View
4
Download
0
Category
Preview:
Citation preview
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
High Temperature Material Laws of High Strength (S460) Steel
Prof. Dr.-Ing. Jörg LangeInstitute for Steel Structures
and Fracture MechanicsTechnische Universität Darmstadt
STAHLBAU
STAHLBAU
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
7,8
8,2
15,0 15,0 15,0 15,0
Penthouse
1981
BMW AG in Berlin
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
60,0
15,0
7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5 7,5
120,0
Tensile forces H resulting from sagging composite beams
Protected beams carrying compressive forces15,0
15,0
15,0
1,2
5
2,5
2,5
2,5
2,5
2,5
B
B
1,2
5
Unprotected beams sagging under fire
H H
Protected beams
Protected beams
Beams and girders “level above ground floor“
AA
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Paint shop for Airbus A380 – Hamburg 2004
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Frame of the main door
Door Airplane
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Deflections under self weight and fire
Am/V mostly less than 30
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Fire load „Airplane“- Paintshop according to DIN 18230-1 (May 1998)
Fire load for one A380 – painting area
Kind of fire load: Mass
(KG) m - Factor Heating value
(kWh/kg) Energy
contents (kWh)
Airplane – primary structure 153.000 1 8,63 1.320.390
Hydraulic Oil 1.400 1 9,8 13.720
Tires 1.100 1 12,2 13.420
Chairs 17.000 1 7,686 130.660
Additional plastic 39.200 1 12,2 478.240
Additional load inside building 7.900 1 10,0 79.000
Kerosine (after emptying) 400 1 11,7 4.680
Paint 600 1 9,0 5.400
Tools etc. 12.500 1 8,0 100.000 Sum 2.145.510
This results in a specific fire load qr = 273,4 kWh/m2, in an area of 7.848 m2.
= 17 kg/m² wood
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Reduction of the yield strength of S460
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 100 200 300 400 500 600 700 800 900 1000
Θ [°C]
f y(Θ
) / f y(20°C) [-]
SFB 148 (1986): StE 47
Winter (1990): StE 460 TM
Arbed (1989): StE 460 TM
Outinen (2000): S460 M
EC3-1-2
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Chemical composition
Fine grain built due to Nb, Ti, V
S460 N:
Final rolling at 900°C
S460 M:
Final rolling at 800°CAustenite cannot re-crystallize due to Niob
⇒ fine grain ferrite
⇒ reduction of carbon
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
S460 N
S460 M
Equal grain size(G = 8)
S460 N:Round grain, linear distribution of perlite (dark)
S460 M:Uneven distribution,Distorted grainless perlite (less carbon)
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Test methods
σ
ε
εs
Θ= const
F
F
Steady State Tests(+ creep):
Θ = const.εs, εk, εth separated
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
σ
ε
εsεs + εk
Θ= const
F
F
Test methods
Steady State Tests(+ creep):
Θ = const.εs, εk, εth separated
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
σ
ε
εsεs + εk
Θ
F = const
FΘ= const
F
F
Test methods
Transient State TestsΘ ≠ const
εs, εk and εth included
Steady State Tests(+ creep):
Θ = const.εs, εk, εth separated
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
σ
ε
εsεs + εk
ε– εth = εs + εk
Θ
F = const
FΘ= const
F
F
Transient State TestsΘ ≠ const.
