TINH TOAN LIEN KET KHOP DAM - COT DANG BAN Sl/CJNTHEO TIEU CHUAN EUROCODES
ABSTRACT
The article introduces the method of calculating the loading capacity of non-preloaded and preloaded bolt according to Eurocode 3. It also presents the fomulars to calculate the shear capacity, bearing capacity and tension capacity of bolt. It also studies the failure mechanism of fin plate connection using the bolts and the method of calculating of this
connection. Comparisions between Eurocode 3 andTCXDVN 338-2005 are also discussed.
TSVu Quoc Anh Th.S Pham Dai Luofng Khoa Xay dung Trirdng Dai hoc Kien true Ha Noi
1. Gidi thieu
Nhufng nam qua, ngay cang c6 nhieu cac to chufc, cong ty nUdc ngoai dau tif vao Viet Nam d nhieu linh vUc khac nhau, trong do CO ITnh vifc xay dung. TCr thifc te do, ngay cang co nhieu cong trinh dU0c yeu cau thiet ke khong phai theo tieu chuan Viet Nam ma theo cac tieu chuan cua nudc ngoai nhu tieu chuan AISC (My), BS (Anh), JIS (Nhat), Eurocode... Khi thiet ke nhUng cong trinh theo tieu chuan nUdc ngoai cac k y s u thiet ke cua Viet Nam gap nhieu kho khan de tiep can, hieu sau cac quan niem, cong thUc tinh toan. Do vay viec nghien cUu tim hieu cac phuong phap tinh toan ket cau theo he thong tieu chuan nU6c ngoai noi chung va cua Chau Au noi rieng la can thiet.
Ket cau thep ngay cang ducjc sU dung rong rai trong nhieu loai cong trinh xay dung dan dung, cong nghiep, nha cao tang, thap v6 tuyen, cau cong... Lfu diem noi bat cua ket cau thep la cho phep thdi gian thi cong nhanh, kha nang kiem soat chat che chat lUcJng ket cau cong trinh trong qua trinh san xuat, thi cong lap dung rat de dang va thuan loi. Ket cau thep duoc chia thanh cac mo dun khac nhau, duoc san xuat trong nha may, sau do mang den cong trudng tien hanh lap dung, noi ghep chung lai bang cac moi noi lien ket (thudng la lien ket bang bu long) de tao thanh he ket cau hoan chinh. Viec tinh toan cac moi noi lien ket bu long dam bao cac dieu kien an toan ve ben, mdi, on dinh cho toan he ket cau la het sUc quan trpng, lien quan trUc tiep tdi tuoi thp cua cong trinh. Viec chpn kieu lien ket cung het sUc quan trpng trong thiet ke ket cau thep. Ngoai viec lUa chpn de dam bao cac dieu kien an toan ve ket cau, ngudi thiet ke cdn phai can nhac den cac dieu kien lap dung thuc te tai cong trUdng sao cho viec lap dung de dang, nhanh chdng va an toan nhat. Hien nay mot so kl sU thiet ke cdn chUa hieu sau, chua nam rd dupc
Vu QuocAnh Pham Oai Luang
cac kieu lien ket va phuong phap tinh toan bu Idng lien ket. Bai viet gidi thieu phuang phap tinh toan mot dang lien ket rat hay gap trong thuc te: lien ket khdp dam vdi cot dang ban sUdn.
2. Cau tao va nguyen ly lam viec cua bu long
Ve cau tao, bu Idng dupc chia thanh 2 loai chinh: Bu Idng t h u d n g va bu Idng cudng dp cao.
Bu long thudng dUgic dung chu yeu trong ket cau nhe, cac cau kien nhu giang, xa gd, dam tudng, dan nhip nhd va cac ket cau tuong t u khac ma tai trpng khdng Idn va tTnh. Bu Idng thudng dUpc tinh toan de cd the chju dupc lUc keo va lUc cat tac dung len than bu Idng. Ung suat chay f ^ va Ung suat keo cue han f^^ ddi vdi bu Idng cap dp ben 4.6, 5.6, 6.8, 8.8, 10.9 dUOc cho trong bang 1.
Mat cat yeu nhat cua bu Idng tai vi tri ranh ren. CUdng dp bu Idng thudng dUdc tinh toan theo dien tich chiu Ung suat cua than bu Idng. Dudng kinh tiet dien nay (6^J duoc xac dinh bang trung binh cdng cua dudng kinh Idi than bu Idng (dJ va dudng kinh trung binh (d^).
