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        <title>Wyatt的個人網站 Blog</title>
        <link>https://wyatt180.com/blog</link>
        <description>Wyatt的個人網站 Blog</description>
        <lastBuildDate>Fri, 01 May 2026 00:00:00 GMT</lastBuildDate>
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        <language>en</language>
        <copyright>Copyright © 2026 Wyatt Lu</copyright>
        <item>
            <title><![CDATA[2026的Z7]]></title>
            <link>https://wyatt180.com/blog/2026/05/01/風刃Z7</link>
            <guid>https://wyatt180.com/blog/2026/05/01/風刃Z7</guid>
            <pubDate>Fri, 01 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[今天看到廢文小天地的風刃Z7影片]]></description>
            <content:encoded><![CDATA[<p>今天看到<a href="https://trashposts.com/" target="_blank" rel="noopener noreferrer">廢文小天地</a>的風刃Z7影片<br>
<!-- -->我真的好驚訝啊<br>
<!-- -->在這個小小部落格圈竟然有人玩跑跑卡丁車誒<br>
<!-- -->我是一個很晚期才開始玩跑跑的玩家，在倒閉前半年開始玩跑一，然後跑二從開服到關服，現在在國服等跑三<br>
<!-- -->所以完全不認識Z7車，只知道他光罩很大而已<br>
<!-- -->所以我就也想來嘗試跑看看<br>
<a href="https://www.youtube.com/watch?v=V_jYb8hJFao" target="_blank" rel="noopener noreferrer">城鎮高速公路 1分46秒84 風刃Z7</a>
皮皮的路線真的很好啊，我刷了三個多小時學習Z7的跑法後才終於跑進46<br>
<!-- -->對於主要跑跑生涯在跑二的我來說，Z7真的很難跑誒，集氣量實在是太少了<br>
<!-- -->但今天看到有人在玩跑跑真的超級開心的，現在高中同學真的是沒一個玩過</p>
<p>之後會出一篇文章講<strong>曾經的午後間奏</strong>(畢業歌)的和弦進行，不現在講的原因是我也忘了，要去查一下<br>
<!-- -->如果有人有看到這篇文章一定要去<a href="https://rickyblog.bearblog.dev/" target="_blank" rel="noopener noreferrer">Ricky的部落格</a>詳細的歌曲解析喔</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[生產力]]></title>
            <link>https://wyatt180.com/blog/2026/04/29/生產力</link>
            <guid>https://wyatt180.com/blog/2026/04/29/生產力</guid>
            <pubDate>Wed, 29 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[這篇文章的觀點與分享都是我的個人經驗，有看到文章的人不要隨便相信，因為每個人的方法一定都不一樣]]></description>
            <content:encoded><![CDATA[<p><em><strong>這篇文章的觀點與分享都是我的個人經驗，有看到文章的人不要隨便相信，因為每個人的方法一定都不一樣</strong></em></p>
<p>其實我真的不太知道這個主題要寫什麼，但我還是很想要投稿，所以還是寫點東西吧。<br>
<!-- -->四月應該算是我人生生產力的高峰期吧，完成了所有申請大學的備審資料還有一首畢業歌，我就稍微分享一下我這個月對生產力的感受吧。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="拖延大法交差了事">拖延大法+交差了事<a href="https://wyatt180.com/blog/2026/04/29/%E7%94%9F%E7%94%A2%E5%8A%9B#%E6%8B%96%E5%BB%B6%E5%A4%A7%E6%B3%95%E4%BA%A4%E5%B7%AE%E4%BA%86%E4%BA%8B" class="hash-link" aria-label="Direct link to 拖延大法+交差了事" title="Direct link to 拖延大法+交差了事">​</a></h2>
<p>備審要趕到全部四月做，其實是我自己的問題啦</p>
<p>照理來說是高一高二高三要先在每個學習紀錄學習歷程，在最後勾選要用來當作審查資料的檔案，但我高一高二實在太懶，再加上對於僅有的一些紀錄也不滿意，所以決定全部重做了。</p>
<p>我這時候我要講一下我自己在國中時期就在用的技巧─拖延大法。</p>
<p>我感覺我如果在很早就開始做準備，我心裡會覺得反正還有很多時間，所以反而效率低。然而在繳交期限來臨前開始做的話，反而會因為時間的急迫性和心理壓力，用最高效的時間做出最好的作品(至少以我來說啦)。<br>
<!-- -->另外在急迫的時間中，我還會搭配交差了事的心態，不知道為什麼，每次這樣都能做的最好。</p>
<p>我知道這聽起來超級奇怪，但我就是這樣的。</p>
<p>印象很深刻的是國中表演藝術課程的兩次作品<br>
<!-- -->第一次是一個配音作品，找到組員後要幫卡通配音，用剪輯軟體接在一起。</p>
<p>當時我們組員就覺得這實在太無聊了，全部人都沒有興致，亂錄一通(雖然這樣說但也還是認真的錄)，想說作業交一交就好了，在期限截止前幾小時趕上。</p>
<p>結果我們的效果超好的誒，大家在別無選擇的情況下反而做事效率最高，記憶沒錯的話我們在三天內幫一集完整多拉A夢配音＋後製。</p>
<p>另一個表藝課的作品是即時MV演出，選定一首歌後在舞台上搭配音樂演繹MV內容</p>
<p>由於我們組有一個成員有導演夢，所以非常熱情於這次的作品，所以很早就開始規劃時程、畫分鏡、演練等等的</p>
<p>結果我們最後的成果反而有點不知所云，亂糟糟的，節奏很糟糕。</p>
<p>現在的備審資料也是一樣的道理，高一高二時間太多反而不知道在幹嘛，到最後緊要關頭反而有效率的生出了很多我很滿意的文章。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="為什麼">為什麼<a href="https://wyatt180.com/blog/2026/04/29/%E7%94%9F%E7%94%A2%E5%8A%9B#%E7%82%BA%E4%BB%80%E9%BA%BC" class="hash-link" aria-label="Direct link to 為什麼" title="Direct link to 為什麼">​</a></h2>
<p>其實我也不知道真正的原因是什麼，我也懶得去查，所以我就講講我的推論。</p>
<p>我想是因為人在期限將至別無選擇時，就會在自己的<strong>能力範圍內</strong>，做出期限內能做出最滿意的作品</p>
<p>然而在時間很多的狀況下，我反而會鬆懈，且會想著要做很多<strong>能力範圍外</strong>的準備，以及完整的計劃與執行</p>
<p>這樣反而會造成想在每一步都做到完美，想太多，最後一事無成的境地</p>
<p>所以我後來就選擇好好利用我拖延症和交差了事的特性，用更高的效率完成組品。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="這篇文章也是一樣">這篇文章也是一樣<a href="https://wyatt180.com/blog/2026/04/29/%E7%94%9F%E7%94%A2%E5%8A%9B#%E9%80%99%E7%AF%87%E6%96%87%E7%AB%A0%E4%B9%9F%E6%98%AF%E4%B8%80%E6%A8%A3" class="hash-link" aria-label="Direct link to 這篇文章也是一樣" title="Direct link to 這篇文章也是一樣">​</a></h2>
<p>看看今天日期，4/29</p>
<p>必須的繳交文章了</p>
<p>好啊來寫</p>
<p>結果我覺得我寫得還不錯</p>
<p>雖然一定有語句不通順的地方，但我想講的東西都講完了</p>
<p>就這樣吧</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[四重奏練習法]]></title>
            <link>https://wyatt180.com/blog/2026/04/26/四重奏練習法</link>
            <guid>https://wyatt180.com/blog/2026/04/26/四重奏練習法</guid>
            <pubDate>Sun, 26 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[今天是四重奏練習法第一天]]></description>
            <content:encoded><![CDATA[<p>今天是四重奏練習法第一天<br>
<!-- -->無聊在看yt的時候不小心看到wiwi的四重奏練習法編曲的影片<br>
<!-- -->我想說今天就來試試看<br>
<!-- -->今天選Autumn Leaves練習<br>
<!-- -->配置一台midi的鋼琴、一個organ當旋律、一個真的double bass、midi的鼓<br>
<!-- -->真的還蠻好玩的<br>
<!-- -->結果其實不算太難聽誒(我覺得啦)<br>
<!-- -->接下來每天花大約十分鐘練習<br>
<!-- -->看幾天後可以好聽到我覺得可以發的程度<br>
<!-- -->真的好好玩誒</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[自主學習計畫成果]]></title>
            <link>https://wyatt180.com/blog/2026/04/26/自主學習計畫成果</link>
            <guid>https://wyatt180.com/blog/2026/04/26/自主學習計畫成果</guid>
            <pubDate>Sun, 26 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[之前上傳了材料力學的學習筆記，其實後來幾天我就把基礎html學完了，還把它做成了動態圖表，當成自主學習成果。我覺得真的非常酷，我做的是應力應變關係曲線的動態圖，有四個滑桿可以拉，也有預設四種材料可以直接套用正確的數值。有看到的話大家可以滑滑看，真的很有趣。]]></description>
            <content:encoded><![CDATA[<p>之前上傳了材料力學的學習筆記，其實後來幾天我就把基礎html學完了，還把它做成了動態圖表，當成自主學習成果。我覺得真的非常酷，我做的是應力應變關係曲線的動態圖，有四個滑桿可以拉，也有預設四種材料可以直接套用正確的數值。有看到的話大家可以滑滑看，真的很有趣。</p>
<iframe src="/mfe.html" width="800px" height="800px" style="border:none;border-radius:8px" scrolling="no"></iframe>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[班導的話]]></title>
            <link>https://wyatt180.com/blog/2026/04/22/班導的話</link>
            <guid>https://wyatt180.com/blog/2026/04/22/班導的話</guid>
            <pubDate>Wed, 22 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[今天數學課的時候]]></description>
            <content:encoded><![CDATA[<p>今天數學課的時候<br>
<!-- -->老師說了一句話<br>
<!-- -->雖然我有通過<br>
<!-- -->但從我們這個老師嘴裡說出最有說服力</p>
<blockquote>
<p>開心也是過一天，不開心也是過一天，那我當然要開心過一天啊</p>
</blockquote>
<p>我們的老師是一種極樂天歡樂教學的老師<br>
<!-- -->上課會一直呵呵呵呵呵笑嘻嘻<br>
<!-- -->我會把這句話記起來的</p>]]></content:encoded>
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        <item>
            <title><![CDATA[材料力學Day 2]]></title>
            <link>https://wyatt180.com/blog/2026/04/21/材料力學Day2</link>
            <guid>https://wyatt180.com/blog/2026/04/21/材料力學Day2</guid>
            <pubDate>Tue, 21 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[今天是第二天，有感覺內容變難了些]]></description>
            <content:encoded><![CDATA[<p>今天是第二天，有感覺內容變難了些<br>
<!-- -->但是還在可控範圍內<br>
<!-- -->兩天總共花了三小時<br>
<!-- -->我覺得ＯＫ了<br>
<!-- -->該開始學html和javascript來圖形化了<br>
<!-- -->昨天的東西有很多瑕疵但我也懶得管了<br>
<!-- -->在網站上看起來很怪但我本地看還不錯<br>
