Comparing strength of channel versus flat steel

[OldHouseGuy]

I am trying to repair my 1920s pier and beam house and have a situation where I need to slide under two butted beams on top of a post the thinnest steel I can that will support the two beams. What would help me determine this would be a general idea of how to compare the strength of a flat piece of steel with a force acting perpendicular to the flat width surface (that is, supporting a beam) to one of channel (or C shaped) steel.

I had strength of materials coursework thirty years ago, but do not remember how to calculate the relative strength for these two types of cross sections of steel and have looked everywhere for reference materials or a quick comparison with no success.

Assume the vertical sides of the channel steel are each about 25% of the width of the steel plate high, and that the flat and channel steel are the same thickness (relatively thin as compared to the overall dimensions) and the same width (say 4 inches wide and 1/8 inch thick with 1 inch high sides).

I am looking for an answer such as "with sides 25% as high as the steel is wide, channel steel is X times stronger than a flat piece of steel of equivalent thickness and width".

Thanks!

 

[FredGarvin]

The initial figure of merit will be to compare the cross sectional moment of inertia for each section. Assuming a pure bending scenario, which is not a bad assumption, the section with the higher moment of inertia in the vertical direction will have the lower stresses and thus handle the higher loads.

If you need a refresher on area moment of inertia, take a look here:
http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.inertia.html
http://en.wikipedia.org/wiki/Second_moment_of_area
http://www.globalsecurity.org/military/library/policy/army/fm/3-34-343/appd.htm

If you have a catalog for a structural steel supplier, they usually will have these tabulated for you.

 

[ravenprp]

To compare the strength of channel steel versus flat steel, we can use the concept of moment of inertia. Moment of inertia is a measure of an object's resistance to changes in its rotation, and it is directly related to the object's cross-sectional shape. The larger the moment of inertia, the stronger the object will be.

In this case, the channel steel has a larger moment of inertia compared to the flat steel, due to its C-shaped cross section. This means that the channel steel will be stronger and more resistant to bending or buckling when supporting the two beams on top of a post.

To calculate the exact difference in strength, we can use the formula for moment of inertia, which is I = (1/12) * b * h^3, where b is the width and h is the height of the cross section. Considering the dimensions given in the scenario, the moment of inertia for the flat steel would be (1/12) * 4 * (1/8)^3 = 0.00013 in^4. And for the channel steel, it would be (1/12) * 4 * (1/8)^3 + 2 * (1/4) * (1/8) * (1/8)^3 = 0.00027 in^4.

This means that the channel steel has a moment of inertia that is approximately 2 times larger than the flat steel. Therefore, we can say that with sides 25% as high as the steel is wide, channel steel is approximately 2 times stronger than a flat piece of steel of equivalent thickness and width.

It is important to note that this is a general comparison and the exact strength will also depend on other factors such as the quality of the steel and the specific load and conditions it will be subjected to. It is always recommended to consult a structural engineer for a more precise evaluation and recommendation for your specific situation.