Ida Mascolo
580 California St., Suite 400
San Francisco, CA, 94104
Horizontal Force Capacity of a Hemi-Spherical Dome
2021, Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015)
https://doi.org/10.7712/120121.8513.19613visibility
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Abstract
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The paper investigates the horizontal force capacity of hemi-spherical domes through mathematical modeling and analysis. It defines various parameters and equations essential to understanding the structural mechanics involved. Results illustrate the critical limits of force tolerance under varying conditions, contributing to the field of structural engineering by providing guidelines for design and safety assessments.
Key takeawaysAI
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- The study focuses on the horizontal force capacity of hemi-spherical domes.
- The critical parameter identified is the slenderness ratio, S e λ, which is 0.45.
- Understanding this capacity is essential for structural engineering applications.
- The findings contribute to the design standards for dome structures.
- Further research may explore the implications of varying S e λ values.
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Available online at www.eccomasproceedia.org
Eccomas Proceedia COMPDYN (2021) 614-625
COMPDYN 2021
8th ECCOMAS Thematic Conference on
Computational Methods in Structural Dynamics and Earthquake Engineering
M. Papadrakakis, M. Fragiadakis (eds.)
Streamed from Athens, Greece, 28 - 30 June 2021
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ISSN:2623-3347 © 2021 The Authors. Published by Eccomas Proceedia.
Peer-review under responsibility of the organizing committee of COMPDYN 2021.
doi:10.7712/120121.8513.19613
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i Mv }t2/ p Hm2 Q7 i?2 HQ / 7 +iQ` λ- i?2 "oS T`Q#H2K 7Q`KmH i2/ BM i?2b2 i2`Kb
/KBib mMB[m2 bQHmiBQM r?B+?- ?Qr2p2`- /Bb`2; `/b i?2 +QMbiBimiBp2 `2bi`B+iBQMb UdVX h?2M
i?2 2[mBHB#`BmK T`Q#H2K Q7 i?2 mMBH i2` H K2K#` M2 S ;Qp2`M2/ #v Sm+?2`Ƕb 2[m iBQM U8V
+ M #2 `2/m+2/ iQ 7Q`K@}M/BM; T`Q#H2KX q2 b2 `+? BM M bbB;M2/ M@T ` K2i2` 7 KBHv
Q7 b? T2 7mM+iBQMb f (x1 , x2 , α1 , α2 , ..., αn )- +QMbi` BM2/ iQ #2 2MiB`2Hv +QMi BM2/ rBi?BM i?2
/QK2 pQHmK2 M/ bm+? i? i i?2 >2bbB M Bb /2}MBi2 UBX2X +QMp2t TQHvMQKB H 7mM+iBQMV-
i?2 QMHv QM2 i? i T`QpB/2b bQHmiBQM Q7 i?2 i` Mbp2`b2 2[mBHB#`BmK 2[m iBQM U8V r?B+?
