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.