Advanced Computational Analysis ACA REPORT REPORT NO: S Dr M Lacey BSc PhD CEng MIMechE On Behalf Of Fairground Inspection Services Ltd.

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1 Advanced Computational Analysis ACA REPORT REPORT NO: S Title: Structural Verification Of Static 4-Person Bungee Trampoline Device Client: Mr Jonathan Crick Author: Dr M Lacey BSc PhD CEng MIMechE On Behalf Of Fairground Inspection Services Ltd. Date: 8 th August 2009 ADIPS Registration No.: A, Main Road, Gedling, Nottingham NG4 3HP Tel (0115) m.lacey@aca-consultants.co.uk 1

2 Summary This report describes the structural verification of the static 4-person, bungee trampoline amusement device, as manufactured by Jonathon Crick. The structural model of the bungee trampoline device was generated from drawings provided by Mr Jonathan Crick. The design review verification was performed against ride calculations and verification provided by Mr C. Pettinger. The analysis detailed below was carried out based on loadings form various combinations of ride operation, based on a maximum single passenger mass of 90 kg, bouncing with a maximum inertial acceleration equivalent to 2g. The results of the analysis and the comparison of these results with those provided by Mr C. Pettinger, show that all structural and mechanical components have adequate loadcarrying capacity, based on the loading prescribed above. Page 2 Of 33 ACA Engineering Consultants S1369-1

3 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 11 Recommendations 13 Figures 14 Appendix A 23 Appendix B 25 Appendix C 26 Appendix D 28 Appendix E 29 Appendix F 30 Calculations 31 Page 3 Of 33 ACA Engineering Consultants S1369-1

4 Description Of Ride The static 4-person bungee trampoline is an amusement device capable for use either by adult or child participants. The ride is lightweight and fully transportable. It 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 bungee ropes are 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 6.5 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 when bouncing. A typical view of the 4-person bungee trampoline is shown in figure 1.1. Page 4 Of 33 ACA Engineering Consultants S1369-1

5 Method Of Analysis The analysis of the 4-person bungee trampoline device was performed using the ANSYS finite element program. The structural model of the device was generated from drawings and sketches provided by Mr Jonathan Crick. The analysis of the bungee-trampoline structure was performed with regard to the initial design verification carried out independently by Mr C. Pettinger (not reported here). 1) Structural Analysis The finite element model of the device was generated using a combination of BEAM4, LINK10, CONTACT52, SHELL63, MASS21 and MPC184 element types. The BEAM4, 3- dimensional prismatic beam elements were used to model the aluminium poles. The crosssectional properties of these elements were set to those of the pole members, as appropriate. The LINK10, 3-dimensional, tension-only elements were used to model the steel guy ropes which constrained the top of each support pole and the bolts connecting the centre post support angles to the base plate. 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. Additionally these elements were used to model the contact at the pivot pins, to ensure the correct degree of permitted free rotation at these points. The SHELL63, 3- dimensional plate elements, were used to model the centre tube and the central base plate components. The element thickness was set to the local section wall or plate thickness, as appropriate. The MASS21, 3-dimensional mass elements, without rotational inertia, were used to model the mass of the hoist motors. The MPC184, rigid beam elements were used to model the correct connectivity between the hoist motors and their mounting angles. The finite element model comprised a total of 8740 elements (1612 beam elements, 16 tension-only elements, 998 contact elements, 6082 shell elements, 16 mass elements and 16 rigid beam elements) and 8990 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 deflexion analysis was performed, to ensure increased accuracy in predicting deflexions and also to include any Page 5 Of 33 ACA Engineering Consultants S1369-1

6 secondary bending or tension effects in the results. Hence the analysis was non-linear (due to the use of non-linear element types) and the model reached convergence to within 0.5% of the overall load on the structure. A total of 4 load cases were analysed for the structure, viz. load cases 1 to 4. For each load case, from 1 to 4, the number of passengers was increased by one. Hence load case 1 represented a single passenger. Load case 2 represented 2 passengers, situated adjacent to each other. Load case 3 represented 3 passengers, to examine the maximum out-of-balance load condition. Finally load case 4 represented a full complement of participants, bouncing simultaneously, which represented the maximum load condition. In addition to the loads described above, the self-weight loading of the structure was included automatically by the finite element program, for all load cases, based on the steel and aluminium densities shown below and an acceleration due to gravity of 9.81 m/s 2. Page 6 Of 33 ACA Engineering Consultants S1369-1

