fem analysis of tension stru ctures with · pdf fileappr o 2. ex th e and i t with a m. t h...
TRANSCRIPT
![Page 1: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/1.jpg)
The 2012 World Congress on Advances in Civil, Environmental, and Materials Research (ACEM’ 12)Seoul, Korea, August 26-30, 2012
FEM ANALYSIS OF TENSION STRUCTURES WITH EXPERIMENTAL WIND ACTION
Fabio Rizzo1), Piero D'Asdia2), Federica Speziale3) 1), 2), 3) Dept. of Engineering and Geology
(Inter-University Centre for Building Aerodynamics and Wind Engineering) University of Chieti-Pescara, Viale Pindaro 42, 65127 Pescara, Italy
ABSTRACT This paper describes the design of a tension structures to cover a sport arena. Wind tunnel details are used to evaluated wind action static and dynamic in order to perform non linear static and dynamic analyses. Wind forces in time histories are evaluated from pressure coefficients acquired in wind tunnel and time histories of displacements are evaluated in order to study the dynamic deformed shape. An interesting comparison between the existent structure, realized with a spatial reticular steel structure, and the tensile-structure proposed, puts in evidence the high performance of this second kind of structure and its low dead load. This is a very important characteristic in a particularly vulnerable seismic zone. 1. INTRODUCTION
Sports arenas, indoor swimming pools, skating park, conference spaces are buildings that need to cover large spans without intermediate supports. Tension structures, and hyperbolic paraboloid shape in particular, are the most flexible structures to realize free spaces. Furthermore, such structures meet the requirements of today’s market in terms of lightness, innovation of materials and cost-effectiveness. Thus, considering the developments obtained in the research aimed at parameterization of the structural responses of hyperbolic paraboloid cables nets illustrated in a previous proceeding (Rizzo et all ACEM 12), this paper shows a design of a tension structure covering a sport arena located in Chieti (Italy). This project is based on aerodynamic wind tunnel and its detail is used to evaluated wind action static and dynamic in order to perform non linear static and dynamic analyses. Finally, to complete this study, the present work describes an interesting comparison between the existent structure, realized with a spatial reticular steel structure, and the new structure, realized with a tension structure to put in evidence the high structural performance of this second kind of structure and its low dead load. In fact, such structures have a ratio between live loads and dead loads which is
1) PhD, Researcher 2) Professor 3) PhD student
![Page 2: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/2.jpg)
opposappro 2. EX
Theand itwith am. Thand th Table
Geom
Roof m
Roof s
SuppoSuppo
In 20consethis rauxiliaThanspans
site of theoach in stru
XISTING S
e sport aret is the maa spatial rehe main infhe structur
e 1: Palatric
etrical para
material
structural w
ort structureort structure
07, Palatrequence, treason a nary spacesks to the hs, this struc
e one of tructural ana
STRUCTUR
ena used foain compleeticular steformation ral model a
calle existi
meter
weight
e e material
icalle was the capacitnew desigs dedicatedhigh perforctural typo
raditional halysis.
RE
or this projex of the ceel structurregarding are reporte
ng structu
Exis
Square pBeam hi
Steel: S2
1.00 kN/- roof - struc- syste
ConcreteConcrete
Fig. 1
restored ty of the an has beed to caterinrmance of ology is cho
heavy stru
ject, calledcity dated 1e with squthe existin
ed below (F
re.
sting structu
plan: 73x73 gh (including
235
/m2: weight: 0.30
ctural weightems weight:
e bleacherse: C25/30
Existing s
in order toarena is deen proposeng, meetintension st
osen to rea
ctures and
d “Palatrica1980. The are footpri
ng structureFig. 1).
ure data
m g roof): 2.30
0 kN/m2 t: 0.50 kN/m2
0.20 kN/m2
structural m
o respect ecreased: fed, in partg and busructures in
alize a new
d this dete
alle”, is locexisting s
int of dimee are sum
m
2
Steel: B45
model
FIBA and from 3500 ticular an iness activ
n covering w idea of Pa
ermines a
ated in Chtructure is
ensions of amarized in
50C
fire regula to 2400 sexpansion
vities are dmedium aalatricalle.
different
hieti (Italy) realized
about 73 n Table 1
ation. As seats; for n and an esigned.
