i

MECHANICAL ENGINEERING DESIGN 1 (MECN2014)

Title: BRIDGE DESIGN PROJECT

Group Number: 44

Names: Phuti Balty Tjale (607911)

Masego Erens (569332)

Thabo Lepota (568571)

Humphry Tlou (681141)

Date: 15 September 2015

Table of Contents Executive summary .......................................................................................................................1

1. Introduction ...........................................................................................................................2

1.1 Task as given ............................................................................................................................. 2

1.2 Literature review ....................................................................................................................... 2

1.3 Material strength ....................................................................................................................... 3

1.4 Material availability .................................................................................................................. 4

1.5 Glue information ....................................................................................................................... 4

1.6 Competition requirements and rules ......................................................................................... 5

2. Task as understood ................................................................................................................6

3. Product Requirements and Specifications (PRS) ...................................................................7

3.1 Requirements ............................................................................................................................ 7

3.2 Constraints ................................................................................................................................ 7

3.3 Criteria ...................................................................................................................................... 8

4. Functional Analysis ...............................................................................................................9

5. Concept development and analysis ...................................................................................... 10

5.1 Concept 1 ................................................................................................................................ 10

5.2 Concept 2 ................................................................................................................................ 11

5.3 Concept 3 ................................................................................................................................ 12

5.4 Concept 4 ................................................................................................................................ 12

6. Concept selection ................................................................................................................. 14

7. Detailed design development ................................................................................................ 16

7.1 Calculation of forces on each member .................................................................................... 16

7.2 Buckling .................................................................................................................................. 18

8. Design Specifications ........................................................................................................... 21

8.1 Performance Specification ............................................................................................................ 22

8.2 Recommendations ......................................................................................................................... 22

9. References ........................................................................................................................... 23

10. Appendices .......................................................................................................................... 24

1

Executive summary

This report outlines the design process followed in the construction of a cardboard paper bridge –

built from only cardboard paper of 300gsm and glue. The primary aim of the task was to design

the bridge that is engineered to complete the task of supporting loadings at its mid-span while

flat and when tilted to an angle of 30˚ to the horizontal with a maximum deflection of 5mm.

Initially, individual concepts of the bridge were designed separately. Team members

brainstormed and integrated ideas for the concepts. New sketches were created from the

individual concepts and discussions were held regarding the proposed function of the

components and the overall bridge. In total, four concepts were proposed and a selection matrix

used to identify which of the four scored the most in terms of the criteria used. Stress, buckling

and deflection calculations were incorporated to determine which would withstand the most

loads and strength of each.

The most suitable design came out as the third concept. It has fewer members than the rest but

can withstand the most forces. The deflection thereof was found to be 1.866mm downwards

under a load of 5kg and the component through which the axle that will have the rope attached to

it will go has very minimal chances of tearing since it is attached to the bottom of the deck of the

bridge. The highest stressed member in has a load of 33.04N but with a critical load of 2.89kN,

thus the possibility of members failing is minimal.

It is manufactured by cutting the specified paper size with a knife cutter and folding until

specified thickness. Only triangular and cylindrical members are used, which are easy to fold

out. Holes the same size and shape as the cross-section of each member are drilled to the specific

member and location they have to be connected to. Glue is smeared onto the joints before they

are attached to members.

The overall design lacks resemblance to an actual bridge in terms of the small details which

make it possible to use a bridge. Hand or side rails could be introduced to avoid passengers of

vehicles from falling over. Lane markings on the road to indicate a proper road surface would

also enhance aesthetics. Careful attention should be paid to the dimensions used so that one can

carefully estimate the mass of the bridge without weighing (which is only done after it is built).

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1. Introduction

1.1 Task as given

A project has been assigned where it is expected of us to design a cardboard bridge from

cardboard paper that has a maximum weight of 300 gsm and restricted dimensions of 841mm x

1189mm (A0). The bridge must be able to support a minimum mid-span load of 3kg without any

sign of structural failure with a maximum deflection of 5mm. A truck having the dimensions:

125mm (H) x 75mm (W) must pass through without any obstruction. The bridge will be capable

of spanning a river that is 500mm wide while it has a supporting structure which may not extend

20mm below the straight level support line (point where it rests on the testing station). The

support structure of the bridge will have a 5mm pin connection to support one side of a bridge

while the other bridge support will have a smooth horizontal surface to support the other side of

the bridge. In addition, the bridge has to pivot about the pinned connection to an angle of 30° to

allow boats to pass under the bridge with sufficient clearance.

