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3 Tensile Data Analysis 3 A Note on Importing Data The files generated in the lab are tab-limited so that they easily paste into the worksheets. Importing data using Data>Get External Data> is not required. You should have something similar to: The EXCEL workbook Steel6150Tens.xls containing a completed example is located in the HELP folder. Formulas and References Relative and Absolute Formulas start with =. Remember that when a formula is copied, the cell addresses change. This is one of the most powerful features of spreadsheet programs. When the formula in C32, =A32 * B32, is copied to cell C33, it becomes =A33 * B33, and so on

4 Tensile Data Analysis 4 down the column. The value in column C is the product of the values in columns A and B in the same row. This task is an example of a relative reference; wherever the cell is copied, the result is the product of the values in the two cells to the left of it. Often, an operation is performed on many cells with a constant value. To compute engineering stress, the load in each row is divided by the original cross-sectional area. One method (not recommended) is to type the calculated area in the formula. It is a better technique to use the address of the cell that contains the area data. To make a reference absolute (constant), place \$ in front of the column and row. For the example above, =\$A\$32 * B32 copied to C33 results in =\$A\$32 * B33. This feature may be used efficiently in our example. First compute the cross-sectional area and make the cell address a constant divisor in the formulas employing the \$ designations. Another way to specify a constant is to name the cell. This is especially convenient when many different data sets are being analyzed. In the current sheet, locate Specimen diameter: in Column A (A12). Highlight the adjacent cell in column B (B12). From the menu bar (top of screen), choose Insert>Name>Define. Excel may suggest a name based on column A. Since there may be more than one 6150 steel specimen, call this one Stl6150a and add diameter. Name: Stl6150a_diameter (highlighted); cell address = B12 in the current Sheet (bottom of the Define Name frame.) (Note: Names are not case sensitive.) Click OK. Note that the Name Box on the formula bar now displays the name rather than the column and row.

5 Tensile Data Analysis 5 Accessing the Define Name window is the only way to delete names and edit their ranges. Names may also be entered on the Formula Bar. The final diameter is displayed in cell B26. The formula bar displays the cell address in the Name Box and contents. Type the desired name in the Name Box and press Return. An entire range of cells may be highlighted and assigned a name in this manner. Names and their ranges may not be edited using this technique. NOTE: Names must start with a letter or underscore, but may not be the same as a possible cell address. The most recent versions of EXCEL designate cell addresses using up to 3 letters and 7 digits, e.g., abc Therefore, Stl6150 and Al2024 are invalid names. Some valid alternatives are Stl6150a, _Stl6150, Steel6150, Stl_6150, and Al_2024. Pi The constant, pi, is PI(). Note the empty parenthesis. A good technique is to enter functions in lower case. If the formula is correct, EXCEL converts it to caps. If not, it remains in lower case indicating an error. Area Arrow right ( ) to cell D12 and type in Area:. Set this label to align right with Format>Cells>Alignment, Horizontal: Right. In column E enter the formula for area, πd 2 /4. Start the formula with = pi() *. To enter the diameter, click on the cell you just named (Stl6150a_diameter). Square with ^2, then divide by 4 ( /4 ). The result is: = PI() * Stl6150a_diameter^2 /4 Name this cell (E12) Stl6150a_area. Type the units mm^2 in column F. The use of names may appear to be trivial here. When large amounts of data are compiled, names can be very useful. For example, data, including diameter, from 15 tests could be summarized in a table on the 17 th spreadsheet of the workbook. For the test 6150a, simply enter the formula =6150a_diameter. The process may be streamlined with database functions, so that the diameter for each test will (nearly) automatically be reported in the table. Your completed worksheet can be copied as a new worksheet, and then data from another test can be pasted. Since the data formats are the same, the new diameter is in the right place and the corresponding area and other formulas are immediately recalculated. Now stresses can be calculated. Find the label Time (sec) in column D. On the same row, in column E (E31), enter Stress (MPa).

