3. Specialty in design SLS, tension, compression

quartzaardvarkΠολεοδομικά Έργα

29 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

58 εμφανίσεις

© 3 Prof. Ing. Josef Macháček, DrSc.
3 (2E14) 1
3. Specialty in design
SLS, tension, compression
Dissimilarities in design as compared with design of carbon steels structures. SLS, ULS.
Classification of cross sections, members in tension, compression, buckling.
Principal dissimilarities of stainless steel and carbon steel design:
• Stress-strain diagram of stainless steels depends on direction and sign of
stresses (the material is anisotropic) and is non-linear:
- in design, however, common values of yield and ultimate stresses (f
y
, f
u
) are used,
- substantial work hardening due to cold working may be utilized,
- secant modulus of elasticity E = 200 000 MPa is used for deflection calculations,
- in detailed FEM calculations the two-phase Gardner-Nethercot model (for σ ≤ f
y
and σ > f
y
)
may be used.
• stability (buckling) is checked more rigorously due to anisotropy,
• high ductility and growth of strength during quick loading is advantageous
in design for explosions and seismicity,
• the behaviour under fire is better,
• chromium-rich oxide passive self-repairing layer protects steel from corrosion.
3 (2E14) 2
T [º C]
stainless steel
carbon steel
l
l
Δ
[x10
-3
]
Relative thermal expansion
λ
a
[W/(mºK)]
T [º C]
stainless steel
carbon steel
Thermal conductivity
θ
a
[J/(kgºK)]
T [º C]
stainless steel
carbon steel
Specific heat capacity
Behaviour under fire
(c) 0.000 012
(s) 0.000 017
5000
425
27.3
54
598
450
0.0178
650
0.0236
14.6
29.8
© 3 Prof. Ing. Josef Macháček, DrSc.
3 (2E14) 3
SLS (Serviceability limit states)
• Criteria for deflections and vibrations are the same as for carbon steel.
• Effective cross section shall take into account shear lag of wide flanges and
buckling of compression parts:
Approximately (conservatively) it can be taken the same as for ULS.
• Secant modulus of elasticity E
s,ser
= (E
s,1
+ E
s,2
)/2 should be used, which
depends on stresses in tension (i = 1) and compression (i = 2) flanges and
direction of rolling. Conservatively it may be taken from cross-section with
maximum stresses (neglect the variation of E
s,ser
along span):
n
f
E
,
E
E








+
=
y
serEd,i,
serEd,i,
is,
σ
σ
00201
RO coefficient (given in Eurocode tables).
E.g.:for Grade 1.4301:
longitudinal direction n = 6
transverse direction n = 8
for duplex Grade 1.4462 n = 5
for austenitic and duplex steels E = 200 000 MPa
3 (2E14) 4
ULS (Ultimate limit states)
• Higher partial material factors are used: γ
M0
= γ
M1
= 1,1; γ
M2
= 1,25.
• Cross section classification (4 Classes) adopts more strict slenderness
(for details see Eurocode EN 1993-1-4 tables).
The procedure of classification is the same as for carbon steel.Example:
Internal compression parts:
t
c
t
c
osa ohybu
h
c
t
axis of bending
For example:
slenderness c/t: bending compression
Class 2 common steel ≤ 83,0ε ≤ 38,0ε
stainless steel ≤ 58,2ε ≤ 26,7ε
Class 3 common steel ≤ 124,0ε ≤ 42,0ε
stainless steel ≤ 74,8ε ≤ 30,7ε
y
f
E
210000
235