1.2 Literature review

Bridge design is constantly revolutionized by the significant demand of bridges by the

community or public. While bridges are in demand, many factors which affect the quality of the

designs thereof have imposed a competitive innovation of various types of bridges which have

different capabilities.

The wooden truss bridges were used since 1700s because of their high level of strength. They

were also used for railroad bridges mainly because of the heavy loads they can support, however

they were not preferred since they are very difficult to construct, requires a high maintenance

which is costly and difficult to widen if necessary [1].

Nevertheless, beam bridges came to the rescue since they are simplest to design and build. These

beam bridges consist of vertical piers and horizontal beam, while their strength depends on the

strength of the roadway so their strength can be increased by additional piers which are mainly a

firm combination of concrete and steel. The steel enhances the strength of concrete when

stretched under tension [2]. The weight of the beam bridges pushes straight down on the piers

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[3].Although beam bridges can be quite long, the span or distance between adjacent piers is

usually small. However beam bridges have a limited span and do not allow large ships or heavy

boat traffic to pass underneath [1].

For that reason, newly innovated suspension bridges were designed and built in 1801 in

Pennsylvania. Suspension bridges are strong, have a long span distance and allow large ships and

heavy boats traffic to pass underneath the bridge [1]. Since suspension bridges are suspended

from the cables, as traffic passes on the road, the weight is carried by the cables which transfer

the force of compression to the two towers and the cable also have the constant force of tension

which are stretched because the roadway is suspended from them. However they are very

expensive because they take a long time to build and require a large amount of materials [1].

It is clear from the existing bridges that various factors which may affect the functionality,

strength and criteria of the bridges are considered for the improvement of bridge designs.

1.3 Material strength

Cardboard paper is generally stronger than the average normal paper. In tension it does not snap

easily when pulled from both ends with equal forces but components made from it will buckle

easily under a compressive loading [6]. The tensile properties of paper are measured by clamping

a strip between two grips and applying a tensile load until the strip breaks but it is difficult to

obtain the exact value of the tensile strength of cardboard paper. Tensile strength is defined as

the breaking force divided by the width of the strip and has the units 𝑁/𝑚 [6]. The modulus of

elasticity of cardboard paper is also very difficult to obtain due to paper being very thin and

snapping too quickly during testing.

Due to the manufacturing process of paper, the elastic modulus 𝐸 thereof is significantly

anisotropic, which makes it very different from most materials. The manufacturing process

results in paper 𝐸𝑥 > 𝐸𝑦. This means that the elastic modulus of fibres in the longitudinal

direction is larger than that of the fibres in the transverse direction [7]. Experimentally the

modulus of elasticity of paper board (100 − 400 gsm) for the 𝑥(MD) and 𝑦(CD) directions have

been determined to be 5420𝑀𝑝𝑎 and 1900𝑀𝑝𝑎 respectively. Thus combining the two gives an

average of 5724.5𝑀𝑝𝑎.

4

The other factors that influence the strength of cardboard paper are the moisture content of the

paper (thus air humidity), paper directionality, folding endurance, stiffness and effects of

recycling. The moister the cardboard becomes, the weaker it gets [8]. All types of paper gain or

lose moisture due to ambient humidity and the properties of paper change with the moisture

content. Paper fibres become weakened through every recycling cycle, thus virgin paper will

inherently be stronger than recycled paper. The ability of paper to resist being bent is what

stiffness is. When a strip of paper is subjected to continuous folding under tension it will

eventually break. The number of folds it can endure before it breaks is the measure of the

endurance resistance of paper. Cardboard paper is stiffer when bent and folded across the grain

than along the grain (machined direction) [8].

