The calculation of effective section properties is important because it allows the engineer to include the post-buckling capacity of the member and reduce material used. Effective section properties take into account the fact that post-buckling stress will render a certain portion of the cross-section ineffectual. The difficulty in calculating effective section properties arises from a classic "chicken-and-egg" scenario. For example, the moments of inertia are needed to calculate the stress conditions under moments to determine the effective width of each segment, while the effective width of each segment is needed to determine the moments of inertia. This means that an extremely tedious and time-consuming series of calculations are required to iterate to a solution despite the fact that the equations involved are straight-forward.

Recently, a computer program has been developed that automates the process of determining effective properties of sections with arbitrary shapes. The program, called Geometric Analysis of Sections (GAS), uses an iterative procedure to compute the stress distribution and corresponding effective properties until the results converge. The effective properties of the section are computed according to the element effective width calculation results. The element effective width calculations are based on the Cold-Formed Steel Design Manual and Automotive Steel Design Manual published by the American Iron & Steel Institute. The program includes a graphical preprocessor, which allows the user to create and edit the cross section graphically using a keyboard, mouse or digitizing tablet. Among other uses, this tool makes it easy to calculate the properties of a complex section prior to finite element analysis thus greatly reducing the time required to perform the analysis.

In the AISI Cold-Formed Steel Design Manual, the effective width concept is used to account for the post-buckling strength of a thinwalled section. The post-buckling strength is the additional load carried by elements of the cross section, after they have buckled locally, by means of a redistribution of stress. Under the effective width concept, only certain portions of the plate width are considered to be effective in carrying loads after exceeding the local buckling stress and the nonuniformity of stress distribution in the element is accounted for by replacing the actual plate width by a reduced effective width such that the total area under the stress distribution curve is the same.

The effective width of a cross section element is a function of a number of parameters such as boundary condition, stress condition, material and width to thickness ratio, etc. The stress distribution cannot be computed until the cross section property is calculated. Therefore, it is necessary to assume a certain stress distribution and compute the associated effective property. This process can be an iterative process, which is shown in the examples in the Cold-Formed Steel Design Manual. The iterative nature of the effective property calculation makes the manual calculation tedious and time consuming.

To facilitate the effective property calculation for coldformed steel cross sections, American Iron and Steel Institute sponsored the development of GAS and its integration into the Computerized Application and Reference System (CARS), a computerized version of the Automotive Steel Design Manual by AISI.

In the hand calculation examples in the Cold Formed Steel Design Manual, stress distribution is obtained first based on the assumption that the whole cross section is effective. Accordingly, effective width of each segment in the cross section is computed. If the results indicate that any element is not fully effective, the calculation becomes iterative. The stress distribution in the subsequent calculation is obtained by moving the principal axis. This technique simplifies the effective width calculation and stress distribution calculation for simple cross sections. For cross sections with arbitrary shape, flanges and webs are difficult to identify and stress distribution can be very complicated. Therefore, a more general procedure should be developed to compute the effective properties of cross sections with arbitrary shape.

The following procedure is developed and implemented in GAS to compute the effective cross section properties:

1. Compute the normal stress distribution assuming all the segments are fully effective.

2. Calculate the effective width of each segment.

3. Calculate the cross section properties of the section based on the effective portion of each segment.

4. Compute the stress distribution using the calculated effective section.

5. Calculate the effective width of each segment based on the revised stress distribution.

6. Calculate the cross section properties of the section based on the effective portion of each segment.

7. Repeat Steps 4 and 6 until the area and moments of inertia of the effective section converge.

The difference between GAS's procedure and the manual example's procedure is that GAS computes the equivalent stress distribution in each iteration based on the effective property results from the last iteration. After the stress distribution is obtained, GAS computes the effective width of each element in the cross section according to the procedures and equations presented in the Cold-Formed Steel Design Manual and the Automotive Steel Design Manual. Both manuals classify the effective width calculation by the element type, which is a combination of the element boundary condition and the stress condition in the element. GAS handles the following seven element types:

1. Uniformly compressed stiffened elements

2. Stiffened elements with a stress gradient

3. Unstiffened elements in compression

4. Uniformly compressed elements with an edge stiffener

5. Uniformly compressed elements with a single intermediate stiffener

6. Edge stiffened elements with intermediate stiffeners or stiffened elements with more than one intermediate stiffener

7. Curved elements

Both manuals cover the first six element types. The calculation procedures for curved elements are from the Automotive Steel Design Manual. The inclusion of edge and intermediate stiffeners complicates the program algorithm because they have to be evaluated as a group of entities unlike the stiffened or unstiffened elements which can be evaluated entity by entity.

A practical computer program needs more than a good solution engine -- the user interface is equally important. GAS's features in user interface include: graphical input, dual systems of units, material database, graphical results, parametric study and cross section database. The cross section in GAS can be a combination of four kinds of entities: points, lines, arcs and welds. These entities can be created and edited graphically using a keyboard, mouse or digitizing tablet.

Two units systems are offered in GAS, English and SI. GAS's dual units feature allows the user to design entirely in either system of units or design in one system and then convert to the other since GAS allows the user to toggle back and forth instantly between English and SI units. The user can design in English units then convert on the fly to SI and not lose that all important feel for the numbers that have taken the user years to acquire. In addition, a unit conversion utility is provided for on-line units conversion.

GAS provides a database management utility, MAP (Material Archive Program), to manage commonly used materials or user-defined materials. When materials are assigned to entities in a cross section, material properties are automatically associated with the analysis. This feature enables engineers to choose and use the right materials for optimal product performance.

The effective properties are shown in two windows. One window shows the centroid and the principal axes of the effective section and the effective portion of the section is highlighted. The other window contains the numerical values of the effective properties.

Using GAS, trend analysis or single calculation permits parametric study to be performed by varying dimensions of the section. The results of a parametric study can be shown in an XY plot. The parametric study capability of GAS allows the engineer to conduct the "what if" analysis for the optimal design.

Instead of using one data file for one cross section, GAS uses a database utility to manage the cross section information. This feature allows a long description name, longer than 8 characters under DOS limitation, for the cross section for better identification.

In summary, an algorithm to compute the effective properties of a cross section has been developed and implemented in the program GAS. By utilizing the computer processing power to perform iterative calculations and by implementing the interactive and graphical tools of the graphical user interface, the structural engineer is freed from repetitive and tedious calculations and allowed to focus his or her energy on the more creative aspects of the design process.