εs, εk and εth included
Steady State Tests(+ creep):
Θ = const.εs, εk, εth separated
Test methods
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
S460N - direkter Vergleich stationär-instationär
0
50
100
150
200
250
300
350
400
450
500
0 0,5 1 1,5 2 2,5 3
Dehnung [%]
Sp
an
nu
ng
[N
/mm
²]
500°
600°
700°
800°
500-stat
600-stat
700-stat
800-stat
Comparison steady state tests – transient state test
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Curve fitting using a nonlinear function
according to Anderberg (1983) and Rubert/Schaumann (1985)
fy,Θ
fp,Θ - c
εp,Θ εy,Θ εy,Θ + d
E0,Θ
EV,Θ
fp,Θ
d
a
b
c
εεεε
σσσσ
Ellipse:
cf)d(aa
bΘ,p
2Θ,y
2 −+ε−+ε−=σ
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Analytical Stress-Strain-Relationship
Fitting of parameters
according to least square
method
λδ
δε−ε+ψ=
ΘΘΘΘ )()EE(a
,p,y,V,0
λδ
λ−+−ψ=
ΘΘΘΘ )ff()EE(b
,p,y,V,0
δ
−+−ε−ε−=
ΘΘΘΘΘΘΘ2
,p,y,p,y,p,y,V )ff()ff()(Ec
λ
ε−ε−−ε−ε=
ΘΘΘΘΘΘΘΘΘ2
,p,y,0,V,p,y,p,y,V )(EE)ff()(Ed
Hilfswerte )f;f;;;E;E(f,, ,p,y,p,y,V,0 ΘΘΘΘΘΘ εε=ψλδ
mit ΘΘΘ =ε ,0,p,p E/f
Θε≤ε ,p : Θε=σ ,0E
ΘΘ ε≤ε<ε ,y,p : cf)d(aa
b,p
2,y
2 −+ε−+ε−=σ ΘΘ
03,0,y ≤ε<ε Θ : ΘΘΘ ε−ε+=σ ,V,y,y E)(f
Geometry of the ellipse:
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Examples for curve fitting
0
100
200
300
400
500
600
0 0,005 0,01 0,015 0,02 0,025 0,03
Dehnung [-]
Sp
an
nu
ng
[N
/mm
2]
200°C
500°C
700°C
mit Berücksichtigung
des Fließplateaus
S460 N
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Analytical Stress-Strain-Curve for S460 N
0
50
100
150
200
250
300
350
400
450
500
0 0,005 0,01 0,015 0,02 0,025 0,03
Dehnung [-]
Sp
an
nu
ng
[N
/mm
2] 200°C
100°C
400°C
500°C
600°C
700°C
800°C900°C
300°C
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
0
50
100
150
200
250
300
350
400
450
500
0 0,005 0,01 0,015 0,02 0,025 0,03
Dehnung [-]
Sp
an
nu
ng
[N
/mm
2]
600°C
700°C
800°C
900°C
500°C400°C100°C
200°C 300°C
Analytical Stress-Strain-Curve for S460 M
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Comparison of examples for S460 N und S460 M
0
50
100
150
200
250
300
350
400
450
500
0 0,005 0,01 0,015 0,02 0,025 0,03
Dehnung [-]
Sp
an
nu
ng
[N
/mm
2] 500°C
600°C
800°C
S460 NS460 MEC3-1-2
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Comparison of results for S460 N und S460 M
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
1,1
0 100 200 300 400 500 600 700 800 900
Temperatur [°C]
Rt2
,0 /
fy(2
0°C
) [-
]
S460 N
S460 M
EC3-1-2
• increased strength of S460 M compared to S460 N
(yielding at higher temperatures)
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Comparison to EC3-1-2
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
1,1
0 100 200 300 400 500 600 700 800 900
Temperatur [°C]
Rt2
,0 /
fy(2
0°C
) [-
]
S460 N
S460 M
EC3-1-2
• EC3-1-2 overestimates the S460 N
⇒ Will this lead to unsafe structures?
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Ultimate Load Design
Calculation of the ultimate load at various temperatures and various slendernesses.Comparison of the new model to EC3-1-2
w0
N N
q0
V0
L = s
K
Θ Θ
w0= L/1000
q0 = 8 N w0 / L2
V0 = 4 N w0 / L
Nb,fi,Θ,Rk = ?
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 20 40 60 80 100 120 140
λ = L/iy
κfi (
be
z.
au
f N
fi,8
00
°C,R
k,E
C3)
eigenes Werkstoffmodell - S460 N
Werkstoffmodell nach EC3-1-2
y
z
y
z
Calculation of Ultimate Load
800°C – Buckling perpendicular to y-axis (HEA 300)
Institute for Steel Structures and Fracture MechanicsInstitute for Steel Structures and Fracture Mechanics
Summary
• Higher strength of S460 M compared to S460 N
at 400°C ≤ Θ ≤ 900°C.
• Material laws according to EC3-1-2 are ok for
S460 M but not for S460 N.
Recommended