1.4 Material availability

Cardboard A0 sheets are readily available and do not require any additional work on them. Most

printer shops and gift shops (which also have a number of glues) sell these at a price of

approximately R50 per sheet. There are plenty of such shops in close vicinity thus it will not be a

problem to acquire all the material needed for the construction of the bridge. Literally only two

materials are needed for the entire construction; glue and cardboard.

1.5 Glue information

Glues are part of a larger family called adhesives. The two classes are distinguished by the fact

that glue comes from organic compounds while adhesives are chemical-based. Adhering

materials called epoxies, caulks, or sealants are also chemical compounds that have special

additives to give them properties suitable for particular jobs or applications [4].

It is every group’s responsibility to choose their own glue type to use on their construction of the

bridge but with the exception of super glue and epoxy. The glue is selected in such a way that it

will bond to every component of the bridge; making the joints very strong in order to keep the

bridge rigid and stable without causing the cardboard to warp.

There’s a quite a variety of glue types to choose from. In order to select glue, certain types of

glues had to be investigated to check which product best suits our design. In order to select

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adhesives, mechanical properties were the simpler way to see which glue best suits our design.

The criterion used to select glue is the following: weight distribution, drying time, transparency

and colour after drying, strength and temperature resistance [5]. The one glue that fits our

criterion is white glue. The fact that it’s friendly to use, not toxic cheap unless ingested, readily

available and cleans up with water which is a solvent in them makes them the top contenders for

the design.

1.6 Competition requirements and rules

- The project should be done by groups of a maximum of four members with each member

spending at least 50 hours working on it.

- Strictly only a single sheet of A0 cardboard paper with dimensions 841mmx1189mm can

be used for all the parts of the bridge.

- Any glue other than super glue and epoxy glue are allowed for any joining needed.

- The scoring equation that will be used to assess the constructed bridge is the following:

𝑺𝒄𝒐𝒓𝒆 = 0.3 (0.35

𝐵𝑟𝑖𝑑𝑔𝑒 𝑚𝑎𝑠𝑠) + 0.4(𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐿𝑜𝑎𝑑) + 0.3(𝑆𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 𝐹𝑎𝑖𝑙𝑢𝑟𝑒)

6

2. Task as understood

A bridge constructed out of cardboard paper has to be designed by groups of four. This should be

done from a single A0 sheet of 300gsm cardboard paper and must span a river that is 500mm

wide. The height at any location above the deck or road way must be greater than 125mm with a

width that is greater than 75mm in order to allow a truck of the dimensions; 125mm (H) x75mm

(W) to pass through. It must be capable of supporting a load of at least 3kg at the mid-span

without sustaining deflection of more than 5mm below its lowest point. The bridge should have

provisions for three 5mm axle pins at the mid-span, one end (below road surface and acting as a

pivot for the bridge) and somewhere on the bridge to allow attachment of a cable hoist. It should

be able to pivot about a pinned connection to an elevation of 30° to the horizontal for allowance

of boats to pass below it. Finally at this tilted position, it must sustain a 0.5kg weight attached to

the mid-span for about 10s. The bridge must be designed in such a way that the strength to

weight ratio is as high as possible to not compromise on weight even when optimizing its

strength.

7

3. Product Requirements and Specifications (PRS)

3.1 Requirements

Must span a 500mm wide river

A truck with the dimensions (125mm H × 75mm W) must be able to go through

the bridge with ease

Must pivot about pinned connection

Must be able to support a load of up to 3kg

Must be able to hold a suspended 0.5 kg mass for at least 10 seconds while being

tilted to an angle of 30˚

Provision must be made at the mid-span and one end of the bridge for a 5mm

diameter axle pin

3.2 Constraints

Bridge must be manufactured using only single sheet of A0 cardboard

Weight specification of the cardboard must not exceed 300gsm

The dimensions of the cardboard must be 841 mm × 1189 mm

The design components must be joined together by any type of glue except for

super glue and epoxy glue

The bridge must be able to hold a weight without a deflection greater than 5 mm

at most

Width of the bridge cannot exceed length of pin (i.e. must be less than 100mm)

Supporting structure may not be extended for more than 20mm below the straight

level support line

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3.3 Criteria

Mass of the bridge should be at most or preferably 0.35kg (for a good score on

the equation)

