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 2
Now, let's investigate some other characteristics of the beam. Specifically, assume that the beam will be steel, 6 feet long, fixed at both ends, with a maximum concentrated load of 2000 lbf at the center. You want to determine the deflection and stress values. You can merge another case from Roark's Formulas into the existing model.

Select Interactive Roark's Formulas from the Applications Menu. Find and select Table 8.1, Case 1d.

 

 
Click Load File(s). When prompted, choose Merge. This will combine the cross section variables and formulas with the beam loading formulas. The new variables will appear at the end of the Variable Sheet, ready for inputs.

First, notice that the current unit for the beam length (L) is inches (in), even though the beam is 6 ft long. You can use the built-in calculator in TK Solver to convert between inches and feet. Enter 6*12 and TK Solver does the multiplication for you.

There is another way to convert the units. Move to the Unit field for the variable L and enter ft. The value automatically changes. Change the unit to meters by entering m. The value changes again.

 

 
The Unit Sheet supplied with Interactive Roark's Formulas includes a list of unit conversions.

Make the Unit Sheet active and take a look.

 

 
Close the Unit Sheet. Enter the remaining inputs on the Variable Sheet:
 
Load distance from left end (a)36 in
Load (W) 2000 lbf
Young's Modulus (E) 3E7 psi
 
(You could also enter L/2 as the input for a. TK Solver will automatically handle the unit conversion even though L is displayed in meters.)

If you didn't remember the Young's Modulus for steel, you could have checked the Material Properties table that is automatically loaded with each case. You can look at the Material Properties table by clicking the Tables drop-down list in the TK Solver Object Bar, then clicking on the name of the Materials interactive table, as shown.

 

 
The table should appear as shown below.
 

 
For various types of stel, the Young's Modulus ranges from 2.66E7 to 3E7.

Close the table and enter one more input.

 
This tells TK Solver the location along the beam at which the shear, moment, slope, deflection, and stress will be calculated and reported. By default, the model automatically solves for the two ends. By entering a value for x, you get a solution at any other location. 

Solve.

TK Solver generates the following results.

 

 
Let's change the beam from steel to aluminum. Make the Materials Table active again. Notice that materials 1-4 are various types of aluminum. Use number 4. Close the table and enter 4 on the Variable Sheet as an input for the variable named matnum.

Blank the current value for E. TK Solver will automatically look up the value from the table.

Solve.

The change in materials has significantly increased the deflection.

 

 
To see a plot of the results, make the Plot Sheet active, highlight the name Stress, and press F7, or press the Plot button on the Toolbar.