Portique_autonome_en.. - Unicycle
Portique_autonome_en.. - Unicycle
Portique_autonome_en.. - Unicycle
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UNICYCLE<br />
Free-Standing Trapeze Rig<br />
Technical Verification Report
Cont<strong>en</strong>ts<br />
1 Introduction __________________________________________________ 3<br />
2 G<strong>en</strong>eral Diagrams _____________________________________________ 3<br />
3 Dim<strong>en</strong>sional Details ____________________________________________ 5<br />
4 Coordinates of Points at Refer<strong>en</strong>ce Point X, Y, Z above ________________ 6<br />
5 Nature of Compon<strong>en</strong>ts _________________________________________ 6<br />
6 Anticipated treatm<strong>en</strong>t of the structure ______________________________ 7<br />
7 Hypotheses and justifications ____________________________________ 8<br />
8 Justification of states of pressure considered ________________________ 8<br />
9 Verification of str<strong>en</strong>gth compon<strong>en</strong>ts _______________________________ 9<br />
10 Verification of str<strong>en</strong>gth of elem<strong>en</strong>ts ______________________________ 12<br />
11 Verification of overall stability __________________________________ 14<br />
12 Comm<strong>en</strong>ts on maint<strong>en</strong>ance and monitoring _______________________ 15<br />
13 Verification of equipm<strong>en</strong>t and devices ____________________________ 15<br />
14 Points of anchorage _________________________________________ 15<br />
15 Comm<strong>en</strong>ts on level of safety ___________________________________ 15<br />
16 Refer<strong>en</strong>ces ________________________________________________ 16<br />
Cont<strong>en</strong>ts
1 Introduction<br />
The sector of circus arts is moving more and more towards sport and leisure<br />
activities. The demand for authorised products is therefore important and the<br />
societies that op<strong>en</strong> in this sector must satisfy certain expectations.<br />
However, the disciplines of performance must also adhere to artistic constraints<br />
that are sometimes contrary to recognised safety methods.<br />
It is therefore very important that the validation of security of these apparatus is<br />
adapted with accumulated practical experi<strong>en</strong>ce. With a goal, one day, to reach<br />
the establishm<strong>en</strong>t of a specific standard of security, it is necessary that the<br />
reasoning of checks of this equipm<strong>en</strong>t is detailed and explicit. The choice of<br />
methods and coeffici<strong>en</strong>ts must be justified, and the degree of security expected<br />
must take into account the specifics involved in the particular use of the<br />
equipm<strong>en</strong>t.<br />
Above all, the apparatus must <strong>en</strong>sure the safety of all persons. One must not<br />
assume the ultimate flexibility of the equipm<strong>en</strong>t; taking into account the possible<br />
limitations is important.<br />
2 G<strong>en</strong>eral Diagrams<br />
Page 3
NOTE: In the verifications that follow, only the Freestanding Rig 3m60 will be<br />
considered. The narrow version (2m60) causes, by the way of its geometry,<br />
incomparable str<strong>en</strong>gths.<br />
Page 4
3 Dim<strong>en</strong>sional Details<br />
The coordinates of these differ<strong>en</strong>t points are tak<strong>en</strong> at refer<strong>en</strong>ce point X,Y,Z,<br />
