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:
-
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.
-
yt1
= distance from ANA to highest part of all
the Material 1 components, make negative if below ANA,
plus
if otherwise
-
yb1
= distance from ANA to lowest part of all the
Material 1 components, make negative if below ANA,
plus
if otherwise
-
yt2
= distance from ANA to highest part of all
the Material 2 components, make negative if below ANA,
plus
if otherwise
-
yb2
= distance from ANA to lowest part of all the
Material 2 components, make negative if below ANA,
plus
if otherwise
-
E1
= Modulus of Elasticity for Material 1 (in
the same units as shown in the spreadsheet)
-
E2
= 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 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.
-
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.
-
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:
-
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.
-
Ic
value - moment of inertia of the transformed area
about its own neutral axis.
-
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.
-
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:
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:
Terms:
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End 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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