<!-- -->之後要大翻新網站再說</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="第二課筆記">第二課筆記<a href="https://wyatt180.com/blog/2026/04/21/%E6%9D%90%E6%96%99%E5%8A%9B%E5%AD%B8Day2#%E7%AC%AC%E4%BA%8C%E8%AA%B2%E7%AD%86%E8%A8%98" class="hash-link" aria-label="Direct link to 第二課筆記" title="Direct link to 第二課筆記">​</a></h2>
<p>銅棒的應力應變曲線圖<br>
<img decoding="async" loading="lazy" alt="sas" src="https://wyatt180.com/assets/images/stressandstrain-bfc9bfe3acfceb2e7536318c8c3a7270.jpg" width="1292" height="970" class="img_ev3q"></p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="延展性和脆性">延展性和脆性<a href="https://wyatt180.com/blog/2026/04/21/%E6%9D%90%E6%96%99%E5%8A%9B%E5%AD%B8Day2#%E5%BB%B6%E5%B1%95%E6%80%A7%E5%92%8C%E8%84%86%E6%80%A7" class="hash-link" aria-label="Direct link to 延展性和脆性" title="Direct link to 延展性和脆性">​</a></h3>
<ol>
<li>延展性：變形可以很大量，破壞之前會產生很大的永久應變。eg.結構鋼</li>
<li>脆性材料：變形很小，超過彈性極限就斷掉 。</li>
</ol>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="percent-elongation-percent-reduction">Percent elongation Percent reduction<a href="https://wyatt180.com/blog/2026/04/21/%E6%9D%90%E6%96%99%E5%8A%9B%E5%AD%B8Day2#percent-elongation-percent-reduction" class="hash-link" aria-label="Direct link to Percent elongation Percent reduction" title="Direct link to Percent elongation Percent reduction">​</a></h3>
<p>伸長率：</p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><msub><mi>L</mi><mn>1</mn></msub><mo>−</mo><msub><mi>L</mi><mn>0</mn></msub></mrow><msub><mi>L</mi><mn>0</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">\frac{L_1-L_0}{L_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3335em;vertical-align:-0.4451em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8884em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre><br>
<!-- -->截面積縮小率：<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><msub><mi>A</mi><mn>0</mn></msub><mo>−</mo><msub><mi>A</mi><mn>1</mn></msub></mrow><msub><mi>A</mi><mn>0</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">\frac{A_0-A_1}{A_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3335em;vertical-align:-0.4451em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8884em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre><br>
<strong>若沒有明顯Yield point</strong>：就把linear區域的線往右移0.002，沒有為什麼，是經驗<br>
<strong>受壓和受拉曲線不同</strong><p></p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="loading-and-unloading加載與卸載">Loading and Unloading加載與卸載<a href="https://wyatt180.com/blog/2026/04/21/%E6%9D%90%E6%96%99%E5%8A%9B%E5%AD%B8Day2#loading-and-unloading%E5%8A%A0%E8%BC%89%E8%88%87%E5%8D%B8%E8%BC%89" class="hash-link" aria-label="Direct link to Loading and Unloading加載與卸載" title="Direct link to Loading and Unloading加載與卸載">​</a></h3>
<p>把力放上去和把力拿掉</p>
<ul>
<li>從<strong>原來加載曲線</strong>回到原點，稱為彈性<br>
<!-- -->哪裡是彈性區間，在能回到原點的曲線範圍內叫做<strong>彈性區間 Elastic</strong>
<strong>線彈性</strong>：彈性區間是斜直線Linear</li>
<li>超過彈性區間後進入<strong>塑性 Plastic</strong><br>
<!-- -->在超過彈性區間後會怎麼unloading呢？<br>
<!-- -->會沿著<strong>初始斜率</strong>回來(Stress and strain curve在x=0的微分)<br>
<!-- -->這種超過彈性區間的unload應變叫做<strong>殘文應變</strong>或<strong>永久應變</strong>(Residual Strain)<br>
<!-- -->因為他回不去了<br>
<!-- -->發生明顯改變
展現<strong>Plasticity</strong>行為
如果又在load，就會沿著初始斜率回去然後接回原本的curve，彈性極限會被往前推一點點到Ｂ，但<strong>塑性區域減小</strong>，因為永久應變已經在那裡了回不去了，多的只剩E到B<br>
<img decoding="async" loading="lazy" alt="lau" src="https://wyatt180.com/assets/images/loadandunload-36eefae384537fd0e20d26c42834f0c7.jpg" width="1262" height="534" class="img_ev3q"></li>
</ul>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="潛變creep">潛變Creep<a href="https://wyatt180.com/blog/2026/04/21/%E6%9D%90%E6%96%99%E5%8A%9B%E5%AD%B8Day2#%E6%BD%9B%E8%AE%8Acreep" class="hash-link" aria-label="Direct link to 潛變Creep" title="Direct link to 潛變Creep">​</a></h3>
<p>長時間固定載荷下會產生<strong>額外的應變</strong>，伸長量會隨時間增加<br>
<!-- -->好像就是潛在的變化的感覺<br>
<!-- -->一開始會幾乎線性伸長，然後隨著時間推進達到極限。叫做<strong>潛變</strong><br>
<!-- -->繃緊的材料，一開始應力線性上長，在長時間後鬆掉，應力減少。也叫做潛變。<br>
<img decoding="async" loading="lazy" alt="creep" src="https://wyatt180.com/assets/images/Creep-9eb1c269f626d7edae1c8c464ba276ab.jpg" width="1128" height="823" class="img_ev3q"></p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="虎克定律-hookes-law">虎克定律 Hooke's Law<a href="https://wyatt180.com/blog/2026/04/21/%E6%9D%90%E6%96%99%E5%8A%9B%E5%AD%B8Day2#%E8%99%8E%E5%85%8B%E5%AE%9A%E5%BE%8B-hookes-law" class="hash-link" aria-label="Direct link to 虎克定律 Hooke's Law" title="Direct link to 虎克定律 Hooke's Law">​</a></h3>
<p>Linear elasticity(線彈性)：應力應變曲線為線彈性且線性，符合虎克定律。<br>
</p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo>=</mo><mi>E</mi><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\sigma=E\epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.0576em">E</span><span class="mord mathnormal">ϵ</span></span></span></span></code></pre><br>
<!-- -->E是彈性模數modulus of elasticity或楊氏模數(單位：N/<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>m</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">m^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></code></pre>, Pa)<br>
<!-- -->在線Linear彈性範圍難，不是Linear的都不行<p></p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="poissons-ratio">Poisson's Ratio<a href="https://wyatt180.com/blog/2026/04/21/%E6%9D%90%E6%96%99%E5%8A%9B%E5%AD%B8Day2#poissons-ratio" class="hash-link" aria-label="Direct link to Poisson's Ratio" title="Direct link to Poisson's Ratio">​</a></h2>
<p>Def : 桿件受到拉利伸長時，橫向收縮。此橫向變化過程就是Poisson's Ratio</p>
<h1><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ν</mi><mo>=</mo><mo>−</mo><mfrac><mrow><mi>l</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>l</mi><mtext> </mtext><mi>s</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>a</mi><mi>x</mi><mi>i</mi><mi>a</mi><mi>l</mi><mtext> </mtext><mi>s</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>i</mi><mi>n</mi></mrow></mfrac><mo>=</mo><mo>−</mo><mfrac><msup><mi>δ</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mi>δ</mi></mfrac></mrow><annotation encoding="application/x-tex">\nu=-\frac{lateral\,strain}{axial\,strain}=-\frac{\delta'}{\delta}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0637em">ν</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em"></span><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mord mathnormal mtight">ia</span><span class="mord mathnormal mtight" style="margin-right:0.0197em">l</span><span class="mspace mtight" style="margin-right:0.1952em"></span><span class="mord mathnormal mtight">s</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight" style="margin-right:0.0278em">r</span><span class="mord mathnormal mtight">ain</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0197em">l</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight" style="margin-right:0.0278em">er</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight" style="margin-right:0.0197em">l</span><span class="mspace mtight" style="margin-right:0.1952em"></span><span class="mord mathnormal mtight">s</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight" style="margin-right:0.0278em">r</span><span class="mord mathnormal mtight">ain</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.3185em;vertical-align:-0.345em"></span><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9735em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0379em">δ</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0379em">δ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8278em"><span style="top:-2.931em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre></h1>
