Portique_autonome_en.. - Unicycle

UNICYCLE
Free-Standing Trapeze Rig
Technical Verification Report

Contents
1 Introduction __________________________________________________ 3
2 General Diagrams _____________________________________________ 3
3 Dimensional Details ____________________________________________ 5
4 Coordinates of Points at Reference Point X, Y, Z above ________________ 6
5 Nature of Components _________________________________________ 6
6 Anticipated treatment of the structure ______________________________ 7
7 Hypotheses and justifications ____________________________________ 8
8 Justification of states of pressure considered ________________________ 8
9 Verification of strength components _______________________________ 9
10 Verification of strength of elements ______________________________ 12
11 Verification of overall stability __________________________________ 14
12 Comments on maintenance and monitoring _______________________ 15
13 Verification of equipment and devices ____________________________ 15
14 Points of anchorage _________________________________________ 15
15 Comments on level of safety ___________________________________ 15
16 References ________________________________________________ 16
Contents

1 Introduction
The sector of circus arts is moving more and more towards sport and leisure
activities. The demand for authorised products is therefore important and the
societies that open in this sector must satisfy certain expectations.
However, the disciplines of performance must also adhere to artistic constraints
that are sometimes contrary to recognised safety methods.
It is therefore very important that the validation of security of these apparatus is
adapted with accumulated practical experience. With a goal, one day, to reach
the establishment of a specific standard of security, it is necessary that the
reasoning of checks of this equipment is detailed and explicit. The choice of
methods and coefficients must be justified, and the degree of security expected
must take into account the specifics involved in the particular use of the
equipment.
Above all, the apparatus must ensure the safety of all persons. One must not
assume the ultimate flexibility of the equipment; taking into account the possible
limitations is important.
2 General Diagrams
Page 3

NOTE: In the verifications that follow, only the Freestanding Rig 3m60 will be
considered. The narrow version (2m60) causes, by the way of its geometry,
incomparable strengths.
Page 4

3 Dimensional Details
The coordinates of these different points are taken at reference point X,Y,Z,
shown above and placed at point A.
Eg: H has coordinates: 270; 0; 620 (the last coordinate being the height).
Page 5

4 Coordinates of Points at Reference Point X, Y, Z above
Units in cm
A 0 0 0 E 0 0 52 I -137 -273 0
B 270 0 0 F 270 0 52 J -137 273 0
C -13 0 18 G 0 0 620 K 419 273 0
D 283 0 18 H 270 0 620 L 419 -273 0
5 Nature of Components
• Braces: IG, JG, KH, LH
Strap 35x1.5mm with tightener ratcheded.
CMR ≥ 2750 daN, extension break-off ∼ 8%, E ∼ 11000N/mm 2
• Poles and tubes: GC, HD, FL, FK, EI, EJ
Tube ∅ 60x2mm, sleeve ∅ 55x3mm NFA49643, quality 2
• Cables: AB
Steel cable ∅ 11mm 6x36 wires
CMR≥ 5800daN
• Yards GH
Profile ∅ 60x2mm + 30x30x2mm spacing of 100mm between axles
Linked by 6 flats of 25x55x6mm
NFA 49643 quality 2
• Pulleys: BL, BK, AI, AJ
Tube ∅ 40x2mm, NFA 49541
• Principal compression tube: CD
Tube ∅ 82.5x3.2mm, NFA 49643, quality 2
Page 6

• Caisson blocks: ACE, BDF
Rigid, together consisting of different profiles and of sheet metal of 2.5mm
(effective traction).
NFA 49643, quality 2 and ≥ E 24-2
6 Anticipated treatment of the structure
• Weight applied on the centre of structure GH
Suspension of two persons. The mass to take into account is based on the 95 th
percentile for the curve of the distribution of weight that can be expected. In this
case, a mass of 168kg is considered. The frame can possibly tolerate one
person swinging. To take this into account, one multiplies the weight (94daN)
by a dynamic factor of 2, and by an acceleration of 10m/s 2 following an angle of
45 o . (See hypotheses and justifications.)
Page 7

7 Hypotheses and justifications
The considerations that follow are drawn from different norms applicable within
the sport (gymnastics and climbing) and are supported by the behaviour and
experience of this type of equipment. (See references.)
1. The weight of the group of people is taken into account as a load based on
the probability calculation (95 th percentile) applied to the expected distribution of
weight, according to the number of people.
Number of people Weight for adults (kg) Weight for children (kg)
1 94 70
2 180 130
Given that there is a difference in weight between a base and a flyer, the sum of
their weight can be estimated at 168kg.
2. The dynamics appropriate for swinging (centrifugal acceleration) leads to a
maximum vertical strain when a flyer passes directly below the point of
suspension so that the horizontal strain is at a maximum within the zones
approaching 45 o .
As hypothesis, one considers that the combination of strain to account for are,
on one hand, the vertical load of bodies increased by a dynamic C d +2, and on
the other hand, a dynamic acceleration of 10m/s 2 within a 45 o angle beneath the
horizontal. Combinations are to be verified separately.
3. The factor of overall security (γα=1.2) to apply to these variable strains
stems from the norm NF EN 913
“Material de gymnastique, Exigences generales de securite.”
Q d = γ q x Q k
Q d = 1.2 x Q k x C d
4. To estimate the ground-based acceleration, one takes 10m/s 2 ⇒ 1kg = 1daN
5. f y ≥ 235 N/mm 2 , f u hypotheses and justifications ≥ 360 N/mm 2
6. In view of the finesse of fundamental components, the effect of wind has
been disregarded.
8 Justification of states of pressure considered
In view of the specific treatments and configurations of the use of this
equipment, experience has shown that the combinations and approaches to
consider are the following:
Page 8