_ d „ + d , „
' " " ^ ^ (2.1) Nguyen ly truyen tai trpng trong lien
ket bu Idng chiu cat: lUc cat dupc truyen qua do kha nang chiu ep mat cua thep ban, kha nang chiu cat va ep mat cua bu Idng. Loai lien ket nay phu thudc nhieu vao cUdng dp bu long, cUdng dp thep ban va khoang each tU mep bu Idng den tim bu Idng.
Nguyen ly truyen tai trpng trong lien ket chju cat ddi vdi bu Idng cudng dp cao:
luc cat dupc truyen qua luc ma sat giQa cac ban thep, lUc ma sat nay do luc siet cua bu Idng ep chat cac ban thep lai vdi nhau. LUc ma sat phu thudc nhieu vao dang be mat tiep xuc cua ban thep. Vi vay khi tinh toan lien ket bu Idng cUdng dp cao ngudi kT sU thiet ke phai chu y den dang be mat tiep
5 8 ^i^nisni^i 8.2010
Bang 1: Cap dp ben cua b u l d n g [5]
Cap b u I d n g fyb (N/mm^) fub (N/mm^)
4.6 240 400
5.6 300 500
6.8 480 600
8.8 640 800
10.9 900 1000
Hinh 1: IVIat cat ngang bu long va dien tich hulu hieu
Bang 2: Cdng thUc tinh toan kha nang chju lUc cua bu Idng [5]
Dang pha huy
Kha nang chju cat tren mdt mat phang
Kha nang chjuep mat
Kha nang chju keo
Kha nang chong c h p c t h u n q To hpp cua luc cat va keo
Bu Idng
F..^"-^-N3.1)
Vdi;
- Mat phang cat la mat phang di qua phan cd ren cua bu Idng (A d cdng thUc nay la dien tich hQu hieu As) + Vdi cap dp ben 4.6, 5.6,8.8: a . = 0.6.
+ Vdi cap dp ben 4.8, 5.8,6.8 va 10.9: a„ = 0.5
- Khi mat phang cat di qua phan khdng ren cua bu Idng (A la dien tich toan phan cua bu Idng - dien tich phan khdng ren):
Ov = 0.6
'',,„,,k,a.f„d. (3.2) Vdi:
- a b i a n h o n h a t c u a a j , - "'' h o a c i : TrUdng hop ciing hudng phUdng truyen life:
Bu Idng ngoai cung ttj = ' ; 3do Pi 1 Bu long phia tronq a^ = -
^ 3do 4 Trudng hpp vudng gdc vdi phuong truyen lUc
Bu Idng ngoai cung kl la nhd nhat cua 2,8 ^ - 1 , 7 hoac 2.5
do Bu Idng phia trong kl la nhd nhat cua 1,4 '^^ -1,7 hoac 2.5
4)
F,,„d = ^ ^ ' ' ' (3.3)
1'M2
Vdi k2 = 0.63 vdi bu Idng cd dang mu Cac trudng hop khac k = 0.9 Bp, Rd = 0.6jid„,tpfu/YM2 (3.4)
Fv,sd_^ F,5, ^ ^ F 1 4F
"t
prpr
p
'•-v'X'-A'^^r Hinh 2: Bu long thifdng, chju ep matCHIU EP l/.AT
rf'
UJJ.- 'V—r
'••i.KdOAI\G Hg
flinh 3: Bu long cudng dp cao
xuc, loai son phu ddi vdi vat lieu djnh sU dung.
3. Tinh toan kha nang chju-li/c cua bu long
Khi tinh toan bu Idng ta can luu y mdt sd diem sau:
• Ludn ludn phai kiem tra mat phang truyen tai trpng cat qua than bu Idng hay phan ren cua bu Idng
• Kha nang chju cat cua bu Idng giam khi khi ti sd giUa Ung suat chay tren Ung suat keo dUt Idn.
• Kha nang chiu ep mat cua ban ma lien ket phu thudc vao khoang each cac bu Idng va khoang each tU mep ban thep den tim bu Idng.
• Kha nang chju keo cua bu Idng giam khi dudng truyen tai trpng bj lech tam.
