Equivalent Area Method for Composite Cross Sections
(Metric 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:
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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.
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yt1
= distance from ANA to highest part of all
the Material 1
components, make negative if below ANA, plus
if otherwise |
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yb1
= distance from ANA to lowest part of all the
Material 1 components,
make negative if below ANA, plus
if otherwise |
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yt2
= distance from ANA to highest part of all
the Material 2
components, make negative if below ANA, plus
if otherwise |
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yb2
= distance from ANA to lowest part of all the
Material 2 components,
make negative if below ANA, plus
if otherwise |
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E1
= Modulus of Elasticity for Material 1 (in the same units as shown in
the spreadsheet) |
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E2
= Modulus of Elasticity for Material 2 (in the same units as
shown in the spreadsheet)
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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 1-15
of the spreadsheet; or if a structural shape for which
tabular data is available and for
non-rectangular geometric shapes for which area property
calculations can be made, put these later items into the bottom rows
of the spreadsheet that are numbered 16-30.
item description - describe the item in "Description" field,
also use "Misc. Member Information" field for entering more data if
required.
qi 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. |
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For plating
& flat bar components (Rows 1-15
on
this spreadsheet) the
inputs are:
bi value -
transverse dimension of plating or flat bar member
hi value -
vertical dimension of plating or flat bar member
ri 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.
ni 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. |
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Rows 16-30
on this spreadsheet apply to structural shaped components
with area property data
available from tables or these
input rows can also apply to non-rectangular geometric shapes
where the area properties can be directly
calculated by using formulas. The following inputs are required
for this type:
hi value - put
in the component's height (it's measurement perpendicular to the
ANA).
yi
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 non-rectangular geometric shape; this is the computed
distance from bottom edge of the component to component's vertical
centroid
Ai value -
cross section area, value taken from a table or computed separately.
Ii value -
moment of inertia about its own neutral axis, this value taken from
a table or computed separately.
ri 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:
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A value
- total transformed area of the composite cross section.
|
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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.
|
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Ic
value - moment of inertia of the transformed area
about its own neutral axis. |
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SMtop1
value - available section modulus applicable to flexural stresses at the
highest fibers of Material 1 |
 |
SMbot1
value - available section modulus applicable to flexural stresses at the
lowest fibers of Material 1 |
 |
SMmin1
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. |
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SMtop2
value - available section modulus applicable to flexural stresses at the
highest fibers of Material 2 |
 |
SMbot2
value - available section modulus applicable to flexural stresses at the
lowest fibers of Material 2 |
 |
SMmin2
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:
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A blank template for you to input data. |
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A set of instructions on how to perform the
analysis. |
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A sample calculation already filled out. It
is recommended that each cell within the sample calculation be examined
to fully grasp the techniques involved. |
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A drawing of the sample cross section . |
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A sheet containing the products standard "Use Terms." |
Suggested
Reading or References:
Terms:
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User License Terms.
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Minimum
System Requirements: Windows 95/98/NT/2000/XP/Vista/Windows7
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Sample:
A sample calculation and
cross section are shown below.
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Additional Comments:
The inputs may seem a bit
complicated at first. But they are really easy to obtain and are clearly explained
within the template instructions.
To assist with this process, there is a small simple diagram located on
the spreadsheet, that shows the geometric information that is
required as inputs.
This spreadsheet is geared toward metric units
of measure commonly used in the United States. For determining
moment of inertia and section modulus in metric units go the the
English units
composite section equivalent area method spreadsheet.
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