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Take the Spaghetti Test to Understand the Strength of Compression Members

Which brought to mind one of my seminar questions:

The Strength of a Compression Member:

a) Depends only on the cross sectional area, i.e. the amount of “meat” of the member.

b) Does depend on the cross sectional area, but more importantly, depends on unbraced length. The longer the unbraced length, the weaker the member.

c) There is an unbraced length for any given compression member beyond which the strength is so low that the member is not allowed by code.

The correct answers are b) and c).

The point of the question is to introduce the concept of unbraced length. But first, what is a compression member?

A compression member is any structural member that experiences compressive (squeezing) forces. Posts and columns are prime examples. Studs are also compression members, but if used in an exterior wall, studs also must resist bending stresses from wind loads. For now, we’ll only concern ourselves with pure compression members, i.e. no wind loads or other bending stresses.

Take for example the temporary 2x4 posts holding up the subject porch. How much compressive force can a 2x4, standing alone (no plywood sheathing attached) hold? It depends a lot on length. If short, say two-feet or less, a 2x4 can hold approximately 4,500 lbs. — over two tons. If long, however, the story changes dramatically. That same 2x4, six feet long, can hold only 900 lbs. If eight feet long, that same 2x4 cannot be used at all per code! In our porch example, the two 10-foot 2x4s standing alone were overstressed the instant they were installed.

This concept can be easily demonstrated using a plain piece of uncooked spaghetti. Try to break a one-inch-long piece of spaghetti by pushing on the end. Be careful you don’t poke a hole through your finger — that short column of spaghetti can take a very large load. Now, take an 8-inch-long piece and it will break with very little compressive force — it buckles in the middle. Now, take another 8-inch piece and hold (brace) the middle with finger and thumb, restraining it from buckling (moving sideways). Now you can apply a lot of compressive force again before failure. By bracing the middle, you shortened the column’s unbraced length and in effect made two short columns.

Another way to determine the strength of posts, columns and studs is by using computer software, such as ConstructionCalc’s Wood Column Calculator (shameless plug, ding!). The loads determined above were found that way in about 15 seconds.

To summarize, the strength of compression members (posts, columns and studs) depends on their size, but more importantly, on their length. So if you ever see a long, slender, unbraced column, beware. Buckling and failure may not be far behind.

Tim K. Garrison P.E. of ConstructionCalc.com has authored books and short courses and lectures on topics relevant to builders. Got a technical or management issue? E-mail buildersengineer@constructioncalc.com. Tim reads every one.

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The views expressed in this article represent the personal views, statements and opinions of the author and do not necessarily represent the views, statements, opinions or policies of the National Association of Home Builders. NAHB does not necessarily endorse any of the views expressed by the author and NAHB is not responsible for any direct or indirect consequences arising out of the views expressed in this article.

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