The design must be for ease of manufacture (e.g. 2D development components

that can be cut out and folded easily)

It must be able to be tested with ease

The cost of the bridge should preferably not exceed R100

Number of components should not be too high to avoid needing more material

than allowed

The design should be aesthetically pleasing

Load carrying capacity must be greater than 3kg

A high stiffness (strength to weight ratio must be high )

The different 2D components must be easy to assemble

Deflection is minimum

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4. Functional Analysis

START

Place bridge on

station for

testing

Insert pivot

axle through

bridge

Load bridge

with minimum

weight

Is the

deflection

≤5mm?

Hook rope to

axle placed at

top corner

Stop increasing

loads and then

remove

Pull rope until

bridge is tilted

30° to

horizontal

Keep increasing

load

Place the 0.5kg

load Is the

load

≤3kg?

STOP

Is there

imminent

failure?

No

No

No

Yes

Yes

Yes

Wait 10s

Remove weight

and bridge

from station

10

5. Concept development and analysis

It is common knowledge in structural engineering that to obtain optimum rigidity in a structure

that is under loading it is best to make use of triangulation in it. The concept designs that follow

have been developed in light of this fact, thus triangular trusses have been incorporated in all of

the concepts as much as possible to take advantage of their rigidity. Cutting triangles from

cardboard can also be done fairly easily than most shapes.

5.1 Concept 1

Figure 1

The well-known bridge that inspired this concept is the Warren Bridge. The basic design of this

concept is taking two trapeziums and joining them across the width of the bridge at the top joints

and midway through the bridge to make a complete bridge. This is done by having one beam

defining the height of the bridge that runs from end to end. The advantage with this is that there

will be fewer joints at the top of the bridge which suggests that there will be fewer points where

failure is most probable to occur.

A hole for the 3mm diameter axle pin that functions as a pivot is cut out from the material as part

of a component during manufacturing and thus the pin does not rest on any joints. Whereas the

axle pin to which the rope will be attached rests on the short member at the top right corner joint.

Although the weight of the pin before being pulled rests on a member it will not cause significant

buckling as the member onto which it rests is very short in comparison to the others. The joints

of the bridge are made more rigid by cutting out gusset plates according to the size and shape of

each joint in a particular position on the bridge. All the members forming a specific joint are

Height of the

bridge all

throughout is

160mm

Hole (±3.5mm) for

axle by which

bridge pivots

Road level

(where

cardboard

sheet will

rest)

The two

trapeziums

are the basic

structure

3mm diameter axle goes

through here and rests on the

short member

One of three beams

joining both trapeziums

of the bridge together

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attached to these cut out gusset plates. These ensure less likelihood of failure at the joints due to

loading.

When loading is at the top of the bridge, normally trusses would follow the configuration

outlined by the dotted lines on the sketch. Since loading is the bottom, they have been placed in

such a way that they spread out to the bottom

5.2 Concept 2

Figure 2

In this concept the main objective was to come up with a bridge that has a strong member that

can bare the weight rather that most of it being taken by the lower deck. Another consideration

that led to this design was that when it tilts there will be a moment introduced so more mass was

moved at the back of the pivot to counteract this moment.

The advantage with this one is that where the axles will be positioned is strong and made of thick

material unlike being put at the joints. This minimizes stresses at the joints and ensures minimal

chances of failure at the axle locations. Another advantage is that while tilting, the problem of

having the part of the bridge to the left of the pivot being squashed to the ground is eliminated.

The disadvantage is that there are too many joints and thus as far as manufacturing is concerned

it might pose as a challenge. One other disadvantage is that the hollow members will be weak,

making it easier for failure at the joints.

The left side and right side are exactly

identical. Some members might have not

been excluded from the right side for

simplicity.

