跟讀練習: Statics: Lesson 46 - Distributed Loads Using Centroids - 通過影片學習英語口語

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hey welcome back team today we're talking about distributed loads we've finished chapter set chapter 9

which was Centroids

and now I'm kind of going to jump you back to chapter 4 to talk about distributed loads

because really distribute loads I think it's kind of out of place until you talk about Centroids

and then they really make sense okay we know about Centroids center of volume, center of mass, center of area,

center of weight, center of pressure, right?

Distributed loads has a lot to do with that, okay?

So when you say a distributed load, what is a distributed load?

Well, it's like me standing on the floor, okay?

My weight is distributor over the size of my foot.

Or it's like this textbook.

If I lay this textbook on the table,

this textbook has weight, but that weight is not a point load or a concentrated load like we've been used to, right?

Like that.

That's what we're used to.

But this book actually has the weight spread out all over the whole thing

so that that weight is distributed across an area that's why we call it a distributed load some things

that you might see for

that um maybe maybe a snow load on a roof let's say you were designing a roof

or a building

and you needed to account for the snow load

now in texas where we are there we don't get a lot of snow

so we don't have to worry about that but

if you're up north then you have like a three or four foot storm that dumps that much snow

that could be a tremendous amount of weight on the roof.

If that kind of snow hit Texas,

it would collapse most buildings in Texas because they're just not designed to take that kind of weight on the roof.

So the distributed load looks something like this.

You'll see it given in some kind of weight per length.

In this case, 100 pounds per feet.

So for every foot I go, I'm going to accumulate 100 pounds of weight.

That's what the distributed load looks like.

And this is what we call a rectangular distributed load.

So it's even across the whole thing, okay?

So how do we deal with that?

I know how to deal with that, but I don't know how to deal with that, okay?

And so it would go something like this, right?

You would calculate the size of the distributed load by looking at how much of it you have.

So it's 100 pounds per feet over four feet.

So that would be 400 pounds.

And where do you apply that?

What we're doing here is we're converting a distributed load into a concentrated load just to simplify things

so that we can solve it as a regular old statics problem.

So that would be 400 pounds, right?

So you do 100 pounds per feet times four feet, right?

The feet cancel out and I'm left with just pounds, okay?

So that's where that comes from.

And then where do you apply it?

At the center, okay?

So distributed loads are all around us.

Let me give it to you this way.

Let's say that you want to go dancing, okay?

And you can go dancing, you can dance with me

or you could dance with lovely linda okay now i am full man size okay 220 pounds

that's full man size but lovely linda she's only 120 pounds okay

so who are you gonna dance with well before

we make up our mind let me tell you one thing me and Linda, we're both really bad dancers, okay?

And we're going to step on your foot, okay?

Now, I only go dancing in my cowboy boots, right?

And the heel of my cowboy boots is four inches by three inches, okay?

And so, lovely Linda, she only dances in her stiletto high heels because it makes her legs look good, you know what I mean?

And those little stilettos have a little high heel

that is a quarter of an inch by a quarter of an inch okay

now you're going to get stepped on i guarantee you that

because we're not that good at dancers okay

so let me tell you something you'll run into in solids

and that is stress okay

and stress is what we call the intensity of the force okay

so stress is p over a in other words the force divided by the area

that it's distributed over So in my case, you'd have 220 pounds divided by 3 times 4, 12 inches squared.

Now that's going to give me PSI, okay?

Where lovely Linda, lovely Linda over here is 120 pounds divided by a quarter times a quarter.

That is 0 .0625 inches squared.

And let's see what we get here.

So, if you're dancing with me, you get 220 divided by 12, you're going to feel 18 .3 PSI, okay?

but if you're dancing with linda over there 120 divided by 0 .0625 you're going to feel

1 ,920 psi okay now i don't know what the sheer stress of skin is

but you may be you know if i step on you it's going to hurt

but if she steps on you she may be standing on the floor like through your foot, right?

Punctured a hole right in you.

So, that's distributed load.