6 Tensile Data Analysis 6 Definition of units of Stress 1 Pa = N/m 2 Or, 1 MPa = 10 6 Pa 1 mm = 10-3 m 1 mm 2 = 10-6 m 2 1/ mm 2 = 10 6 /m 2 Therefore, Stress (Pa) = Stress (MPa ) = Load (N ) Area (m 2 ) Load (N ) Area (mm 2 ) Note that the test load (column B) data are recorded in units of kn (1000N). Therefore, Enter the formula (Stress = ) Stress (MPa ) = Load (kn ) Area (mm 2 ) * 1000 In the Stress column (E), highlight the cell below Stress(MPa) (E32). Start the formula with =. In the same row, click on the load value (B32). Then type * 1000 /. Click on the cell with the area (Stl6150a_area). For the cell E32, the formula is: = B32 *1000 / Stl6150a_area Stl6150a_area is an absolute reference (constant). The load (Column B) is a variable. Copy the formula to derive stress from the load data Copy the formula in E32 down the column to the last row of data. One way to copy the formula down the column is to highlight the cell to be copied (E32), and then move the cursor to the bottom-right corner of the cell. Note that a + sign appears. You may copy the formula by dragging this corner down the column. That is a long drag! There must be a better way! When the + sign appears, double click on it. The column will be filled until an empty cell in column B is encountered. Scroll down the column with the down arrow ( ). Note the display of the formula for different cells in the formula bar. Save your work. Plotting the Data There are a lot of numbers organized in columns. A picture is worth a thousand words or a whole table of numbers! Next, we will create a graphical image of the data. In EXCEL, plots (graphs) are called Charts. (Perhaps, because the spreadsheet is rooted in accounting?!) Select the two columns of data. Click on the letter at the top (column label) of the strain column to highlight the entire column (C). Press and hold control [command ( ) for Mac], then click

7 Tensile Data Analysis 7 the top of the stress column (on the E ). Both columns are selected and highlighted. (Column D is not selected.) Depending on the version, click on the Gallery icon, then Charts or select Chart Wizard on the toolbar. Choose XY (Scatter), then select points only. [NOTE: Line charts are designed for equally spaced data. Do NOT use here!!!]. The details of your display may be different from this presentation. Note: In general, use only points with no lines for experimental data and lines with no points for correlations and theoretical constructions. If you get only a plot, right-click on the chart and then Select Data. Click Next> if available. The Range contains ALL of the charting (plotting) data. Series contain data for individual plots. For this test, the Series in: choice is Columns. The initial selection was all of column C and all of column E, so the range starts at row 1. Useful data start at row 32. In the Data Range box, change the \$1 references to \$32 for both C and E to get: ='6150Tens'!\$C\$32:\$C\$404,'6150Tens'!\$E\$32:\$E\$404 The X and Y scale ranges will adjust automatically. Click Next> if available. Enter title (Steel 6150 Stress-Strain) and axis labels (Strain and Stress (MPa)). Note that a preview appears in the window. Press Next>. Have the chart appear in the same worksheet. Press Finish>, then Save the workbook. On recent versions, changes are performed using the Formatting Palette. If the palette is not visible, select View on the top menu bar, then Formatting Palette. Chart Options and Chart Data are the most useful. It s okay, but it needs work. Save! Extraneous Data There is a point around Strain = 0.08, Stress = 0 that does not belong to the test. Between the time that the test computer requested data from the testing machine and the time the machine reported data, the specimen failed. This point is not part of the test and must be eliminated. Eliminate the point by the deleting the data in the cells on row 404 or delete the entire row. To find the last row, click on a cell within the recorded stress-strain data, and then press End, then arrow down ( ). The last data entry in the column is highlighted. Delete the data or the entire last row. Ascertain that the point has vanished from the graph.

10 Tensile Data Analysis 10 References S. C. Block, EXCEL for Engineers and Scientists, 2nd Ed., Wiley & Sons (New York), J. P. Holman, What Every Engineer Should Know About EXCEL, CRC Press (Boca Raton), Credits Originally authored as A little help handout by Jessica Crompton, BSME 2002, MS September 9, 2002.

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