shown above and placed at point A.<br />
Eg: H has coordinates: 270; 0; 620 (the last coordinate being the height).<br />
Page 5
4 Coordinates of Points at Refer<strong>en</strong>ce Point X, Y, Z above<br />
Units in cm<br />
A 0 0 0 E 0 0 52 I -137 -273 0<br />
B 270 0 0 F 270 0 52 J -137 273 0<br />
C -13 0 18 G 0 0 620 K 419 273 0<br />
D 283 0 18 H 270 0 620 L 419 -273 0<br />
5 Nature of Compon<strong>en</strong>ts<br />
• Braces: IG, JG, KH, LH<br />
Strap 35x1.5mm with tight<strong>en</strong>er ratcheded.<br />
CMR ≥ 2750 daN, ext<strong>en</strong>sion break-off ∼ 8%, E ∼ 11000N/mm 2<br />
• Poles and tubes: GC, HD, FL, FK, EI, EJ<br />
Tube ∅ 60x2mm, sleeve ∅ 55x3mm NFA49643, quality 2<br />
• Cables: AB<br />
Steel cable ∅ 11mm 6x36 wires<br />
CMR≥ 5800daN<br />
• Yards GH<br />
Profile ∅ 60x2mm + 30x30x2mm spacing of 100mm betwe<strong>en</strong> axles<br />
Linked by 6 flats of 25x55x6mm<br />
NFA 49643 quality 2<br />
• Pulleys: BL, BK, AI, AJ<br />
Tube ∅ 40x2mm, NFA 49541<br />
• Principal compression tube: CD<br />
Tube ∅ 82.5x3.2mm, NFA 49643, quality 2<br />
Page 6
• Caisson blocks: ACE, BDF<br />
Rigid, together consisting of differ<strong>en</strong>t profiles and of sheet metal of 2.5mm<br />
(effective traction).<br />
NFA 49643, quality 2 and ≥ E 24-2<br />
6 Anticipated treatm<strong>en</strong>t of the structure<br />
• Weight applied on the c<strong>en</strong>tre of structure GH<br />
Susp<strong>en</strong>sion of two persons. The mass to take into account is based on the 95 th<br />
perc<strong>en</strong>tile for the curve of the distribution of weight that can be expected. In this<br />
case, a mass of 168kg is considered. The frame can possibly tolerate one<br />
person swinging. To take this into account, one multiplies the weight (94daN)<br />
by a dynamic factor of 2, and by an acceleration of 10m/s 2 following an angle of<br />
45 o . (See hypotheses and justifications.)<br />
Page 7
7 Hypotheses and justifications<br />
The considerations that follow are drawn from differ<strong>en</strong>t norms applicable within<br />
the sport (gymnastics and climbing) and are supported by the behaviour and<br />
experi<strong>en</strong>ce of this type of equipm<strong>en</strong>t. (See refer<strong>en</strong>ces.)<br />
1. The weight of the group of people is tak<strong>en</strong> into account as a load based on<br />
the probability calculation (95 th perc<strong>en</strong>tile) applied to the expected distribution of<br />
weight, according to the number of people.<br />
Number of people Weight for adults (kg) Weight for childr<strong>en</strong> (kg)<br />
1 94 70<br />
2 180 130<br />
Giv<strong>en</strong> that there is a differ<strong>en</strong>ce in weight betwe<strong>en</strong> a base and a flyer, the sum of<br />
their weight can be estimated at 168kg.<br />
2. The dynamics appropriate for swinging (c<strong>en</strong>trifugal acceleration) leads to a<br />
maximum vertical strain wh<strong>en</strong> a flyer passes directly below the point of<br />
susp<strong>en</strong>sion so that the horizontal strain is at a maximum within the zones<br />
approaching 45 o .<br />
As hypothesis, one considers that the combination of strain to account for are,<br />
on one hand, the vertical load of bodies increased by a dynamic C d +2, and on<br />
the other hand, a dynamic acceleration of 10m/s 2 within a 45 o angle b<strong>en</strong>eath the<br />