7mH}HHb i?2 "oS b r2HH b i?2 +QM+ pBiv +QM/BiBQMb UdVX h?2 T ` K2i2`b αi + M `2T`2b2Mi-
7Q` 2t KTH2- i?2 bBx2- i?2 TQbBiBQM Q` i?2 bvKK2i`v Q7 i?2 bi`2bb K2K#` M2 SX h?2
`2bi`B+iBQM QM i?2 >2bbB M 2Mbm`2b i? i i` Mbp2`b2 2[mBHB#`BmK 2[m iBQM U8V Bb 2HHBTiB+ M/
i?2M 2 bv iQ bQHp2 #v 61J@HBF2 MmK2`B+ H bi` i2;vX h?2M- iQ bb2bb i?2 mHiBK i2 HQ /
+ T +Biv Q7 i?2 /QK2- BX2X i?2 HQ / 7 +iQ` λ- r2 + M b2 `+? 7Q` i?2 K tBKmK p Hm2 Q7 λ
rBi?BM i?2 72 bB#H2 `2;BQM bm+? i? i +QM+ p2 bQHmiBQM Q7 i?2 "oS bQ /2}M2/ 2tBbib UBX2X
F ∈ Sym− VX
9 LmK2`B+ H TTHB+ iBQMb
h?2 ;Q H Q7 i?Bb b2+iBQM Bb iQ BHHmbi` i2 ?Qr i?2 K2i?Q/ rQ`Fb i?`Qm;? irQ i`BpB H
2t KTH2bX HH 2t KTH2b +QMbB/2` ?2KBbT?2`B+ H /QK2 rBi? i?B+FM2bbĜ` /Bmb ` iBQ Ut/LV
2[m H iQ 0.2X Ai Bb HbQ bbmK2/ i? i- rBi?Qmi HQbb Q7 ;2M2` HBiv- i?2 ?Q`BxQMi H HQ / p Bb
b2iiH2/ iQ #2 +QMbi Mi T2` T`QD2+i2/ `2 M/ 2[m H iQ {λp, 0, −p} /2}MBM; i?2 HQ /BM;
bm`7 +2 Sp b
Sp = {(x1 , x2 , fp (x1 , x2 )) , (x1 , x2 ) ∈ Ω} ; UNV
r?2`2 fp (x1 , x2 ) Bb i?2 T ` #QHQB/ U6B;X kV
x1 2 + x2 2
fp (x1 , x2 ) = L 1 − ; URyV
t2
L Bb i?2 KB//H2 ` /Bmb Q7 i?2 /QK2XLQi2 i? i- 7Q` +QMp2MB2M+2 Tm`TQb2b- HH i?2 ;2QK2i`B+ H
/BK2MbBQMb `2 /BK2MbBQM HBx2/ rBi? `2bT2+i iQ i?2 `272`2M+2 H2M;?i LX
6B;m`2 k, GQ /BM; bm`7 +2 Sp
h?2 Sm+?2`Ƕb 2[m iBQM ;Qp2`MBM; i?2 2[mBHB#`BmK T`Q#H2K U8V Bb T ` K2i`B+ HHv bQHp2/
7Q` i?2 b? T2 f (x1 , x2 , α1 , α2 , ...) #v mbBM; i?2 S.1b iQQH BKTH2K2Mi2/ BM J i?2K iB+ Ü
Uo2`bBQM 12V (9k) M/ # b2/ QM i`B M;mH ` 6BMBi2 1H2K2Mi /Bb+`2iBx iBQM USH2 b2 `272` iQ
(kd) 7Q` KQ`2 /2i BHbVX
9XR 1t KTH2 R
AM i?2 }`bi 2t KTH2 r2 +?QQb2 M BMBiB H K2K#` M2 b? T2 +Q``2bTQM/BM; iQ i?2 T ` #QHQB/
URyVX h?Bb b? T2 Bb 7mHHv +QMi BM2/ rBi?BM i?2 /QK2 i?B+FM2bb #mi Bi Bb MQi /2T2M/2Mi QM
i?2 ;2QK2i`B+ H T ` K2i2`b αi X h?2 K tBKmK p Hm2 Q7 λ i r?B+? i?2 bi`2bb +2 b2b iQ #2
M2; iBp2 b2KB@/2}MBi2 +QM+ p2 bm`7 +2 Bb λ = 0.35X 6B;X j b?Qrb i?2 T`BM+BT H bi`2bb2b
618
*X PHBpB2`B- X * bi2HH MQ- AX 1HB M/ AX J b+QHQ
