aca - bungeetrampoline.com computational analysis aca report report no: s1364-1 title: ......

Advanced Computational Analysis

ACA REPORT

REPORT NO: S1364-1

Title: Structural Verification Of Single-Person Bungee Trampoline

Amusement Device

Client: Mr Jonathan Crick Author: Dr M Lacey BSc PhD CEng MIMechE On Behalf Of Fairground Inspection Services Ltd. Date: 9th March 2008 ADIPS Registration No.: 0815130-2

4A, Main Road, Gedling, Nottingham NG4 3HP

Tel (0115) 9533931 e-mail: [email protected]

Summary

This report describes the structural verification of the single-person, bungee trampoline

amusement device, as manufactured by North Dean Fabrications, on behalf of Mr Jonathan

Crick.

The structural model of the bungee trampoline device was generated from drawings and

sketches provided by Mr John Grimes, on behalf of Mr Jonathan Crick. The design review

verification was performed against initial calculations provided by Mr Chris Pettinger, for the

structure of the ride.

The analysis detailed below was carried out based on a maximum single passenger

mass of 90 kg, bouncing with a maximum inertial acceleration equivalent to 2g.

The results of the analysis show that all structural and mechanical components have

adequate load-carrying capacity, based on the loading prescribed above.

© ACA Engineering Consultants S1364-1 2 Of 26

Index Page

Summary 2

Description Of Ride 4

Method Of Analysis 5

1) Structural Analysis 5

2) Material Properties And Component Capacities 7

Results 9

Conclusions 10

Recommendations 12

Figures 13

Appendix A 19

Appendix B 21

Appendix C 22

Calculations 23


Description Of Ride

The single-person bungee trampoline is an amusement device capable for use either by

adult or child participants. The ride is lightweight and fully transportable and can easily be

erected and dismantled for use on any suitable site, either outdoors or indoors (providing

adequate headroom height is available).

The ride operates by first positioning the passenger on the trampoline. The passenger

harness is then fitted and attached to the bungee ropes, on either side of the passenger. The

number of bungee ropes used is adjusted, depending on the estimated passenger mass, to give

the appropriate ‘feel’ to the bounce of the participant, without exerting excessive inertial forces

on the passenger. This is carried out based on the experience of the ride operator.

During the ride the participant bounces vertically until reaching a maximum height of

approximately 6 m. At this point the participant experiences a feel of partial weightlessness. As

the passenger moves progressively higher with each bounce, the winding motor reduces the

effective length of the ropes, to permit the passenger to release progressively more potential

energy with each bounce.

The downwards motion of the participant, at the lowest point, is arrested by a

combination of the contact between the participant and the trampoline and the moderate

tension in the flexible bungee ropes. Note that it is not always necessary for the participant to

make full contact with the trampoline; in some instances the vertical motion is arrested only by

the bungee ropes. In this case the flexibility of the bungee ropes would ensure that the

maximum inertial forces are reduced.

It is difficult to estimate the maximum passenger forces exerted by the device, due

principally to the wide variation possible in participant mass. However an acceptable guide

would be approximately 2g absolute maximum inertial acceleration, which would give the ride

participant a sensation of twice body mass.

A typical view of the single-person bungee trampoline is shown in figure 1.1.


Method Of Analysis

The analysis of the single-person bungee trampoline device was performed using the

ANSYS finite element program. The structural model of the device was generated from

drawings and sketches produced by Mr John Grimes, on behalf of Mr Jonathan Crick.

In view of the fact that no structural assessment had been performed by either the

manufacturer or ride owner, a retrospective structural analysis was performed by Mr

Christopher Pettinger, which enabled this design review to be carried out. Mr Pettinger’s

analysis is not reported here, but the results of the present analysis are compared with those of

Mr Pettinger below.

1) Structural Analysis

The finite element model of the device was generated using a combination of BEAM4,

LINK10 and CONTACT52 element types. The BEAM4, 3-dimensional prismatic beam

elements were used to model the steel base frame of the device and the aluminium support

poles. The cross-sectional properties of the elements were set to those of the frame and support

pole members, as appropriate. The LINK10, 3-dimensioal, tension-only elements were used to

model the steel guy ropes which constrained the top of each support pole. This element can

sustain only tensile loads and is removed from the element formulation if the forces are equal

to, or decrease below zero. The cross-sectional area of the element was set to that of the steel

rope, as appropriate. The CONTACT52, 3-dimensional, compression-only contact elements

were used to model the contact between the base frame and ground. The stiffness of these

elements was set to ensure that there was no interpenetration between the frame and the

ground. Also this ensured that should the frame lift from the ground during loading these

elements would be removed from the element formulation.

The finite element model comprised a total of 587 elements (368 beam elements, 6

tension-only elements and 213 contact elements) and 578 nodes. The finite element model of

the device is shown in figure 1.2.

Note that due to the inherent flexibility of the structure a large defelxion analysis was

performed, to ensure increased accuracy in predicting deflexions and also to include any

secondary bending or tension effects in the results. Hence the analysis was non-linear (due to

the use of large deflexion effects and non-linear element types) and the model reached

convergence to within 0.5% of the overall load on the structure.