Eurocode dUa ra edng thUe tinh kha nang chju lUc eua 1 bu Idng chju cat va keo n h u sau: (Bang 3.4 EN 1993-1-8)
4. Kha nang chju trifcrt cua bu ldng cUdng do cao
Ddi vdi eae lien ket chju tai trpng lap hoac tai trpng ddng, khdng dupe phep sU dung bu Idng thudng chju eat va ban ma chju ep mat. Nhu vay, can phai sUdung bu Idng cudng dp cao siet chat de tao lUc ep giUa cac ban ma lien ket. Khi dd tai trpng trong lien ket se 6MC truyen qua lUc ma sat. Khi tai trpng tang vUpt qua kha nang chong trUcrt, cae ban ma se bj trUOt va bu Idng khi dd se chju cat, ep mat.
Khdng nen sU dung bu Idng cUdng dp cao ddi vdi nhUng ket eau dupc bao ve bang Idp son phu be mat vi chung se lam giam he sd ma sat giUa eae be mat tiep xuc dan den lam giam kha nang chju lUc cua lien ket. Ddi vdi trudng hop dae biet
8.20io^i9niiiisi]59
Bang 2.5: Gia tri he sd k^ [5]
M d t a Bu Idng vdi Id tieu chuan
Bu Idng vdi 16 rdng hoac Id d van ngan cd true d van vudng gdc vdi hudng truyen tai trpng
Bu Idng vdi 16 d van dai cd true d van vudng gdc vdi hudng truyen tai trpng
Bu Idng vdi Id d van ngan cd true d van song song vdi hudng truyen tai trpng
Bu Idng vdi 16 d van dai cd true d van song song vdi hudng truyen tai trpng
ks 1,0 0,85
0,7 0,76 0,63
Bang 2.6: Gia trj he so trupt n [16]
Loai be mat ma sat A B C D
He so trUcft m 0,5 0,4 0,3 0,2
1. Cae yeu eau kiem tra va duyet tuan theo mue 2.8, nhdm 7 cua tieu chuan Chau Au 2. Phan loai cua bat ky be mat dupc xU li can dUa tren mau t h i nghiem dai dien cho be mat ket cau djnh sCr dung va can thuan theo muc 2.8, nhdm 7 cua tieu chuan Chau Au
3. Cach xac djnh loai be mat ma sat theo muc 2.8, nhdm 7 cua tieu chuan Chau Au 4. XUly be mat son can phai can phai tinh den de tranh s u t o n hao Ung xuat trong bu Idng eUdng dp cao theo thdi gian.
•n u.
r r
L J 1 1
i ; 1 1 I'l'
J ^
, , n
LJ
Hinh 4: Lien ket noi chong dai [5]
/
I
4 1 •^^i 'M f'''^'
k
( 1
1
/
\
\
]
-t -t.
-«
r7~^
^•;
^
a, dang 1 b, dang 2 Hinh 5: Cac dang pha hoai ban thep [5]
e, dang 3
ket cau yeu cau son phu be mat thi can scf dung loai son dac biet.
Viec siet bu Idng vdi lUc siet bao nhieu cung rat quan trpng trong tinh toan lien ket bu Idng cudng dp cao de tinh toan dupe sd luong bu Idng trong lien ket.
Diem Uu viet chinh eua lien ket loai nay la lien ket ed dp cUng eao, kha nang chju tai trpng thay doi va tai trpng lap eao hon bu Idng thudng. Nhupe diem cua lien ket bu Idng eudng dp cao la cho gia thanh dat, qua trinh gia cdng be mat phUc tap, phai dao tao edng nhan ky thuat dam bao life siet bu Idng theo thiet ke.
Kha nang chju trupt cua bu Idng 8.8 va 10.9dUdelay nhusau:
k,n.^^
(4.1) F - ' '^F
YM3 Trong do:
- k^: lay theo Bang 3 - n : sd mat ma sat tiep xuc.