U V U#V
6B;m`2 j, h?`mbi bm`7 +2 Sp BMbB/2 i?2 /QK2 U V M/ T`BM+BT H bi`2bb2b T`Q}H2 BM i?2 b ;Bii H
TH M2 7Q` λ = 0.38 U#V
T`Q}H2 BM i?2 x2 x3 @b ;Bii H TH M2 7Q` p Hm2 Q7 λ = 0.38 i? i H2 /b iQ i2MbBH2 bi`2bb2b
mTrBM/ rBi? `2bT2+i iQ i?2 /B`2+iBQM Q7 i?2 ?Q`BxQMi H 7Q`+2X
AM Q`/2` iQ QTiBKBx2 i?2 K2K#` M2 b? T2 f (x1 , x2 ) = Sp - r2 ? p2 //2/ iQ fp +QMp2@
MB2Mi b? T2 7mM+iBQM Δf (x1 , x2 , α1 , α2 , ..., αn ) - i? i Bb +m#B+ BMi2`TQH iBM; bTHBM2 7mM+iBQM
rBi? M TT`QT`B i2 b2i Q7 +QMi`QH TQBMib α1 , α2 , .., αn UBX2X K tBKmK ?2B;?i- KB//H2 ` /Bmb
M/ BM~2tBQM TQBMi Q7 K2K#` M2 b? T2VX "v MmK2`B+ HHv bQHpBM; i?2 T ` K2i`B+ 2[mBHB#@
`BmK 2[m iBQM 8 r2 Q#i BM +H bb Q7 K2K#` M2 7Q`Kb /2T2M/BM; QM i?2 HQ / 7 +iQ` λX
"v `2; `/BM; i?2 HQ / 7 +iQ` λ b i?2 Q#D2+iBp2 7mM+iBQM- i?2 T ` K2i2`b α1 , α2 , ..., αn `2
}M HHv QTiBKBx2/ #v K tBKBxBM; λ(α1 , α2 , ..., αn )X
h?2 bQ QTiBKBx2/ K2K#` M2 b? T2 f (x1 , x2 , α1 , α2 , ..., αn ) 2M #H2b bB;MB}+ Mi BM+`2 b2
BM i?2 K tBKmK p Hm2 Q7 λ i r?B+? i?2 i?`mbi bm`7 +2 Bb +QMi BM2/ 2MiB`2Hv BMbB/2 i?2
/QK2 M/ +QM/BiBQMb UdV ?QH/- M K2Hv λ = 0.42X
6B;X 9 b?Qrb i?2 +Q``2bTQM/BM; T`Q}H2 Q7 i?2 T`BM+BT H bi`2bb2b +Q``2bTQM/BM; iQ i?2
QTiBKBx2/ bQHmiBQM BM i?2 x1 x3 @+Q`QM H M/ BM i?2 x2 x3 @b ;Bii H TH M2bX h?2 +QMiQm` THQi
Q7 i?2 T`BM+BT H UKBMBKmK M/ K tBKmKV T`QD2+i2/ bi`2bb p Hm2b M/ i?2 +Q``2bTQM/BM;
BbQbi iB+ HBM2b `2 HbQ `2TQ`i2/X
9Xk 1t KTH2 k
AM i?Bb 2t KTH2 r2 M Hvx2 /QK2 r?B+? /BbTH vb +2`i BM T ii2`M Q7 +` +F- /m2 iQ
?Q`BxQMi H +iBQMb r?B+? 2t+22/ i?2 HBKBi p Hm2X AM bm+? + b2 i?2 bi`2bb K2K#` M2 Bb
MQi +QMi BM2/ 2MiB`2Hv BM i?2 /QK2 U6B;bX 8VX h?2`27Q`2- r2 HHQr 7Q` bK HH 2MH `;2K2Mi
Q7 i?2 2ti` /Qb bm`7 +2 M/ HQQF 7Q` i?2 BMi2`b2+iBQM Q7 i?2 K2K#` M2 bm`7 +2 rBi? i?2
Q`B;BM H 2ti` /Qb bm`7 +2 Se X AM i?Bb + b2- i?2 K tBKmK HQ / 7 +iQ` bm+? i? i i?2 bi`2bb
Bb M2; iBp2 b2KB@/2}MBi2 Bb λ = 0.45X h?2 +QMiQm` THQi Q7 i?2 KBMBKmK M/ K tBKmK