The components

coloured with black are

thick components with

a thickness that is a lot

more than the other

members

6 mm diameter

holes through

which 5mm

diameter axles will

be slit This arm also runs along the right

side of the bridge and supports a

lot of the downward load

12

5.3 Concept 3

Figure 3

The thinking behind this design was to remove as many members as possible, thus as many

joints as possible. In doing that it would result in a simple bridge that can be manufactured from

2D rolled sheets of paper instead of having too many members supporting loads. The advantage

with this design is that a lot of the members are cylindrical, which is easier to manufacture as one

just rolls paper to the desired dimensions. Another advantage is that when tilted the axle will lift

the component from the bridge but there is no potential for it to tear from the bridge unlike with

the previous design. Disadvantage is that aesthetic wise is not up to scratch, it lacks some

creativity

5.4 Concept 4

The diagonal and upright

members are triangular in

cross section.

Since this design has very fewer

members than the others, the

members can be made less

hollow

These members are

cylindrical

6mm diameter hole by

which the bridge will pivot

This curved part is thicker

than all the other part on

the bridge

The rope will be

hooked to axle slit

through here

Road level

Beam running beneath

the bridge

13

The advantage with this design is that below the deck of each bridge runs a beam looking like

corrugated cardboard. This will be constructed of two cardboard sheets sandwiching triangular

trusses folded from another cardboard paper. This beam together with the trusses above the deck

will absorb the load placed at the mid span of the bridge. Another advantage is due to the curved

section. It was introduced to allow for easy rotation, thus it is definite that no material after the

hole will touch the ground.

The disadvantages with this design are that the curve might be difficult to construct physically.

There are too many members and therefore many joints, hence there will be too much stresses

induced in the hole drilled into the joint to allow an axle for the rope to be put through.

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6. Concept selection

To thoroughly select the best design concept, Matrix selection table is constructed where in all

the proposed ideas are judged according to the proposed criteria stated in the PRS. Below is a

tabulated data of all the three concepts.

Weightings start from 1-5

Scoring 5 = Excellent

4 = Good

3 = Average

2 = poor

1 = very poor

For a concept meeting a certain criteria specified in the requirements outstandingly it will receive

a score of 5, and if it meets averagely it will be accredited a score of 4. A concept scoring below

3 is attributed as a poor concept for a particular criterion.

Table 1: Matrix Selection

Criteria Weighting Concept

1

Concept

2

Concept

3

Concept 4

Weight 4 3(× 4) 3(× 4) 4(× 4) 4(× 4)

Manufacturability 5 3(× 5) 3(× 5) 4(× 5) 3(× 5)

Effective cost 4 3(× 4) 3(× 4) 4(× 4) 3(× 4)

Max load Support 5 4(× 5) 3(× 5) 4(× 5) 3(× 5)

Deflection 5 3(× 5) 2(× 5) 4(× 5) 2(× 5)

Aesthetics 4 3(× 4) 4(× 4) 3(× 4) 4(× 4)

Stiffness 4 2(× 4) 2(× 4) 3(× 4) 2(× 4)

Material

Consumption

5 3(× 5) 3(× 5) 2(× 5) 2(× 5)

Total Rating 109 103 126 102

15

From the matrix above it is observed that all concepts have relatively high total rating with very

little differences. All the concepts appear to be meeting the criteria of effective cost very well.

Although concept 1 can support relatively huge load, it’s not easy to be manufactured. Thorough

analysis revealed that concept 3 of the bridge meets meet most of the criteria listed above in the

matrix selection, with zero deflection, average aesthetic and can support at a load of 4 kg which

is greater than the one specified in the design requirement, hence this concept is selected as the

best among all the proposed designs.

16

7. Detailed design development

7.1 Calculation of forces on each member

Assumptions made for force analysis:

The load placed at the mid-span is 5kg and shared between the two vertical posts equally.