horizontal. Combinations are to be verified separately.<br />
3. The factor of overall security (γα=1.2) to apply to these variable strains<br />
stems from the norm NF EN 913<br />
“Material de gymnastique, Exig<strong>en</strong>ces g<strong>en</strong>erales de securite.”<br />
Q d = γ q x Q k<br />
Q d = 1.2 x Q k x C d<br />
4. To estimate the ground-based acceleration, one takes 10m/s 2 ⇒ 1kg = 1daN<br />
5. f y ≥ 235 N/mm 2 , f u hypotheses and justifications ≥ 360 N/mm 2<br />
6. In view of the finesse of fundam<strong>en</strong>tal compon<strong>en</strong>ts, the effect of wind has<br />
be<strong>en</strong> disregarded.<br />
8 Justification of states of pressure considered<br />
In view of the specific treatm<strong>en</strong>ts and configurations of the use of this<br />
equipm<strong>en</strong>t, experi<strong>en</strong>ce has shown that the combinations and approaches to<br />
consider are the following:<br />
Page 8
. One person susp<strong>en</strong>ded and swinging at the c<strong>en</strong>tre of the yard GH.<br />
. Two people susp<strong>en</strong>ded at the c<strong>en</strong>tre of the yard GH.<br />
These approaches should not be considered in a combined fashion as they<br />
occur only in distinct configurations of use.<br />
Furthermore, the instructions for use that accompany this material strictly<br />
restrict usage to these configurations.<br />
9 Verification of str<strong>en</strong>gth compon<strong>en</strong>ts<br />
. One person susp<strong>en</strong>ded and swinging at the c<strong>en</strong>tre of the yard GH.<br />
(The least favourable case in considered.)<br />
Load to be considered: vertical force = 94 daN x 2 x 1.2<br />
. B<strong>en</strong>ding of the yard GH<br />
Hypothesis: That the participation of bores is neglected and that the flat<br />
sections are maintained.<br />
Inertia of the section:<br />
Areas: A squared profile: 4x28x2 = 224mm 2<br />
A rounded profile: Πx30 2 -28 2 = 364mm 2<br />
C<strong>en</strong>tre of gravity:<br />
224/(224+364) = 38mm above the axis of the circular section<br />
I squared profile: (30 4 -26 4 )/12 = 2.9418cm 4<br />
I rounded profile: π x (60 4 – 56 4 )/64 = 15.3423cm 4<br />
I = 2.94 + 62 2 x 224 + 15.34 + 38 2 x 364 = 156.95cm 4<br />
Curt stress:<br />
V sd = 94x2x1.2 = 225daN<br />
V pl.Rd = (2x364mm 2 /π) x 235N/mm 2 / √3x1.1 = 2858.2 daN<br />
V Sd ≤ 50% V pl.Rd ⇒ Curt stress is not tak<strong>en</strong> into account.<br />
Mom<strong>en</strong>tum:<br />
M sd = 94daNx 2x 1.2x 3.7m = 20181Nm<br />
4<br />
For this type of profile, security is considered by:<br />
W pl.Rd ≥ 1.2 x W el.Rd<br />
Therefore,<br />
W el.Rd = Ι = 20389mm 3<br />
Y max<br />
M e.Rd = W pl.Rd x 235 = 5228Nm<br />
1.1<br />
M sd = 40% M c.Rd<br />
Page 9
. Curvature of posts GE and HF:<br />
Q d = 225daN + 30 daN (dead wights of the yard) = 255 daN<br />
N due to pre-existing pressure = 200 daN x 2 x cos (26.2 o ) = 359 daN<br />
As hypothesis, the initial t<strong>en</strong>sion in the braces is tak<strong>en</strong> as T I = 200 daN which repres<strong>en</strong>ts an<br />
important pre-existing pressure.<br />
The profile is of class b, therefore fyb and βΑ = 1 are used.<br />
N b.Rd = χ x β Α x Α x fγ<br />
γM1<br />
_ 6000<br />
λ = λ = 20.6 = 3.01<br />
λ 1<br />
π √E<br />
f y<br />
⇒ χ = 0.0988<br />
⇒ N b.Rd = 364.4mm2 x 235 x 0.0988 = 769.15daN<br />
1.1<br />
⇒ N sd = 225+30 + 2 x 200daN x cos26.2 o = 486.5 daN = 63.5% N b.Rd<br />