7 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 = N/mm 2 (Young s modulus) ν = (Poisson s ratio) σ 0.2 = 326 N/mm 2 (0.2% Proof strength) ρ = 2710 kg/m 3 (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 S235 structural steel (as specified by the device manufacturer), as follows: E = N/mm 2 (Young s modulus) ν = 0.28 (Poisson s ratio) σ y = 235 N/mm 2 (Yield strength) ρ = 7850 kg/m 3 (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 fleck shock cords have a length of 230 cm and a diameter of 12 mm and 10 mm, for the high and low stiffness cord respectively. 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 fleck shock cords is shown in Appendix C. The pulleys used for the bungee ropes are of Easy Pulley product description, manufactured to EN These pulleys have a maximum load-carrying capacity of 30 kn. The certificate of conformity for the pulleys is shown in Appendix D. Page 7 Of 33 ACA Engineering Consultants S1369-1

8 e) The climbing ropes are a 9 mm superstatic configuration, manufactured to EN 1891A and EN 1891B.. The certificate of conformity for the bungee ropes is shown in Appendix D. f) The carabiners are Offset D Screw type, manufactured to EN 362. The certificate of conformity for the carabiners is shown in Appendix D. g) The support jacks have a capacity of 2350kg each. The certificate of conformity for the jacks is shown in Appendix E. h) The steel ropes are a standard 6x19 configuration, with a fibre core, to BS 302. i) 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. Page 8 Of 33 ACA Engineering Consultants S1369-1

9 Results Stresses In Centre Load Case Stresses In Main Stresses In Bottom Stresses In Long Stresses In Short Stresses In Base Tube No. Legs (N/mm 2 ) Legs (N/mm 2 ) Props (N/mm 2 ) Props (N/mm 2 ) Plate (N/mm 2 ) (N/mm 2 ) (fig 2.2) 6.2 (fig 2.3) 27.2 (fig 2.4) 38.7 (fig 2.5) (fig 2.6) (fig 2.1) Table 1 Results For Stresses Load Case No. Maximum Deflexion (mm) Maximum Tension In Guy Maximum Reaction Under Maximum Reaction At Main Ropes (kn) Central Base (kn) Legs (kn) (fig 3.1) Table 2 Results For Deflexions, Guy Rope Loads And Reactions Page 9 Of 33 ACA Engineering Consultants S1369-1

10 Note: i) The stresses quoted in table 1, for the legs and props, are the most severe combination of bending and axial stress in any structural component. The stresses in the continuum of the centre tube and base plate are the von-mises stresses. ii) The deflexion quoted in table 2 is the vector sum of the individual Cartesian deflexion components. iii) The max reaction of kn is equivalent to an average pressure on the ground of kn/m 2 when typically a 300x300 mm base area is used. iv) The determination of the structural capacities of the various components of the device and the assessment of the critical joints is shown in calculation sheets 1 to 3. Page 10 Of 33 ACA Engineering Consultants S1369-1

