Equivalent Area Method for Composite Cross Sections
(U. S. A. Units)
Description
For a two material composite section, this spreadsheet
computes the transformed cross sectional
area properties
using the
equivalent area method. The section evaluated can be simple
cross section consisting of only two members; or a complex section, like a
ship or boat cross section that is made up of
a numerous components (including
structural shapes like tees, angles, and flat
bars). Area properties from this sheet are
often used
for obtaining available section modulus values and
flexural stress values for the two materials
present in the cross section.
Electronic
Document Type: Microsoft^{} Excel^{}
spreadsheet
Cost:
$35.00 US funds
Number of
Pages: single sheet
Inputs:

Location of
ANA (Assumed Neutral Axis)  indicate your selected location at
bottom of spreadsheet in the
provided text box. Usually it is best
to select at lowest point of cross section, so that all vertical arms
values are positive.

y_{t1}
= distance from ANA to highest part of all
the Material 1 components, make negative if below ANA,
plus
if otherwise

y_{b1}
= distance from ANA to lowest part of all the
Material 1 components, make negative if below ANA,
plus
if otherwise

y_{t2}
= distance from ANA to highest part of all
the Material 2 components, make negative if below ANA,
plus
if otherwise

y_{b2}
= distance from ANA to lowest part of all the
Material 2 components, make negative if below ANA,
plus
if otherwise

E_{1}
= Modulus of Elasticity for Material 1 (in
the same units as shown in the spreadsheet)

E_{2}
= Modulus of Elasticity for Material 2 (in
the same units as shown in the spreadsheet)

For each
cross section
component the following inputs are required:
decide on component type  if a plating member,
or other rectangular shape, put it in a
top row, that is in rows 115
of the spreadsheet; or if a structural shape for which
tabular data is available and for
nonrectangular geometric shapes for which area property calculations
can be made, put these later items into the bottom rows
of the spreadsheet that are numbered 1630.
item description  describe the item in "Description" field,
also use "Misc. Member Information" field for entering more data if
required.
q_{i }value  put
in quantity of components that have
the same centroid height. It is important make different component
listings (put them in new rows on the spreadsheet)
for same type components that are at different vertical distances
from the ANA (like side shell stiffeners).
Mat'l Type  Enter 1 if component is composed of Material 1;
or enter 2 if the component is made from Material 2.

For plating
& flat bar components (Rows 115
on this spreadsheet) the
inputs are:
b_{i} value 
transverse dimension of plating or flat bar member
h_{i} value 
vertical dimension of plating or flat bar member
r_{i} value 
insert this value in table based on figure in the spreadsheet. Note
that this distance is always perpendicular to the ANA.
Sign convention is important for this
item. It is plus if this distance if above the ANA, otherwise it is
negative.
n_{i }value 
insert this value in table based on figure in the spreadsheet. Note
that this distance is always perpendicular to the ANA. This distance
is radius of gyration of this flat member and it is
used to compute it's moment of inertia.

Rows 1630
on this spreadsheet apply to structural shaped components
with area property data
available from tables or these
input rows can also apply to nonrectangular geometric shapes
where the area properties can be directly
calculated by using formulas. The following inputs are required
for this type:
h_{i} value  put
in the component's height (it's measurement perpendicular to the ANA).
y_{i}
value  If from tabular data; this is shortest distance from
shape centroid to component's closest edge, this measurement is
perpendicular to the ANA. If based on
nonrectangular geometric shape; this is the computed distance from
bottom edge of the component to component's vertical centroid
A_{i} value 
cross section area, value taken from a table or computed separately.
I_{i} value 
moment of inertia about its own neutral axis, this value taken from a
table or computed separately.
r_{i} value 
insert the perpendicular distance from the component's centroid to the
ANA. This value is illustrated in the figure on the spreadsheet.
Sign convention is important for this
item.
It is plus if this distance if above the
ANA, otherwise it is negative.
Outputs:

A value
 total transformed area of the composite cross section.

r value
 location of transformed area centroid, vertical distance from the
ANA. A plus value indicates the centroid is above the ANA and negative
indicates the assemblies centroid is below the ANA.

I_{c
}value  moment of inertia of the transformed area
about its own neutral axis.

SM_{top1}
value  available section modulus
applicable to flexural stresses at the highest fibers of Material 1

SM_{bot1}
value  available section modulus
applicable to flexural stresses at the lowest fibers of Material 1

SM_{min1}
value  available section modulus
"normally" used to compute flexural stresses present in the framing
assembly. This is often called the "Least"
(or governing) section modulus and it applies only to Material 1.

SM_{top2}
value  available section modulus
applicable to flexural stresses at the highest fibers of Material 2

SM_{bot2}
value  available section modulus
applicable to flexural stresses at the lowest fibers of Material 2

SM_{min2}
value  available section modulus
"normally" used to compute flexural stresses present in the framing
assembly. This is often called the "Least" (or governing) section
modulus and it applies only to Material 2.
Items Included with the Product:
A blank template for you to input data.

A set of instructions on how to perform the
analysis.

A sample calculation already filled out. It
is recommended that each cell within the sample calculation be examined
to fully grasp the techniques involved.

A drawing of the sample cross section .

A sheet containing the products standard "Use Terms."
Suggested
Reading or References:
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Minimum System Requirements: Windows 95/98/NT/2000/XP/Vista/Windows7/later Windows OSs including Windows 11
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Sample:
A sample calculation and
cross section are shown below.
