CE 115 Introduction to Civil Engineering Graphics and Data Presentation Application in CE Materials Dr. Fouad M. Bayomy, PE Professor of Civil Engineering University of Idaho Moscow, ID 83844-1022
Graphics and Data Presentation Application in CE Materials Objective The objective of this module is to introduce students to basics of data presentation using a computer graphic tool such as MS-Excel. It is assumed that students have some knowledge of how to use the MS-Excel spreadsheet software. Why Do Engineers Need to Present Data? A Picture is better than a thousand words, it is that simple. Let me take an engineering example where a CE material engineer may need to understand the effect of age on the increase of strength of Portland cement concrete (PCC) mixtures. All of us know that when you place concrete to build a driveway, you will have to block the driveway until you make sure that the concrete of the driveway has gained sufficient strength to support vehicles. Let us investigate the gain of strength with time. The following table (Table 1) shows data of a PCC mix. Table 1 Gain of Strength with Time Time, day Compressive Strength, psi 1 619 3 1374 7 2111 14 2642 28 3022 56 3256 84 3342 112 3387 140 3415 180 3439 200 3448 Looking at the numbers in Table 1, one can see that strength does increase with time. But that is all. To understand better the rate of strength increase and the critical time(s) that may have more profound effect on strength, it would be better to plot the data to be able to visualize the information. The following graph, Figure 1, shows same information on a graphical form. Comp. Strength, psi 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0 50 100 150 200 Time, day Figure 1 Gain of Compressive Strength with Time From the graph, an engineer can predict that after about 90 days, the concrete does not gain much strength as it does in the first three weeks. If the vehicles operating on the driveway will impose stresses about 2500 psi, then the engineer may recommend that at least the driveway shall blocked to traffic until at least 10-days to allow the concrete to gain such level of minimum
required strength. This simple example signifies the importance of presenting the data in a graphical form. While the table and the graph have same data, the graph makes it more visual and allows the engineer to interpolate and predict the in-between values. Types of Graphs There are several types of graphs that engineers use for data presentation. The following is a list of most common forms. (Students should list more graph types as they find in Excel Chart option) Bar / Column graphs Line graphs x - y plots 3D effects Bar / Column Plots In the following we will do an example of each type of the mentioned chart types. Let us create the data table as shown in Figure 2. Steps: 1. Open the Microsoft Excel spreadsheet software. 2. In columns A and B insert the data entry in columns A and B as shown in Figure 2. 3. Select the data range by highlighting the range (A1:B7) as shown in Figure 3. 4. With range selected, click on the chart wizard icon or by selecting the chart from the Insert menu. 5. Follow the windows instructions to create a column chart as shown in Figure 4. Let us now try to present the data in another graphical form. After spending some time trying to present the data in Figure 2 in other forms, answer the following question: Q: What are other types of charts that you can use to present the data? A: Q: Can you use the x-y scatter plot to present the data in Figure 2? Yes or No Why? A:
Figure 2 Strength Data in an Excel sheet Figure 3 Selecting the Data Range
Figure 4 Bar Chart for the Data in Range A2:B7 X- Y Plots: This type of data presentation is suitable for continuous functions. For example, the increase of strength with time, as presented in Figure 1. The increase of a person weight with the amount of food he/she eats, the increase or decrease of electrical bill with the weather temperature. This type of information is not discrete. In the Example of Figure 2, the strength of each mix is totally independent of other mixes. Thus, the bar or column graph was used to depict the various strength values of these mixes. It does not matter which mix we plot first. Thus, the plot does not depend on the order where to replace the mix name on the x- axis nor the value. The Excel software will place these bars at equal distances, just for convenience. The name of the mix, whether you call it A or any thing else, it will not affect the plot you get. Let us now work with the example that was presented in Figure 1. Open a new sheet and type in the data given in Table 1 in columns A and B. See Figure 5. Select the data range A2:B14 (Columns A and B) and while selected, click the Chart Wizard icon. Follow the instructions of the Excel Windows to create an x-y plot of the Strength vs. Time relationship as shown in Figure 5.
The plot shown is done using linear scale on both x and y axes. Therefore, sometime this may not be convenient since the change of strength is so rapid in the early days. To expand that period, we may choose to use Log scale on the x axis instead. This will allow us to flatten the curve in the early days as shown in Figure 6. Figure 5 X-Y Plot for Strength-Time Results Figure 6 X-Y Plot of the Strength-Time Results (semi-log plot)
Data Fitting and Regression Analysis Another example of using the x-y plots, is representing the data in a format so that we can fit simulate its physical or mechanical behavior by a mathematical equation. It is typically referred to as a regression model or regression equation. This helps engineers to determine, experimentally, material properties that describe certain phenomenon of material behavior. The following example is for modeling the creep behavior of an engineering material. Creep is a very slow process in which a material continues to deform with time under constant stress. Materials that exhibit creep deformation are time-dependent. The relationship that governs the progress of creep deformation, ε c with time of loading (t) can be written in the form: ε c = α (t) β.. (1) Where, α and β are called creep parameters. Once the engineer determines the creep parameters for a given material, he can predict the creep deformation at any time. The data in columns A and B in the Excel sheet shown in Figure 7, is obtained from a creep test performed on a polymer material. The deformation is represented in creep strains (deformation per unit length, mm/mm). The chart in Figure 7 shows the relationship on a linear scale. The figure shows the creep deformation progress is fast at initial times and slows down until it reaches a steady state development. Figure 7 Creep Deformation with Time
The data can be represented on a log-log scale, in which a power relationship transfers to a linear relationship by taking the logarithmic values. In this case, equation 1 can be written in the form Log ε c = Log α + β.log (t).. (2) So, plotting the same data on log-log-scale allows for determining the creep parameters α and β where α is determined from the intercept of the y-axis at t=1, and β is the slope of that linear relation on log-log scale chart, as shown in Figure 8 From the shown fitted data, it is found that the creep parameters for this material are: α = 400 mm/mm β = 0.15 Figure 8 Creep Deformation with Time (Semi-Log)
Take Home Quiz Do this quiz and submit it to the course coordinator (Dr. Richard Nielsen) on the date indicated in the course schedule Purpose: Problem: Data: Synthesizing how to use graphics to support your engineering decisions. A civil engineering material engineer designed a concrete mix to be used in a floor of an industrial store house where heavy machinery is to be transported. Due to the expected heavy loads, the engineer decided to modify the concrete mixture by adding steel fibers to it. One of the main challenges to design the mix was to determine how much steel fibers that should be add to achieve the required increased strength without detrimental effect on the mix? Therefore, a laboratory program was established to test mixes with different steel fiber contents to answer this question. Results are listed below. Compressive Strength of Concrete Mixes Normal Steel Fiber Added Mix Time, 0 2% 4% 6% 8% 10% Days 7 2111 2462 3166 3869 3377 2814 14 2642 3082 3962 4843 4226 3522 28 3022 3525 4532 5540 4835 4029 90 3354 3913 5031 6149 5366 4472 180 3439 4013 5159 6306 5503 4586 Required: Present the data in a suitable format so that you are able to reach an engineering decision on how much steel fiber you should add if the minimum required 28-day strength is 5000 psi. Compare the 28-day strength of all mixes. How does the time affect the increase in strength of these different mixes? Hints: To answer the main question, plot the 28-day strength versus steel fiber content for all mixes. To determine the effect of time, plot the strength versus time for all mixes. Questions: Contact Dr. Fouad Bayomy, BEL 131