and large
![Page 3: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/3.jpg)
3. HY
FigGeomshape
Table
α = L
1
Tensi
Cablevaryinmembwhichconstrectansystewith ainclinecablethey c
YPERBOL
g. 2 illustrametric and e are repor
(a)
e 2: Geome
L1/L2 ρ =
1/6
A1 [cm2] 5.71
ion structu- - -
e net, withng from +brane is fh has the tituted by ngular crom presenta distanceed about 2
e shoot. Thchanged th
LIC PARAB
tes a virtuamechanic
rted in Tab
Fig. 2 Gr
etric and m
= f2/f1 γ = Lmax
re is formean hyperba border sa cable-sta
h a distanc12.60 to +fixed for pfunction ofour arcs
oss sectionted tubular of 4 m (820° respeche stays aheir sectio
BOLOID R
al three-dimc parameteble 2 (Rizzo
round floor
mechanic p
Square plaGeo
= H/Lmax 2
MecA2
cm2 2.31
ed by: olic parabo
structure;ayed systece of 2 m+26.00 m. points throof absorbin having tn 500x900r steel col8 m in corct to the vere made ons if are p
ROOF DES
mensional ers of hypo 2011).
r (a), Virtua
parameters
ane models ometric para
f1 f2
[cm] [cm4.44 8.89
chanic para
oloid cable
em for anchm, is ancho
Cable neough mechng the forche same
0x30 mm, umns (500responden
ertical; in thof high-streparallel to t
SIGN
view of thperbolic pa
(b)
al three-dim
s of hyperb
with Hb=1/6ameters L1
m] [cm]9 80.00
ameters ε1
0.006294
es net;
horage. ored to boet is coverhanical coces transmcurvature made of
0x30 mm)nce of the his way it ength steethe bearing
e project aaraboloid r
mensional
bolic parabo
6 L
L2 [cm]
80.00
order strucred with Pnnections.
mitted fromof the rosteel S35
and a caentrance)opposes, f
el with E=1g cables (Ø
and its groroof with a
view (b)
oloid roof.
H [cm]
1/6 Lmax
ε2
0.00765
cture at anPTFE (Tefl
Border sm the cabloof. They 55. The aable-stayed. The colufor the form16500 KN/Ø 40) or p
und floor. a square
Hb [cm]
1/6 Lmax
2
n altitude lon); this structure, e net, is have a
nchoring d system umns are m, to the /cm2 and arallel to
![Page 4: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/4.jpg)
the stA2 anfor loavaluefor staof thesag astays inveschara
Table
Geomparam
Bearin
Stabili
Stays
Stays
Colum
Borde
Struct
tabilizing ond A3 indicaad bearing
es of cable ays; L is the stabilizinand of stab
2 are partigate wind
acteristics.
e 3: Input p
etrical meter
ng cables
izing cables
1
2
mn
er structure
tural weight
one (Ø 30).ate the cabg cables, fo
strain reshe length og cables; bilizing caballel to thed action on
project data
Square pThicknes
A1 = 5.7
s A2 = 2.3
A3 = 10.5
A3 = 8.0
Cross se
Cross se
0.18 kN/m- roof w- struc- syste
. These chble area vaor stabilizinpectively f
of stays; L1f1 and f2 isbles sag.
e stabilizingn the tensio
a.
In
plan: 80x80 mss: 0.15 m
1 cm2 ε1
1 cm2 ε2
50 cm2 ε3
0 cm2 ε3
ection (tubula
ection (rectan
m2: weight: 0.10
ctural weight:ems weight:
aracteristicalues obtaing cables for load be1 is the spas, respectiStays 1 ag cables. Fon structur
nput project
m
= 0.006294
= 0.007652
= 0.010500
= 0.003500
ar): 40x2 cm
ngular): 50x9
kN/m2 (mem: 0.06 kN/m2
0.02 kN/m2 (
Fig. 3 FE
cs are sumned by preand for sta
earing cablan of the bively, the vre parallel Fig. 3 showre while in
t data
T1 = 592
T2 = 720
T3 = 181
T3 = 462
90x3
mbrane) (dead load +
(separated fr
EM model
mmarized ineliminary days; ε1, ε2, es, for sta
bearing cabvalues of l
to the bew the FEMTable 4 ar
2.99 KN L
0.93 KN L
19.1 KN
2.00 KN
Materia
Materia
+ connectionrom cables n
n Table 3 wdesign, res
and ε3 indabilizing cables, L2 is load beari
earing cablM model rere reported
L1=80 m
L2=80 m
L = 25.8
L = 25.8
al: steel S35
al: steel S35
ns) net)
where A1, pectively icate the bles and the span ng cable les while
ealized to d its main
f1=4.44 m
f2=8.89 m
840 m
840 m
55
55
![Page 5: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/5.jpg)
4. HY
4. Noactionanglethe mvaluenumeresultsuctioobtaintime wind Table
Wind 0
Wind 9
YPERBOL
1. Non-lineon-linear sn evaluatees, 0° and 9mean (Cp,m
es for eacherical procts are showon displacened from nhistory caltunnel data
e 5: Non-lin
0°
90°
Fi
Ta
LIC PARAB
ear static astatic analyed using th90°. The w), minimum Thiessen
cedure (Guwn in Tablements). Tnon-linear lculated wa.
