GENG 1001Assignment 1

Members:

Nathaniel Joseph Mcadam c3137132

Aung Kyaw Thet c3120444

Yeo Tian Jie Daniel c3124147

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.

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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

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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.

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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.

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F F

200 N

200 N

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 = 00 = F + F - 200 2F = 200F = 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).

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B D F H

CA E G I

100RA RI

72o

15 cm

11 cm

15 cm

72o

FAB

FAC

50 N

Model 1

Reaction Forces

- MA = 0 (Clockwise as +ve)0 = 100 * 0.15 – RI * 0.3RI = 50 N

- My = 0 0 = RA – 100 + RI0 = RA – 100 + 50RA = 50 N

Forces in each truss

Joint A

- Fy = 00 = 50 – FAB * Sin 72o

FAB = 52.57 N

- Fx = 00 = – FAB * Cos 72o + FAC

0 = – 52.57 * Cos 72o + FAC

FAC = 16.25 N

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72o 72o

FAB

FBD

FBC

72o 72oFAC FCE

FBC FCD

72o 72o

FCD

FBD

FDE

FDF

72o 72oFCE FEG

FDE FEF

100 N

Joint B

- Fy = 00 = FAB * Sin 72o - FBC * Sin 72o

0 = 52.57 * Sin 72o - FBC * Sin 72o

FBC = 52.57 N

- Fx = 00 = FAB * Cos 72o + FBC * Cos 72o - FBD

0 = 52.57 * Cos 72o + 52.57 * Cos 72o - FBD

FBD = 32.5 N

Joint C

- Fy = 00 = FBC * Sin 72o - FCD * Sin 72o

0 = 52.57 * Sin 72o – FCD * Sin 72o

FCD = 52.57 N

- Fx = 00 = - 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 = 00 = FCD * Sin 72o – FDE * Sin 72o

0 = 52.57 * Sin 72o – FDE * Sin 72o

FDE = 52.57 N

- Fx = 00 = 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 = 00 = FDE * Sin 72o + FEF * Sin 72o – 1000 = 52.57 * Sin 72o + FEF * Sin 72o – 100 FEF = 52.57 N

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72o 72o

FEF

FDF

FFG

FFH

72o 72oFEG FGI

FFG FGH

72o

FGH

FFH

FHI

- Fx = 00 = - 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 = 00 = - FEF * Sin 72o + FFG * Sin 72o

0 = - 52.57 * Sin 72o + FFG * Sin 72o

FFG = 52.57 N

- Fx = 00 = 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 = 00 = - FFG * Sin 72o + FGH * Sin 72o

0 = - 52.57 * Sin 72o + FGH * Sin 72o

FGH = 52.57 N

- Fx = 00 = - 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 = 00 = - FGH * Sin 72o + FHI * Sin 72o

0 = - 52.57 * Sin 72o + FHI * Sin 72o

FHI = 52.57 N

- Fx = 00 = FFH – FGH * Cos 72o – FHI * Cos 72o 0 = 32.5 - 52.57 * Cos 72o - FHI * Cos 72o

FHI = 52.57 N

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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 N52.57 N

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.

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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

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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].

Materials Ultimate Tensile Strength MPa Young’s Modulus (GPa)

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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.

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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

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Figure 4.6 Front View

Figure 4.7 Top View

Figure 4.8 Side View

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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.

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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

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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.

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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.

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9.0 Appendix

9.1 Model 2

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Model 3

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Receipt 1

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Evident 2

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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&MatlProp=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

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