 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 3
Suppose you decide to stick with the aluminum beam but you're concerned about the deflection. You'd like to limit the deflection to -.1 in by resizing the beam cross section. For example, if you increase the dimension of side b, the deflection should decrease. The problem is, how much do you change side b? The answer is to let TK Solver backsolve for the solution.

Enter -.1 as the input for the variable y. Blank the input for the variable t1b.

Solve.

What? No solution? Don't panic! As you may know, TK Solver includes both a Direct Solver for basic algebraic manipulations and an Iterative Solver for more complex situations.

This must be a job for the Iterative Solver!

To invoke the Iterative Solver, just place a G in the Status Field of the t1b variable. This indicates that the value in the input field will be the initial guess for t1b.

Solve again. Success! The beam design has been optimized.

 Variable Sheet St Input Name Output Unit Comment Roark's Formulas for Stress and Strain Section 3: Hollow Rectangle DIAGRAM 'y Generate section diagram? ('n=no) 1 axis Neutral Axis (1,2) t1b 2.7483 in Side b 1.3125 t1bi in Hollow Side bi 2.75 t1d in Side d 2 t1di in Hollow Side di A 4.9328 in^2 Area, A t1y 1.375 in Centroid to Extremity, y I 3.888 in^4 Area moment of inertia I%c 2.8276 in^3 Elastic Section Modulus, I/c t1r .8878 in Radius of Gyration, r Z 3.8835 in^3 Plastic Section Modulus, Z SF 1.3734 Shape Factor, SF SF 2.75 in Depth Left end fixed, right end fixed Table 8.1 Case 1-Roark's Formula Concentrated Intermediate Load case 'CASE_1d End Restraints Reference Number 4 matnum Material Number (See Material Table) matl "Aluminum plot 'y Generate plots ? 'n=no (Default=yes) 1.8288 L m Length of beam 36 a in Load distance from left end 2000 W lbf Load E 1E7 psi Young's Modulus z '_ in Neutral axis to stress point AT SECTION: 36 x in Distance from left end V 1000 lbf Transverse shear M 18000 lbf-in Bending moment theta 0 rad Slope Angle -0.1 y in Deflection st '_ psi Fiber stress at stress point sty 6365.741 psi Max Fiber stress at extremity y AT LEFT END: RA 1000 lbf Vertical reaction MA -18000 lbf-in Bending moment thetaA 0 rad Slope Angle yA 0 in Deflection AT RIGHT END: RB 1000 lbf Vertical reaction MB -18000 lbf-in Bending moment thetaB 0 rad Slope Angle yB 0 in Deflection

To see a plot of the results, make the Plot Sheet active, highlight the name Section1, and press F7. 