Equivalent Area Method for Composite Cross Sections
(English 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

• 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.
  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 1-15 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 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:
  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 non-rectangular 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: 

• HMC Article entitled "Composite (Laminated) Section Analysis,
  Equivalent Area Method"

• A. I. S. C. Manual of Steel Construction

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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 English or Imperial units of measure commonly used in the United States.  For determining moment of inertia and section modulus in metric units go the the metric units composite section equivalent area method spreadsheet.