Copy the rules into MathLook for a better view. Close MathLook after observing the equations.

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1 Sample : Torsion on a Sha The Sha Design example is found the Sample Applications, Engeerg and Science section of the TK Solver Library. When it loads, the Variable and Rule Sheets appear as shown below. Status Input Name Output Unit Comment ID L J Txy theta G ^4 lbf/^2 lbf/^2 lbf* ****** SHAFT TORSION ***** outside diameter side diameter length of sha polar moment of ertia torsional shear stress angle of twist torsional modulus of elasticity torsional moment St * * * Rule Txy = */(2*J) J = pi()*(^4-id^4)/32 theta = *L/(G*J) Copy the rules to MathLook for a better view. Close MathLook aer observg the equations. Txy= 2 J π 4 - ID 4 J = 32 theta = L G J Sample puts are provided on the Input Column of the Variable Sheet. Observg the rules, we see that the first rule has only one unknown, J, so TK can solve for it. The second rule will then have a sgle unknown, ID, and the third rule will have a sgle unknown, theta. Press F9 to have TK solve the model. The solutions appear the Output Column. Status Input Name Output Unit Comment ID L J Txy theta G ^4 lbf/^2 lbf/^2 lbf* ****** SHAFT TORSION ***** outside diameter side diameter length of sha polar moment of ertia torsional shear stress angle of twist torsional modulus of elasticity torsional moment Change the put for to 2 and solve aga.

2 TK is able to solve for J but then encounters an Exponentiation Argument Error the second rule. St > * Rule Txy = */(2*J) J = pi()*(^4-id^4)/32 theta = *L/(G*J) In this case, J is computed as 6. Multiplyg 6 times 32 and dividg by pi, we get With put as 2, TK is le with the equivalent of = 6 ID^4, and it responds with the error message. Input 0 for ID, blank the value of, and solve. TK provides no solution. None of the rules has only one unknown, so TK cannot solve them directly. Type a G the status column for the variable and solve. This tells TK to try to solve the problem iteratively, startg with a guess for. By default, TK uses the last value of as the guess unless we enter a different value. In this case, 2 works fe. Status Input Name Output Unit Comment ID L J Txy theta G ^4 lbf/^2 lbf/^2 lbf* So, this is the smallest value of that we can put, given the other values. Next, let s assume we have a solid sha (ID=0) with of 2. Assumg the same as before (40000 lbf*), we can blank the value of Txy and compute the stress seems too high. Input for Txy and blank the value of. Solve aga. Status Input Name Output Unit Comment ID L J Txy theta G ^4 lbf/^2 lbf/^2 lbf* Suppose we want the torsional shear stress to be no greater than for any shas we use. Assumg solid shas (ID = 0), what is the maximum allowable for different values? We can use TK to generate a table and plot of solutions. Launch the List Solver Wizard from the Wizards Menu. ****** SHAFT TORSION ***** outside diameter side diameter length of sha polar moment of ertia torsional shear stress angle of twist torsional modulus of elasticity torsional moment ****** SHAFT TORSION ***** outside diameter side diameter length of sha polar moment of ertia torsional shear stress angle of twist torsional modulus of elasticity torsional moment

3 Select as the Independent Variable and as the Dependent Variable. Fill the list with values startg with 0.5 steps of 0.25 up to 4. Name the table and plot Txy. They are shown below. Element [] Let s take a look at the units used this model. They are summarized on the Variable Sheet. The basic length dimension is ches (). The variable L is currently displayed feet () aer conversion from. Open the Variable Sheet and right-click on the variable L to open the subsheet and confirm this. Then close the subsheet. Display Unit: Calculation Unit:

4 A more efficient way to check the units for all variables is to use the Object Units Summary Wizard. As you scroll down the Variable Sheet, it summarizes the units for each variable. The model currently has three units of length available. We add more usg the Units Import Wizard. Select the unit type Length and the wizard presents the followg form. Click the box to Select all unit conversions and then click on Export to TK. Close the wizard screen.

5 When you have fished importg units, open the Unit Sheet to see a complete list of all the units and conversion factors currently the model. Here is the Unit Sheet as the model itially loads. From To Multiply By Add Offset Comment rad lbf/^2 lbf* mm MPa lbf* Pull down the Plots list the Objects Bar and brg up the Txy plot. Right-click on the plot to access the subsheet and make the followg edits. Display Scale: Display Zero Axes: Display Grid: Display Legend: Le Chart Scalg: Title: Subtitle: X-Axis Label: Y-Axis Label: Yes None Yes Yes Y-log Sha Torsion Txy = psi Close the plot subsheet and observe the changes to plot.

6 00000 Sha Torsion Txy = psi [lbf*] [] Close the plot and brg up the Variable Sheet. We will assign formats to values. Click on the properties icon on the Toolbar bar and then click the thumbtack the properties box to keep it on the screen. Enter d3 for the format and then click the General Format tab near the top of the box and make the edits shown below.

7 Switch to the variable ID by clickg on its row of the Variable Sheet. If you clicked the thumbtack, the properties box should rema on the screen but will now display the properties for ID. Click on the Variable tab the property box and assign the format d3 to it as well. Contue this process, assigng the d3 format to all the variables. Your Variable Sheet should appear as shown below. Status Input Name Output Unit Comment ID L J Txy theta G Now let s lk this model with Excel ^4 lbf/^2 lbf/^2 lbf* ****** SHAFT TORSION ***** outside diameter side diameter length of sha polar moment of ertia torsional shear stress angle of twist torsional modulus of elasticity torsional moment Organize the sheets (close, resize, etc.) and save the model as a new file called sample. The Excel Wizard searches the TK Variable Sheet to see which variables are puts and outputs. Be sure to save the model with the Variable Sheet set up as you would like it to be transferred over to Excel. Start Excel and then use File New to select the TK Solver template file. The lkg wizard will automatically be launched and will prompt us for the name of the TK file to lk. We can enter the path and name or we can browse.

8 Aer your path and file names are entered, click the Next button to advance to the next screen. All the put variables the model are listed. If we want some of these puts to be held constant when workg Excel, we can remove the check from those variables. In this case, let s keep them all. Click the Outputs button to specify which outputs to view Excel. In this case, check all three outputs.

9 Click the Next button to view the next screen. In this example, let s check all three boxes. Click the Fish button and the wizard creates the lked terface between the Excel spreadsheet and the TK model. By default, the wizard places the outputs to the right of the puts but we are free to cut and paste the cells a new position, as shown below.

10 \tk4\sample.tkw Input Value Unit Comment 2 outside diameter ID 0 side diameter L length of sha Txy lbf/^2 torsional shear stress G lbf/^2 torsional modulus of elasticity Output Value Unit Comment J ^4 polar moment of ertia theta angle of twist lbf* torsional moment Change the put for to 3 and observe that the is recomputed. Next, change the stress value (Txy) to and see how the outputs change. The cells are now lked with the TK Solver model. \tk4\sample.tkw Input Value Unit Comment 3 outside diameter ID 0 side diameter L length of sha Txy lbf/^2 torsional shear stress G lbf/^2 torsional modulus of elasticity Output Value Unit Comment J ^4 polar moment of ertia theta angle of twist lbf* torsional moment Invoke the Solver Add In from the Tools menu and make the entries shown below. We can also use the Excel Solver Add In to backsolve as we might have done TK Solver. The new is

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