2<br />
. Curvature of the principal compressions tube CD:<br />
N b.Rd = χ x β Α x Α x fγ<br />
γM1<br />
_ 3964<br />
λ = λ = 28.05 = 1.5<br />
λ 1<br />
π √E<br />
⇒ χ = 0.3422<br />
f y<br />
⇒ N b.Rd = 797.2mm 2 x 235 x 0.3422 = 5828daN<br />
1.1<br />
⇒ N sd = 3.89 x 255 + 2790 = 3782 daN = 65% N b.Rd<br />
. Resistance of caisson blocks blocks ACE and BCF:<br />
. with flexion<br />
M e.Rd = 2.5mm x100mm x 235 x 0.1m = 5340Nm<br />
1.1<br />
which would correspond with ⇒ N sd = 5012daN in the principal<br />
compression tube.<br />
⇒ The cassion exists if the tube resists!<br />
Page 10
. with pressure of tube CD at base of caisson<br />
P Rd = 2x π x 40mm x 2.5mm = 628mm 2<br />
V eff.rd =<br />
235 x 628 = 7749daN<br />
√3 x 1.1<br />
V sd = 3782 daN = 49% V eff.rd<br />
. with force of lower foot at A and B<br />
Smaller perimeter requires:<br />
A Veff = 2 x16mm x8mm = 256mm 2<br />
V eff.rd =<br />
235 x 256 = 3157.5daN<br />
√3 x 1.1<br />
V sd = 1138 daN = 36% V eff.rd<br />
. Curvature of upper tubes of feet EI, EJ, FL, FK<br />
N b.Rd = χ x β Α x Α x fγ<br />
γM1<br />
_ 3100<br />
λ = λ = 20.6 = 1.6<br />
λ 1<br />
π √E<br />
⇒ χ = 0.3079<br />
f y<br />
⇒ N b.Rd = 364.4mm2 x 235 x 0.3079 = 2397daN<br />
1.1<br />
⇒ N sd = 1.483 x 255 + 1065 = 1443 daN = 60% N b.Rd<br />
. Resistance of cable AB:<br />
Qd÷4 + T ii x sin 63.8 o<br />
N sd = tg9.7 o + T i x cos 63.8 o = 11384daN<br />
With T i = 200daN and Q d = 255daN<br />
N rt.d (Ø10.6mm 6 x 36) ≥ 5800daΝ<br />
⇒ N sd = 20%N t.Rd<br />
Page 11
10 Verification of str<strong>en</strong>gth of elem<strong>en</strong>ts<br />
. Breakdown of linkage posts – yard.<br />
This breakdown is tak<strong>en</strong> from the points G to H.<br />
The semi-rigid linkage is made from means of two metal plates of 8mm<br />
thickness, bolted together as a safety mechanism (lock-nuts).<br />
The installation holes, of which one is oversized, permits a slight rotation at the<br />
support of the yard. The mechanism allows that if a necessary case arises, the<br />
rotation of the support barely influ<strong>en</strong>ces the behaviour of the posts. (Assembly<br />
of type articulated.)<br />
In the verifications above, it has be<strong>en</strong> considered that this linkage is articulated.<br />
This is what assists us in certifying our security in regards to the resistance of<br />
the yard.<br />
Page 12
Verification of assembly:<br />
Verification of pliers<br />
22.5 ≤ 30 ≤ 12 x 8 OK!<br />
22.5 ≤ 30 ≤ 12 x 8 OK!<br />
45 ≤ 65 ≤ 400 OK!<br />
Verification of cutting of metal plates<br />
V sd = 225 + 30 = 225daN<br />
L v.eff = 30 +65 +22.5 = 117.5<br />
A v.eff = 117.5 x 8 = 940mm 2<br />
V eff.Rd = 235 / √3 x 940 = 11594daN = 11.5T<br />
1.1<br />
V sd = 2.2%V eff.Rd<br />
Verification of cutting bolts:<br />
F v.sd = 225 = 127.5 daN<br />
2<br />
The bolts are class 8.8<br />
Cutting<br />
F v.Rd =<br />
0.6x800x115 = 4416 daN<br />
1.25<br />
Diametric stress (tak<strong>en</strong> at caisson level t=5mm)<br />
α = 30 + 0.66<br />
3x15<br />
F b.Rd =<br />
Conclusion<br />
2.5x0.66x800x14x5 = 7392 daN<br />
1.25<br />
⇒ F v.sd at yard level GH = 3% F v.Rd<br />
⇒ F v.sd at cassion level AE BF = 1433daN x cos9.7<br />
o<br />
+ 1422.5daN + 32% F v.Rd<br />
Page 13
11 Verification of overall stability<br />
Verification of the stability of inversion with regard to support point I, J, K and L.<br />
The least favourable circumstance is naturally the case of swinging. Therefore,<br />