All joints are fixed joints

Thickness of the axles is neglected (thus dealing with point loads)

Area of contact between surface and bridge is negligible, thus reaction is a point load

Thickness of members ignored

↺ + ∑𝐵 = 0; −𝐴𝑦(0.68) + 24.53(0.42) + 24.53(0.26) = 0

𝐴𝑦 = 24.53𝑁

↑ + ∑𝐹𝑦 = 0; 𝐵𝑦 + 24.53 − 24.53 − 24.53 = 0 ∴ 𝐵𝑦 = 24.53𝑁

260 260 160

𝐴𝑦 2.5(9.81)

𝐵𝑥

2.5(9.81) 𝐵𝑦

𝐶

𝐵

𝐷

𝐹 𝐸

𝐴

193 304

𝐴𝑦

𝐹𝐴𝐸

𝐹𝐴𝐶

36.59∘

Joint A

17

↑ + ∑𝐹𝑦 = 0; 𝐹𝐴𝐶 sin(36.59∘) + 24.53 = 0

𝐹𝐴𝐶 = −41.15𝑁 = 41.15(𝐶)

→ + ∑𝐹𝑥 = 0; 𝐹𝐴𝐶 cos(36.59∘) + 𝐹𝐴𝐸 = 0

−41.15 × cos(36.59∘) + 𝐹𝐴𝐸 =

𝐹𝐴𝐸 = 33.04𝑁

→ + ∑𝐹𝑥 = 0; 𝐹𝐴𝐶 cos(36.59∘) + 𝐹𝐶𝐷 = 0

−(−41.15) × cos(36.59∘) + 𝐹𝐶𝐷 = 0

𝐹𝐶𝐷 = −33.04𝑁

𝐹𝐶𝐸 = 𝐹𝐶𝐹 𝐹𝐵𝐷 = 𝐹𝐴𝐶 𝐹𝐴𝐸 = 𝐹𝐸𝐹 = 𝐹𝐵𝐹

↑ + ∑𝐹𝑦 = 0; 𝐹𝐶𝐸 − 24.53 = 0

𝐹𝐶𝐸 = 24.53𝑁

36.59∘ 𝐶 𝐹𝐶𝐷

𝐹𝐶𝐸 𝐹𝐴𝐶

Joint C

𝐹𝐸𝐹 𝐹𝐴𝐸

𝐹𝐶𝐸

24.53𝑁

𝐸

Joint E

18

7.2 Buckling

𝑃𝑐𝑟 =𝜋2𝐸𝐼

(𝐾𝐿)2

Where 𝑃𝑐𝑟 = critical or maximum axial load on the column just before it begins to buckle

𝜎𝑐𝑟 = critical stress, which is an average normal stress in the columns moments before it buckles

𝐸 = modulus of elasticity for the material

𝐼 = least moment of inertia for the column’s cross-sectional area

𝐿 = unsupported length of the column, whose ends are pinned

𝑟 = smallest radius of gyration of the column, determined from 𝑟 = √𝐼 𝐴⁄ , where I is the least

moment of inertia of the column’s cross-sectional area

The members that are under compression are 𝐴𝐶, 𝐶𝐷 and 𝐷𝐵. In the following calculation the

maximum axial load on the column before it begins to buckle will be assessed.

Since the joints of the members are glued together it is assumed that the ends of the members are

fixed, thus the effective length 𝐿𝑒 (𝐾𝐿) is calculated using 𝐾 = 0.5.

𝑃𝑐𝑟 =𝜋2𝐸𝐼

(𝐾𝐿)2=𝜋2(5724.5 × 106)(3.78 × 10−9)

(0.5 × 0.16)2= 33.37𝑘𝑁

17𝑚𝑚 9𝑚𝑚

𝐼 =𝜋

64(𝑑04 − 𝑑𝑖0

4)

=𝜋

64(174 − 94) = 3777.77𝑚𝑚4

= 3.78 × 10−9𝑚4

𝑟 = √𝐼 𝐴⁄ = 3777.77

𝜋4(172 − 92)

= 4.81𝑚𝑚

19

𝜎𝑐𝑟 =𝜋2𝐸

(𝐾𝐿𝑟 )

2 =𝜋2(5724.5 × 106)

(0.5

0.00481)2 = 5.23 𝑀𝑝𝑎

𝑃𝑐𝑟 =𝜋2𝐸𝐼

(𝐾𝐿)2=𝜋2(5724.5 × 106)(1.183 × 10−9)

(0.5 × 0.304)2= 2.89𝑘𝑁

𝜎𝑐𝑟 =𝜋2𝐸

(𝐾𝐿𝑟 )

2 =𝜋2(5724.5 × 106)