- n: he sd trUcrt duoc lay theo Bang 4 -Vdi bu Idng cap dp ben 8.8; 10.9 6uc3c siet chat theo mue 2.8, nhdm 7 cua tieu chuan,
Gia tri F ^ duoc tinh theo cdng thUc:
= 0,7f .„A. (4.2)
5. Lien ket noi chong dai
Eurocode qui djnh ddi vdi lien ket cd khoang each Lj giQa eae tam bu Idng Idn hon 15d (xem hinh ve dudi) thi kha nang chju cat cua bu Idng F^i,^ tinh toan theo Bang 2 dupe nhan vdi he so giam (5,^,
L - 1 5 d
B , , = 1 — ! nhung 0,75<p,<1(5.1) 200d '•
6. Kiem tra pha hoai ban thep Ban thep bj pha hoai dudi tac dung eua lUc cat tai vj tri hang bu Idng dpe theo mat chju eat cung vdi lUc keo tai vj tri hang bu Idng dpe theo mat chju keo.
Ddi vdi nhdm bu Idng chju tai trpng dung tam, kha nang chju pha hoai ban thep Vef,1,Rd dupe tinh theo edng thUc:
VeWRd = t A „ , h^i + ( 1 / ^ / 3 ) ^ ^ „ /YMO (6.1) Trong do: A^^ la dien tich thuc tren mat chju keo.
A^^ la dien tich thUc tren mat chju cat.
Doi vdi nhdm bu Idng chju tai trpng lech tam, kha nang chju pha hoai ban thep V^^^jj^ dupe tinh theo edng thUe:
Veff,2,„d = 0 , 5 t A„, / Y „ , + ( 1 / ' y 3 ) ^ A „ . l/dfiil 7. Tfnh toan lien ket khdp dam - cot dang ban sUdn (Fin Plate Connection)
7.7. Sado dgng lien ket
Eurocode coi cac lien ket dang nay la lien ket khdp vdi gia thiet lien ket khdng chju momen, ehi ehju luc eat. Khi tinh toan can tinh toan kiem tra vdi 2 trudng hpp:
tinh toan kha nang chiu lue cua bu Idng va kha nang ehju lUc cua dudng han lien ket.
Trong npi dung eua bai viet nay, tac gia xin chi dua ra cac cdng thUe tinh toan
Hinh 6: Lien ket ban si/on chiu lUc cat theo phuflng diJng; 1 .Ban sUdn; 2.Dam; 3. Cot do; 4. Dam dS
e O ^ ^ ^ l ^ i i l ^ ^ 8.2010
a. Bu long bj cat 6(tt
PH4N Bl PHA HOAI
d. Pha hoai tai mep ngoai ban thep Hlnh 7: Mot so dang pha hoai ciJa lien ket
n ^ -
b. Pha hoai do ep mat
e. Ban s u a n bi chay d e o
c. Pha hoai tren tiet dien thii'c
f. Pha hoai tai vi tri han
\<—'^^
'M
^ , b , &]\i
A Pi eij_
-0-
iI
-6-
< > Z
j^
T
T/le
n2= 1
Hinh 8: Cac kich thi/dc chinh cua lien ket dang ban sudn
lien quan den bu Idng lien ket, cac cdng thUe kiem tra cac thanh phan khac n h u kiem tra dudng han, kiem tra ban thep lien ket, kiem tra on djnh ban canh, on djnh ban bung... khdng de cap den trong ndi dung nay.
7.2. Cdc thong so cdn tinh todn Dang pha huy
Bu Idng chju cat V,,^, Ban ma chju ep mat V^^^
Ban ma ehju eat tai tiet dien thuc V^^^
Ban ma chju xe rach V„^^
Bung dam chju ep mat V^^^
Bung dam chiu cat tai tiet dien thUe V„^^
Bung dam ehju xe rach V^^^
7.3. Cdc thong so dau vdo
n2= 2
Cac gia trj thdng so dau vao nhu hinh ve:
b Chieu rdng ban ma lien ket h Chieu cao ban ma lien ket
p
t Chieu day ban ma lien ket g^ Khoang each giQa dam va cot z Khoang each tU trpng tam cum bu Idng den mep cdt
n^ Sd hang bu Idng (theo phuong ngang) n^ Sd cdt bu Idng (theo phUOng dUng) 7.4. Khd ndng chiu cat ciia bu long Kha nang chju eat cua bu Idng dupc tinh theo cdng thUe
nF.M
(7.1) V„.