we consider an acceleration of 10m/s 2 applied to a mass of 94kg, following an<br />
angle of 45 o . (See hypothesis and justifications.)<br />
Here, the mass of the frame, 2.60m, is considered, as it is weaker and therefore<br />
unfavourable in terms of stability.<br />
M Qd = 115 x 2.462m = 2777Nm<br />
M Gd = 125 x 2.73m = 3412Nm<br />
M Gd ≥ M Qd ok! M Qd = 81%M Gd<br />
Page 14
12 Comm<strong>en</strong>ts on maint<strong>en</strong>ance and monitoring<br />
Ev<strong>en</strong> though the principal bolts are self-locking, it is still necessary to regularly<br />
check the state of assembly and equipm<strong>en</strong>t, to control the level of corrosion and<br />
to undertake, if required, replacem<strong>en</strong>t of defective bolting.<br />
13 Verification of equipm<strong>en</strong>t and devices<br />
The <strong>en</strong>tirety of the accessories and devices used correspond with security<br />
norms guaranteed by the manufacturers.<br />
. All the rapid links integrated within the principal structure have a<br />
breaking stress point ≥ 2000 daN.<br />
. The cable has a breaking stress point ≥ 5800 daN.<br />
. The straps are treated in order to make them more resistant to abrasion<br />
and have a breaking stress point ≥ 3300 daN.<br />
. The <strong>en</strong>tirety of the bolting is treated against corrosion (stainless steel<br />
optional), and the lock-nuts are systematically used in strategic places.<br />
. The safety surface (mattress) that accompanies this product (optional) is<br />
made by a leader in the gymnastic sector. Its design and d<strong>en</strong>sity is<br />
specifically adapted for the freestanding trapeze rig.<br />
14 Points of anchorage<br />
In case of usage of non-autonomous rig but anchored to the ground:<br />
The system of anchorage is very specific to the constraints of the site and t the<br />
nature of the ground. Non-autonomous usage is not the subject of the pres<strong>en</strong>t<br />
verifications. The maximum t<strong>en</strong>sion calculated for the straps is 750daN. Their<br />
implem<strong>en</strong>tation in the rule of the art is left to the responsibility of the<br />
<strong>en</strong>trepr<strong>en</strong>eur.<br />
The calculations of verification of the yard, the poles as well as the details and<br />
the bolts are to be tak<strong>en</strong>, of course, with care.<br />
15 Comm<strong>en</strong>ts on level of safety<br />
In this report, a series of favourable factors have not be<strong>en</strong> tak<strong>en</strong> into account.<br />
For example, all the loads have be<strong>en</strong> considered localised and c<strong>en</strong>tral.<br />
However, this is practically never the case: a trapeze is attached at two points,<br />
spaced by 1.2m; the bearer distributes his load over 40cm.<br />
Nevertheless, to favour safety and to protect oneself during a non-habitual<br />
usage of the equipm<strong>en</strong>t, we preferred not to take these situations into account.<br />
Page 15
16 Refer<strong>en</strong>ces<br />
. Eurocode 3 “calcul des structures <strong>en</strong> acier >> + DAN (NF P 22-311).<br />
December 19922<br />
. NF EN 913 Materiel de gymnastique, exig<strong>en</strong>cies g<strong>en</strong>erales de securite et<br />
moethodes d’essai. May 1996.<br />
. Donnees ds differ<strong>en</strong>ts constucteurs: Spanset, Tubeurop, OUTA, Stein, Klocker<br />
& Co., etc.<br />
Page 16