© 3 Prof. Ing. Josef Macháček, DrSc.
3 (2E14) 5
Eurocode 1993-1-4 recommends to use the following factors ε:
austenitic steel 1.4301 f
y
= 210 MPa ε = 1,03
austenitic steel 1.4401 f
y
= 220 MPa ε = 1,01
duplex steel 1.4462 f
y
= 460 MPa ε = 0,70
c
c
t
t
Outstand flanges:Tubes:
For example parts in uniform compression:
slenderness c/t: common steel stainless steel
Class 2 cold formed ≤ 10,0ε ≤ 10,4ε
welded ≤ 10,0ε ≤ 9,4ε
Class 3 cold formed ≤ 14,0ε ≤ 11,9ε
welded ≤ 14,0ε ≤ 11,0ε
Tubes in compression: slenderness d/t :
Class 2 ≤ 70ε
2
≤ 70ε
2
Class 3 ≤ 90ε
2
≤ 280ε
2
d
t
3 (2E14) 6
Reduction factor ρfor Class 4 cross sections (buckling factor) is lower (more
strict) than for carbon steel:
internal compression parts:
outstand compression parts:
1
125,0772,0
2
≤−=
pp
λλ
ρ
1
231,01
≤−=
2
pp
λλ
ρ
for welded 0,242
0
0,2
0,4
0,6
0,8
1
0 0,5 1 1,5 2 2,5
slenderness λ
p
reduction factor
ρ
common steel, internal parts
common steel, outstand parts
stainless steel, internal parts
stainless steel, outstand parts
stainless steel, outstand parts (welded)
Note:
It is obvious, that distinction
between rolled and welded
parts is senseless.
© 3 Prof. Ing. Josef Macháček, DrSc.
3 (2E14) 7
Tension, simple compression
- as for carbon steel:
Resistance of the net cross section:
M0yRdc,Rdt,
/
γ
fANN
=
=
Buckling in compression
- as for carbon steel:
M1yeffRdb,
/
γ
χ
fAN
=
Reduction factors are taken from worse buckling curves and some buckling
curves slightly differ in comparison with common steels.
[ ]
1
1
5,0
22

−+
=
λφφ
χ
(
)
[
]
2
0
15,0 λλλαφ +−+=
cr
yeff
N
fA

M2uRdt,
/γfAkN
netf
=
acc. number and spacing of bolts
( )
[ ]
3,0/31
0
=+= udrk
f
but
r number of bolts in section/total bolt number,
u = 2e
2
but ≤ p
2
(common edge bolt spacing).
1≤
f
k
3 (2E14) 8
Values of and for flexural, torsional and torsional-flexural buckling:
α
0
λ
0.200.34
All members
Torsional and
torsional-flexural
0.200.76Welded open sections
(minor axis)
0.200.49Welded open sections
(major axis)
0.400.49Hollow sections
(welded and seamless)
0.400.49Cold-formed open
sections
Flexural
Type of memberBuckling mode
α
0
λ
© 3 Prof. Ing. Josef Macháček, DrSc.
3 (2E14) 9
Mind (!) for possibility of torsional or torsional-flexural buckling:
Procedure as for other thin-walled profiles: determination of „space“ buckling (in general N
cr,xyz
):
• torsional critical (buckling) force for doubly symmetrical cross-section (where L
cr,x
is buckling length for torsion, y
O
, z
O
coordinates of shear centre S to centroid G):
• torsional-flexural critical force for cross-section symmetrical about z-z (y
0
= 0):
Column resistance is frequently determined by torsional or torsional-flexural buckling when its
boundary conditions differ for various buckling directions (i.e.for various buckling lengths with
respect to axis x (torsional buckling), y, z (plane or torsional-flexural buckling).
Thin-walled cross-sections from stainless steels
Procedures according to Eurocode EN 1993-1-4 shall be used:
i.e. use of effective width A
eff
, covering effects of local and distortional buckling.








+=
2
xcr,
w
2
t
2
0
xcr,
1
L
IE
GI
i
N
π
2
0
2
0
2
z
2
y
2
0
zyiii +++=
( )
cr,zxcr,
2
cr,zxcr,cr,zxcr,xzcr,
4)(
2
1
NNNNNNN β
β
−+−+=
2
0
0
1








−=
i
z
β
y
z
G ≡ S
y
z
G
S
(i
y
, i
z
radii of gyrations)