Petr Konečný, M.S.
Parametric study of the Safety of a Steel Bar
using SBRA Method
Structural Mechanics Division
Department of Civil Engineering
VŠB – TU Ostrava
Czech Republic
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
Parametric Study
• The safety of 26 steel bars exposed to tension and designed according to LRFD Code was investigated by students in California using SBRA Method (see Probabilistic Engineering Mechanics 14, 1998)
• The safety of the same set of steel bars designed according to Eurocode was evaluated using SBRA in 2001 at VŠB - TU Ostrava.
• The steel bars are exposed to different mutually uncorelated load effect combinations.
• Probabilities of failures Pf are compared
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
Loadings
0,0
25,0
50,0
75,0
100,0
1 6 11 16 21 26Cases
Loading. [kN]
Dead
Long lastingSnow
Wind Short lasting
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
0,000000
0,000500
0,001000
0,001500
0,002000
1 6 11 16 21 26
A [m2]
EC SBRA LRFD
G+Q G+2QG G+3Q G+4Q G+5Q G+6Q
Cross-sectional area - A [m2 ]
Cases
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
0,000000
0,000500
0,001000
0,001500
0,002000
1 6 11 16 21 26
A [m2]
EC SBRA LRFD
G+Q G+2QG G+3Q G+4Q G+5Q G+6Q
Cross-sectional area - A [m2 ]
Cases
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
0,000000
0,000500
0,001000
0,001500
0,002000
1 6 11 16 21 26
A [m2]
EC SBRA LRFD
G+Q G+2QG G+3Q G+4Q G+5Q G+6Q
Cross-sectional area - A [m2 ]
Cases
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
Probability of failure Pf
0,000001
0,00001
0,0001
0,001
0,01
1 6 11 16 21 26
Pf
EC LRFD SBRA
G+Q G+2QG G+3Q G+4Q G+5Q G+6Q
Cases
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
0,000001
0,00001
0,0001
0,001
0,01
1 6 11 16 21 26
Pf
EC LRFD SBRA
G+Q G+2QG G+3Q G+4Q G+5Q G+6Q
Probability of failure Pf
Cases
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
0,000001
0,00001
0,0001
0,001
0,01
1 6 11 16 21 26
Pf
EC LRFD SBRA
G+Q G+2QG G+3Q G+4Q G+5Q G+6Q
Probability of failure Pf
Cases
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
Summary and Observations
Both codes, LRFD and Eurocode, lead in the presented parametric study to a wide range of probabilities of failure Pf depending on the actual load effects combination.
Significant differences between the probabilities of failure, in case of the LRFD design and Eurocode design, can be observed.
More attention should be given to the substance of the load effects combination analyses in order to explain the observed differences.
Simulations based approach SBRA can serve as tool in such investigation.
Thank you for your attention
Petr Konečný, M.S.
Structural Mechanics Division
Department of Civil Engineering
VŠB – TU Ostrava
Czech Republic
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
iidi
jjdj
SBRA QQGGS var,,var,,
Loading EC SBRA1
S SSBRA1
Dead Gk 1,35 G.Gk Gd.Dead1.disLong lasting Qk1 1,5 Q.Qk Qd.Long1.disSnow Qk2 1,5 0,6 0Q.Qk Qd.Snow1.dis
Wind Qk3 1,5 0,6 0Q.Qk Qd.Wind1.disShort lasting Qk4 1,5 0,7 0Q.Qk Qd.Short1.disShort lasting Qk5 1,5 0,7 0Q.Qk Qd.Short1.disShort lasting Qk6 1,5 0,7 0Q.Qk Qd.Short1.dis
Load effects combinations S
ikiiQi
kQ.,jkjGj
EC QΨQGS .,0.1
1.1,, EC
SBRA Rest of the Rest of the
incidental loadsincidental loads1.st incidental load1.st incidental loadDead loadDead load
HistogramHistogramExtrem of the Extrem of the loadload
Incidental loadsIncidental loadsDead loadDead load
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
0 ,000001
0 ,00001
0 ,0001
0 ,001
Pf
EC3 LRFD SBRA
G +Q G +2QG G +3Q G +4Q G +5Q G +6Q
Probability of failure Pf
G
G+1×Q G+2×Q G+3×Q G+4×Q
G+5×Q
G+6×Q
Euro-SiBRAM’2002 Prague June 24 to 26, 2002
Cross-sectional area - A [m2 ]
0 ,000000
0 ,000200
0 ,000400
0 ,000600
0 ,000800
0 ,001000
0 ,001200
0 ,001400
0 ,001600
0 ,001800
0 ,002000
A [m
2 ]
EC3 SBRA LRFD
G +Q G +2QG G +3Q G +4Q G +5Q G +6Q
G G+1×Q G+2×Q G+3×Q G+4×Q
G+5×Q
G+6×Q