T`BM+BT H bi`2bb2b M/ i?2 +Q``2bTQM/BM; BbQbi iB+ HBM2b `2 `2TQ`i2/ BM 6B;bX 8- BM T `iB+mH `
i?2 K tBKmK T`BM+BT H bi`2bb HKQbi p MBb? 7Q` x1 ∈ (−17, −5)- H22r `/ rBi? `2bT2+i iQ
i?2 ?Q`BxQMi H +iBQMX LQiB+2 i? i i?2 BbQbi iB+ HBM2b +Q``2bTQM/BM; iQ x2`Q T`BM+BT H
bi`2bb2b- `2 HKQbi bi` B;?i- K2 MBM; i? i i?2 bm`7 +2 T`Q}H2 BM bm+? /B`2+iBQMb +QMbBbib
Q7 7mMB+mH ` HBM2bX AM 6B;X 8# i?2 T`Q}H2 Q7 i?2 +m`p2 Q7 BMi2`b2+iBQM Q7 i?2 QTiBKBx2/
K2K#` M2 bm`7 +2 rBi? i?2 Q`B;BM H 2ti` /Qb bm`7 +2 Si Bb b?QrM U#H +F HBM2bVX
8 *PL*Gl.AL: _1J_Ea
h?Bb T T2` T`2b2Mib M2r T ` K2i`B+ TT`Q +?- # b2/ QM i?2 J2K#` M2 1[mBHB#`BmK
M HvbBb- iQ i?2 bb2bbK2Mi Q7 i?2 HQ / + ``vBM; + T +Biv Q7 K bQM`v /QK2b Q` p mHib
mM/2` ?Q`BxQMi H #Q/v 7Q`+2bX "v mbBM; i?2 J1 i?2 HQ / TTHB2/ iQ /QK2 +QKTQb2/ Q7
619
*X PHBpB2`B- X * bi2HH MQ- AX 1HB M/ AX J b+QHQ
U V U#V
U+V U/V
U2V U7V
6B;m`2 9, PTiBKBx2/ i?`mbi bm`7 +2 S +Q``2bTQM/BM; iQ i?2 QTiBK H p Hm2 Q7 λ U Vc T`BM@
+BT H HBM2b Q7 +m`p im`2 U#Vc T`BM+BT H bi`2bb T`Q}H2 BM i?2 +Q`QM H TH M2 U+Vc T`BM+BT H
bi`2bb T`Q}H2 BM i?2 b ;Bii H TH M2 U/Vc +QMiQm` THQi Q7 KBMBKmK M/ K tBKmK T`BM+BT H
T`QD2+i2/ bi`2bb p Hm2b U2-7V
mMBH i2` H >2vK M K i2`B H Bb HmKT2/ iQ HQ /BM; bm`7 +2 Sp M/ Bb + ``B2/ #v i?`mbi
bm`7 +2 S +QMi BM2/ BMbB/2 i?2 K bQM`vX "v +? M;BM; Bib b? T2 f i?`Qm;? i?2 imMBM; Q7
}MBi2 MmK#2` Q7 ;2QK2i`B+ T ` K2i2`b- i?2 ;2M2` HBx2/ K2K#` M2 bi`2bb # H M+BM; i?2
HQ /b b r2HH b Bib T`QD2+iBQM QM i?2 TH M7Q`K +? M;2X h?2 QTiBK H p Hm2 Q7 i?2 ;2Q@
K2i`B+ T ` K2i2`b- BX2X i?2 QTiBK H b? T2 7mM+iBQM Q7 i?2 bi`2bb K2K#` M2- Bb Q#i BM2/
#v K tBKBxBM; i?2 ?Q`BxQMi H HQ / KmHiBTHB2` λ- rBi? i?2 +QMbi` BMib i? i i?2 ;2M2` HBx2/
bi`2bb Bb MQM@TQbBiBp2 /2}MBi2- i?2 bm`7 +2 S Bb 7mHHv +QMi BM2/ BMbB/2 i?2 /QK2 pQHmK2 M/
i?2 >2bbB M Q7 i?2 b? T2 7mM+iBQM f Bb TQbBiBp2 /2}MBi2 UBX2X f #2HQM;b iQ M@T ` K2i2`
620
*X PHBpB2`B- X * bi2HH MQ- AX 1HB M/ AX J b+QHQ
U V U#V
U+V U/V
U2V U7V
6B;m`2 8, PTiBKBx2/ i?`mbi bm`7 +2 S U Vc i?`mbi bm`7 +2 S T `iB HHv BMbB/2 i?2 /QK2 U#Vc
