Corrugated plates

Purpose of calculation
Calculation of section properties of Corrugated Plates

Comments
This calculation sheet is a combination of various formulas from books as noted. The SANS code used is similar to British standards.It is recommended that profile to be drawn in CAD to determine correct dimensions when critical working limits are encountered.

References
Strengths of Material (V Elliot)
Southern African Steel Construction Handbook (Table 13.7)
SANS 0162-2: 1993. The structural uses of steel Part 2: Limit states design of cold formed steelworks

Validation
Corrugation properties is checked by modelling profile with Solid Edge V20 & physical properties function.

Calculation Reference
Strengths of Material Elliot

Southern African Steel Construction Handbook

Limit states design of cold formed steelworks

Corrugated plates, commonly used in construction and engineering, have a wavy pattern that increases their stiffness and load-bearing capacity. Calculating the section properties of corrugated plates can be complex due to their geometry. However, here is a general approach to estimate the section properties:

1. Simplify the corrugated profile: Divide the corrugated profile into a series of flat or curved segments to simplify the calculations. For example, you can approximate the profile as a series of trapezoids and/or triangles.

2. Calculate the area (A) and centroid (C) of each segment: For each segment, calculate its area and centroid. For example, the area of a trapezoid can be calculated using:

A = (1/2) * (b1 + b2) * h

Where b1 and b2 are the lengths of the parallel sides, and h is the height.

3. Determine the overall area (A_total) and centroid (C_total) of the corrugated profile: Sum the areas of all segments to find the total area. To find the overall centroid, use the formula:

C_total = (Σ(Ai * Ci)) / A_total

Where Ai is the area of each segment and Ci is the centroid of each segment.

4. Calculate the moment of inertia (I) for each segment about the centroidal axis: For each segment, calculate the moment of inertia about the centroidal axis. For example, the moment of inertia of a trapezoid about its centroidal axis can be calculated using:

Ix = (1/12) * (b1 + b2) * h^3 / (b1 + b2)

5. Determine the overall moment of inertia (I_total) of the corrugated profile using the parallel axis theorem: The parallel axis theorem states that the moment of inertia of a shape about an axis parallel to and at a distance d from the centroidal axis can be calculated using:

I_total = Σ(Ii + Ai * di^2)

Where Ii is the moment of inertia of each segment about its centroidal axis, Ai is the area of each segment, and di is the distance between the centroid of each segment and the overall centroid.

By following these steps, you can estimate the section properties of corrugated plates. Note that this is an approximation, and for more accurate results, you may need to use specialized software or numerical methods, such as the finite element method.