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  • 1.  Factors affecting Safety Index

    Posted 01-28-2019 01:59 PM
    Edited by Tirza Austin 01-28-2019 02:00 PM
    Hi Everyone.

    I want to know your opinion about the factors which affect suggesting a value for Safety Index by a Code.

    Best regards,

    Rasoul Eskandari S.M.ASCE


  • 2.  RE: Factors affecting Safety Index

    Posted 01-31-2019 03:44 PM
    Edited by Tirza Austin 01-31-2019 03:43 PM
    In the United States (at least in building structures), we use slightly different terminology. The factors of safety are based on risk category. Risk category is essentially how important the building is to public health, welfare, and safety (i.e. a hospital has a higher risk category than an unoccupied warehouse). Below is an article that explains these.

    I also found this thread which discusses the used of the "safety index" in Europe based on the Eurocode (I did not fact check, only posted it for reference purposes): https://www.researchgate.net/post/How_can_I_measure_a_reliability_index_for_civil_engineering_structures

    Stephanie Slocum P.E., M.ASCE
    Engineers Rising LLC

  • 3.  RE: Factors affecting Safety Index
    Best Answer

    Posted 02-01-2019 10:18 AM
    Dear Rasoul,

    I'm glad you asked this question. It's an important topic that Engineers need to know about its rigorous background.
    Load Factors are calibrated based on statistical analysis of probability of failure vs. a target safety within financial limitations. I had the opportunity in working with the team that did load factors study for subway stations design in Toronto, back in 1994. The Rapid Transit Expansion Program (RTEP) in Toronto, commissioned us to make a load factors study specifically tailored to subway stations, since neither the bridge code nor the building code seem to represent deep underground stations. Our team included ANDRZEJ S. NOWAK, an expert on load factors, who did earlier calibrations of other codes in USA and for Ontario Bridge Highway Design Code (OHBDC, 1991); other members of the OHBDC calibration team as well as several experts from the concrete industry and academia. Under Nowak's direction, we studied a large number of existing subway structures, of various locations and dates of construction. Parameters related to loads and to resistance were measured for variances: soil cover, soil properties, water levels, concrete thicknesses, concrete strengths (cores taken), structural analysis and design performed. Statistical analysis carried out to find the normal distribution curves for load effects (Q). And resistance (R) for various load factor possibilities such that the safety margin (R-Q) should meet a Reliability Index Beta that is determined based on how critical the structure is vs. cost of reaching that level of reliability. Beta is the number of standard deviations away from failure. A larger Beta requires increasing R, which requires larger load factor; and vise versa.

    From "Calibration of the Ontario Highway Bridge Design Code 1991 edition" by Nowak and Grouni, 1993; available online at: http://www.nrcresearchpress.com/doi/10.1139/l94-003#.XFJ-Hunsbrc

    The following table, from the above reference, lists the probabilities of failure vs. Beta:

    A summary of design philosophy is presented on The Canadian Highway Bridge Design Code, Commentary on CAN/CSA-S6-06, C1.4.2.1. 

    CHBDC load factors are based on Beta = 3.5 corresponding to Pf = 1/4300

    Building codes might be using Beta = 4.0 corresponding to Pf = 1/31,500 given that early signs of structural distress in buildings might not be as visible as it is for bridges.

    As to subway stations, it was suggested at one point to use Beta = 4.25 corresponding to Pf = 1/100,000 because of the difficulty and extra cost involved in subway structure. I think it was settled at Beta = 4.0. However, even if its Beta was the same as that of the building code, its required load factors can be different due other considerations.

    The determination of Beta, or Pf relies not only on Engineers but on practical and economic considerations. The pyramids of Egypt, probably have an infinite Beta as they are supposed to stay for ever, even if they took tens of thousands of laborers for a whole generation. We don't have that luxury; we have to work hard at calibrating our load factors!

    Neil Kazen, M.Eng., M.Sc., P.Eng.
    Retired Structural Engineering Manager, Transportation Division, SNC-Lavalin
    Toronto, Ontario, Canada

  • 4.  RE: Factors affecting Safety Index

    Posted 02-06-2019 09:58 PM
    Edited by Tirza Austin 02-06-2019 09:57 PM
    Following up on the discussion so far.  In Australia, Europe, Russia and Canada there are standards explaining the basis of the probabilities behind the country standards
    AS/NZ 1170.0,  EN 1990,  CAN/CSA S408, GOST 27751-2014

    The greatest uncertainty I have found in reliability analysis is the ability to provide better methods of analysis. With the more common use of non-linear analysis (AISC Direct Analysis Method ) Structures that we once thought to be safe have been found not to be safe.  Sometimes ignorance is dangerous.

    David Thompson P.E., M.ASCE
    KTA Structural Engineers Ltd.
    Calgary AB
    (403) 246-8827

  • 5.  RE: Factors affecting Safety Index

    Posted 02-11-2019 12:22 AM
    Edited by Neil Kazen 02-11-2019 01:46 AM
    Thank you David for highlighting the none-linear analysis impact. As design becomes more complex, the probability of error increases. That requires recalibration of load factors.

    As an example, new structural analysis software capabilities are allowing soil-structure integrated analysis; soil resistance to lateral side sway in underground structures is included in the analysis. This none-linear analysis allows for major savings in structural design. But the fact that it relies on more analysis of soil, adds extra layers of calculations, where each layer has its own uncertainty, that should be factored in the probability analysis mentioned in my previous message. The load factors need to be re-calibrated accordingly.

    Neil Kazen, M.Eng., M.Sc., P.Eng.
    Retired Structural Engineering Manager, Transportation Division, SNC-Lavalin
    Toronto, Ontario, Canada