Fig. 3.2. Calculating with variables and functions.

For example, to define a value of say 10 to a variable, say t, click anywhere in the worksheet and type t: (the letter t followed by a colon).

Mathcad will show the colon as the definition symbol: = and will create an empty placeholder to its right. Then type 10 in the empty placeholder to complete the definition for t.

To enter another definition, press return [J] to move the crosshair below the first equation. For example, to define acc as -9.8 type acc:-9.8. Then press [J] again.

Now that the variables acc and t are defined, they can be used in other expressions. For example, to calculate the magnitude of Oft2, type acc/2*tA2. The caret symbolA represents raising to a power, the asterisk * is multiplication, and the slash / is division.

To obtain the result, type = for Mathcad to return the result as shown in Figure 3.2.

3.3.3 Entering text

Mathcad handles text as easily as it does equations [2]. To begin typing text, click in an empty space and choose Text Region from the Insert menu or simply type ". Mathcad will then create a text box in which you can type, change font, format and so on as you would when using a simple Windows based word processor. The text box will grow as the text is entered.

Now type, say, 'Equation of motion'; see Figure 3.3. To exit text mode simply click outside the text box.

3.3.4 Working with units

Mathcad's unit capabilities take care of many of the usual chores associated with using units and dimensions in engineering analysis and design calculations [2]. Once the appropriate definitions are entered, Mathcad automatically performs unit conversions and flags up incorrect and inconsistent dimensional calculations.

Fig. 3.3. Entering text.

The SI system is used and, although Mathcad version 11 or greater recognises most of the common units used in practice, by default a result will be displayed using its fundamental units. If the result is to be expressed in other units compliant with the SI system, this will be achieved by clicking the unit placeholder at the end of the result and inserting the units to be used. You can also define your own units if you so wish, and to assign units to a number, simply multiply the number by the name or letter(s) that defines the unit.

To illustrate the above, calculate the magnitude of the bending moment M at the built-in end of a cantilever of length L = 2 m induced by a force of P = 10 kN acting at its free end. To do this, click anywhere in a Mathcad worksheet and type the following:

Then type M=. As soon as the = sign is typed, Mathcad will compute the result and also display the units of M (as shown in Figure 3.4). The default unit for force times distance is joule and to display the answer in kN m, click the placeholder to the right of 10 and insert kN*m.

Several of the equations given in EC5 [3] are empirical and dimensionally incorrect. In such circumstances, to obtain the correct result from the Mathcad equation, each symbol within the equation must be made dimensionless by dividing by its associated units and the units used for the symbol to be imported into the equation must use the units defined in EC5.

For example, to obtain the yield moment of a bolt, My Rk, EC5, equation (8.30) must be used. The equation is structured to give the answer in N mm units providing the tensile strength of the bolt, /u>k is in N/mm2 and the bolt diameter, d, is in mm units. The equation is

>& Mathcad [Untitled:! J

0 0

Post a comment