Download Full Text (1.3 MB)


Background: The method of designing partially composite sandwich wall panels (SWPs) relies strongly on the use of percent of composite action. Calculating these values proves to be a complex and virtually inaccessible process for practicing engineers, resulting in the reliance on proprietary software or connector-system manufacturers for the necessary values. We simulated percent composite action data, including several relevant variables, to examine the relationship and determine if simple and accessible methods of calculation could be created. Methods: Code from collaborating engineers used to calculate percent composite action with the Iterative Sandwich Beam Theory (ISBT) method was translated into R, a free software. Large data sets (five million observations each) were simulated using the ISBT method, including eight potential explanatory variables and two response variables, percent of deflection composite action (Def.%.Cmp) and percent of cracking composite action (Crk.%.Cmp). Data sets were created for two possible explanatory variable ranges, the “common” range and the full theoretical range. Data were analyzed and cleaned, and traditional variable selection techniques were applied. Ordinary least squares (OLS), quantile regression, and pruned regression trees were fit to the data in an attempt to provide simplified models for calculation. Results: The simple regression methods were unfit for the data sets simulated using the full theoretical ranges for explanatory variables, which exhibited very loose relationships between explanatory and response variables, so the main analysis was run for the common range data sets. Strong relationships were found between predictor variables wall height in inches (variable L), average elastic stiffness of the connectors (kip/in) (variable K) and percent composite action response variables. We found models were most effective with transformations for the response variables ((Def.%.Cmp)1.5 and (Crk.%.Cmp)2). The mean relative absolute error rates were high for OLS, quantile models and traditional pruned regression trees (Def.%.Cmp min.=0.302 max.=0.490, Crk.%.Cmp min.= 0.246 max.=0.490), but the median relative absolute error rates were much lower (Def.%.Cmp min.=0.0744 max.=0.233, Crk.%.Cmp min.= 0.0605 max.=0.156). This indicated inconsistency in prediction; we found that all of the simple regression models tended to overestimate the values of percent composite on the lower and upper tails of the data, indicated by the predicted/observed ratios being over 1. Pruned regression trees were used to estimate coefficients for K, by producing regression trees for (Def.%.Cmp)1.5/K and (Crk.%.Cmp)2/K. Using these new regression trees, we reduced our error drastically compared to our linear models (Def.%.Cmp mean absolute prediction error=0.104 median absolute prediction error=0.0772, Crk.%.Cmp mean absolute prediction error= 0.171 median absolute prediction error =0.0663), and our prediction to observation ratios reduced to roughly 1, indicating less severe overestimation. Conclusions: We found the full theoretical range of variables to produce data too unstable for simple regression methods. Variables L and K were found to be significant and useful in predicting percent composite action. The implemented regression methods were not able to be produced at this stage of research to be of practical use, either from being too inaccurate or too complicated for our purposes. However, the ISBT method for calculation is now available in freely software, allowing for accessibility for practicing engineers.

Publication Date



Logan, UT


sandwich wall panels, concrete, composite action


Statistics and Probability

Creating Transparent and Accessible Methods For Approximating the Composite Strength of Concrete Sandwich Wall Panels