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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: Prior to purchase, read our 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.

 


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.