<p>通常在0.25在0.35之間<br>
<!-- -->理論最大值為0.5</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="最後強調">最後強調<a href="https://wyatt180.com/blog/2026/04/21/%E6%9D%90%E6%96%99%E5%8A%9B%E5%AD%B8Day2#%E6%9C%80%E5%BE%8C%E5%BC%B7%E8%AA%BF" class="hash-link" aria-label="Direct link to 最後強調" title="Direct link to 最後強調">​</a></h2>
<ol>
<li>Linear elastic線彈性</li>
<li>homogeneous均值</li>
<li>isotropic等相性</li>
</ol>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[自主學習]]></title>
            <link>https://wyatt180.com/blog/2026/04/20/自主學習</link>
            <guid>https://wyatt180.com/blog/2026/04/20/自主學習</guid>
            <pubDate>Mon, 20 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[因為我覺得我高一和高二的自主學習都和科系太沒有關係了，所以決定高三找個主題重新做。我找到了交大開放式課程的材料力學，這是土木大二必修，所以我打算自學個兩三堂，然後學習利用HTML, JavaScript圖形化，一次學兩個很重要的東西，今天是看的第一堂課，以下是筆記，放在這裡記錄。]]></description>
            <content:encoded><![CDATA[<p>因為我覺得我高一和高二的自主學習都和科系太沒有關係了，所以決定高三找個主題重新做。我找到了交大開放式課程的材料力學，這是土木大二必修，所以我打算自學個兩三堂，然後學習利用HTML, JavaScript圖形化，一次學兩個很重要的東西，今天是看的第一堂課，以下是筆記，放在這裡記錄。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="第一課筆記">第一課筆記<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E7%AC%AC%E4%B8%80%E8%AA%B2%E7%AD%86%E8%A8%98" class="hash-link" aria-label="Direct link to 第一課筆記" title="Direct link to 第一課筆記">​</a></h2>
<p>為何要學<br>
<!-- -->了解一個材料的強度safety勁度serviceability與穩定性stability<br>
<!-- -->算好會受到多少力，選擇材料，看是否適合</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="基本假設">基本假設<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E5%9F%BA%E6%9C%AC%E5%81%87%E8%A8%AD" class="hash-link" aria-label="Direct link to 基本假設" title="Direct link to 基本假設">​</a></h3>
<p>所有材料都是<br>
<!-- -->桿件視為可變形固體</p>
<ul>
<li>連續的continuity</li>
<li>均勻的uniformity</li>
<li>等相性的isotropic</li>
<li>微小變形infinitesimal<br>
<!-- -->其他的都不算，因為太難算了<br>
<!-- -->如果沒有這些假設會太難用手算</li>
</ul>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="四種元件">四種元件<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E5%9B%9B%E7%A8%AE%E5%85%83%E4%BB%B6" class="hash-link" aria-label="Direct link to 四種元件" title="Direct link to 四種元件">​</a></h3>
<ul>
<li>連桿link</li>
<li>軸承shaft</li>
<li>梁beam</li>
<li>柱column<br>
<!-- -->![[Pasted image 20260420113912.jpg]]<br>
<!-- -->各種力</li>
</ul>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="ch1-伸長壓縮與剪切tension-compression-and-shear">Ch1 伸長壓縮與剪切Tension, Compression, and Shear<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#ch1-%E4%BC%B8%E9%95%B7%E5%A3%93%E7%B8%AE%E8%88%87%E5%89%AA%E5%88%87tension-compression-and-shear" class="hash-link" aria-label="Direct link to Ch1 伸長壓縮與剪切Tension, Compression, and Shear" title="Direct link to Ch1 伸長壓縮與剪切Tension, Compression, and Shear">​</a></h2>
<p>stress strain displacement <em>on</em> component and structure <em>leads to</em> failure</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="靜力學statics">靜力學Statics<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E9%9D%9C%E5%8A%9B%E5%AD%B8statics" class="hash-link" aria-label="Direct link to 靜力學Statics" title="Direct link to 靜力學Statics">​</a></h3>
<p></p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>B</mi></msub></mrow><annotation encoding="application/x-tex">F_B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0502em">B</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></code></pre> ：作用在Ｂ點的力<br>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex-error" title="ParseError: KaTeX parse error: Can't use function '$' in math mode at position 4: A_x$̲$A_y" style="color:#cc0000">A_x$$A_y</span></code></pre>：Ａ被固定住，實線箭頭加一撇，就是反作用力下標是Ｘ方向和Ｙ方向<br>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>M</mi><mi>A</mi></msub></mrow><annotation encoding="application/x-tex">M_A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.109em">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></code></pre>：彎矩(<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi><mo>∗</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">N*m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.109em">N</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">m</span></span></span></span></code></pre>)作用在Ａ點上，一個讓他力平衡的旋轉力<br>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>q</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">q_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0359em">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></code></pre>：分布載重(<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mi>N</mi><mi>m</mi></mfrac></mrow><annotation encoding="application/x-tex">\frac{N}{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.109em">N</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre>)，在二維，有一條線均勻把力施加在L型上面<br>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>q</mi></msub><mn>2</mn></mrow><annotation encoding="application/x-tex">F_q2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.0359em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span><span class="mord">2</span></span></span></span></code></pre>：分布載重總合力<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>q</mi><mn>1</mn></msub><mo>∗</mo><mi>L</mi></mrow><annotation encoding="application/x-tex">q_1*L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6597em;vertical-align:-0.1944em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0359em">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal">L</span></span></span></span></code></pre>，虛線箭頭<br>
<!-- -->![[Pasted image 20260420132117.jpg]]<p></p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="垂直應力normal-stress-sigma">垂直應力Normal Stress <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span></span></span></span></code></pre><a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E5%9E%82%E7%9B%B4%E6%87%89%E5%8A%9Bnormal-stress-sigma" class="hash-link" aria-label="Direct link to 垂直應力normal-stress-sigma" title="Direct link to 垂直應力normal-stress-sigma">​</a></h3>
<p>內部的應力eg. I'm stress我心中很緊張<br>
<!-- -->A prismatic bar截面積形狀固定<br>
<!-- -->大長管子兩邊受到拉力P後， 截取中間一小段，力均勻分布在中間，他的應力就是</p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo>=</mo><mfrac><mi>P</mi><mi>A</mi></mfrac></mrow><annotation encoding="application/x-tex">\sigma=\frac{P}{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre>(受力/截面積)(單位：<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mi>N</mi><msup><mi>m</mi><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\frac{N}{m^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463em"><span style="top:-2.786em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.109em">N</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre>，帕Pa)<br>
