1) The document describes the development of a folding bridge design through multiple concepts and testing. Initial concepts using cardboard failed due to buckling and stress concentrations. 2) Further concepts incorporated triangular cross-sections and a primary folding mechanism. A secondary folding mechanism was later added to reduce the folded size. 3) Analysis was performed to understand deflection caused by hinges and optimize hinge and material thickness. Changes made after testing improved stiffness. The final design met requirements with a factor of safety of 17.

1. z
Ying Cheung
13019879
Product Design Technology
Product Design Engineering:
“Escape to Freedom” - Bridge
P1

2. Contents
P2
P3 Introduction
P4 Initial Concept (1/4 scale)
P5 2nd Concept (1/8 scale)
P6 Triangular Profiles Testing
P7 Folding Concept (Primary)
P8 Torsional Impact On Folding Structure
P9 Folding Concept (Secondary)
P10 Design Requirements Of Folding Concept
P11 Stabilising Secondary Fold Mechanism
P12 Fixture To The Balcony
P13 Hinge Dimensions
P14 Hinge Clearance Impact On Overall Deflection
P15 Overall Deflection Caused By Hinges
P16 Angle Of Deflection
P17 Improvement Made After Competition
P18 Change In Material Thickness Impact on
Bridge’s Stiffness
P19 Mass Of Bridge
P20 Centre Of Mass
P21 Factor Of Safety
P22 Deflection
P23 Deploy The Bridge To Escape
P24 Summary
Overall Design
And Feature
Development
Relationship
Between Hinges
And Deflection
Changes Made To
The Bridge After
Submission
Final Design
Details And
Summary

3. P3
Introduction
To construct a bridge that fits on the balcony and travels forward
6m and then 2m at 90°
 The bridge must not intersect with the No-Go-Zone.
 Made of Aluminium 2024-0
 Under 2.5m when folded
 Allow user of 80kg to walk on
 Deploy under 5 mins

4. Initial Concept (1/4 scale)
 Failure due to;
 manufacturing error,
 Torsional stress,
 open cross section profile
Improvement can be made;
 Create a closed cross section
profile, to resist torsion and
buckling
 Buckling occur during the testing of the
1/4 scale card model.
P4
Destructive testing of the first card-board bridge (1/4 scale) and
understanding of failure
Side
view
Bottom
view
Cross section profile
Ribs

5. 2nd Concept (1/8 scale)
 Shear failure at the “hook” during
the testing of the 1/8 scale card
model.
 Failure due to;
 Under-Engineering
 Stress concentration
 Corrugation of cardboard
Improvement can be made;
 Create profile with larger
contact surface area to
reduce stress
concentration,
 Increase “h” value to
increase second moment of
area to reduce stress.
The cross section of this design
is triangular to create a closed
profile in order to resist torsion
and buckling
P5
After changing the cross-section profile into a triangle, and
observing failure through destructive testing
Ribs
Previous profile Triangular profile

6. Triangular Profiles Testing
P6
Using Solidworks simulation to test and identify which profile is
suitable for this torsion scenario.
Cross section
Cross section
Cross section
This configuration has more uniform stress range
(1.16e+1 – 8.72e+2 Mpa).
And lower stress at the intersection between the bridge
and dog-leg
Profile used in the 2nd concept

7. Folding Concept (Primary)
 However the collapsed bridge is
relatively large and balky.
 Not meeting the maximum size
standard – 2.5m (full scale)
Further development;
 Create internal folding
structure to reduce
overall size. Flat pack
idea.
P7
Concept of primary folding mechanism to allow the bridge
become portable.
Detach the dog-leg off the bridge
Balcony
Top view
Side view
3.3 m
The folding concept is to
“roll” up the parts to reduce
the size

8. Torsional Impact On
Folding Structure
As the torsional force
applied, the support plates
collide with the section on
it’s left to resist the torsional
motion
The centre point of the torsional motion is
unknown however the plates are added to
location as far away as possible to have
greater mechanical advantage against
torsion
 Torsion will force the folding
parts to shift, this will cause
misalignment and result
large deflection
Support plates are joined to the
section on it’s right
P8
Rotation of parts caused by torsion will affect the performance of
the bridge.

