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