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Just a quick question for you. Well hopefully.

A contractor has installed a retaining wall with colorbond fence on top. In the contract he stipulated that he would use 65mm x 65mm x 1.6mm powder coated steel posts.

He has, by mistake, installed, 76mm x 38mm x 1.6mm powder coated steel posts.

The whole fence is now leaning over and has failed. Now given that these posts are cemented into the sandy soiled ground, which of the posts would be stronger?

The posts have been installed standing up. I.E. the 76mm has the fence attached to it and the 38mm is facing each of the gardens.

Any help gratefully received.

Thanks

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    $\begingroup$ Homework? In spite of the fact that answers have been fed to you, I would suggest that for the sake of your future career, you attempt to actually understand the answers, rather than happily finishing your homework and memorizing the answer for the next test. $\endgroup$ – TimWescott Nov 8 '19 at 18:56
  • $\begingroup$ No I am actually a house owner who is being sued by the contractor because I refused to pay the final payment of $2k because the contractor installed the wrong posts, along with stealing 15 bags of concrete from the order from the supplier which should have gone into the ground to support the fence that is now being propped up by my neighbours car port, which is now causing cracking where it is bolted onto the side of her house. If the car port was not there the fence would be falling over. All this and he is suing me for non payment. So I think I would prefer it to be homework :p $\endgroup$ – Neil Nov 9 '19 at 8:37
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    $\begingroup$ Sorry about that -- if you ever take up writing test or homework questions as a hobby, you did a good job of it -- you captured all of the salient details up front, with just enough obfuscating detail so that students that slept through the lectures would go down rabbit holes. $\endgroup$ – TimWescott Nov 9 '19 at 17:24
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The incorrect posts are weaker as it is the dimension perpendicular to the fence which is critical. It sounds like you have a breach of contract here so you should ask them to replace with the originally specified posts without further charges to you.

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Sue, but I'd suggest getting a lawyer, or at least consulting with one. Mostly because lawsuits can hinge on seemingly the stupidest little things. I'm not even sure you want to bring up the fact that the posts are inadequate -- it should be enough that they are not what's stipulated in the contract. If you do bring it up, I'm pretty sure (and a lawyer would know) that you either need a book of building standards that would demonstrate inadequacy, or an expert witness (who in the US would need to have a professional engineer's license; you'd need the equivalent where you are).

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First, there are different ways a post can fail. For instance, the post could buckle (though rather unlikely, as the compressive load on the post isn't that high) failure of the footing, which is mostl depending on the embedment depth. However, I assume the most likely case is failure due to bending.

So, for case 1, the cross-section is square, with sides $a=b=65mm$, which in turn relates to a CS-area $A=416 mm^2$ and area moment of inertia $I_x=I_y=272'003 mm^4$.

And for case 2: $a=76mm$, $b=38mm$, $A=365mm^2$, $I_x=271'188mm^4$ and $I_y=91'848mm^4$.

When comparing the two cross-sections, assuming a linear-elastic material behaviour, in case 2 the cross-sectional area (roughly corresponding to compressive strength, without considering buckling) is reduced by about $12\%$. On the other hand, the "strong" moment of inertia $I_x$ is about the same, though the "weak" moment of inertia $I_y$ is reduced to about $34\%$ of the square post's value. This translates to the post having about one third of the specified posts bending resistance.

Thus i think it is likely, that if a post with the dimensions specified in the contract was used, it would not have failed.

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The thinner section (38mm) was not as strong as the post originally specified (68mm sq.).

This has allowed the wind loading (guess) to cause the fence to fail.

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