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 P f are compared

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Loadings Dead Long lasting Snow Wind Short lasting

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Cross-sectional area - A [m 2 ] Cases

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Cross-sectional area - A [m 2 ] Cases

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Cross-sectional area - A [m 2 ] Cases

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Probability of failure P f Cases

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Probability of failure P f Cases

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Probability of failure P f 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 P f 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 Loading histograms Histogram Short1 Histogram Long1.dis Histogram Snow1.dis Histogram Dead1.dis Histogram Wind1.dis

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Load effects combinations

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Design of the shapes A EC (m 2 ) Cross-sectional area is designed by Anthill TM program for design probability of failure P d = 0, A SBRA (m 2 ) Histogram Area-S Histogram T235fy01 [MPa] Histogram T235fy01 [MPa] Histogram Area-S

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Assesment by SBRA Reliability function : RF = ( R - S ) Probability of failure P f Is determined by Anthill TM program for 2 mil. simulation R – tensile bearing resistence [kN] S – load effects combinations [kN] Probability of failure : P f (RF<0) < P d

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Warp Inputs Designed shapes Probability of failure Pf Conclusions Snímek 16

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Loading ECSBRA 1   SS SBRA 1 DeadG k 1,35  G.G k G d.Dead1.dis Long lastingQ k1 1,5  Q.Q k Q d.Long1.dis SnowQ k2 1,50,6  0  Q.Q k Q d.Snow1.dis WindQ k3 1,50,6  0  Q.Q k  Q d.Wind1.dis Short lastingQ k4 1,50,7  0  Q.Q k  Q d.Short1.dis Short lastingQ k5 1,50,7  0  Q.Q k  Q d.Short1.dis Short lastingQ k6 1,50,7  0  Q.Q k  Q d.Short1.dis Load effects combinations S EC SBRA Rest of the incidental loads 1.st incidental load Dead load Histogram Extrem of the load Incidental loads Dead load

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Probability of failure P f G G+1×Q G+2×QG+3×Q G+4×Q G+5×Q G+6×Q

Euro-SiBRAM’2002 Prague June 24 to 26, 2002 Cross-sectional area - A [m 2 ] G G+1×Q G+2×QG+3×Q G+4×Q G+5×Q G+6×Q