. One person suspended and swinging at the centre of the yard GH.
. Two people suspended at the centre of the yard GH.
These approaches should not be considered in a combined fashion as they
occur only in distinct configurations of use.
Furthermore, the instructions for use that accompany this material strictly
restrict usage to these configurations.
9 Verification of strength components
. One person suspended and swinging at the centre of the yard GH.
(The least favourable case in considered.)
Load to be considered: vertical force = 94 daN x 2 x 1.2
. Bending of the yard GH
Hypothesis: That the participation of bores is neglected and that the flat
sections are maintained.
Inertia of the section:
Areas: A squared profile: 4x28x2 = 224mm 2
A rounded profile: Πx30 2 -28 2 = 364mm 2
Centre of gravity:
224/(224+364) = 38mm above the axis of the circular section
I squared profile: (30 4 -26 4 )/12 = 2.9418cm 4
I rounded profile: π x (60 4 – 56 4 )/64 = 15.3423cm 4
I = 2.94 + 62 2 x 224 + 15.34 + 38 2 x 364 = 156.95cm 4
Curt stress:
V sd = 94x2x1.2 = 225daN
V pl.Rd = (2x364mm 2 /π) x 235N/mm 2 / √3x1.1 = 2858.2 daN
V Sd ≤ 50% V pl.Rd ⇒ Curt stress is not taken into account.
Momentum:
M sd = 94daNx 2x 1.2x 3.7m = 20181Nm
4
For this type of profile, security is considered by:
W pl.Rd ≥ 1.2 x W el.Rd
Therefore,
W el.Rd = Ι = 20389mm 3
Y max
M e.Rd = W pl.Rd x 235 = 5228Nm
1.1
M sd = 40% M c.Rd
Page 9

. Curvature of posts GE and HF:
Q d = 225daN + 30 daN (dead wights of the yard) = 255 daN
N due to pre-existing pressure = 200 daN x 2 x cos (26.2 o ) = 359 daN
As hypothesis, the initial tension in the braces is taken as T I = 200 daN which represents an
important pre-existing pressure.
The profile is of class b, therefore fyb and βΑ = 1 are used.
N b.Rd = χ x β Α x Α x fγ
γM1
_ 6000
λ = λ = 20.6 = 3.01
λ 1
π √E
f y
⇒ χ = 0.0988
⇒ N b.Rd = 364.4mm2 x 235 x 0.0988 = 769.15daN
1.1
⇒ N sd = 225+30 + 2 x 200daN x cos26.2 o = 486.5 daN = 63.5% N b.Rd
2
. Curvature of the principal compressions tube CD:
N b.Rd = χ x β Α x Α x fγ
γM1
_ 3964
λ = λ = 28.05 = 1.5
λ 1
π √E
⇒ χ = 0.3422
f y
⇒ N b.Rd = 797.2mm 2 x 235 x 0.3422 = 5828daN
1.1
⇒ N sd = 3.89 x 255 + 2790 = 3782 daN = 65% N b.Rd
. Resistance of caisson blocks blocks ACE and BCF:
. with flexion
M e.Rd = 2.5mm x100mm x 235 x 0.1m = 5340Nm
1.1
which would correspond with ⇒ N sd = 5012daN in the principal
compression tube.
⇒ The cassion exists if the tube resists!
Page 10

. with pressure of tube CD at base of caisson
P Rd = 2x π x 40mm x 2.5mm = 628mm 2
V eff.rd =
235 x 628 = 7749daN
√3 x 1.1
V sd = 3782 daN = 49% V eff.rd
. with force of lower foot at A and B
Smaller perimeter requires:
A Veff = 2 x16mm x8mm = 256mm 2
V eff.rd =
235 x 256 = 3157.5daN
√3 x 1.1
V sd = 1138 daN = 36% V eff.rd
. Curvature of upper tubes of feet EI, EJ, FL, FK
N b.Rd = χ x β Α x Α x fγ
γM1
_ 3100
λ = λ = 20.6 = 1.6
λ 1
π √E
⇒ χ = 0.3079
f y
⇒ N b.Rd = 364.4mm2 x 235 x 0.3079 = 2397daN
1.1
⇒ N sd = 1.483 x 255 + 1065 = 1443 daN = 60% N b.Rd
. Resistance of cable AB:
Qd÷4 + T ii x sin 63.8 o
N sd = tg9.7 o + T i x cos 63.8 o = 11384daN
With T i = 200daN and Q d = 255daN
N rt.d (Ø10.6mm 6 x 36) ≥ 5800daΝ
⇒ N sd = 20%N t.Rd
Page 11