<em>與壓力的差別</em>：應力在內部，壓力在外部，剛好單位一樣而已。<br>
<strong>拉應力</strong>正<br>
<strong>壓應力</strong>負<br>
<!-- -->Stree一定要均勻分布才<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span></span></span></span></code></pre>才成立，P必須作用在他的<strong>形心</strong>     ![[Pasted image 20260420133721.jpg]]<br>
<!-- -->Finite element simulation<br>
<!-- -->把一段東西切成很多小小小塊<br>
<!-- -->中間應力中等高，適用<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo>=</mo><mfrac><mi>P</mi><mi>A</mi></mfrac></mrow><annotation encoding="application/x-tex">\sigma=\frac{P}{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre>。
圓柱兩邊應力不均勻，不適用公式，越界進形心越高，距圓柱愈遠應力越小，接近0甚至比中間小。<br>
<!-- -->![[Pasted image 20260420134447.jpg]]<p></p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="垂直應變normal-strain-epsilon">垂直應變Normal Strain <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">ϵ</span></span></span></span></code></pre><a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E5%9E%82%E7%9B%B4%E6%87%89%E8%AE%8Anormal-strain-epsilon" class="hash-link" aria-label="Direct link to 垂直應變normal-strain-epsilon" title="Direct link to 垂直應變normal-strain-epsilon">​</a></h3>
<p>A prismatic Bar，材料均值<br>
<!-- -->受到兩邊的力，他的伸長量是</p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi></mrow><annotation encoding="application/x-tex">\delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord mathnormal" style="margin-right:0.0379em">δ</span></span></span></span></code></pre>，應變是<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">ϵ</span></span></span></span></code></pre>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi><mo>=</mo><mfrac><mi>δ</mi><mi>L</mi></mfrac></mrow><annotation encoding="application/x-tex">\epsilon=\frac{\delta}{L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">ϵ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0379em">δ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre><br>
<!-- -->也就是因為P的力造成的伸長量<br>
<!-- -->伸長量/原本的長度就是<strong>應變</strong><br>
<!-- -->長度/長度(沒有長度)<br>
<!-- -->拉的是正、壓的是負(跟應力一樣)<p></p>
<h4 class="anchor anchorWithStickyNavbar_LWe7" id="examples">Examples<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#examples" class="hash-link" aria-label="Direct link to Examples" title="Direct link to Examples">​</a></h4>
<h4 class="anchor anchorWithStickyNavbar_LWe7" id="eg1-">e.g.1 :<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#eg1-" class="hash-link" aria-label="Direct link to e.g.1 :" title="Direct link to e.g.1 :">​</a></h4>
<p>Given that </p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.1389em">P</span></span></span></span></code></pre> = 27kN, diameter of the bar <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord mathnormal">d</span></span></span></span></code></pre> = 50mm = 0.05m. Please determine the stress in the bar.<p></p>
<h4 class="anchor anchorWithStickyNavbar_LWe7" id="ans--sigmafracpa-frac27000pi00252--138106--138mpa">Ans : <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo>=</mo><mfrac><mi>P</mi><mi>A</mi></mfrac></mrow><annotation encoding="application/x-tex">\sigma=\frac{P}{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre>= <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>27000</mn><mrow><mi>π</mi><mo>∗</mo><msup><mn>0.025</mn><mn>2</mn></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{27000}{\pi*0.025^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0359em">π</span><span class="mbin mtight">∗</span><span class="mord mtight">0.02</span><span class="mord mtight"><span class="mord mtight">5</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463em"><span style="top:-2.786em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">27000</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre> = <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>13.8</mn><mo>∗</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><annotation encoding="application/x-tex">13.8*10^6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">13.8</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8141em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">6</span></span></span></span></span></span></span></span></span></span></span></code></pre> = <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>13.8</mn><mi>M</mi><mi>P</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">13.8MPa</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord">13.8</span><span class="mord mathnormal" style="margin-right:0.109em">M</span><span class="mord mathnormal" style="margin-right:0.1389em">P</span><span class="mord mathnormal">a</span></span></span></span></code></pre><a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#ans--sigmafracpa-frac27000pi00252--138106--138mpa" class="hash-link" aria-label="Direct link to ans--sigmafracpa-frac27000pi00252--138106--138mpa" title="Direct link to ans--sigmafracpa-frac27000pi00252--138106--138mpa">​</a></h4>
<h4 class="anchor anchorWithStickyNavbar_LWe7" id="eg2-">e.g.2 :<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#eg2-" class="hash-link" aria-label="Direct link to e.g.2 :" title="Direct link to e.g.2 :">​</a></h4>
<p>The bar has original length </p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal">L</span></span></span></span></code></pre> = 2.0 m. When it is subjected to a load in tension, it might elongate(伸長) by 1.4mm. Please determine the strain of the bar.<p></p>
<h4 class="anchor anchorWithStickyNavbar_LWe7" id="ans--epsilonfracdeltalfrac1410-32710-4007">Ans : <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi><mo>=</mo><mfrac><mi>δ</mi><mi>L</mi></mfrac><mo>=</mo><mfrac><mrow><mn>1.4</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow><mn>2</mn></mfrac><mo>=</mo><mn>7</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>=</mo><mn>0.07</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">\epsilon=\frac{\delta}{L}=\frac{1.4*{10}^{-3}}{2}=7*{10}^{-4}=0.07\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">ϵ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0379em">δ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.3629em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0179em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1.4</span><span class="mbin mtight">∗</span><span class="mord mtight"><span class="mord mtight"><span class="mord mtight">10</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913em"><span style="top:-2.931em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8484em"></span><span class="mord"><span class="mord"><span class="mord">10</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8484em"><span style="top:-3.0973em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">4</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em"></span><span class="mord">0.07%</span></span></span></span></code></pre><a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#ans--epsilonfracdeltalfrac1410-32710-4007" class="hash-link" aria-label="Direct link to ans--epsilonfracdeltalfrac1410-32710-4007" title="Direct link to ans--epsilonfracdeltalfrac1410-32710-4007">​</a></h4>