9. Folding Concept
(Secondary)
Combining both the primary
and secondary folding
mechanisms together to
collapse the bridge down to
smaller size – 1.88m
P9
Introducing secondary folding structure to reduce size of the
folded bridge in order to meet the brief’s requirement – under
2.5m (full scale)
3.3 m 1.88 m
Using 4-bar-linkage to as
secondary to minimise the size
of the bridge to flat-pack
 Previously without the
secondary fold result 3.3m
in folded size and unable to
meet the maximum limit of
2.5m

10. Design Requirements Of
Folding Concept
Tapered beam able to provide linear axis and flat
surfaces for folding
Ideal beam curve
Walking surface
with constant width
Twisted surface
 It is difficult to manufacture
a twisted piece and to
make it collapsible
 Since the ideal beam curved was replaced the stress
concentration will increase. However this was sacrificed so that
the structure can be folded
P10
Front view
Identifying requirements needed for the secondary fold to be
feasible
 Hinges require a linear pivot axis
Hinge axis

11. Stabilising Secondary Fold
Mechanism
P11
The Fold mechanism is required to be stabilised or else the structure
will collapse
The 2 possible consequences of not
having a stabiliser for the secondary
folding structure
A B
Providing both tensional and
compressive support to avoid
failure in both figure “A” and
“B”.
Fr = 400N
θ = 46:
(for compression calculation)
Fθ = 576N
θ = 44:
(for tensional calculation)
Fθ = 555N
Fc = Compressive force
9.9N
Fc = Tensional force
9.9N
The forces are relatively small and neglectable however both the
compressive and tensional reinforcements are required to be installed
for reassuring that the structure will not collapse during operation.

12. Fixture To The Balcony
 As the bridge is fixed
to the balcony, the
edge of the balcony
is likely to shear the
fixture.
To avoid the balcony cutting into and shear the
fixture, a bottle-cap-remover design was used
in order to have control of the location where
the force exert.
With a side effect of this design, it allows
clearance to slot on to the balcony.
P12
Failure of the 2nd concept
Identify failure occur on the fixture to the balcony and identify
features needed to minimise the chance of failure.
< Torsional stress is greater beam stress on the
same profile therefore the fixture will be stronger
if it is converted into a beam.

13. Hinge Dimensions
Shear surfaces = 5
H1 H2 H3
 The stress shown in the FEA
suggest that the hinges in “H1”
are the most likely to fail due to
low Fos value
P13
Identifying the dimension of the hinges through trial and error due to
complicated scenario – difficulty of applying both shear equation and
torsion equation onto the pin of the hinge
Deformation of the
pin during operation
Diameter (inner)
(mm)
Diameter (outer)
(mm)
Number of shear faces
Max FEA stress
(Mpa)
Fos
H1 50 100 5 37.96 1.9
H2 50 100 5 25.06 2.99
H3 50 100 4 20.47 3.66
Outer diameter
Inner diameter
Diameter of the pin
Although the stress operating of the pins are different, however they
are under the yield stress by at least 1.9 times therefore it is unlikely to
yield.

14. Hinge Clearance Impact On
Overall Deflection
The clearance between the pin
and the bracket of the hinge is
set to be 0.5 mm
 the clearance of the hinges
will have impact on the
overall deflection
Deformation results caused by
hinges;
 H1 11.1mm
 H2 3.74mm
 H3 2.9mm
 H4 2.48mm
Total 20.22mm
H1 H2 H3
H4
 The closer the hinge to the fixture
the more deflection it will cause due
to the mechanical advantage
P14
Clearance on both
brackets therefore the
result deformation x2
Hinge clearance allow parts to shift, the movement will cause the
bridge to deflect. Referencing to “clearance deformation”
calculation within the process book

15. Overall Deflection Caused By
Hinges
P15
H1 H2 H3
H4
The pin with in the hinge will deform during operation and allow parts
to shift, the movement will cause the bridge to deflect. Referencing to
“Hinge Stress Analysis” calculation within the process book
 The sum of the
deformation caused
by hinges is
32.24mm
By adding all the values together –
Total estimate value (without clearance) = 12.02mm
H1
H2
H3
H4
The image above shows how the pin of
the hinge is deformed.
The overall deformation values were
extracted from Autodesk Simulation
Mechanical
- Hinges were made without clearance
Referring to “Hinge Clearance Impact On Overall Deflection”
= 20.22mm
3.2 cm is visible deformation however user is still
enabled to walk on the bridge therefore no
actions need to be taken