V(1 + an)'+(Pn)'
Trong do: F^„^ dupe tinh theo cdng thUc:
= ^ ^ ^ ^ v d i h e s 6 v „ =1,25(7.2) - Vdi lien ket cd 1 hang bu Idng (n^
1;n = n,) a = 0;p = 6z
n(n-i-1)p,
- Vdi lien ket cd 2 hang bu Idng (n^
2;n = 2n,)
a = ^ ; P = ^ ( n , - 1 ) t r o n g d d 21 21
1 = Lp^-F-n,(n?-1)pf 2'' 6
7.5. Khd ndng chiu ep mat cua bdn md lien ket
Kha nang ehju ep mat cua ban ma lien ket dupe tinh theo edng thUc
n 1 + a n pn
(7.3)
' b.Rd.ver J \ b.Rd.hor
Trong d d F 6MC tinh theo edng thUe:
b.Rd
kjttj^d.t
YM2 (7.4)
- Kha nang chiu ep mat eua 1 bu Idng theo phuong thang dUng tren ban ma lien ketF^„^ duoc ti'nh theo:
b.Rd.ver
k,a,f„pd.tp
(7.5) Trong d d
a b = m i n | ( ^ ) ; ( ^ - 4 ( ^ ) ; 1 3d„ 3d„ 4 f„„
k, = m i n ( 2 , 8 - ^ - l , 7 ) ; ( 1 , 4 ^ - 1 , 7 ) ; ( 2 , 5 )
d„ d„ j
8.2010^E^ni[|iSlj61
- Tuong t u n h u vay, kha nang chju ep mat cua 1 bu Idng theo phuong ngang tren ban sUdn lien ket F. „,„ duoc tinh theo:
b,Kd,nor
kiabfu,pd-tp
' b.Rd.hor
Trong do YM
(7.6)
3d„ 3d„ 4 ; 1 k, = m i n ( 2 , 8 - ! - - 1 , 7 ) ; ( 1 , 4 -
dn d, -1,7);(2,5) 7.6. Khd ndng chiu cdt cua bdn lien ket tgi tiet dien thuc
Kha nang ehju eat tai tiet dien thue:
" R d 3 - " v n e t rr
v3.Y„2
v d i A „ , , = V h , - n , d „ ) (7.7) 7.7. Khd ndng chiu xe rdch cda bdn lien
ket (Block Shear)
Ddi vdi nhdm bu Idng chju tai trpng lech tam, kha nang ehju pha hoai ban thep V „ , , = V „ „ , duoc tinh theo cdng thUe:
Rd,4 ef,2,Rd • ^
= 0,5tA„,/Y„2 + +(l/^/3)f A„ / ) (7.8) Trong do: A^^ la phan dien tich thuc ehju keo
- Trudng hpp 1 hang bu Idng theo phuong dUng {n^= 1):
- Trudng hop 2 hang bu Idng theo phuong dUng (n^ = 2):
A „ , = t p ^ P , + e , - 3 ^
A^^ la phan dien tieh thuc chju cat A"" = t (h - e - ( n -0,5)dJ
nv p p 1 1 ' ' 0
7.8. Khd ndng chiu ep mat bdn bung ddm
Kha nang ehju ep mat cua ban bung dam dUPc tinh theo cdng thUe
v . ;
1 + a n pn
(7.9)
t h U c :
yM2 (7.10) - Kha n a n g e h j u e p m a t eua 1 b u I d n g
theo phuong t h i n g dUng tren ban bung dam duoc lien ket F^„, tinh theo:
b.Rd.ver
k^cUdt ,7^„)
YM2 Trong dd:
= min ( Pi 3d„
k, = m i n (2,8
- ) ; i
-1,7);(1,4i^-1,7);(2,5) do
- TUPng t u nhU vay, kha nang chju ep mat cua 1 bu Idng theo phuong ngang tren ban bung dam dupc lien ket f^^^^^^, tinh theo:
p . k i O b U i - d - t w
•"b.Rd.hor ~
1'f^2 (7.12)
Trong dd:
«b=min|(-^);(£^-l);(M-1
3d„ 3d„ 4 f „ „ k , = min (1,4 . ^ - 1 , 7 ) ; (2,5)
I, d„
7.9. Khd ndng chiu cdt cua bdn bung ddm tgi tiet dien thUc
Kha nang chju cat cua ban bung tai tiet dien thuc: ,
t hi
vdi A ,, . = A . - n,d„t ,,
v,b,net v.b 1 0 w,bl
(7.13) 7.70. khd ndng chiu phd hoai ciia bdn bung ddm(Block Shear)
Ddi vdi nhdm bu Idng chju tai trpng lech tam, kha nang chong pha hoai ban
quy djnh phai kiem tra ddng thdi chiu cat va keo theo edng thUc eho san.Trong TCVN thi lai eho phep kiem tra tUng trudng hop ehju eat va chju keo rieng biet.
