Critique of Lower-Margin Equations in Concrete Design Codes and of Their Effect on Structural Safety Software

Abstract It is generally agreed that engineered structures, whether bridges or aircraft, should be designed to have failure probability no higher than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="10 Superscript negative 6" display="inline" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:math> per lifetime. The safety analysis of concrete structures based on the current design codes cannot guarantee meeting this goal. While sophisticated probabilistic models have been developed to deal with the randomness of loads, the uncertainty of material failure has been relegated to empirical understrength (or capacity reduction) factors. The problem is that the design equations of all design codes have traditionally been formulated as lower-margin equations, set at the lower margin of the test data cloud (which lies, depending on structure size, 25% to 40%, below the data mean, in the case of shear strength of RC beams). The load factors are applied to these lower-margin equations while the offset of the mean and the variance of the database remain buried in the code committee documents. Moreover, probabilistic modeling of the mechanics of failure processes, which determines structural strength, has been incorrectly employed, and the probability density function (pdf) required to extrapolate to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="10 Superscript negative 6" display="inline" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:math> has been chosen arbitrarily, often as the lognormal pdf for mathematical convenience. Although the lognormal pdf may be an acceptable approximation for a database of concretes with very different strengths, it is shown to be physically impossible to model the strength distribution of one-and-the-same concrete (i.e., a concrete of the same design strength and composition). These traditional concepts have rendered the current failure probability predictions of the structural safety and reliability software for reinforced concrete structures meaningless. However, experience of many decades shows that the frequency of structural failures has not been excessive. The explanation is that many designs must have had excessive safety margins, thus becoming uneconomical, while the benefit of sophisticated commercial software applicable to the randomness of applied loads gets wasted. A sine qua non of the remedy is that the values of the coefficient of variation of the database and of the offset of the database mean from the code equation accompanying each design code equation must be revealed. This could be done in the code Commentary.