   # Determine the shape factor f for a cross section in the shape of a double trapezoid having the dimensions shown in the figure. Also, check your result for the special cases of a rhombus ( b 1 = 0) and a rectangle ( b 1 = b 2 ). ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

#### Solutions

Chapter
Section ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 6, Problem 6.10.1P
Textbook Problem
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## Determine the shape factor f for a cross section in the shape of a double trapezoid having the dimensions shown in the figure.Also, check your result for the special cases of a rhombus (b1= 0) and a rectangle (b1= b2). To determine

The shape factor of diagram given.

### Explanation of Solution

Given information:

A shape of double trapezoid with dimension shown in figure below.

From this diagram,

We know that shape factor of a trapezoid is given by:

SFtrapezoid=a+b+( ba 2 )2+( h)22π(b+a)h......(i)

So, in the given question:

a=b1b=b2h=h2

Putting this value in equation ....(i)

Therefore, SFtrapezoid=b1+b2+( b 2 b 1 2 )2+( h 2 )22π( b 1+ b 2)h2

For special cases: rhombus

When b1=0

Putting this value in equation

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