(0.5

0.00327)2 = 2.42 𝑀𝑝𝑎

7.3 Deflection

Assumptions

Moment of inertia of the beam is 4 times that of each cylinder it comprises of and load acts

directly at the mid-span of the beam:

16𝑚𝑚

60°

13.86𝑚𝑚

𝐼 =𝑏ℎ3

32

=1

32(13.863)(16) = 1183.33𝑚𝑚4

= 1.183 × 10−9𝑚4

𝑟 = √𝐼 𝐴⁄ = 1183.33

12(16)(13.86)

= 3.27𝑚𝑚

24.525𝑁 24.525𝑁

49.05𝑁

680 𝑚𝑚

20

𝐸𝐼𝑑2𝑣

𝑑𝑥2= 𝑀(𝑥) = 24.525𝑥

𝐸𝐼𝑑𝑣

𝑑𝑥=24.525

2𝑥2 + 𝐶1 ⟹ 𝐸𝐼𝑣 =

24.525

6𝑥3 + 𝐶1𝑥 + 𝐶2

𝑎𝑡 𝑥 = 0, 𝑣 = 0 𝑎𝑛𝑑 𝑎𝑡 𝑥 = 0.68, 𝑣 = 0

∴ 0 = 0 + 𝐶2⟹ 𝐶2 = 0

0 =24.525

6(0.68)3 + 𝐶1(0.68) ⟹ 𝐶1 = −1.89006

Due to the symmetry of arrangement, it can easily be seen that 𝑣𝑚𝑎𝑥 occurs at 𝑥 = 0.68 2⁄ :

∴ 𝐸𝐼𝑣 = (24.525

6) 𝑥3 − 1.89006𝑥

𝐼 =𝜋

64(234 − 154) = 11251.61𝑚4 = 1.125(10−8)𝑚𝑚4 ⟹ 𝐼𝑡𝑜𝑡 = 4.50(10

−8)𝑚𝑚4

𝑣𝑚𝑎𝑥 =1

𝐸𝐼𝑡𝑜𝑡[(24.525

6) (0.34)3 − 1.89006(0.34)] = −1.87𝑚𝑚

From the appendix, the displacement of the joint F was calculated to be −3.55(10−3)𝑚𝑚. The

negative sign indicates that it is displaced upwards. It makes complete sense since the member

DF is in tension and thus pulls the joint upwards. Since the joint F is identical to joint E the same

calculation applies.

The resultant deflection of the entire bridge should be approximately 1.866𝑚𝑚 downwards.

𝑥

𝑀 𝑉 24.525𝑁

↑ + ∑𝐹𝑦 = 0; −𝑉 + 24.525 = 0

∴ 𝑉 = 24.525𝑁

↺ + ∑𝐴 = 0; −24.525(𝑥) +𝑀 = 0

∴ 𝑀(𝑥) = 24.525𝑥

21

8. Design Specifications

The following is a selection matrix on the best material to use for the building of the Bridge.

Since the Constrain in the PRS require the bridge to be constructed out of a cardboard of

maximum size of 300gsm, it was necessary to determine the best cardboard size that will be

suitable for the construction of the components for the selected design.

The cardboard material was selected based on the ability to be folded in triangular or round

shapes because these were easier to construct as compared to rectangular or square shapes.

Table 2: Material Selection Matrix

Material Size 240gsm 300gsm

Components

Road surface

Vertical triangular

beam

Diagonal triangular

beam

Horizontal shafts with

protrusions

Hook

22

8.1 Performance Specification

Components Specification

Road surface Allow smooth mobility of transport and persons

Hook Provide allowance for lifting the bridge

Vertical triangular

column

Prevent the bridge from failing in compression, when subjected to a

downward load.

Diagonal triangular

column

Provide a tensile upward force, thus resist the bridge from failing at

the ends.

Top Protruded

horizontal column

Ensures that the bridge becomes more rigid and stable

Bottom Horizontal

column

Prevent the bridge from failing in the middle and minimizes

deflection

8.2 Recommendations

The bridge built, performed very well, and indeed it was well designed with very ingenious

ideas. Modification that can be applied to improve the bridge is to include side or hand rails for

mobility guidance along the road surface. Including diagonal members between the two

horizontal members on both sides of the bridge will increase the rigidity of the bridge especially

at the top. To Prevent buckling or deflection of the bridge, it would be necessary to constrain the

horizontal columns by introducing flat sheets at both ends.