If you take a big load and you distribute it over a bigger area, the intensity of the force is much less,

whereas a smaller load even over a very small area, the intensity of the load is very high, okay?

So, when do we see this kind of stuff in real life?

Let's say, I've got me a truck drawn over here.

Let's say you go to the hardware store, okay?

You're building a new house and they're going to deliver it to you

and so what they do is they go out

and they stack up two by fours okay

and two by fours look like this okay and let's say that two by fours were i don't know

500 pounds per foot

and then the little guy at the hardware store thought he'd be clever

there was going to be some cinder blocks on there

so he stacked them like up high but then he went every row, he stacked them one less.

So he had like this triangular load here.

Okay.

Very clever little brick stacker guy.

And what we do on triangular loads is we only give you the tallest point.

So let's say that's 700 pounds per foot.

100

At this end, it's zero pounds per feet, isn't it?

101

And then, I don't know, for some reason on that job site, they also were asking for a whole pallet full of helium okay maybe helium

102

and so that load is like this 200 pounds per feet

103

but it's going upwards right it's it's pulling upwards okay so

104

and if we look at this you might say well okay

105

uh find the reactions on the tires okay

106

so we could say over here maybe we have a by and then over here,

107

I have an AY, and I could solve for those reaction forces on those tires

108

if I can convert those distributed loads into concentrated loads.

109

Well, this first one, let me just, let me, let's make up some numbers here.

110

This looks like 15 feet.

111

I'm going to do numbers that I can do in my head.

112

How about that?

113

20 feet.

114

Okay.

115

And this is 20 feet, which would make this back here 13 feet.

116

Okay.

117

It's a 53 foot trailer.

118

That's how long, that's how long most flatbed tractor trailers are, 53 feet.

119

Okay.

120

So this bit up here is 500 times 20.

121

That's going to be 10 ,000, isn't it?

122

And where would I apply that?

123

Right there.

124

So that's 10 ,000 pounds.

125

And I would apply that right in the center of

126

that rectangle because the centroid of a rectangle is half the base, right?

127

Then this guy, and all I'm doing, think about this as an area.

128

Think about the 500 as the height, and the 20 as the width, and I'm finding the area.

129

You can't go out with a tape measure and measure that area, but it's an area, okay?

130

This area here is 700 tall by 20, but it's a triangle, so I'm going to treat it like an area.

131

I've got to divide that by two, so that would be like 700 times 10, which would be 7 ,000.

132

And where would you put that 7 ,000 pounds?

133

Well, I put it like right there.

134

Okay.

135

Why right there?

136

Well, it's at one third the base of the triangle, right?

137

So this distance right here would be 20 over three.

138

Okay.

139

That's centroid stuff, isn't it?

140

and then over here oh the only tricky part about this is the arrows are going up instead of down

141

so this is 200 times 13 which would be 2600 and I would put that right there Okay.

142

2 ,600 pounds.

143

And it's in the middle of the 13.

144

And so now, now I've got three concentrated loads where I used to have distributed loads.

145

I can solve that like a regular old statics problem, right?

146

Take the moment at A and I got 400 times two rotating me negative.

147

I got 500 times six rotating me negative plus BY times seven rotating me positive

148

and just solve it like every problem we've done.

149

So distributed load problems should be really easy for you if you know what a centroid is,

150

because all you gotta do is calculate the area of this shape, 100 times four, right?

151

Apply that load at the centroid of that shape and then just work it like a regular old statics problem, okay?

152

So when I come back, we'll work one of those problems in the next video and maybe that'll make more sense to you.

153

So hope that helps.