<h4 class="anchor anchorWithStickyNavbar_LWe7" id="eg-3">e.g. 3:<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#eg-3" class="hash-link" aria-label="Direct link to e.g. 3:" title="Direct link to e.g. 3:">​</a></h4>
<p><strong>Given :</strong><br>
</p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mn>240</mn><mi>k</mi><mi>N</mi><mo>=</mo><mn>240</mn><mo separator="true">,</mo><mn>000</mn><mi>N</mi></mrow><annotation encoding="application/x-tex">P=240kN=240,000N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.1389em">P</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord">240</span><span class="mord mathnormal" style="margin-right:0.0315em">k</span><span class="mord mathnormal" style="margin-right:0.109em">N</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em"></span><span class="mord">240</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">000</span><span class="mord mathnormal" style="margin-right:0.109em">N</span></span></span></span></code></pre><br>
<!-- -->outer diameter <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>=</mo><mn>130</mn><mi>m</mi><mi>m</mi><mo>=</mo><mn>1.3</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">d_2=130mm=1.3*{10}^{-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">130</span><span class="mord mathnormal">mm</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">1.3</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8484em"></span><span class="mord"><span class="mord"><span class="mord">10</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8484em"><span style="top:-3.0973em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></code></pre><br>
<!-- -->inner diameter <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>d</mi><mn>1</mn></msub><mo>=</mo><mn>90</mn><mi>m</mi><mi>m</mi><mo>=</mo><mn>9</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow><annotation encoding="application/x-tex">d_1=90mm=9*{10}^{-2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">90</span><span class="mord mathnormal">mm</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8484em"></span><span class="mord"><span class="mord"><span class="mord">10</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8484em"><span style="top:-3.0973em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></code></pre><br>
<!-- -->length <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mo>=</mo><mn>1</mn><mi>m</mi></mrow><annotation encoding="application/x-tex">L=1m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal">L</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">1</span><span class="mord mathnormal">m</span></span></span></span></code></pre><br>
<!-- -->shorten of the length <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi><mo>=</mo><mn>0.55</mn><mi>m</mi><mi>m</mi><mo>=</mo><mn>5.5</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\delta=0.55mm=5.5*{10}^{-4}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord mathnormal" style="margin-right:0.0379em">δ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">0.55</span><span class="mord mathnormal">mm</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">5.5</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8484em"></span><span class="mord"><span class="mord"><span class="mord">10</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8484em"><span style="top:-3.0973em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span></span></code></pre><br>
<strong>Find :</strong>
(1) compressive stress <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span></span></span></span></code></pre><br>
<!-- -->(2) strain <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">ϵ</span></span></span></span></code></pre><p></p>
<p><strong>Ans :</strong>
力均勻分布在那個Tube上面，Tube被均勻往下壓。<br>
<!-- -->(1)</p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo>=</mo><mfrac><mi>P</mi><mi>A</mi></mfrac></mrow><annotation encoding="application/x-tex">\sigma=\frac{P}{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mfrac><mi>π</mi><mn>4</mn></mfrac><mo stretchy="false">(</mo><msubsup><mi>d</mi><mn>2</mn><mn>2</mn></msubsup><mo>−</mo><msubsup><mi>d</mi><mn>1</mn><mn>2</mn></msubsup><mo stretchy="false">)</mo><mo>=</mo><mfrac><mi>π</mi><mn>4</mn></mfrac><mo stretchy="false">(</mo><msup><mn>130</mn><mn>2</mn></msup><mo>−</mo><msup><mn>90</mn><mn>2</mn></msup><mo stretchy="false">)</mo><mo>=</mo><mn>6912</mn><mi>m</mi><msup><mi>m</mi><mn>2</mn></msup><mo>=</mo><mn>6912</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup><msup><mi>m</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">A=\frac{\pi}{4}(d_2^2-d_1^2)=\frac{\pi}{4}(130^2-90^2)=6912mm^2=6912*{10}^{-6}m^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.1591em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0359em">π</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-2.4519em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal">d</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-2.4519em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.1591em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0359em">π</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord">13</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord">9</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8141em"></span><span class="mord">6912</span><span class="mord mathnormal">m</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">6912</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8484em"></span><span class="mord"><span class="mord"><span class="mord">10</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8484em"><span style="top:-3.0973em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></code></pre>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo>=</mo><mfrac><mi>P</mi><mi>A</mi></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>240000</mn><mi>N</mi></mrow><mrow><mn>6912</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>−</mo><mn>34.7</mn><mi>M</mi><mi>P</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">\sigma=\frac{P}{A}=\frac{-240000N}{6912*{10}^{-6}}=-34.7MPa</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">6912</span><span class="mbin mtight">∗</span><span class="mord mtight"><span class="mord mtight"><span class="mord mtight">10</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em"><span style="top:-2.7916em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">240000</span><span class="mord mathnormal mtight" style="margin-right:0.109em">N</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em"></span><span class="mord">−</span><span class="mord">34.7</span><span class="mord mathnormal" style="margin-right:0.109em">M</span><span class="mord mathnormal" style="margin-right:0.1389em">P</span><span class="mord mathnormal">a</span></span></span></span></code></pre><br>