16. Angle Of Deflection
P16
Using Solidworks Section Properties to analyse the polar moment of
inertia of the cross-section at every 500mm of the bridge to calculate
the deflection angle
length
(mm)
polar moment of inertia
(J) (m^4)
deflection
(rad)
deflection
(deg)
0 0.000534286 0 0
500 0.000599333 5.80348E-05 0.000364643
1000 0.000669455 0.000103912 0.000652897
1500 0.000744845 0.000140092 0.000880221
2000 0.000825692 0.000168499 0.001058712
2500 0.000912188 0.000190652 0.001197904
3000 0.001004522 0.000207753 0.001305352
3500 0.001102887 0.000220762 0.001387085
4000 0.001207472 0.000230446 0.001447935
4500 0.001318468 0.000237427 0.001491794
5000 0.001436066 0.000242204 0.001521814
5500 0.001560457 0.000245187 0.001540554
6000 0.001691832 0.000246706 0.001550101
Total = 0.014399012
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 1000 2000 3000 4000 5000 6000 7000
Deflection(deg)
Length from Balcony (mm)
Angle of deflection was
calculated by rearranging the
torsion equation
The graph shows the amount of
deflection caused by each of the
cross sections
0.014° of deflection is very small therefore the user
can walk on the without inconvenient.

17. Improvement Made After
Competition
P17
As the bridge was loaded with weight, a small displacement was
spotted along the secondary folding structure, the bridge structure
was weaken by the displacement.
The secondary fold mechanism was removed from
the 2 rear parts, this change stabilise the shear
motion to reduce the overall deformation
 When the bridge is loaded, 2 forces exerted by the
wall (blue arrows), that cause a shear motion. Small
changes made near the balcony will have significant
change to the overall performance.
5526N
The force – 5526N was calculated in the
“Free Body Diagram” within the process
book
A thread was used as reinforcement
to reduce the displacement of the
secondary fold mechanism to
reduce the overall deformation of
the bridge
No secondary fold
 2 secondary folding mechanism needed to be kept so
that the bridge don’t exceed the size requirement
when folded

18. Change In Material Thickness
Impact on Bridge’s Stiffness
P18
Material Thickness
(mm)
End of bridge deformation
(mm)
Stress
(Mpa)
Mpa/deformation
ratio
25 6.109 17.483 2.861843182
3 0.769 3.485 4.531859558
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 5 10 15 20 25 30
Mpa/deformation
ratio
Material Thickness (mm)
Changing material thickness to reduce weight of the bridge and
identify the impact on the stiffness on the bridge
Bridge with material
thickness of 25 mm
Weight: 1670kg
Bridge with material
thickness of 3 mm
Weight: 196 kg
The graph shows that by
reducing the material
thickness the stiffness of
the bridge has increase
significantly
The extra 22mm on top of
the 3mm has become a
burden to the bridge
By reducing the material thickness, unnecessary
weight was removed so that the bridge it self has
become lighter and stiffness has increased

19. Mass Of Bridge
P19
Calculate mass of the bridge made of Aluminium 2024-0
The volume value obtained
from Solidworks Mass
Properties
Volume = 70389712.29 mm^3
0.0703 m^3
Mass = Volume X Density
0.0703 X 2780
195.7kg
 The weight of the
bridge is too much
compare to how
much a single
human can carry
The maximum combined pulling force exert by a
male is approximately 1019N (556+643)
Therefore minimum of 2 people are required to
carry the bridge.