near static
(a)
ig. 4 Defor
able 4: Cha
E
NodeCable
Fram
BOLOID R
analysis ysis were he mean ewind actionm (Cp,min) apolygon. T
umbel 197e 5 whereThen resudynamic a
with the tim
analysis -
δ, Cp,ma
[m]
0.104
0.060
rmed shape
aracteristic
lements
es number:e elements:
me elements:
ROOF DES
performedexperimen
n applied oand maximThis value74) (Cook δ represelts were canalysis, p
me history
vertical dis
ax
e Cp,m 0° (
cs of FEM m
n
18
30
3
SIGN
d applying,ntal pressun the FEM
mum (Cp,ma
is then exk 1978, 1nts vertica
compared performed of pressur
splacemen
δ, Cp
[m
0.26
0.35
b). Deform
model
n.
805
028
84
on a FEMure coefficM model wa
ax) pressurxtended to 979, 1980
al displacemwith the sby applyin
re coefficie
nt.
p,min
m]
60
50
(b)
med shape
M model, ients for tas calculatre coefficie
all net no0). Static ments (in tstructural rng the entents obtain
δ, C
[m
0.2
0.2
Cp,m 90° (b
the wind two wind ted using ent point des by a analysis
this case response tire force ned from
Cp,m
m]
50
68
b)
![Page 6: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/6.jpg)
4.2 Dufreque7504 0.003correcanalythe tespeedgeomintegr1681 with aFig. 6N3 (ccabledecresince than crecorddispla
2. Non-lineuring expeency of 25values w
39 secondct time ste
ysis. This isechnical cds, a U10
metric scaleration steppressure t
a length of 6 (a) showscheck nodee). As can ease movin
the bordecables, in ded in theacements o
ear dynamirimental w52 Hz and
were acquis. Wind t
ep on a reas done by ccode beingvalue is de of the is equal totime histor469 value
s 3 time hises indicate be seen ng away fer structurthis area w
e middle oof node N2
(a) Fig. 6
ic analysiswind tunnel d with an ared with aunnel dataal full-scalecomparingg considereterminedmodel is o 0.24 s. Aries were as. (Majiowstories acqed in Fig. 5
by the trfrom the fre generallwould occof cables2 by applyi
Fig. 5 C
Time Hist
s tests, pre
acquisitiona time stea acquisitie and the
g wind tunnred. In pa (calculateestablishe
A time histoapplied withwiecki 1994quired by p5) for windend of timflow separly consistsur vertical net. Fig. 6ng force tim
Check node
tory (a) Ca
ssure time time step
ep equal tion must step integ
nel speedsarticular, aed as 10 ced (in thisory is applih 7504 valu4). pressure tad angle atme historieration zones of steel
displacem6 (b) illustme history
es N1, N2
ble joint di
e histories p of 29.7 sto 29.7/75be scaledration to b with real s
after calcucm on the s case 1:1ed to eachues plus a
aps close t0° (paralle
es, the pree (containibeams tha
ments muchtrates the
y.
and N3
(b) splacemen
were acquseconds. A504, appro to determ
be used in speed accolating winmodel sc
100 (λl=10h node. In tn additiona
to the nodeel to the stessure coeing N1). Hat are much lower thahistory of
nts (b)
uired at a A total of oximately mine the dynamic ording to d tunnel
cale), the 00)). the this case, al “ramp”
e N1, N2, tabilizing efficients
However, ch stiffer an those f vertical
![Page 7: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/7.jpg)
Fig. 8calcuFig. 7
The pressof disresultdispla Table
Min
8 (a) (b) ilated on c
7. The cabl
greatest ssure displasplacements of non-liacements a
e 6: Non-lin
Stab
displacemen
[m]
0.1152
llustrates table S1 (ses were di
(a) Fig. 7
(a) Fig. 8 V
suction discement is ts, were snear staticas reported
near dynam
ilizing cable
nts Ma
the trend stabilizing ciscretized
7 Stabilizin
Vertical dis
splacemenequal to aummarized
c analysis fd in Table
mic analysi
es S1
ax displacem
[m]
0.1971
of absolutcable) andin 41 node
ng cable S1
placement
nt is equaabout 11 cmd in Tablefor Cp,min th7. (Simiu,
is results.
