

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 1Roark'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 
lbfin 
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 
lbfin 
Bending moment 


thetaA 
0 
rad 
Slope Angle 


yA 
0 
in 
Deflection 





AT RIGHT END: 


RB 
1000 
lbf 
Vertical reaction 


MB 
18000 
lbfin 
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. 