11 Conclusions The stresses determined from the present analysis are concomitant with those predicted by the Mr C. Pettinger verification report on this ride. The results of the analysis performed by Mr Pettinger are based on a closed form analysis of the structure, using similar loads and accelerations to those described in the present study. The small discrepancies between the predictions from Mr Pettinger s report and the present study arise mainly from the method of analysis used in each case. The non-linear analysis carried out in the present study uses a non-linear approach, which more accurately predicts stresses and deflexions. 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 poles provide a maximum utilisation factor of approximately 28 % on the buckling capacity of the poles (based on a limit state analysis to BS 8118, see calculations sheets 1 to 2), which clearly is adequate. This maximum utilisation factor occurs in the bottom leg poles, for load case 3 The maximum stress in the centre tube provides a minimum factor of safety of approximately 7.7, based on the 0.2% proof strength for the aluminium grade used. Similarly the central base plate has a factor of safety of approximately 2.2. Hence these components are satisfactory under the worst case loading conditions used for the analysis. The maximum deflexion in the structure represents approximately 1 /85 of the overall height of the device (for load case 3). Whilst this would be excessive for a static structure the deflexions result from dynamic loads and result from sway of the structure, rather than vertical deflexion. Hence, since the stresses are relatively low in these components the dynamic deflexion is fully recoverable and will be acceptable. In terms of fatigue in parent metal the combined bending and axial stresses are in all cases less then the recommended limits indicated in BS8118. Therefore the structure should have an adequate fatigue life, but this will depend on the usage of the device. The analysis of the critical pin connections, shown in calculation sheet 3, demonstrates that the stresses in the pin connection has adequate strength for the proposed maximum loading. Page 11 Of 33

12 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. Page 12 Of 33

13 Recommendations From the results of the analysis clearly there are 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 cracks. 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. The details shown in Appendix F provide a regular inspection régime for care and maintenance of the device and it is recommended that this régime be strictly adhered to. 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 kn/m 2, based on a 300 mm x 300 mm footprint. 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. Additionally the operator must ensure that there is a recognisable boundary around the ride, at a safe distance, to ensure that spectators are clear of the motion envelope of the ride participants. Page 13 Of 33

14 Figure 1.1 Typical View Of Static 4-Person, Bungee Trampoline Device Page 14 Of 33

15 Figure 1.2 Finite Element Model Of Static 4-Person Bungee Trampoline Page 15 Of 33

16 Figure 2.1 Stresses In Main Legs, Due To Load Case4 Maximum Stress = 12.5 N/mm 2 Page 16 Of 33

17 Figure 2.2 Stresses In Bottom Legs, Due To Load Case 3 Maximum Stress = 72.8 N/mm 2 Page 17 Of 33

18 Figure 2.3 Stresses In Long Props, Due To Load Case 3 Maximum Stress = 6.2 N/mm 2 Page 18 Of 33

19 Figure 2.4 Stresses In Short Props, Due To Load Case 3 Maximum Stress = 27.2 N/mm 2 Page 19 Of 33

20 Figure 2.5 Stresses In Centre Tube, Due To Load Case 3 Maximum Stress = 38.7 N/mm 2 Page 20 Of 33

21 Figure 2.6 Stresses In Base Plate, Due To Load Case 3 Maximum Stress = N/mm 2 Page 21 Of 33

22 Figure 3.1 Overall Deflexions In Structure, Due To Load Case 3 Maximum Deflexion = mm Page 22 Of 33

23 Appendix A Certificate Of Conformity For Aluminium Support Poles Figure A1 Conformity Certificate For Aluminium Grade 6082 T6 Support Poles Page 23 Of 33

24 Figure A2 Chemical Analysis And Mechanical Test Certificate For Aluminium Grade 6082 T6 Support Poles Page 24 Of 33

25 Appendix B Conformity Certificate For Passenger Harness Figure B1 Conformity Certificate For Passenger Body Harness Page 25 Of 33

26 Appendix C Certificate Of Conformity For Fleck Shock Cords Figure C1 Conformity Certificate For Fleck Shock Cords 12 mm diameter. Page 26 Of 33

27 Figure C2 Conformity Certificate For Fleck Shock Cords 10 mm diameter Page 27 Of 33

28 Appendix D Certificate Of Conformity For Pulleys, Carabiners and Climbing Ropes. Figure D1 Conformity Certificates For Pulleys, Carabiners and Climbing Ropes. Page 28 Of 33

29 Appendix E Certificate Of Conformity For Support Jacks. Figure E1 Conformity Certificates For Support Jacks. Page 29 Of 33

