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safety in structural design Notes-Part1-2012.pdf

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McMaster University
Civil Engineering
Ghani Razaqpur

Safety in Structural Design There are three main reasons for including safety considerations in structural design: ▯ The strength of materials or structural components may be less than expected ▯ Overloads may occur ▯ The consequences of failure may be very severe Methods of Defining Safety in Structural Design There are two basic methods: (1) Factor of Safety or Working Stress Design Method Factor of Safety = (Ultimate Resistance/ Service Load) = R/S This assumes that both resistance R and load S are well defined, but in fact both the resistance and load of structures vary. Resistance Variation The resistance R varies because it is affected by: ▯ Variations in materials strength (variations in composition, microstructure, quality control, in-situ versus laboratory conditions, variations in environmental and operational conditions, variations caused by testing methods, presence of residual stresses) ▯ Variations in member sizes and geometry ▯ Variations in workmanship and type of failure ▯ Variations due to simplified assumptions in design, Each of these may not affect equally the strength of all types and sizes of members, but nevertheless they are there. The following histogram shows typical variation of the yield strength of structural steel with mean strength of 394.4 MPa. Note that strengths as low as 338 and as high as 487 MPa are reported. Therefore, the use of the mean value does not ensure a safe design. Variability of Steel Yield Stress ▯ f' 2▯ c 2▯ ▯ ▯ Variability of Concrete Compressive Strength Load Variation The load S is difficult to determine with certainty because in real life applied loads are not constantly controlled; therefore, their magnitude and distribution can vary widely. Live loads will have higher variability than dead loads. Structures cannot be designed for unreasonably high loads nor can material strength be assumed unreasonably small despite a small probability of occurrence of either event during the design life of a structure. Designing for such extreme values will make structures costly. Since neither R nor S can be precisely and uniquely determined, the factor of safety concept as defined earlier lacks clarity. To clarify the matter, one may define F.S. as _ R Central Factor of Safety = Mean Resistance / Mean Load = _ S or Rd Nominal Factor of Safety = Design Resistance/ Service Load = Sd where R ds the capacity computed according to the design code and S ds the service load given in the local or national design (building, bridges, etc.) code. For example, in concrete design, the factor of safety was traditionally defined as: F.S. = Yield Strength of Reinforcement / Allowable Steel Stress or F.S.= Concrete Strength/Allowable Concrete Stress Drawbacks of Factor of Safety Method ▯ It does not account adequately for the variability of loading and resistance ▯ It does not account adequately for variations in loadings which increase at different rates or have different signs ▯ It does not determine the ultimate load capacity ▯ It does not rationally consider consequences of failure For these reasons, this format was abandoned in Canada in the seventies and was replaced by the limit states design format. Limit States Design Limit State: when a structure or element becomes unfit for its intended use, it has reached a limit state. Limit states design process involves: ▯ Identification of all potential modes of failure (limit states) ▯ Determination of acceptable levels of safety against occurrence of each limit state ▯ Consideration by the designer of the significant limit states Important Limit States in Canadian Standards ▯ Durability: The structure should withstand environmental effects without premature and excessive deterioration. ▯ Fire resistance: The structure must have sufficient fire resistance as specified in governing building codes ▯ Ultimate limit states: These refer to the structural collapse of structural components or entire structure. Due to the serious consequences of such collapse, it must have a very low probability of occurrence. The limit states covered under this category include: ▯ Loss of equilibrium (tipping, sliding, or other rigid body movement ▯ Rupture (failure of part or entire structure) ▯ Progressive collapse (Localized failure in one part leading to the overload of other parts and to complete collapse of the structure). ▯ Formation of plastic mechanism (Development of adequate plastic hinges, leading to an unstable structure) ▯ Instability ( Loss of equilibrium caused by excessive deformations or high loads, such as buckling) ▯ Fatigue (Fracture of members due to repeated cycles of service loads) ▯ Serviceability limit states: Failure involving disruption of the function or normal operation of a structure. Since this does not involve loss of life, a higher probability of failure may be acceptable. The limits covered by this category are: o Excessive deflections o Excessive crack width o Uncomfortable vibration and movement ▯ Special limit states: This deals with limit states which lead to damage or failure due to abnormal conditions or loadings. This may include structural effects of vehicular or aircraft collision, or of explosion as well as long-term physical or chemical instability. Probabilistic Basis of CSA Limit States Design Format Let R denote the resistance of a member and S the load effects on the same member. Let R and S have probability distributions as shown below, then the safe and unsafe load and resistance combinations can be established using the given probability distributions. fS(s) S ▯ S, R S Probability Distribution Functions for Load S and Resistance R If R ▯ S, safe If R < S unsafe Let Y= margin of safety = (R-S), and its probability distribution function is plotted below. The total probability of Y < 0, is the shaded area in the figure below. The probability of failure,fP , is the chance that a certain R and S combination will give a negative Y value, i.e. f = probability of (Y <0) P f shaded area / total area under the curve ▯▯ y ▯ Proofability Distribution Y 0 + _ Let the function Y have a mean of Y and a standard deviation ▯ , from the above figure y we can see that _
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