports. Therefore, it is important to consider Young’s Modulus of materials which will be
used for the bridge in order to define the deflection that could give under traffic loads [3] [5].
13. 10
Materials Ultimate Tensile Strength MPa Young’s Modulus (GPa)
Timber 40 10-40
Steel 200 180- 210
Concrete 30 17 - 30
Stone 25 20 - 70
Table 4.2
Weight
The weight of the material that is used for the bridge is crucial according to the design criteria
of this assignment. To define the weight of materials, the density of the material is to be
defined which will be shown in density (kg per cubic meter). The lower the density is, the
lighter the material will be. The following table shows the density of different materials
which are considered to use in the bridge design [4] [7].
Materials Density (kg per cubic meter)
Timber Around 1000 kg ( Depending moisture content)
Steel 8000 kg
Concrete 2400 kg
Stone 2515 kg
Table 4.3
Steel has the highest young modulus and tensile strength followed by timber. On the other
hand, steel density out weight all materials. Despite being not being the strongest, timber
durability is more than well equipped for this assignment. It could also be observed that the
cheapest, lightest and easiest availability form of material is timber. Therefore, timber will be
selected as the most suited material for this assignment.
14. 11
4.2 Final bridge construction
The following pictures taken were the end product of our construction. The final
measurements of the truss were measured to be 10cm wide, 30cm long and 11.8 cm high. The
truss came in at a weight of 104.72 grams.
Figure 4.5 Isometric View
16. 13
5.0 Cost Analysis
Below in Table 5.1 is a summary of the expenses for the design of the truss.
Item No. of Units Unit Price Total Price Appendix
Popsicle sticks (100 per pack) 1 $1.98 $1.98 Receipt 1
Wood Glue 1 $7.70 $7.70 Evident 2
Table 5.1: Cost summary
Many options were though up regarding the method to merge the trusses together. Options
such as duct tape, cable ties, strings, glue are some of the suggestion put into considerations.
Ultimately, it was decided that the structure of the bridge should be rigid body therefore the
method to merge the truss should be similar to welding. Among all the suggestions, glue is
the only one that could resemble welding and it is also affordable and easily obtained.
There is multiple type of adhesive bonding available in the market ranging from liquid glue,
stick glue, super glue, epoxy, wood glue etc. To save cost, epoxy was omitted while the
common glue is known to be weakest in bonding wood. The only two type of glue left is the
super glue and the wood glue. Super glue was also rejected due to the nature of the glue.
When super glue dries it becomes very brittle and cracks easily. Due to this wood glue was
selected, as there is some form of elasticity with it. To test out which is better, both type of
glue is purchased and tested on. It was discovered that despite super glue is quicker in drying
as compared to wood glue, super glue snaps the moment it exceed a certain threshold whereas
wood glue still held together due to it elasticity. Even though super glue is much cheaper than
wood glue, the group decided to opt for durability and used the wood glue for the bridge.
17. 14
6.0 Results and Discussion
6.1 Results
During testing day, the bridge could withstand most of the load with ease. However, before
the last three loaded was added to the stack, one side of the bridge adhesive starts to give way
and the bridge is slowly being compressed at its side. However, the trusses on both side of the
bridge were uncompromised and therefore held the load without collapsing. The judges
decided to carry on and continue adding the remaining loads to the stack. Once the entire load
was added, the bridges still held on despite the connection between one sides of the truss is
caved in. It was decided by the judging panel that the bridge passes and could withstand the
entire load.
Figure 6.1
18. 15
Figure 6.2
6.2 Discussion
Since this test put loads in the middle of the connection between trusses. It was felt by the
group members that this bridge test could not truly test the durability of the trusses. The
reasons being that before the trusses could even be broken; its connections between trusses
will fail first. This is because when the load is place between trusses, it is being compress
horizontally. The true strength in the trusses lies in its vertical strength. Perhaps in the future,
slight adjustment could be made to the test. One suggestion is put load on the truss instead of
the bridge. Another suggestion could be to put the bridge under a load test machine whereby
the machine will slowly crush the bridge till it fails and the result will be shown in the
computer, how strong it truly is.
19. 16
7.0 Personal Contribution and Reflection
For this assignment, the task is distributed evenly among the members. Each member
participated in the meeting. Each member has calculated fully on one truss design. The
building and purchasing of construction material was done together. The report is distributed
into three sections evenly and was thereafter collated together.
Aside from learning the technical part of the assignment, it also allows each member to
experience the advantages of teamwork. By being in a team, opinion and ideas is shared
therefore further improve the quality of work for the assignment. Due to the team unity, the
task was accomplished much faster pace as compared to doing it alone. It was overall a fun
experience especially when it comes to the building of the bridge.
8.0 Conclusions and Future Development
This assignment is just a stepping-stone and a glimpse in what to expect in the working
world. It teaches that team unity is crucial in projects as the saying goes two head is better
than one. To achieve a common goal, it is crucial to be able to work well with every team
member. For this assignment, due to the time constraint and restrictions, it is difficult to
research and get enough data to get a better truss design and better malleable construction
material. Perhaps in the future, with sufficient funding and proper software, new alien design
can be tested out to further improve the truss design.
28. 25
10.0 References
1. Bridge Conference (2006). Construction materials used for Bridges. Retrieved from
http://www.bridgeconference2006.com/?q=node/60
2. Maine Welding Company (2008). Metals Mechanical Properties. Retrieved from
http://mewelding.com/metals-mechanical-properties/
3. Brantacan Bridge (2013). Bridge Material. Retrieved from
http://www.brantacan.co.uk/materials.htm
4. The Physic Factbook (2001). Density of Concrete. Retrieved from
http://hypertextbook.com/facts/1999/KatrinaJones.shtml
5. efunda (2014). Properties of common solid Material. Retrieved from
https://www.efunda.com/materials/common_matl/common_matl.cfm?MatlPhase=Solid&Mat
lProp=Mechanical
6. The Engineering Tool Box (2014). Modulus of Elasticity. Retrieved from
http://www.engineeringtoolbox.com/young-modulus-d_417.html
7. SI Metric (2011). Density of Material. Retrieved from
http://www.simetric.co.uk/si_materials.htm