3-Trong Eurocode cdn cd qui dinh dae biet ve tinh toan mdi ndi qua dai va qua day (lien ket ndi chdng dai). Khi moi ndi cd chieu dai hay chieu day Idn qua trj sd qui djnh thi kha nang chiu cat cua bu Idng phai dupe giam di bang mdt he so tUong Ung (Cdng thUe 5.1). Trong TCVN khdng ed cac qui djnh nay.
4- Trong Eurocode cd qui djnh cu the edng thUe tinh toan chdng pha hoai xe rach ban thep (block tearing) tai trj tri hang bu Idng lien ket (Cdng thUe 6.1 & 6.2).
Trong TCVN khdng ehi rd cdng thUe tinh
toan nay. • thep V „ , , =
thUe:
V „ , = V .
V dupc tinh theo cdng
= 0,5t,bA,/YM2 +
H-(1/V3)f,i,Av/yMo (7.14) Trong dd: A^^ la phan dien tieh thUc
chju keo
- Trudng hpp 1 hang bu Idng theo phupng dUng {n^= 1):
A „ , = t „ , b i [ e , , - ^
- Trudng hpp 2 hang bu Idng theo phupng dUng (n^ = 2):
A n , = t „ , J p j + e , i , - 3 ^ A la phan dien tich thuc chiu cat A l = t„.bi(e,,, + ( n , - 1 ) p ; - ( n ; - 0 , 5 ) d „ ) Sau khi tinh toan eac kha nang khang cat cua cac thanh phan tham gia trong lien ket, gia trj nao nhd nhat thi kha nang ehju eat eua lien ket chinh bang kha nang chju luc cua thanh phan yeu nhat.Theo dd dang pha huy cua lien ket cung chinh la sU pha huy tU thanh phan yeu nhat eua lien ket.
8. IVIot vai nhan xet ve phUOng phap tinh toan bu long theo Eurocode va TCXDVN 338:2005
Qua qua trinh nghien eUu tieu chuan Eurocode, tac gia nhan thay each tinh theo Eurocode kha phUe tap va ehi tiet. Khi so sanh mdt so qui dinh va edng thUc tinh toan giCfa Eurocode va TCXDVN 338: 2005, tac gia cd mot so nhan xet n h u sau:
1- Khi tinh toan kha nang chiu ep mat eua 1 bu Idng, Eurocode xet den rat nhieu yeu t d anh hudng nhU: dUdng kinh 16, khoang each t U t i m bu Idng den mep ban thep (e,, e^, p,, p^...), ty sd Ung suat ben eua bu Idng va thep ban (f„/f„), khoang each giQa cae bu Idng (p,,)... Trong TCVN khdng qui djnh cu the nhu vay, each tinh theo TCVN don gian hon va ed the tong hpp thanh dudi dang bang tra sSn.
2- Odi vdi bu Idng vUa chju cat, vUa chju keo (trudng hop hay gap ddi vdi bu Idng neo, bu Idng ndi mat bich), Eurocode
TAI LIEU THAM KHAO
1. Boan Binh Kien, "Thiet ke ket cau thep theo tieu chuan Anh B55950: Part 1-2000", Nha xuat ban xay difng. Ha Npi, 2004.
2. Pham Van Hpi; Nguyen Quang Vien, Pham Van Tif; Lifu Van Tadng,"Ket cau thep - Cau kien CO ban" NXB Khoa hpc vaKythuat, HaNpi,2006.
3. TCXDVN 338-2005, "Ket cau thep - Tieu chuan thiet ke".
Ha Npi, 2005.
4. Continuing Education in Structural Connection, "Design of Structural Connection to Eurocode 3 - Frequently Asked Questions", Czech Technical University in Prague, 2004.
5. British Standards Institute, "Eurocode 3-Design of steel structure - Part 1-8: Design of joints", BSI, London, 2006.
6. Trahair, Bradford, Nethercot Gardner, "The behaviour and Design of steel structures to EC3", Taylor & Francis e- Library, NewYork, 2008.
6 2 ^ ^ B f i ; [ i 8 ! i l 8.2010