<!-- -->(2)<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi><mo>=</mo><mfrac><mi>δ</mi><mi>L</mi></mfrac><mo>=</mo><mfrac><mn>0.55</mn><mn>1000</mn></mfrac><mo>=</mo><mo>−</mo><mn>5.5</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\epsilon=\frac{\delta}{L}=\frac{0.55}{1000}=-5.5*{10}^{-4}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">ϵ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0379em">δ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1000</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0.55</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em"></span><span class="mord">−</span><span class="mord">5.5</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8484em"></span><span class="mord"><span class="mord"><span class="mord">10</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8484em"><span style="top:-3.0973em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span></span></code></pre><br>
<!-- -->![[Pasted image 20260420144556.jpg]]<p></p>
<h4 class="anchor anchorWithStickyNavbar_LWe7" id="eg-4">e.g. 4:<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#eg-4" class="hash-link" aria-label="Direct link to e.g. 4:" title="Direct link to e.g. 4:">​</a></h4>
<p><strong>Given :</strong><br>
<!-- -->circular steel rod<br>
<!-- -->length : </p><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal">L</span></span></span></span></code></pre><br>
<!-- -->diameter : <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord mathnormal">d</span></span></span></span></code></pre><br>
<!-- -->bucket weight : <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>W</mi></mrow><annotation encoding="application/x-tex">W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.1389em">W</span></span></span></span></code></pre><br>
<strong>Find :</strong>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>σ</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\sigma_{max}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></code></pre> (account the weight of the rod of itself, rod density <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.0556em">γ</span></span></span></span></code></pre> )<br>
<strong>Ans :</strong>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo stretchy="false">(</mo><mtext>向上</mtext><mo stretchy="false">)</mo><mo>=</mo><mi>W</mi><mo>+</mo><msub><mi>W</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mtext>自重</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F_{max}(向上)=W+W_0(自重)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord cjk_fallback">向上</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em"></span><span class="mord mathnormal" style="margin-right:0.1389em">W</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord cjk_fallback">自重</span><span class="mclose">)</span></span></span></span></code></pre><br>
<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo><mi>W</mi><mo>+</mo><mi>g</mi><mi>γ</mi><mi>A</mi><mi>L</mi><mo stretchy="false">(</mo><mtext>體積</mtext><mo>∗</mo><mtext>密度</mtext><mo>∗</mo><mtext>重力加速度</mtext><mo stretchy="false">)</mo><mo>=</mo><mi>W</mi><mo>+</mo><mi>g</mi><mi>γ</mi><mfrac><mrow><mi>π</mi><msup><mi>d</mi><mn>2</mn></msup></mrow><mn>4</mn></mfrac><mi>L</mi></mrow><annotation encoding="application/x-tex">F_{max}=W+g\gamma AL(體積*密度*重力加速度)=W+g\gamma\frac{\pi d^2}{4}L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.1389em">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em"></span><span class="mord mathnormal" style="margin-right:0.1389em">W</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.0359em">g</span><span class="mord mathnormal" style="margin-right:0.0556em">γ</span><span class="mord mathnormal">A</span><span class="mord mathnormal">L</span><span class="mopen">(</span><span class="mord cjk_fallback">體積</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord cjk_fallback">密度</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord cjk_fallback">重力加速度</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em"></span><span class="mord mathnormal" style="margin-right:0.1389em">W</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1.3629em;vertical-align:-0.345em"></span><span class="mord mathnormal" style="margin-right:0.0359em">g</span><span class="mord mathnormal" style="margin-right:0.0556em">γ</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0179em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0359em">π</span><span class="mord mtight"><span class="mord mathnormal mtight">d</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913em"><span style="top:-2.931em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal">L</span></span></span></span></code></pre><p></p>
<h5 class="anchor anchorWithStickyNavbar_LWe7" id="sigma_maxfracf_maxafracwaggamma-lfrac4wpi-d2ggamma-l"><pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>σ</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo><mfrac><msub><mi>F</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mi>A</mi></mfrac><mo>=</mo><mfrac><mi>W</mi><mi>A</mi></mfrac><mo>+</mo><mi>g</mi><mi>γ</mi><mi>L</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi>W</mi></mrow><mrow><mi>π</mi><msup><mi>d</mi><mn>2</mn></msup></mrow></mfrac><mo>+</mo><mi>g</mi><mi>γ</mi><mi>L</mi></mrow><annotation encoding="application/x-tex">\sigma_{max}=\frac{F_{max}}{A}=\frac{W}{A}+g\gamma L=\frac{4W}{\pi d^2}+g\gamma L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2334em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8884em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1645em"><span style="top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ma</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em">W</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.0359em">g</span><span class="mord mathnormal" style="margin-right:0.0556em">γ</span><span class="mord mathnormal">L</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0359em">π</span><span class="mord mtight"><span class="mord mathnormal mtight">d</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463em"><span style="top:-2.786em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span><span class="mord mathnormal mtight" style="margin-right:0.1389em">W</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.0359em">g</span><span class="mord mathnormal" style="margin-right:0.0556em">γ</span><span class="mord mathnormal">L</span></span></span></span></code></pre><a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#sigma_maxfracf_maxafracwaggamma-lfrac4wpi-d2ggamma-l" class="hash-link" aria-label="Direct link to sigma_maxfracf_maxafracwaggamma-lfrac4wpi-d2ggamma-l" title="Direct link to sigma_maxfracf_maxafracwaggamma-lfrac4wpi-d2ggamma-l">​</a></h5>