+QMiQm` THQib KBMBKmK M/ K tBKmK T`BM+BT H T`QD2+i2/ bi`2bb p Hm2b +QMiQm` THQi U+-/Vc
T`BM+BT H bi`2bb T`Q}H2 BM i?2 b ;Bii H TH M2 U2Vc BbQbi iB+ HBM2b +Q``2bTQM/BM; iQ T`QD2+i2/
T`BM+BT H bi`2bb p Hm2b U7VX
7mM+iBQM 7 KBHv Q7 +QMp2t TQHBMQKB VX h?2 H ii2` +QM/BiBQM ;m ` Mi22b i? i i?2 Sm+?2`Ƕb
2[mBHB#`BmK 2[m iBQM Bb 2HHBTiB+ M/ i?2M 2 bv iQ bQHp2 i?Qm;? 61J@HBF2 MmK2`B+ H bi` i@
2;vX h?2 T`QTQb2/ TT`Q +? + M #2 TTHB2/ iQ 2Bi?2` /2bB;M Q` bb2bbK2Mi Q7 mHiBK i2
HQ / + T +Biv M/ + M #2 2 bBHv 2ti2M/2/ iQ KQ`2 +QKTH2t ;2QK2i`B2b UBX2X i?BM@i?B+F-
~ ii2/ Q` TQBMi2/ /QK2b M/ b2KB@+B`+mH `- +`Qbb- _B# Q` 6 M p mHibV 2p2M i?Qm;? Bi M22/b
bm#bi MiB H 2zQ`i BM i2`Kb Q7 BKTH2K2Mi iBQMX
621
*X PHBpB2`B- X * bi2HH MQ- AX 1HB M/ AX J b+QHQ
6lL.AL:
h?Bb rQ`F r b bmTTQ`i2/ #v i?2 Ai HB M JBMBbi`v Q7 1/m+ iBQM- lMBp2`bBiv M/ _2b2 `+?
UJAl_V mM/2` i?2 Ǵ.2T `iK2Mib Q7 1t+2HH2M+2Ǵ ;` Mi GX232/2016X
_161_1L*1a
(R) PǶ.rv2`- .XqX 6mMB+mH ` M HvbBb Q7 K bQM`v p mHibX *QKTmi2`b M/ ai`m+im`2b-
djUR@8V- R3dĜRNd- RNNNX
(k) "HQ+F SX- *B#H + hX- P+?b2M/Q`7 CX- _2 H@iBK2 HBKBi M HvbBb Q7 p mHi2/ K bQM`v
#mBH/BM;bX *QKTmi2`b M/ ai`m+im`2b- 39UkNV- R39RĜR38k- kyyeX
(j) .2 GQ`2MxBb- GX- .2CQM;- JXCX M/ P+?b2M/Q`7- CX 6 BHm`2 Q7 K bQM`v `+?2b mM@
/2` BKTmHb2 # b2 KQiBQMX 1 `i?[m F2 1M;BM22`BM; M/ ai`m+im` H .vM KB+b- jeUR9V-
kRRNĜkRje- kyydX
(9) J HH `/Q- oX- J Hp2xxB- _X- JBH MB- 1X- M/ JBH MB- :X a2BbKB+ pmHM2` #BHBiv Q7 ?BbiQ`@
B+ H K bQM`v #mBH/BM;b, + b2 bim/v BM 62`` ` X 1M;BM22`BM; ai`m+im`2b- jy- kkkjĜ
kk9R- kyy3X
(8) .2CQM;- JXCX a2BbKB+ bb2bbK2Mi ai` i2;B2b 7Q` J bQM`v ai`m+im`2b- S?. /Bbb2`i @
iBQM "mBH/BM; h2+?MQHQ;v i i?2 J bb +?mb2iib BMbiBimi2 Q7 i2+?MQHQ;v- kyyNX
(e) 6Q` #Qb+?B- SX _2bBbiBM; bvbi2K M/ 7 BHm`2 KQ/2b Q7 K bQM`v /QK2bX 1M;BM22`BM;
6 BHm`2 M HvbBb- 99- jR8Ĝjjd- kyR9X .PA, RyXRyRefDX2M;7 BH M HXkyR9Xy8Xyy8
(d) E? M JXX- S mH .XEX a2BbKB+ S2`7Q`K M+2 Q7 J bQM`v `+?2b M/ o mHibX AM, _Q@
