Interactive Roark’s Formulas: Five Problems and Solutions

Let's load a case from the Interactive Roark's Formulas application and solve a problem. Along the way, you will learn about many of the software's features.


Problem 1

Suppose you are designing a beam having a hollow rectangular section and you need to know the area, moment of inertia, and plastic section modulus. Start up TK Solver and choose Interactive Roark's Formulas from the Applications Menu.

When the RY Menu appears, select and load Table A.1, Case 3.


Enter the following five input values on the Variable Sheet:
Neutral axis parallel to b (axis) 1
Base width b (Arial">t1b in the model) 1.5 in
Base inside dimension bi ( Arial">t1bi) .3125 in
Outside height d (Arial">t1d) 2.75 in
Inside height di (Arial">t1di)  in
Solve by selecting Solve from the Commands Menu, clicking the Solve icon,  or pressing F9.

The solution is displayed below.


Press F7 (you could also select Display Plot from the Commands Menu or click the Plot icon  on the Toolbar) to view a plot of the section with your specified dimensions and neutral axis.

Now, suppose that other considerations require that the area moment of inertia,I, be 2.0 in^4, and that you are willing to adjust the outside dimension of the base,t1b.
Enter 2 as the input value for I and blank the input for the variable t1b by pressing the Spacebar followed by Enter. (You can also blank an input by typing B in the Status field of the variable or double-clicking on the Status field and selecting Blank from the drop-down list box.)
Solve for the new outputs.

TK Solver's unique ability to solve for a variety of combinations of input and output variables is known as backsolving. You will use this feature frequently in checking alternatives and optimizing your designs.
Just for practice, let's backsolve again. Enter an input of 1.6 for the variable t1b, blank the input for I, and solve.