Introduction to Mathcad

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Mathcad is like a digital engineering notebook. Calculations are a critical part of engineering, and documenting these calculations is important. Mathcad is like a digital engineering notebook. Uses and benefits of Mathcad include: Live mathematical notations Units intelligence Powerful calculation capabilities Calculation presentation through graphs, plots, text, and images Source: https://www.ptc.com/en/products/mathcad

Mathcad Interface Ribbon user interface with tabs: Math, Input/Output, Functions, Matrices/Tables, Plots, Math Formatting, Text Formatting, Calculation, Document, & Resources Cursor identifying where you are on the worksheet Worksheet used to write all calculations and other documentation. Think of this as “smart” paper

Typing Calculations Versus Text Math Mode: Do you notice any subtle differences in the Math Mode versus the Text Mode? Text Mode: Both Math and Text Modes can be useful depending on what you are trying to accomplish. Text Mode allows you to input text in the worksheet, like comments or other forms of documentation that you do not need the worksheet to calculate. Math Mode allows you to input data (number and units) that may be used in your calculations. By default the worksheet is written in math mode. You need to tell the worksheet to shift to text mode. Under the Math tab, click Text Block (large block allotted for text) or Text Box (smaller box allotted for text).

Predefined Variables & Units Mathcad has predefined variables for commonly used values. Notice how the predefined variable turns green when you type. After you press = the predefined value appears. You should AVOID redefining the predefined variables by using them for different variables (e.g., setting g=10lbf, because g is already defined as gravity = 9.81 m/s2). Mathcad has predefined units and can move seamlessly between metric and US Customary units. Notice how the units turn blue when you type them or when they appear after the = sign. If using US Customary units, after you press = Mathcad will automatically convert to metric units. You should AVOID redefining the predefined units by using them for different variables (e.g., setting m=10lbf, because m is defined as meters)

Using Mathcad Use the example problem to build a Mathcad Worksheet Example Problem: For the forces and angles depicted below, what is the magnitude of the resultant force (provide answer in lbf), and what is the angle that the resultant force makes with the x-axis (provide answer in degrees)? 𝐹 1 =44.962 𝑙𝑏𝑓 𝐹 2 =850 𝑁 𝜃 1 =0.489 𝑟𝑎𝑑 𝜃 2 =18° First, set up your sheet like you would with any engineering problem – Use Engineering Format Insert text boxes to format the heading, label the problem, type the given information. Format the text in the Text Formatting tab.

Using Mathcad Use the example problem to build a Mathcad Worksheet Example Problem: For the forces and angles depicted below, what is the magnitude of the resultant force (provide answer in lbf), and what is the angle that the resultant force makes with the x-axis (provide answer in degrees)? 𝐹 1 =44.962 𝑙𝑏𝑓 What do you notice about these given values? 𝐹 2 =850 𝑁 𝜃 1 =0.489 𝑟𝑎𝑑 Do you need to convert the units before entering them into Mathcad? 𝜃 2 =18° No! Mathcad can seamlessly translate between the different unit systems. You can type the values as given in the problem. Once the initial format is set for the worksheet, you need to insert the given variables. Why are the equal signs preceded by “:”? When you are assigning a value to a variable, Mathcad needs to know this is your intent. The “=“ on your keyboard is used by Mathcad to calculate values. Assigning values uses a special equal sign “:=“ that you get by pressing <shift> ; To insert θ (or other Greek letters), click symbols section in the Math Tab. To place a subscript press <ctrl> -

You will likely need to do some preliminary calculations before getting to your solution. Notice how text is used like comments to help understand what is being calculated. Using Mathcad Break F1 and F2 into their x and y components. := is used to define the values being calculated = is used to calculate the answer Even though the answer is asked to be in lbf, intermediate calculations can be left in N. Notice, we do not type the units for F1 or θ1 since the units are already stored within the variable. Rule of Thumb: Type a unit whenever you type a number, not when you type a variable! Be aware of the direction of your forces. Since F2y is in the negative direction, you need to put a – sign here. Mathcad is smart, but not that smart!

Using Mathcad Notice R is defined using := then calculated with = To get the square root symbol you press \ To get exponents press ^ Initially the calculation will be given in Newtons Within the calculation box, erase the N and type lbf (must be lbf to calculate force) Notice θ is defined using := then calculated with = To get the division symbol you press / Initially the calculation will be in rad Within the calculation box, a unit box will appear, type deg

Formatting and Other Tips Use the Math Formatting tab to: Highlight math text Change the color of math text Change font type and size Edit the appearance of a number Result Format – General, Decimal, Scientific Notation Display Precision – Change number of decimal places Resources Tab Help feature – large library of information, includes sample text that you can copy and paste into your worksheet help you get started on a calculation. Tutorials – sample exercises to help familiarize yourself with Mathcad. Keyboard shortcuts – list of keyboard shortcuts that will make using Mathcad much easier.