# Error Statistics for Reinforced Concrete Beams

*by*Theodore Zsutty,

**Serial Information**:

*Journal of the Structural Division*, 1963, Vol. 89, Issue 6, Pg. 235-270

**Document Type:**Journal Paper

**Abstract:**

The error statistics that describe the probability distribution function of the ultimate moment resistance of under-reinforced concrete beams are estimated by multiple, linear, regression analysis. Data from 109 specified beam tests are analyzed in order to produce a median prediction equation with a known probability distribution of equation error. This median prediction is compared with the existing design procedure equation to show general agreement in functional behavior. The comparison also permits a calibration of the relative prediction capabilities of each equation. The particular mathematical form of the median prediction equation allows the computation and inclusion of workmanship error in the variance of the resistance of veams in actual structures. The computation of workmanship error variance requires the availability of coefficients of variation of in-place beam properties about specified median values. It is expected that future quality control and workmanship surveys will provide this statistical information. While certain test data inconsistencies, sampling errors, and uncertainty of workmanship error values make it necessary to term all resulting numerical values as preliminary estimates, the regression analysis procedure provides a means of identifying, organizing, and combining the individual components of strength prediction error. The final log-normal error statistics are used to compute an under-strength factor that will provide for a selected high probability of safety under known load conditions.

**Subject Headings:**Reinforced concrete | Concrete beams | Regression analysis | Probability | Probability distribution | Load and resistance factor design | Errors (statistics) | Moment distribution

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