Objective


Sometimes some calculations are implemented as basic code. Mathcad is a useful tool to translate and analyze the behavior of these calculations. The objective of this worksheet is to show how to implement a simple but traceable component for using basic language inside Mathcad.

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This month, we will look at the format required to solve a differential equation or a system of differential equations using one of the command-line differential equation solvers such as rkfixed, Rkadapt, Radau, Stiffb, Stiffr or Bulstoer.

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Mathcad text styles make it easy for you to create a consistent appearance in your worksheets. As an added advantage, text styles enable you to quickly apply text formatting rather than having to make each piece of text the right size and color.

Using text styles across your worksheets make your work consistent and easier for other people to follow.

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CAD software has evolved to make the basic mathematics of product design transparent to users. But design also requires frequent ad-hoc calculations for everything from converting units to testing probability models. These vital calculations were - and often still are - done with calculators or manually on paper.

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Define a function.

Numerically

You cannot substitute the point value into the function before taking the derivative.  The variable t is not recognized by the numeric processor, so Mathcad returns an error.

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Engineering design calculations must be accurate and error free. When performing calculations in Mathcad, it is always helpful to add color to the worksheet to visually identify critical design parameters, equations, and results. Math regions containing such variables and results can easily be highlighted by accessing the properties panel for the region and enabling the Highlight Region option on the Display tab.

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The normal display of a vector or matrix result in Mathcad is shown below. Do you know that you have other options to display your results? You can change the alignment of the result, also called an output table, and show the indices for the rows and columns.

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This sheet shows how you can read the data in the steel shapes data file distributed by the AISC. It is completely data driven, so that all information about the steel shapes is in the Excel files and not in the worksheet.

Here are two list boxes. The first one shows a list of all of the available file names, which should be chosen to be meaningful. When you select one of the files, the second list box is populated with a list of the shapes that can be found in the selected file. Selecting a shape in this list box causes all of the variables from the Excel worksheet to be defined (including their units as listed in the Excel file) for further use. The selections are persistent. When first opening this sheet the file and shape selections remain as they were when the sheet was last saved.

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Sometimes it is necessary to incorporate tolerance into calculations such that the results include maximum, minimum, and nominal values. Often, physical components and device properties do not deliver their exact, nominal values. The sections that follow provide guidance on how to set up a tolerance function in Mathcad and include the defined tolerance in subsequent calculations so that the uncertainty introduced by the component can be considered as part of the design or analysis process. This article demonstrates the concept of using tolerance within Mathcad calculations with a simple RL circuit example.

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Vectors

A vector is simply a matrix with only one column.

Use the Insert Matrix dialog box to create a matrix. This dialog box can be accessed in three ways: Selecting Matrix from the Insert menu; typing the shortcut CTRL+ M.; or selecting the matrix icon (showing a three by three matrix) on the Matrix toolbar. For a vector, the columns field in the dialog box should be set to 1.

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