Upload
ledieu
View
218
Download
2
Embed Size (px)
Citation preview
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
© ACA Engineering Consultants S1364-1 3 Of 26
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.
© ACA Engineering Consultants S1364-1 4 Of 26
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.
© ACA Engineering Consultants S1364-1 5 Of 26
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.
© ACA Engineering Consultants S1364-1 6 Of 26
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.
© ACA Engineering Consultants S1364-1 7 Of 26
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.
© ACA Engineering Consultants S1364-1 8 Of 26
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.
© ACA Engineering Consultants S1364-1 9 Of 26
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
© ACA Engineering Consultants S1364-1 10 Of 26
(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.
© ACA Engineering Consultants S1364-1 11 Of 26
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.
© ACA Engineering Consultants S1364-1 12 Of 26
Figure 1.1 – Typical View Of Single-Person Bungee Trampoline Device
© ACA Engineering Consultants S1364-1 13 Of 26
Figure 1.2 – Finite Element Model Of Single-Person Bungee Trampoline
© ACA Engineering Consultants S1364-1 14 Of 26
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
© ACA Engineering Consultants S1364-1 19 Of 26
Figure A2 – Chemical Analysis And Mechanical Test Certificate For Aluminium Grade 6082 T6
Support Poles
© ACA Engineering Consultants S1364-1 20 Of 26
Appendix B – Conformity Certificate For Passenger Harness
Figure B1 – Conformity Certificate For Passenger Body Harness
© ACA Engineering Consultants S1364-1 21 Of 26
Appendix C – Certificate Of Conformity For Bungee Ropes
Figure C1 – Conformity Certificate For Bungee Ropes
© ACA Engineering Consultants S1364-1 22 Of 26
Figure C2 – Conformity Certificates For Pulleys, Steel Ropes And Carabiners
© ACA Engineering Consultants S1364-1 23 Of 26
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
1) Loading
N 258n1790x9.81xsiloads horizontal opposingnet N 844s1790x9.81xcopolesupport each at force alnet vertic
34ropes bungee of angle included minimum(2g) m/s 19.622x9.81onaccelerati inertial equivalent
kg 90masspassenger loadingPassenger b)
m/s 9.81 ofgravity todueon acceleratian andaboveshown densities materialon based program, FEby lly automatica included loadingweight -Self
weight-Self a)
2
2
====
=
==
=
2) Section Verification
2bc
22
2
e
2c
22total
2bc
N/mm 149p N/mm 9.23170x70000πp
cation)for verifi usedbeen has N/mm 10p stress ecompressiv epermissibl of valuereduced a1969:CP118 BSin given of valuemaximum theexceeds ratio sslendernes this:(Note
17038.2374650.85x
mm 23.382153.5
3147761r
polessupport Aluminium b)
4.7557.9275yieldon safety ofFactor
N/mm 275N/mm 57.9f
N/mm 275pp contact) groundby supportedalterally (fully 0frame base Steel a)
===
=
==
==
==
<=
===⇒=
λ
λ
λ
rySatisfacto
yp
Prepared By: Dr M.Lacey Checked By: Dr M.Lacey
ACA Engineering Consultants
© ACA Engineering Consultants S1364-1 24 Of 26
Contract No. S1364
© ACA 2008 Sheet: 2 of: 3
Advanced Computational Analysis 4a, Main Road, Gedling, Nottingham. NG4 3HP. Telephone 0115 9533931 e-mail:[email protected]
Prepared By: Dr M.Lacey Checked By: Dr M.Lacey
rySatisfacto 1.0 27.0
9.234.21149x
6.410
4.2
pf
1p
fpf
e
cbc
b
c
c <=⎟⎠⎞
⎜⎝⎛ −
+=
⎟⎟⎠
⎞⎜⎜⎝
⎛−
+
3) Connection Verification
rySatisfacto
rySatisfacto
N/mm 165 N/mm 0.17153426010f
mm 15343225z
Nmm 260105202x5M
N/mm 115 N/mm 3.52xπxπx5202x4f
analysis) FE(from N 5202pinon forceshear max polesupport of baseat pin Shear a)
22b
33
xx
max
222q
<==
==
==
<==
=
xπ
4) Fatigue Verification
cycles 0.98x10 weldof life fatigue BS7608, to weld,F classfor
N/mm 6.185
265.9xstressshear net weld
N/mm 65.97.358.6force net weld
N/mm 3.72x126
2x923.4shear todue cefor weldeffective
N/mm 6.586300
0.369x10moment todue force weldeffective
mm 6300126x50group weldof modulusmm 1262x63dispersal) 45(at weldoflength effective
Nmm 0.369x1002x923.4x20on weldmoment bracket mountingmotor at Welda)
8
2
6
2
6
=
==
=+=
==
==
==
==
==
ACA Engineering Consultants
© ACA Engineering Consultants S1364-1 25 Of 26
Contract No. S1364
© ACA 2008 Sheet: 3 of: 3
Advanced Computational Analysis 4a, Main Road, Gedling, Nottingham. NG4 3HP. Telephone 0115 9533931 e-mail:[email protected]
Prepared By: Dr M.Lacey Checked By: Dr M.Lacey
operation of years 03.29300x112500.98x10 weldof life fatigue
ride)per bounces 150nominally (assuming 112508
10x60x150dayper cycles of no.
timecyclemin 8an on operatingyear,per days300 day,per hours 10 ofoperation devicefor
8
==
==
ACA Engineering Consultants
© ACA Engineering Consultants S1364-1 26 Of 26