<p>要找哪裡的應力就切哪裡，靠力平衡找出力。<br>
<!-- -->重要的是如何畫切開來的受力圖。<br>
<!-- -->![[Pasted image 20260420152620.jpg]]</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="為何要學應力stress-sigma-和-應變strain-epsilon">為何要學應力Stress <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span></span></span></span></code></pre> 和 應變Strain <pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">ϵ</span></span></span></span></code></pre><a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E7%82%BA%E4%BD%95%E8%A6%81%E5%AD%B8%E6%87%89%E5%8A%9Bstress-sigma-%E5%92%8C-%E6%87%89%E8%AE%8Astrain-epsilon" class="hash-link" aria-label="Direct link to 為何要學應力stress-sigma-和-應變strain-epsilon" title="Direct link to 為何要學應力stress-sigma-和-應變strain-epsilon">​</a></h3>
<p>應力應變的比值針對材料性質不管幾何<br>
<!-- -->完全針對材料<br>
<!-- -->一開始用<strong>單位伸長量所需的力</strong>當作座標，發線同種金屬斜率不同，表示金屬的伸長量會受到幾何(截面積和長度)影響。<br>
<!-- -->後來發現若使用<strong>應力與應變的比值</strong>就能統一一種材料的性質，去除外型的影響。<br>
<!-- -->![[Pasted image 20260420154158.jpg]]</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="nominal-and-true-stress-strain">Nominal and True Stress, Strain<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#nominal-and-true-stress-strain" class="hash-link" aria-label="Direct link to Nominal and True Stress, Strain" title="Direct link to Nominal and True Stress, Strain">​</a></h3>
<p>![[Pasted image 20260420155242.jpg]]</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="第一堂課總結和心得">第一堂課總結和心得<a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E7%AC%AC%E4%B8%80%E5%A0%82%E8%AA%B2%E7%B8%BD%E7%B5%90%E5%92%8C%E5%BF%83%E5%BE%97" class="hash-link" aria-label="Direct link to 第一堂課總結和心得" title="Direct link to 第一堂課總結和心得">​</a></h2>
<p>因為單純用伸長量與受力會因幾何形狀不同，導致同金屬卻有不同斜率，所以找到應力與應變的比值來讓所有相同金屬性質相同。</p>
<h6 class="anchor anchorWithStickyNavbar_LWe7" id="應力是內部的力在均勻受力的清況下應力sigmafracp力a截面積">應力是內部的力，在均勻受力的清況下<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>應力</mtext><mi>σ</mi><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mtext>力</mtext><mo stretchy="false">)</mo></mrow><mrow><mi>A</mi><mo stretchy="false">(</mo><mtext>截面積</mtext><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">應力\sigma=\frac{P(力)}{A(截面積)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord cjk_fallback">應力</span><span class="mord mathnormal" style="margin-right:0.0359em">σ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span><span class="mopen mtight">(</span><span class="mord cjk_fallback mtight">截面積</span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.485em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.1389em">P</span><span class="mopen mtight">(</span><span class="mord cjk_fallback mtight">力</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre><a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E6%87%89%E5%8A%9B%E6%98%AF%E5%85%A7%E9%83%A8%E7%9A%84%E5%8A%9B%E5%9C%A8%E5%9D%87%E5%8B%BB%E5%8F%97%E5%8A%9B%E7%9A%84%E6%B8%85%E6%B3%81%E4%B8%8B%E6%87%89%E5%8A%9Bsigmafracp%E5%8A%9Ba%E6%88%AA%E9%9D%A2%E7%A9%8D" class="hash-link" aria-label="Direct link to 應力是內部的力在均勻受力的清況下應力sigmafracp力a截面積" title="Direct link to 應力是內部的力在均勻受力的清況下應力sigmafracp力a截面積">​</a></h6>
<h6 class="anchor anchorWithStickyNavbar_LWe7" id="應變是一種比例在材料均值的情況下應變epsilonfracdelta伸長量l_0原長">應變是一種比例，在材料均值的情況下<pre tabindex="0" class="codeBlockStandalone_MEMb thin-scrollbar language-math math-inline codeBlockContainer_Ckt0 theme-code-block" style="--prism-color:#393A34;--prism-background-color:#f6f8fa"><code class="codeBlockLines_e6Vv"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>應變</mtext><mi>ϵ</mi><mo>=</mo><mfrac><mrow><mi>δ</mi><mo stretchy="false">(</mo><mtext>伸長量</mtext><mo stretchy="false">)</mo></mrow><mrow><msub><mi>L</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mtext>原長</mtext><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">應變\epsilon=\frac{\delta(伸長量)}{L_0(原長)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord cjk_fallback">應變</span><span class="mord mathnormal">ϵ</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord cjk_fallback mtight">原長</span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.485em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.0379em">δ</span><span class="mopen mtight">(</span><span class="mord cjk_fallback mtight">伸長量</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></code></pre><a href="https://wyatt180.com/blog/2026/04/20/%E8%87%AA%E4%B8%BB%E5%AD%B8%E7%BF%92#%E6%87%89%E8%AE%8A%E6%98%AF%E4%B8%80%E7%A8%AE%E6%AF%94%E4%BE%8B%E5%9C%A8%E6%9D%90%E6%96%99%E5%9D%87%E5%80%BC%E7%9A%84%E6%83%85%E6%B3%81%E4%B8%8B%E6%87%89%E8%AE%8Aepsilonfracdelta%E4%BC%B8%E9%95%B7%E9%87%8Fl_0%E5%8E%9F%E9%95%B7" class="hash-link" aria-label="Direct link to 應變是一種比例在材料均值的情況下應變epsilonfracdelta伸長量l_0原長" title="Direct link to 應變是一種比例在材料均值的情況下應變epsilonfracdelta伸長量l_0原長">​</a></h6>
<p>但由於現實中不會那麼漂亮，所以這些叫做Nominal Stress and Strain<br>
<!-- -->真實的應力和應變需要用積分處理</p>
<p>感覺大學的課程沒有想性中那麼難，就只是變成原文書和很多符號而已，至少目前上完第一堂開放式課程這樣感覺啦。</p>]]></content:encoded>
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            <title><![CDATA[畢業歌]]></title>
            <link>https://wyatt180.com/blog/2026/04/18/畢業歌</link>
            <guid>https://wyatt180.com/blog/2026/04/18/畢業歌</guid>
            <pubDate>Sat, 18 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[今天是畢業歌投稿繳交期限，我們也停止混音內耗，就這樣了。]]></description>
            <content:encoded><![CDATA[<p>今天是畢業歌投稿繳交期限，我們也停止混音內耗，就這樣了。</p>
<audio controls=""><source src="/assets/medias/畢業歌9.2-1cbfada9af48d3b630810d635a3c4ba8.m4a" type="audio/mp4"></audio>
<p>我真的覺的我們的歌非常好聽，以下是幾個我覺得最好聽的點。</p>
<ol>
<li>第一次主歌靠北根本不重要的和音</li>
<li>第一次副歌的信因因因因因念</li>
<li>間奏的double bass(那是我彈的喔)</li>
<li>間奏接第二次主歌的漸強的恩恩恩吉他聲</li>
<li>第二次pre-chorus的主吉他的藍調音階點綴</li>
<li>整首歌所有的小號</li>
<li>第二次副歌呼嘯綿延的和音</li>
<li>驀然回首那句和的太好聽了</li>
<li>第三次轉調副歌的雙眼星空嗡嗡嗡嗡屋嗡嗡</li>
<li>G大調 -&gt; C大調 -&gt; A大調 -&gt; Gadd2結尾，每一次轉調都超好聽</li>
</ol>
<p>至於人員名單和工作分配等之後上架串流再說，因為現在直接把他們的本名供出來感覺也不好，連我自己都沒有在這公布我的本名了。</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[NBA附加賽和季後賽預測]]></title>
            <link>https://wyatt180.com/blog/2026/04/14/Playoffs</link>
            <guid>https://wyatt180.com/blog/2026/04/14/Playoffs</guid>
            <pubDate>Tue, 14 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[明天就要開打了，我的預測，或者說，猜測，也可以說，我希望他長得樣子。]]></description>