Wind_0°
ments M
te displaced cable P1 es.
1 (a) Beari
ts: cable S
l to aboum. Howeve 6. Then ahat in absoScanlan 1
°
Min displace
[m]
0.0954
ements for(bearing c
(b) ng cable P
(b) S1 (a) cable
t 22 cm er, the meaa comparisolute value996).
Bearing cab
ments
4
r a 0° wincable) as s
P1 (b)
e P1 (b)
and the man results, son was de provide m
bles P1
Max displac
[m]
0.218
nd angle, shown in
minimum in terms one with
maximum
cements
]
81
![Page 8: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/8.jpg)
Table 7: Comparison between non-linear static and dynamic analysis.
Wind_0°
Δf
[m]
Non-linear Static Analysis (Cp,min) 0.218
Non-linear Dynamic Analysis 0.260
CONCLUSION This paper describes a project of a sport arena with medium span using an hyperbolic paraboloid tension structure made of cables net. Results show that is possible to cover 80 m of span with a cables net that weighs 0.4 KN/m2, which presents cables with areas that do not exceed 6 cm2, with a diameter not greater than 3 cm. If you consider that, currently, the same span is covered with a common spatial reticular steel structure, with a height of the single beam that exceeds 1.50 m, with a structural weight four times bigger than the one of the cables net, you can understand how the advantage of using cables net is relevant both in terms of formal and structural lightness. So, the tension structure results less expensive than a traditional one. Then the paper comments static and dynamic non-linear analysis results conducted on cables net. In particular, analysis consider wind action. It is calculated using the pressure coefficients acquired through experimental wind tunnel tests. Such tests have provided pressure coefficients for minimum, mean and maximum values and as time history. These coefficients were used to perform non-linear static analysis with wind action evaluated for mean, minimum and maximum pressure coefficients and to perform non-linear dynamic analysis applying wind action as a time history of force, calculated using the single time histories of the pressure coefficients. It showed that the results of dynamic analysis are very similar to the results obtained with static forces calculated using the mean pressure coefficients, demonstrating that it is possible to simplify experimental data when making a global analysis. So, the paper shows that you can use experimental results obtained in a simplified form even for very deformable structures such as cables nets. This would permit designers to make a preliminary dimension calculation of cables nets with a hyperbolic paraboloid shapes, in the form examined, using appropriate pressure coefficient values. REFERENCES Cook, N.J., Mayne, J.R. (1978), On design procedures for wind loading, Building Research Estabilishment, Garston. Cook, N.J., Mayne, J.R. (1979), “A novel working approach to the assessment of wind loads for equivalent static design”, Journal of Wind Engineering and Industrial Aerodynamics, 4, 149-164.
![Page 9: FEM ANALYSIS OF TENSION STRU CTURES WITH · PDF fileappr o 2. EX Th e and i t with a m. T h and t h Tabl e ... net, with g from + rane is f has the ituted by ... tatic analy d using](https://reader031.vdocuments.us/reader031/viewer/2022030511/5abc0be97f8b9a441d8d96a7/html5/thumbnails/9.jpg)
Cook, N.J., Mayne, J.R. (1980), “A refined working approach to the assessment of wind loads for equivalent static design”, Journal of Wind Engineering and Industrial Aerodynamics, 6, 125-137. Gumbel, E.J., Statistic of extremes, Columbia University, Press: Lieblein J. (1974), Efficient methods of extreme value methodology, Report 74-602, National Bureau of Standards: Washington. Majiowiecki, M., (1994), Tensostrcture: Design and control, Crea, Milano. (in Italian). Rizzo, F., D’asdia, P., Lazzari, M., Procino, l., (2011) “Wind action evaluation on tension roofs of hyperbolic paraboloid shape”, Engineering Structures, Vol. 33, Issue 2, 445-461. Rizzo, F., D’Asdia, P., Ricciardelli, F., Bartoli, G. (2012). “Characterisation of pressure coefficients on hyperbolic paraboloid roofs”, Journal of Wind Engineering & Industrial Aerodynamics, Vol. 102(C), 61-71. Simiu, E., Scanlan, R.H., (1996), Wind effects on structures, Third edition, John Wiley & Sons, New York.