10 Verification of strength of elements
. Breakdown of linkage posts – yard.
This breakdown is taken from the points G to H.
The semi-rigid linkage is made from means of two metal plates of 8mm
thickness, bolted together as a safety mechanism (lock-nuts).
The installation holes, of which one is oversized, permits a slight rotation at the
support of the yard. The mechanism allows that if a necessary case arises, the
rotation of the support barely influences the behaviour of the posts. (Assembly
of type articulated.)
In the verifications above, it has been considered that this linkage is articulated.
This is what assists us in certifying our security in regards to the resistance of
the yard.
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Verification of assembly:
Verification of pliers
22.5 ≤ 30 ≤ 12 x 8 OK!
22.5 ≤ 30 ≤ 12 x 8 OK!
45 ≤ 65 ≤ 400 OK!
Verification of cutting of metal plates
V sd = 225 + 30 = 225daN
L v.eff = 30 +65 +22.5 = 117.5
A v.eff = 117.5 x 8 = 940mm 2
V eff.Rd = 235 / √3 x 940 = 11594daN = 11.5T
1.1
V sd = 2.2%V eff.Rd
Verification of cutting bolts:
F v.sd = 225 = 127.5 daN
2
The bolts are class 8.8
Cutting
F v.Rd =
0.6x800x115 = 4416 daN
1.25
Diametric stress (taken at caisson level t=5mm)
α = 30 + 0.66
3x15
F b.Rd =
Conclusion
2.5x0.66x800x14x5 = 7392 daN
1.25
⇒ F v.sd at yard level GH = 3% F v.Rd
⇒ F v.sd at cassion level AE BF = 1433daN x cos9.7
o
+ 1422.5daN + 32% F v.Rd
Page 13

11 Verification of overall stability
Verification of the stability of inversion with regard to support point I, J, K and L.
The least favourable circumstance is naturally the case of swinging. Therefore,
we consider an acceleration of 10m/s 2 applied to a mass of 94kg, following an
angle of 45 o . (See hypothesis and justifications.)
Here, the mass of the frame, 2.60m, is considered, as it is weaker and therefore
unfavourable in terms of stability.
M Qd = 115 x 2.462m = 2777Nm
M Gd = 125 x 2.73m = 3412Nm
M Gd ≥ M Qd ok! M Qd = 81%M Gd
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12 Comments on maintenance and monitoring
Even though the principal bolts are self-locking, it is still necessary to regularly
check the state of assembly and equipment, to control the level of corrosion and
to undertake, if required, replacement of defective bolting.
13 Verification of equipment and devices
The entirety of the accessories and devices used correspond with security
norms guaranteed by the manufacturers.
. All the rapid links integrated within the principal structure have a
breaking stress point ≥ 2000 daN.
. The cable has a breaking stress point ≥ 5800 daN.
. The straps are treated in order to make them more resistant to abrasion
and have a breaking stress point ≥ 3300 daN.
. The entirety of the bolting is treated against corrosion (stainless steel
optional), and the lock-nuts are systematically used in strategic places.
. The safety surface (mattress) that accompanies this product (optional) is
made by a leader in the gymnastic sector. Its design and density is
specifically adapted for the freestanding trapeze rig.
14 Points of anchorage
In case of usage of non-autonomous rig but anchored to the ground:
The system of anchorage is very specific to the constraints of the site and t the
nature of the ground. Non-autonomous usage is not the subject of the present
verifications. The maximum tension calculated for the straps is 750daN. Their
implementation in the rule of the art is left to the responsibility of the
entrepreneur.
The calculations of verification of the yard, the poles as well as the details and
the bolts are to be taken, of course, with care.
15 Comments on level of safety
In this report, a series of favourable factors have not been taken into account.
For example, all the loads have been considered localised and central.
However, this is practically never the case: a trapeze is attached at two points,
spaced by 1.2m; the bearer distributes his load over 40cm.
Nevertheless, to favour safety and to protect oneself during a non-habitual
usage of the equipment, we preferred not to take these situations into account.
Page 15

16 References
. Eurocode 3 “calcul des structures en acier >> + DAN (NF P 22-311).
December 19922
. NF EN 913 Materiel de gymnastique, exigencies generales de securite et
moethodes d’essai. May 1996.
. Donnees ds differents constucteurs: Spanset, Tubeurop, OUTA, Stein, Klocker
& Co., etc.
Page 16