Have you ever actually taken a moment to think about this?

你有沒有想過這個問題？

This simple technology forms the basis of all our largest structures, and even features in one of the world's most famous photos.

這個簡單的科技為人類史上建造過最大的建築打下了基礎，甚至還成為了世界上最知名照片的主角之一。

But after asking some of my friends, few actually knew the answer to this simple question.

但在問過我的一些朋友們之後，我發現很少有人真的知道這個簡單問題的答案。

The I-beam is designed in that way to handle a maximum bending load while using the least amount of material.

工字樑被設計用來在使用最少原料的同時，承受最高程度的彎折力道。

Let's look at an I-beam supported on either end to understand more.

讓我們從側面來看看工字樑來了解更多吧。

When we apply a uniform load across this beam, the max deflection will occur here in the middle.

當我們對這根橫樑施加均等的力量時，最大撓度會出現在正中央。

We can calculate the deflection with this equation.

我們能利用這個方程式來計算出撓度。

This may look complicated, but it really isn't.

這看起來或許有些複雜，但其實沒那麼困難。

W represents the uniformly distributed load in terms of Newtons per meter; L is the span between supports;

W 代表的是以牛頓米為單位的均等施加的壓力，L則是支撐點之間的跨越長度，

E is the Young's Modulus which as explained in my Material Properties 101 video, describes the stiffness of the material.

E 則是楊氏模量，我曾在我的「物理屬性基本知識」影片中解釋過，這是拿來形容該材料堅韌度的常數。

But the variable we want to focus on is I, which represents the second moment of area, sometimes called the moment area of inertia.

但在這裡我們要特別注意的變數是 I，它代表了面積二次軸矩，有時也被稱為面積慣性矩。

This describes the shape of the beam, more specifically, it describes how the material is distributed throughout the shape.

它代表了橫樑的形狀，更具體來說，它描述了該材質是如何被分布到整個形狀之中的。

These two shapes have the same area, but that area is distributed very differently and that is important.

這兩個形狀有著同樣的面積，但是整個面積的分布方式非常不同，而這就是最重要的地方。

A see-saw is a good analogy for this idea.

我們可以用蹺蹺板來很好地解釋這個概念。

When we place weight in the middle, it is very easy to lift, in fact, if it is placed exactly over the middle, we aren't lifting it at all.

當把重量放置在中間時，我們很輕易地便能將蹺蹺板的一端抬起。實際上，如果我們把重量放在正中間，我們甚至不必費力抬起。

But the further we move that weight to the end, the more difficult it is to lift, due to the increasing leverage.

但隨著我們越把重量移動一端的尾部，我們便會因為槓桿距離加長，因而越難抬起另外一端。

A very similar thing happens with beams in bending.

而橫樑在受到彎折時也會分生相當類似的情況。

Material at the center of the beam, which is called the neutral axis, does not resist bending, and the material furthest away from the center, resists the bending the most.

橫樑正中央的材質被稱為中性軸，它不會抵抗彎折，而越遠離中心點的材料則越能抵抗彎折。

It is called the neutral axis because if we place a bending load downward the same way we did before,

它之所以被稱作中性軸，是因為如果我們像是之前一樣往下施加彎折力道，

the beam will bend in a way that will cause the lower edge to be in max tension and the upper edge to be in max compression,

梁柱將會以一種使底部的邊緣承受最大張力，頂部邊緣承受最大壓力的方式彎折，

and the values of stress gradually decrease to 0 at the neutral axis where there is neither tension or compression.

而壓力的數值會隨著靠近中性軸而趨近於零，該軸上沒有任何的張力或壓力。

Because the tension and compression is maximum the furthest from neutral axis, we want to maximize the amount of material on the outside of the profile where it is needed most.

由於最高的張力與壓力會出現在距離中立軸最遠的地方，我們便希望能盡量把材料用在外側，也就是最需要加強的地方。

The more material further from the neutral axis, the larger the second moment of area will be.

遠離中立軸的材料越多，我們便能獲得越大的面積二次軸矩。

Applying that to the equation, we can see that a larger second moment of area will result in a smaller deflection.

套入到方程式後，我們能看到面積二次軸矩越大，撓度也就越小。

So if we to place this section under the same bending load, it would actually be stronger if we flipped it over 90 degrees, because now more material now located future from the neutral axis.

所以要是我們對右邊的這塊材料施加相同的壓力，把它翻轉 90 度其實會更能支撐力道，因為現在有更多的材料遠離中立軸了。

We could make it even stronger again, by reducing this thickness to a minimum, just enough to resist the shear stress,

我們接著能將它的厚度降低至剛好能抵盪壓力即可，

and placing that material at the the top and suddenly, we're back to the I-beam shape.

並在上面放置更多的材料來讓它變得更能支撐力道，然後我們便回到了左邊的工字樑形狀。

You can see this idea put into action all around you.

在生活的周遭各處都能看到這種概念的應用。

In my last video, I mentioned just one of them when I spoke about the Willis Tower using a bundled tube structure.

在我的上一個影片中，我提到的威利斯大廈所使用的綑綁式管狀結構便是其中之一。

This structure maximizes the amount of steel on the outside of the building to maximize it's resistance to lateral bending from wind and other loads.

這樣的結構在建築外圍使用了盡可能多的鋼鐵，藉此來最大化該建築對強風與其他作用力所造成的側向彎曲抵抗能力。

I will be talking about another application of this technology in my next video,

我將會在下一部影片中提到另一個使用了此種技術的實際應用，

and if you can think of any other examples of the second moment of area being applied in the world around you, be sure to share it in the comments.

如果你能想到生活周遭更多體現了面積二次軸矩的其他例子，歡迎在底下留言分享。

Thanks for watching.

感謝收看。

Like my last video, I wanted to experiment with a shorter format, and it's thanks to sponsors like the TheGreatCoursesPlus that allow me the freedom to do that.

如同我上個影片一樣，我想要實驗看看較短的影片形式，而這都是多虧了有像是 TheGreatCoursesPlus 這樣的贊助商，才能讓我們有這麼做的自由。

They have been a fantastic sponsor of this channel over the last few months.

他們在過去幾個月來一直是本頻道的優良贊助商。

If you'd like to learn more about subjects like this, they have a really great course called Everyday Engineering, and they have a huge range or other topics too.

如果你想要學習更多像是今天這種主題的課程，他們的平台上有個叫做「每日工程學」的超棒課程，上面還有著廣範圍的其他主題。

Their courses give you indepth knowledge and are taught by world renowned educators.

他們的課程能讓你深入學習知識，且皆由世界知名的教育者們教導。

They added a new course by Niel De Grasse Tyson recently or you can learn about photography, history, or cooking.

他們最近剛新增了一門由奈爾·德葛拉司·泰森主持的課程，或是你也能學習攝影學、歷史或是烹飪。

If you'd like to learn more, head over to TheGreatCoursesPLus.com/RealEngineering for your free one month trial.

如果你想要了解更多，就前往 TheGreatCoursesPLus.com/RealEngineering 並取得首月免費試用吧。

If you'd like to see more content from me, the links to my Patreon, Instagram, Facebook, and Twitter accounts are below.

如果你想要觀賞更多來自我的內容，我的 Patreon、Instagram、Facebook 與 Twitter 帳號的連結都放在下面了。