30 Appendix F Manufacturer s Recommended Checks And Inspections Visit Web Site: Under Care Section Page 30 Of 33

31 Advanced Computational Analysis 4a, Main Road, Gedling, Nottingham. NG4 3HP Telephone Client : Mr Jonathan Crick Contract No : S1369 Date : 7 th August 2009 Description : Structural Verification Of Static 4-Person Bungee Trampoline ACA Engineering Consultants 1) Loading a) Self - weight Self - weight loading included automatically by FE program, based on material densities shown above 2 and an acceleration due to gravity of 9.81 m/s b) Passenger loading passenger mass = 90 kg 2 equivalent inertial acceleration = 2x9.81 = m/s (2g) o minimum included angle of bungee ropes = 45 FromFE analysis for a single passenger the loads on each pole will be : horizontal components of vertical component of 2) Section Verification force = N (x - direction), N (z - direction) force = N (negative y - direction) a) Main Legs (to BS8118). Worst case Load Case 4 factored axial load = 1.33x3.2 = 4.26 kn Moment : M Z = 0.44 knm factored ΣM = 0.44x1.33 = 0.59 knm λ = = ps = 30 N/mm PRX 38.2 p 0Sx 255x82960 M RSZ = = = 17.6 knm 6 γ m 1.2x10 P M Z PM Z = + + P M 2P M RX RZ RX RSZ 30x = = 53.8 kn 3 1.2x x0.59 2x53.8x17.6 = 0.11< 1.0 Satisfactory Prepared By: Dr M.Lacey Checked By: Dr M.Lacey ACA 2009 Sheet: 1 of: 3 Page 31 Of 33

32 Advanced Computational Analysis 4a, Main Road, Gedling, Nottingham. NG4 3HP. Telephone Contract No. S1369 ACA Engineering Consultants b) Bottom Legs. Worst case Load Case 3 factored axial load = 1.33x2.4 = 3.19 kn Moment : M Z = 2.84 knm factored ΣM = 2.84x1.33 = 3.78 knm λ = = ps = 29 N/mm PRX 38.2 p0sx 255x82960 M RSZ = = = 17.6 knm 6 γ m 1.2x10 P M Z PM Z = + + PRX M RZ 2PRXM RSZ c) Long Props Worst case Load Case 3 factored axial load = 1.33x2.4 = 3.19 kn Moment : M Z = negligible 0.85x6042 λ = = ps = 18 N/mm 29.4 P 3.19 = = 0.14 < 1.0 Satisfactory PRX 23.4 d) Short Props Worst case Load Case 3 factored axial load = 1.33x3.3 = 4.39 kn Moment : M Z = negligible λ = = 66.8 ps = 80 N/mm P 16.1 P 4.39 = = 0.13 < 1.0 Satisfactory P 34.2 RX RX 29x = = 52.0 kn 3 1.2x x3.78 2x52.0x P RX 80x427 = 3 1.2x10 = 0.28 < x1560 = = 23.4 kn 3 1.2x10 = 34.2 kn Satisfactory Prepared By: Dr M.Lacey Checked By: Dr M.Lacey ACA 2009 Sheet: 2 of: 3 Page 32 Of 33

33 Advanced Computational Analysis 4a, Main Road, Gedling, Nottingham. NG4 3HP. Telephone Contract No. S1369 ACA Engineering Consultants 3) Connection Verification a) Shear pin at base of poles max shear force on pin = 4.26 kn (fromfe analysis load case 4) /2 2 2 f q = x = 36.2 N/mm < 115 N/mm Satisfactory x3 M max = = 6390 Nmm 2 3 πx10 3 z xx = = 98.2 mm f b = = 65.0 N/mm < 135 N/mm Satisfactory 98.2 By inspection all other pins satisfactory, since shear loads are lower b) Bolted Connections To Central Post Max shear on any bracket = 2.56cos56.1 = 1.43 kn By inspection 2 - M8 Grade 8.8 Setscrews Satisfactory Prepared By: Dr M.Lacey Checked By: Dr M.Lacey ACA 2009 Sheet: 3 of: 3 Page 33 Of 33

Advanced Computational Analysis

Advanced Computational Analysis REPORT REPORT NO: S2149-1 Revision B Title: Client: Structural Verification Of Portable 4-Person Bungee Trampoline Amusement Device Mr James Oakey Author: R. Anderson BEng