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本課的詞彙與口語要點

這節口語課以影片“Statics: Lesson 46 - Distributed Loads Using Centroids”為素材。影片中反覆出現的詞有：load, distributed, pounds, feet, weight。這段影片共有 153 個句子、1627 個單詞可供跟讀。講話部分時長為 10:42。說話人語速自然，每分鐘約 152 個詞，接近日常對話。 86% 的單詞屬於英語最常用的 3,000 詞，其餘的詞建議在練習前先學一下。全部 153 個句子中有 40 個是問句，適合練習疑問語調和簡短回答。

影片中的重點詞彙

影片中 15 個值得學習的單詞，附發音和釋義：

單詞	發音	釋義
distribute 動詞	/dɪˈstɹɪbjuːt/	分配
divide 動詞	/dɪˈvaɪd/	分, 分裂
solve 動詞	/sɒlv/	解決 /解決
concentrate 動詞	/ˈkɑn.sən.tɹeɪt/	集中
intensity 名詞	/ɪnˈtɛnsɪti/	強度 /強度, 強烈 /強烈
stack 名詞	/stæk/	堆
heel 名詞	/hil/	腳跟 /腳跟, 後跟 /後跟
textbook 名詞	/ˈtɛkst.bʊk/	課本 /課本, 教科書 /教科書
rotate 動詞	/ˈɹoʊ.teɪt/	旋轉, 轉動
trailer 名詞	/ˈtɹeɪlɚ/	拖車 /拖車
hardware 名詞	/ˈhɑɹdˌwɛɹ/	硬體, 硬體 /硬體
boot 名詞	/but/	靴子, 長靴 /長靴
tire 動詞	/ˈtaɪ̯ɚ/	勞累 /勞累, 累
dancer 名詞	/ˈdænsəɹ/	舞蹈家, 舞蹈演員 /舞蹈演員
triangle 名詞	/ˈtɹaɪˌæŋɡəl/	三角, 三角形

影片中出現的短語動詞

單詞	發音	釋義
make up 動詞	/ˌmeɪk ˈʌp/	組成 /組成
come back 動詞		回來 /回來, 返回
go out 動詞		出, 出口
go up 動詞		上昇 /上升, 上去

值得反覆跟讀的句子

影片中簡短而完整的句子，可以直接用在日常對話裡：

That's what we're used to.
Let's say that you want to go dancing, okay?
Let's say you go to the hardware store, okay?
That's centroid stuff, isn't it?

需要注意的發音

說話人用了 47 次縮略和弱讀形式，例如 I'm, we're, you're。請按聽到的簡短形式來說。

長單詞——注意重音位置: intensity /ɪnˈtɛnsɪti/, rectangular /ɹɛkˈtæŋɡjəlɚ/, triangular /tɹaɪˈæŋ.ɡjə.lɚ/, accumulate /əˈkjuːmjʊˌleɪt/

中文母語者容易讀錯的音：

/v/ — 不要讀成 /w/，上齒輕觸下唇: divide /dɪˈvaɪd/, solve /sɒlv/, clever /ˈklɛv.ɚ/, convert /kənˈvɝt/
詞尾子音 — 要讀清楚，後面不要加母音: distribute /dɪˈstɹɪbjuːt/, pound /ˈpaʊ̯nd/, divide /dɪˈvaɪd/, solve /sɒlv/, concentrate /ˈkɑn.sən.tɹeɪt/
/r/ 和 /l/ 的區別: trailer /ˈtɹeɪlɚ/, triangle /ˈtɹaɪˌæŋɡəl/, rectangular /ɹɛkˈtæŋɡjəlɚ/, rectangle /ˈrɛktæŋɡl̩/, triangular /tɹaɪˈæŋ.ɡjə.lɚ/

如何用這段影片練習

先完整聽一遍影片，不要開口，記下不認識的單詞。
先用 0.75 倍速逐句跟讀，熟練之後再回到正常速度。
錄下自己的聲音並與原聲對比，特別注意 distribute, divide, solve 這類單詞。

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影子跟讀法: 閱讀完整分步指南 →

跟讀練習: Statics: Lesson 46 - Distributed Loads Using Centroids - 通過影片學習英語口語

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本課的詞彙與口語要點

影片中的重點詞彙

影片中出現的短語動詞

值得反覆跟讀的句子

需要注意的發音

如何用這段影片練習

什麼是跟讀法？