20. Centre Of Mass
P20
Identifying the centre of mass of the bridge with Solidworks Centre of
Mass feature.
The centre of mass is located near to the balcony
due to larger amount of material used is greater
near the balcony.
Therefore it has greater mechanical advantage
compare to having the centre of mass at the half
way across the bridge
Height from top of the walk way
Distance from front of
the Balcony
(2106mm)
Distance from side of
the bridge
 The centre of gravity is closer to one side of the
bridge, this suggest that a lot of material is used to
construct the dog-leg

21. Factor Of Safety
P21
height of plank from floor
(mm)
Displacement
(mm)
Load applied
(kg)
110 0 0
87 23 80 (Still)
82 28 80 (Shock load)
Using shock load (user’s footstep) and maximum stress from FEA to
calculate the Factor Of Safety.
Physical demonstration was performed so that
the deformation of the beam can be measure
to calculate force
Load: 80kg
800N
Shock load: 800 X (28/23)
973.9N
Max Stress = 3.485 Mpa
The FEA simulation was set up with 800N
therefore
Stress is proportional to
force therefore when shock
load is applied the stress will
increase by 1.2
Stress = 3.584 X 1.2
4.363 Mpa
Fos = yield stress / operating stress
75 / 4.363
17.2
 The factor of safety shows that the bridge is over engineered by
approximately 17 time. This suggest that the cross section of the
bridge can be reduced to minimise the FOS and weight.
X1.2
Aluminium 2024-0:
Yield stress = 75 Mpa

22. Deflection
P22
Identify the deflection of the bridge after reducing the material
thickness.
0.769mm of deformation for a single body is very little and
hardly noticeable.
referring to the change in stiffness after change in material
thickness,
Autodesk simulation on
the bridge as one solid
body (except the balcony)
Referring to “Hinge Clearance Impact On Overall Deflection”
= 20.22mm
Is proportional to 1/J
The sum of the deformation is
21.mm
As one increases the other decreases
Referring to the “Factor of safety” the Fos value has increased
by 17.2 therefore the deflection will be reduce by 17.2 times
0.014 x (1/17.2) = 0.000813°
These deflection are hardly noticeable and they do not cause
any obstruction of inconvenient to the user during operation

23. Deploy The Bridge To Escape
P23
Step by step of deploying the bridge and assembling the dog-leg
onto the end of the bridge
Time required to deploy the cardboard bridge during the competition
was 29s. The estimate time to deploy for full scale bridge to be
approximately 10 time longer – 4mins 50 seconds
4mins 50s is under the brief requirement however it is very close to the
maximum limit of 5 mins.
*unfold secondary mechanism
*unfold secondary mechanism

24. Summary
P24
• The bridge as a single body is very stiff with estimate
0.77mm of deformation due to the triangular profile.
However the folding mechanisms reduce the stiffness
(increase deformation by estimate 32mm) due to both stress
concentration and clearance on the hinges
- In order to improve the performance of the bridge, keep
the number of hinges and parts to minimal
• A large deformation was detected due to displacement of the
secondary folding mechanism therefore it was removed from
the 2 rear sections of the bridge to reduce deformation – this
change does not exceed the size limit of the folded bridge.
- Changes made to the rear end of the bridge (near the
balcony) will have a greater impact compare to changes
made to the end of the bridge.
• Shock loading force is required to take into account to
calculate maximum load applying onto the bridge.
- Applying realistic interaction between user and the
bridge to capture changes in force, in order to
calculate Factor Of Safety
• The full scale design was designated to have 25mm of material thickness however
the bridge perform much better when the material thickness was changed to 3 mm.
- The material thickness should be considered at early stages so that the factor of
safety can be minimised.
Not interact with the no-go zone ✓
Made of Aluminium 2024-0 ✓
Under 2.25m when folded ✓ 1.88m when folded
Allow user of 80kg to walk on ✓ The bridge can hold up to 17 users of 80kg
Deploy under 5 mins ✓ 29 seconds to deploy the cardboard model

25. The dog-leg has a triangular
fixture that fit around the end of
the bridge to transfer the
moment when the user is
standing at the end
Reinforcement to support the
secondary folding mechanism
(4-bar-linkage) to avoid it
collapsing during operation
Secondary folding mechanism
(4-bar-linkage) to collapse the
parts to minimal size – flat pack
Bottle-Cap-Opener
alike design used to
convert failure mode
of the fixture from
“shear” to “beam”
Reinforcement to transfer the
torsional motion along the
bridge
P13 –
P15
P12 P17
P18
P9 –
P11