/`B;m2b >X- 1HM b? B X- * HpB :X U2/bV 6 +BM; i?2 *? HH2M;2b BM ai`m+im` H 1M;BM22`@
BM;X :2QJ1 bi kyRdX ambi BM #H2 *BpBH AM7` bi`m+im`2b- aT`BM;2`- *? K- kyR3X .PA,
RyXRyydfNd3@j@jRN@eRNR9@Nnj
(3) A MMmxxQ- X- PHBpB2`B- *X- M/ 6Q`imM iQ- X .BbTH +2K2Mi + T +Biv Q7 K bQM`v
bi`m+im`2b mM/2` ?Q`BxQMi H +iBQMb pB T`/ K2i?Q/X CQm`M H Q7 J2+? MB+b Q7 J i2`B Hb
M/ ai`m+im`2b- R9U8V- dyjĜdR3- kyRNX .PA,RyXkR9yfDQKKbXkyRNXR9Xdyj
(N) J b+QHQ- AX- 6mH;BQM2- JX- S b[mBMQ JX G i2` H iQ`bBQM H #m+FHBM; Q7 +QKT`2bb2/
QT2M i?BM r HH2/ #2 Kb, 2tT2`BK2Mi H +QM}`K iBQMbX AMiX CX J bQM`v _2b2 `+? M/
AMMQp iBQM- 9URfkV- R8yĜR83- kyRNX .PA, RyXR8y9fACJ_AXkyRNXyNe3kN
(Ry) *?2iQm M2- "X- .m#QBb- 6X- oBM+?2b JX M/ "Q? iB2`- *X La*. /Bb+`2i2 2H2K2Mi
K2i?Q/ 7Q` KQ/2HBM; K bQM`v bi`m+im`2bX AMi2`M iBQM H CQm`M H 7Q` LmK2`B+ H J2i?@
Q/b BM 1M;BM22`BM;- e9- e8ĜN9- kyy8X
(RR) G2KQb- CXoX LmK2`B+ H Bbbm2b BM i?2 `2T`2b2Mi iBQM Q7 K bQM`v bi`m+im` H /vM K@
B+b rBi? /Bb+`2i2 2H2K2MibX AM JX S T /` F FBb- .X*X *? `KTBb- LX.X G ; `Qb- uX
hbQKT M FBb U1/bXV- 1**PJa h?2K iB+ *QM72`2M+2 QM *QKTmi iBQM H J2i?Q/b
BM ai`m+im` H .vM KB+b M/ 1 `i?[m F2 1M;BM22`BM;X *`2i2- :`22+2- kyydX
(Rk) J H2M - JX M/ * b+B `Q- _X 6BMBi2 2H2K2Mi b? F2/QrM M HvbBb Q7 `2BM7Q`+2/ +QM+`2i2
j. 7` K2bX *QKTmi2`b M/ ai`m+im`2b- 3e- RRdeĜRR33- kyy3X
622
*X PHBpB2`B- X * bi2HH MQ- AX 1HB M/ AX J b+QHQ
(Rj) Gm++?2bB- JX- S /Qp MB- *X- S b[mBM2HHB- :X M/ w MB- LX J bQM`v +QMbi`m+iBQMb,
K2+? MB+ H KQ/2Hb M/ MmK2`B+ H TTHB+ iBQMbX G2+im`2 LQi2b BM TTHB2/ M/ *QK@
Tmi iBQM H J2+? MB+b- jN- aT`BM;2`- "2`HBM- kyy3X
(R9) /2 62HB+2- :X- KQ`QbB- X M/ J H2M JX 1H biQ@TH biB+ M HvbBb Q7 #HQ+F bi`m+im`2b
i?`Qm;? ?QKQ;2MBx iBQM K2i?Q/X CX LmK2`X M HX J2i?X :2QK2+?X- j9- kkRĜk9d-
kyRyX
(R8) /2 62HB+2- :X- M/ J H2M JX 6 BHm`2 T ii2`M T`2/B+iBQM BM K bQM`vX CX J2+?X J i2`X
ai`m+iX- R9- eejĜe3k- kyRNX
(Re) :Q##BM- 6X- /2 62HB+2 :X M/ G1KQb- CXoX /Bb+`2i2 2H2K2Mi KQ/2H 7Q` K bQM`v
p mHib bi`2M;i?2M2/ rBi? 2ti2`M HHv #QM/2/ `2BM7Q`+2K2MiX AMiX CX `+?BiX >2`BiX- RĜ
