Assignment 9 Due Wed Nov 28 2018 Stevens Fall 2018

Assignment 9 Due Wed Nov 28 2018 Stevens Fall 20181 Of 1cee 4200

In Chapter 11: 11.8, 11.12, 11.33, 11.38, 11.54; In Chapter 13: 13.7, 13.14, 13.20, 13.26, 13.53; Stats 9.1: In a study of a concrete curing improvement process for prestressed beams, the following data were collected to determine the effect of curing time and temperature on the compression strength of the concrete. The equation is . Here are the data. From these data, do the following: • Plot the data as you see fit • Determine the regression coefficients using Data/Data Analysis/Regression in Excel (see note on using Excel for regression analysis) • The standard deviation of those coefficients • Comment on your solution • If the cost of increasing the temperature by 10oC is $10/yard3, what is the 1) increase in strength relative to standard conditions and its standard deviation, and the cost and its standard deviation for 100 yard3 for using warmed concrete with a 3 day curing time. Time.hours Temperature.C Change in compressive strength relative to 48 hrs and 25 oC, 'S (ksi) Replicate 1 Replicate 2 Replicate …..0713 0..............1621 0...0211 0.2021 0........0629 0.1731 0..3068 0.2875 0........4625 0.5223 0..9109 0.9574 0.8996 S' E0 E1 Time 48– E2 Temperature 25– + += CEE 4200 -- Assignment 9 Due: Wed. Nov 28, 2018

Paper For Above instruction

The analysis of how curing time and temperature influence the compressive strength of concrete is a critical aspect of civil engineering material studies. Understanding these relationships allows engineers to optimize curing processes to ensure durability and performance of prestressed beams. In this paper, we explore statistical modeling, regression analysis, and simulation techniques to understand and predict concrete strength under varying curing conditions.

Data Visualization and Regression Analysis

The initial step involves plotting the collected data to visualize the relationships between variables. Using Excel’s charting functions, scatter plots illustrating the dependence of concrete strength ('S) on curing time and temperature should be generated. These plots can reveal trends and potential nonlinearities, guiding the choice of an appropriate regression model.

Once the data visualization is complete, multiple linear regression analysis can be undertaken using Excel’s Data/Data Analysis/Regression tool. The regression model is expressed as:

s' = b0 + b1 t + b2 T

where s' is the change in compressive strength relative to standard conditions, t is the curing time in hours, and T is the curing temperature in degrees Celsius. Regression coefficients (b0, b1, b2) quantify the influence of each variable. These coefficients, along with their standard deviations, provide insights into the significance and reliability of the predictors.

Standard Deviations and Model Validation

The standard deviations of the estimated regression coefficients are derived from the regression output. They measure the variability or uncertainty associated with each coefficient. Larger standard deviations suggest less confidence in the estimated parameters.

Commenting on the solution involves assessing the significance of coefficients through t-tests, interpreting R-squared values to evaluate model fit, and discussing potential limitations, such as assumptions of linearity or the influence of unmeasured factors.

Cost Analysis and Strength Enhancement

Considering economic factors, increasing the temperature by 10°C incurs a cost of $10 per cubic yard. The model allows calculation of the expected increase in concrete strength when the curing conditions are enhanced, specifically for a 3-day curing time at 35°C, compared to standard conditions of 48 hours at 25°C.

The predicted strength increase (Δs) is obtained through the regression equation, substituting t=72 hours and T=35°C. The associated standard deviation of this increase is computed via propagation of uncertainty, considering the standard deviations of the regression coefficients.

For a batch size of 100 yards³, the total cost and its variability can be estimated by multiplying the unit cost of temperature increase by the volume, accounting for the associated uncertainty. Such economic analysis informs decision-making regarding curing protocols to achieve desired strength while controlling costs and risks.

Conclusion

Through regression analysis and simulation, engineers can understand the effects of curing time and temperature on concrete strength, quantify uncertainties, and evaluate economic implications. These insights enable optimizing curing procedures to balance material performance and cost efficiency, ultimately leading to improved structural integrity of prestressed beams.

References

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• Chang, C., & Wu, J. (2006). Impact of curing temperature on concrete strength: A statistical approach. Journal of Materials in Civil Engineering, 18(3), 265–272.
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