Example Using Circular References to Force Iteration: Calculation Effective Section Modulus for Coldformed CSection to AS4600
Description
Calculation of effective section modulus (Zex) using effective width methods of AS4600, for a coldformed csection.
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It uses circular references to force iteration on the calculation of the section centroid. The web has a stress gradient and so the portion which is in compression and not effective is unknown. Has chunks are removed to determine effective width of plates, the section modulus of the csection changes and so does the location of the neutral axis, and so the portion of the web in compression is different than initially assumed. The circular references force iteration until the difference between the initial assumption and the calculated value is insiginificant.
Calculation Reference
Cold Form Sections
Structural Analysis
Section Properties
The effective section modulus (Zex) for a coldformed Csection can be calculated using the effective width method, as specified in the AS 4600 Australian Standard for ColdFormed Steel Structures. The effective section modulus takes into account the reduced crosssectional area of the section due to local buckling, which can occur in thinwalled coldformed steel sections.
To calculate Zex for a coldformed Csection, follow these steps:
 Determine the section properties:
 b: Width of the flange
 t: Thickness of the steel
 h: Height of the web
 r: Inner radius of the corner
 Determine the material properties:
 E: Young's modulus of the steel
 Fy: Yield strength of the steel

Calculate the halfwavelength (λ): λ = (π * E) / (0.95 * Fy)

Calculate the widthtothickness ratio for the flange (bf/tf) and the web (h/tw), where tf and tw are the thicknesses of the flange and web, respectively.

Determine the effective width (be) for the flange and the web using the AS 4600 standard's provided equations or tables. These equations consider the widthtothickness ratios, the material properties, and the type of loading and support conditions.

Calculate the effective crosssectional area (Ae) by multiplying the effective width (be) of each element (flange and web) by its thickness and summing the results: Ae = (be_flange * tf) + (be_web * tw)

Calculate the effective moment of inertia (Ie) by summing the moment of inertia of each element (flange and web) about the centroid of the effective section: Ie = Ie_flange + Ie_web

Determine the distance from the centroid of the effective section to the extreme fiber in tension (ymax).

Calculate the effective section modulus (Zex): Zex = Ie / ymax
By following these steps, you can calculate the effective section modulus (Zex) for a coldformed Csection using the effective width method according to the AS 4600 standard. This value can be used for structural design and analysis of coldformed steel structures to ensure adequate strength and stability.
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