23

9. References

[1] Meter, N. V. (2004). Cities/layout L. Bridge Basics, 14-17. Retrieved May 10 2015:

http://www.nbm.org/assets/pdfs/youth-education/bridges_erpacket.pdf

[2] Beam Bridges. (2015). Retrieved May 14, 2015, from Design-technology.org:

http://www.design-technology.org/beambridges.htm

[3] Beam. (2015). Retrieved May 14, 2015, from Warwickallen.com:

http://www.warwickallen.com/bridges/BeamBridges.htm

[4] Mechanical properties of adhesives. (2015). Retrieved May 14, 2015, From

Adhesiveandglue.com: http://www.adhesiveandglue.com/mechanical-properties-adhesives.html

[5] Wood Glue uses and information . (2015). Retrieved May 14, 2015, From

Naturalhandyman.com: http://www.naturalhandyman.com/iip/infadh/infadhe.html

[6] Karlson, H. (2010). Strength Properties of Paper produced from Softwood Kraft Pulp.

Karlstads University: Faculty of Technology and Science. Retrieved 14 May 2015, From:

http://www.diva-portal.org/smash/get/diva2:317178/fulltext01.pdf

[7] Sekulić, B. (2013). Structural Cardboard: Feasibility Study of Cardboard As A Long-Term

Structural Material In Architecture, University of Politècnica De Catalunya. Retrieved 24 June

2015, From: http://upcommons.upc.edu/pfc/bitstream/2099.1/21603/1/BrankoSekulic_TFM.pdf.

[8] Guyana. (2010). Paper and Board packaging: Properties, specifications and sourcing.

Retrieved 24 June 2015, From:

http://www.iica.int/Eng/regiones/caribe/guyana/IICA%20Office%20Documents/tfo_packaging_

workshop/Guyana%20TFO%20Pkg%20W'shp%20Session%203%20-

%20Paper%20and%20Board.pdf

24

10. Appendices

PARTS LIST

DESCRIPTIONPART NUMBERQTYITEM

Cut from 240

gsm,0.09724 metre

squared paper

cover page

11

240gsm paper hollow

rolled tubes.Use ponal

wood glue for every

joint.

bottom_column42

300gsm folded paperbottom beam23

300gsm paper folded

in triangular shapes

vertical triangular

column

44

240gsm rolled solid

paper tubes with two

steps

horizontal shaft with

protrusions

25

240gsm rolled hollow

paper,cuttings made

with a cutting knife

across column26

300gsm paper folded

in triangular shapes

diagonal triangular

beam

47

240gsm paper foldedhook18

1

1

2

2

3

3

4

4

5

5

6

6

A A

B B

C C

D D

full assembly

Humphry Tlou - 681141

2015-09-14

Designed by Checked by Approved byDate

1 / 1

Edition Sheet

Date

6

7

28

3 4

1

5

680,00

160,00

25,50

33,50

40,00

50,00

3

6

,

8

2

°

221,00

1

1

2

2

3

3

4

4

5

5

6

6

A A

B B

C C

D D

acros column

Humphry Tlou - 681141

2015-09-14

Designed by Checked by Approved byDate

1 / 1

Edition Sheet

Date

150,00

9,00

15,00

25,00

160,00

190,00

17,00

9,00

155,00

50,00

25,00

8,00

60,00°

1

6

,

0

0

1

6

,

0

0

16,00

Part 6

Part 5

Part 3

Hole cut to fit vertical triangular column

Hole drill to suit part 5

1

1

2

2

3

3

4

4

5

5

6

6

A A

B B

C C

D D

cover page

Humphry Tlou - 681141

2015-09-14

Designed by Checked by Approved byDate

1 / 1

Edition Sheet

Date

680,00

680,00

23,00

15,00

97,00

92,00

23,00

25,50

Part 1

Part 2

Bottom Support