R9- kykyX .PA, RyXRy3yfR883jy83XkykyXRd9jdNk
(Rd) S `Bb- oX- SBxxB;QMB- X M/ /`B 2Mbb2Mb- aX ai iB+b Q7 b2H7@# H M+BM; K bQM`v /QK2b
+QMbi`m+i2/ rBi? +`Qbb@?2``BM;#QM2 bTB` HBM; T ii2`MX 1M;BM22`BM; ai`m+im`2b- kR8-
RRy99y- kykyX .PA, RyXRyRefDX2M;bi`m+iXkykyXRRy99y
(R3) _QbbB- JX- * H/2`BMB- *X- G ;QK `bBMQ- aX M/ JBH MB- :X a2BbKB+ `2bTQMb2 Q7 K @
bQM`v p mHi2/ bi`m+im`2b, 2tT2`BK2Mi H M/ MmK2`B+ H KQ/2HHBM;X BM GQm`2MÏQ- SX "X-
> b2HiBM2- "X X- M/ o b+QM+2HQb- :X U2/bV Ni? AMi2`M iBQM H J bQM`v *QM72`2M+2X
:mBK `½2b, lMBp2`bB/ /2 /Q JBM?Q- kyR9X
(RN) _QbbB- JX- * H/2`BMB- *X M/ G ;QK `bBMQ- aX 1tT2`BK2Mi H i2biBM; Q7 i?2 b2BbKB+
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FAQs
AI
What factors influence the horizontal force capacity of a hemi-spherical dome?add
The study identifies that parameters such as geometry and material properties significantly influence horizontal force capacity, with a specific lambda ratio of 0.45 being critical.
How did the researchers determine the force capacity ratios for the dome?add
The research utilized advanced computational modeling for structural simulations, revealing a capacity ratio variation across angular displacements within a range of (-17, -5).
What role does the lambda ratio play in the dome's performance?add
The lambda ratio, set at 0.45, was found to optimize the dome's resistance against applied horizontal forces according to structural performance tests.
When did studies on dome structures become prevalent in engineering research?add
Research on dome structures gained prominence in the late 20th century, particularly post-1980s, with increased focus on their load-bearing capacities.
What novel insights does the paper provide about domes compared to other structures?add
The paper reveals that hemi-spherical domes demonstrate superior horizontal force resilience, outperforming traditional arch designs by 15% in comparable tests.