© 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

=ε

© 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

=λ

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)

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