A single load case was analysed for the structure. For this load case the lower ends of

the contact elements were constrained in all translational degrees-of-freedom. Hence the base

contact elements constrained the structure by virtue of the friction at the base. Any fixed

physical positioning of the nodes at the base would render the structure hyperstatic. Hence the

constraints used represent a minimum but sufficient kinematic constraint condition.

The loads on the structure from the participant accelerations were resolved at the points

of contact between the hoisting mechanism and the frame, viz. at the winding motor and the

base, at the diverter pulleys adjacent to the motor and the frame and at the diverter pulleys at

the top of the support poles. The load on the structure was derived from a maximum passenger

of mass 90 kg, accelerating at 19.62 m/s2 (2g). Additionally, as a worst case, the included angle

between the bungee ropes was taken as approximately 34º. This position would be concomitant

with a passenger reaching these accelerations at the bottom of the bounce, in the absence of the

trampoline. Further details of the loading are provided in calculation sheet 1.

In addition to the loads described above, the self-weight loading of the structure was

included automatically by the finite element program, based on the steel and aluminium

densities shown below and an acceleration due to gravity of 9.81 m/s2.


2) Material Properties And Component Capacities

a) The material properties for the aluminium sections used for the analysis were based on

a grade 6082 T6 aluminium, as follows:

E = 70000 N/mm2 (Young’s modulus)

ν = 0.316 (Poisson’s ratio)

σ0.2 = 326 N/mm2 (0.2% Proof strength)

ρ = 2710 kg/m3 (Density)

The material certificate for the aluminium sections is shown in Appendix A

b) The material properties for the steel sections used for the analysis were based on a

grade S275 structural steel (as specified by the device manufacturer), as follows:

E = 207000 N/mm2 (Young’s modulus)

ν = 0.28 (Poisson’s ratio)

σy = 275 N/mm2 (Yield strength)

ρ = 7850 kg/m3 (Density)

c) The harness has a load-carrying capacity of minimum 187 N to 810 N. This is

equivalent to a maximum passenger mass of 82.6 kg. The conformity certificate for the harness

is shown in Appendix B.

d) The bungee ropes are a 9 mm superstatic configuration, manufactured to EN 1891A and

EN 1891B. There is no maximum load-carrying capacity quoted for the bungee ropes, since

this will depend on the configuration used for each passenger. The certificate of conformity for

the bungee ropes is shown in Appendix C.

The pulleys used for the bungee ropes are of ‘Easy Pulley’ product description,

manufactured to EN 122278. These pulleys have a maximum load-carrying capacity of 30 kN.

The carabiners are ‘Offset D Screw’ type, manufactured to EN 362.

The steel ropes are a standard 6x19 configuration, with a fibre core, to BS 302. The

conformity certificates for the pulleys, carabiners and steel ropes are shown also in Appendix

C.


e) The eyebolts used at the top of the support poles have been tested to a capacity of

maximum 750 kg. The eyebolts used at the lower end of the hoist ropes have been tested to a

capacity of maximum 250 kg. These are standard eye bolt configurations.

The results of the analysis are presented below.


Results

Maximum stress in steel base = 57.9 N/mm2 (figure 2.1)

Maximum stress in aluminium support poles = 6.6 N/mm2 (figure 2.2)

Overall structural deflexion = 68.03 mm (figure 3.1)

Maximum contact force between base and ground = 306.22 N

(this is equivalent to an average pressure on the ground of 52 kN/m2).

Note:

i) The stresses quoted above are the most severe combination of bending and axial stress

in any structural component.

ii) The deflexion quoted above is the vector sum of the individual Cartesian deflexion

components.

iii) The determination of the structural capacities of the various components of the device,

the assessment of the critical joints and the fatigue assessment of the critical welds are shown

in calculation sheets 2 - 3.


Conclusions

The stresses determined from the present analysis are concomitant with those predicted

by Mr Pettinger in the retrospective design. The discrepancies between these predictions arise

mainly from the method of analysis used in each case. The analysis carried out by Mr Pettinger

was based on closed-form hand calculations, which cannot predict the stress concentrations and

non-linear deflexions which arise from the finite element analysis. Notwithstanding this the

stresses resulting from each individual analysis are sufficiently close to ensure that there is no

major discrepancy in the resulting stresses and deflexions.

The stresses predicted in the aluminium support poles provide a utilisation factor of

27% on the buckling capacity of the poles, which clearly is adequate.

For the base frame, the members are essentially fully laterally supported by their

contact with ground, via the frictional resistance. Hence the maximum permissible stress in

these members can be taken as the yield strength of the steel (275 N./mm2). Based on this the

resulting stresses in the base frame provide a factor of safety of approximately 4.7. This is

again adequate, based on the maximum loading prescribed.

The maximum deflexion in the structure represents approximately 1/110 of the overall

height of the device. Whilst this would be excessive for a static structure the deflexions result

from dynamic loads (the static deflexion due to self-weight is predicted to be less than 1 mm).

Hence, since the stresses are low in this component the dynamic deflexion is fully recoverable

and will be acceptable.

The weld at the hoist motor support base, which is identified as the critical weld on the

structure, has a fatigue life of approximately 29 years, based on continuous operation of the

device for 300 days per year at 10 working hours per day. Again this acceptable.

The analysis of the critical pin connections, shown in calculation sheet 2 demonstrates

that the stresses in the pin connection has adequate strength for the proposed maximum

loading.

The material and component certificates provided by the manufacturer and owner

demonstrate that all components have adequate load –carrying capacity for the proposed

maximum loading.

Note finally that this report does not cover the verification of the trampoline unit.

Generally most proprietary units are suitable, providing the loading capacity is at least 1800 N


(180 kgf) and the landing area is large enough to ensure that the passenger cannot land beyond

the edge of the trampoline.

It is clear therefore that all components have sufficient strength to provide a satisfactory

working life for the device, based on the assumed maximum loading, providing the

recommendations detailed below are adopted.


Recommendations

From the results of the analysis there are clearly no components on the device which

require specific detailed periodic inspection or other detailed investigation.

Nevertheless it would be prudent to periodically check the integrity of all components

on a regular basis. Hence the operator should periodically (daily) inspect for parent material or

weld cracks. The weld attaching the motor bracket should be non-destructively tested on a bi-

annual basis.

Additionally, all fixing ropes and bungee ropes should be inspected daily and replaced

as necessary if there is any evidence of damage and/or fraying.

Whilst the ride could not be classed as extremely boisterous there would be a category

of people for which the ride would not be suitable. For example it would be suggested that the

following should not be allowed to participate in the ride experience:

Very small children (unless under strict supervision from the operator).

People with a history of neck/back or other skeletal injuries, or other medical problems.

People with a history of heart problems.

Pregnant women.

It would be appropriate to display signage at the ride atrium, indicating the ride would

not be suitable for the above category of participants.

The maximum ground bearing pressure, beneath the ride base, is predicted to be an

average of 52 kN/m2. This bearing pressure is adequate for most sites on consolidated ground.

However it is the responsibility of the ride operator to ensure that the site is capable of carrying

this ground pressure.

For passenger safety and to prevent overturning, the device should not be operated in

wind speeds greater than 8 m/s.

By the nature of the ride, the inertial forces experienced by the ride participants are

governed by the set-up of the bungee rope arrangement, which is strictly under the control of

the operator. It is imperative therefore that only very experienced operators should be allowed

to control the ride.


Figure 1.1 – Typical View Of Single-Person Bungee Trampoline Device


Figure 1.2 – Finite Element Model Of Single-Person Bungee Trampoline


Figure 2.1 – Stresses In Base Frame, Due To 2g Passenger Loading

© ACA Engineering Consultants S1364-1 15 Of 26 Maximum Stress = 57.9 N/mm2

Figure 2.2 – Stresses In Aluminium Support Poles, Due To 2g Passenger Loading

© ACA Engineering Consultants S1364-1 16 Of 26 Maximum Stress = 6.6 N/mm2

Figure 3.1 – Overall Deflexion In Structure, Due To 2g Loading

© ACA Engineering Consultants S1364-1 17 Of 26 Maximum Deflexion = 68.03 mm

© ACA Engineering Consultants S1364-1

18 Of 26 Maximum element Contact Force = 306.22 N (Equivalent To 52 kN/m2 Ground Pressure)

Figure 4.1 – Contact Forces At Base, Due To 2g Passenger Loading

Appendix A – Certificate Of Conformity For Aluminium Support Poles

Figure A1 – Conformity Certificate For Aluminium Grade 6082 T6 Support Poles


Figure A2 – Chemical Analysis And Mechanical Test Certificate For Aluminium Grade 6082 T6

Support Poles


Appendix B – Conformity Certificate For Passenger Harness

Figure B1 – Conformity Certificate For Passenger Body Harness


Appendix C – Certificate Of Conformity For Bungee Ropes

Figure C1 – Conformity Certificate For Bungee Ropes


Figure C2 – Conformity Certificates For Pulleys, Steel Ropes And Carabiners


Client : Mr Jona r than C ick Contract No : S1364

Date : 9th March 2008

Description : Structural Verification Of Single-Person Bungee

Telephone 0115 9533931 e-mail:[email protected] Advanced Computational Analysis 4a, Main Road, Gedling, Nottingham. NG4 3HP

© ACA 2008 Sheet: 1 of: 3

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Prepared By: Dr M.Lacey Checked By: Dr M.Lacey

ACA Engineering Consultants


Contract No. S1364


Advanced Computational Analysis 4a, Main Road, Gedling, Nottingham. NG4 3HP. Telephone 0115 9533931 e-mail:[email protected]


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cycles 0.98x10 weldof life fatigue BS7608, to weld,F classfor

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Contract No. S1364


Advanced Computational Analysis 4a, Main Road, Gedling, Nottingham. NG4 3HP. Telephone 0115 9533931 e-mail:[email protected]


operation of years 03.29300x112500.98x10 weldof life fatigue

ride)per bounces 150nominally (assuming 112508

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