            <content:encoded><![CDATA[<p>明天就要開打了，我的預測，或者說，猜測，也可以說，我希望他長得樣子。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="west">West<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#west" class="hash-link" aria-label="Direct link to West" title="Direct link to West">​</a></h2>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="play-in">Play-In<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#play-in" class="hash-link" aria-label="Direct link to Play-In" title="Direct link to Play-In">​</a></h3>
<p>Warriors vs. Clippers_Clippers<br>
<!-- -->Suns vs. Trail Blazers_Suns<br>
<!-- -->Trail Blazers vs. Clippers_Trail Blazers</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="first-round">First Round<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#first-round" class="hash-link" aria-label="Direct link to First Round" title="Direct link to First Round">​</a></h3>
<p>Trail Blazers vs. Thunder_Thunder 4:0<br>
<!-- -->Lakers vs. Rockets_Lakers 4:3<br>
<!-- -->Nuggets vs. Timberwolves_Nuggets 4:2<br>
<!-- -->Spurs vs. Suns_Suns 4:3</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="second-round">Second Round<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#second-round" class="hash-link" aria-label="Direct link to Second Round" title="Direct link to Second Round">​</a></h3>
<p>Thunder vs. Suns_Thunder 4:1<br>
<!-- -->Nuggets vs. Lakers_Lakers 4:2</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="conference-final">Conference Final<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#conference-final" class="hash-link" aria-label="Direct link to Conference Final" title="Direct link to Conference Final">​</a></h3>
<p>Thunder vs. Lakers_Lakers 4:3</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="east">East<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#east" class="hash-link" aria-label="Direct link to East" title="Direct link to East">​</a></h2>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="play-in-1">Play-In<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#play-in-1" class="hash-link" aria-label="Direct link to Play-In" title="Direct link to Play-In">​</a></h3>
<p>Hornets vs. Heat_Hornets<br>
<!-- -->76ers vs. Magic_76ers<br>
<!-- -->Hornets vs. Magic_Hornets</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="first-round-1">First Round<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#first-round-1" class="hash-link" aria-label="Direct link to First Round" title="Direct link to First Round">​</a></h3>
<p>Pistons vs. Hornets＿Hornets 4:2<br>
<!-- -->Celtics vs. 76ers_Celtics 4:1<br>
<!-- -->Cavaliers vs. Raptors_Cavaliers 4:0<br>
<!-- -->Knicks vs. Hawks_Hawks 4:2</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="second-round-1">Second Round<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#second-round-1" class="hash-link" aria-label="Direct link to Second Round" title="Direct link to Second Round">​</a></h3>
<p>Celtics vs. Hornets_Celtics 4:3<br>
<!-- -->Cavaliers vs. Hawks_Cavaliers 4:1</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="conference-final-1">Conference Final<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#conference-final-1" class="hash-link" aria-label="Direct link to Conference Final" title="Direct link to Conference Final">​</a></h3>
<p>Cavaliers vs. Celtics_Cavaliers 4:2</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="final">Final<a href="https://wyatt180.com/blog/2026/04/14/Playoffs#final" class="hash-link" aria-label="Direct link to Final" title="Direct link to Final">​</a></h2>
<p>Cavaliers vs. Lakers_Cavaliers 4:1</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[好用軟體]]></title>
            <link>https://wyatt180.com/blog/2026/04/11/好用軟體</link>
            <guid>https://wyatt180.com/blog/2026/04/11/好用軟體</guid>
            <pubDate>Sat, 11 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[這篇文來整理我在macOS中用的好用軟體，這些軟體必須有以下條件]]></description>
            <content:encoded><![CDATA[<p>這篇文來整理我在macOS中用的好用軟體，這些軟體必須有以下條件</p>
<ol>
<li>是開源的自由軟體</li>
<li>好用<br>
<!-- -->沒錯就這兩個，單純想分享一下有些好用的東西</li>
</ol>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="monitorcontrol"><a href="https://github.com/MonitorControl/MonitorControl" target="_blank" rel="noopener noreferrer">MonitorControl</a><a href="https://wyatt180.com/blog/2026/04/11/%E5%A5%BD%E7%94%A8%E8%BB%9F%E9%AB%94#monitorcontrol" class="hash-link" aria-label="Direct link to monitorcontrol" title="Direct link to monitorcontrol">​</a></h2>
<p>這是一個讓軟體控制螢幕參數的東西，一般來說macOS要控制外接螢幕音量大小、亮度需要手動去按螢幕上的實體按鈕，用這個就可以用鍵盤或滑鼠直接調。安裝後他會在上面的menu bar顯示一個小小的icon，點進去就可調整外接螢幕亮度跟音量。我通常是使用鍵盤快速鍵F1 F2控制亮度，F10 F11 F12控制靜音、條小音量、條大音量。<br>
<img decoding="async" loading="lazy" alt="長這樣" src="https://wyatt180.com/assets/images/mca-8c267abae59edb3f65d27f731590baa2.png" width="455" height="155" class="img_ev3q"></p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="battery"><a href="https://github.com/actuallymentor/battery" target="_blank" rel="noopener noreferrer">Battery</a><a href="https://wyatt180.com/blog/2026/04/11/%E5%A5%BD%E7%94%A8%E8%BB%9F%E9%AB%94#battery" class="hash-link" aria-label="Direct link to battery" title="Direct link to battery">​</a></h2>
<p>這是一個控制筆電充電量的軟體，可以控制充電到多少％就停止，也就是跟macOS26.4的新功能一模一樣的東西，絕對不要為了控制電量安裝新作業系統啊。<br>
<img decoding="async" loading="lazy" alt="長這樣" src="https://wyatt180.com/assets/images/batterya-c4af8e0b748fdb5cae613cf1cb9ecee9.png" width="376" height="173" class="img_ev3q"></p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="boring-notch"><a href="https://github.com/TheBoredTeam/boring.notch" target="_blank" rel="noopener noreferrer">Boring Notch</a><a href="https://wyatt180.com/blog/2026/04/11/%E5%A5%BD%E7%94%A8%E8%BB%9F%E9%AB%94#boring-notch" class="hash-link" aria-label="Direct link to boring-notch" title="Direct link to boring-notch">​</a></h2>
<p>MacBook上面都有一個醜醜的瀏海，這是讓那個醜醜瀏海變成動態島的軟體，幾乎沒有實質幫助，就是很帥很酷這樣。這個我最近才開始用，所以對他得耗電量還不了解，但總之很帥，然後可以很快Airdrop這樣。<br>
<img decoding="async" loading="lazy" alt="na" src="https://wyatt180.com/assets/images/na-70573e8bc3ced9a8680da2c392df2063.png" width="522" height="74" class="img_ev3q"><br>
<img decoding="async" loading="lazy" alt="nam" src="https://wyatt180.com/assets/images/nam-ac6c849523c36a6bfc61eda93a0baee1.png" width="802" height="158" class="img_ev3q"><br>
<img decoding="async" loading="lazy" alt="naa" src="https://wyatt180.com/assets/images/naa-a7f243df241137060030014b37d48852.png" width="662" height="162" class="img_ev3q"><br>
<!-- -->他的設定有很多詳細的參數可以調，這邊就不多寫，因為我也還不知道怎麼設定好。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="iina"><a href="https://github.com/iina/iina" target="_blank" rel="noopener noreferrer">IINA</a><a href="https://wyatt180.com/blog/2026/04/11/%E5%A5%BD%E7%94%A8%E8%BB%9F%E9%AB%94#iina" class="hash-link" aria-label="Direct link to iina" title="Direct link to iina">​</a></h2>
<p>播放器，這個應該沒有人不知道，反正很厲害，就這樣。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="vienna"><a href="https://github.com/ViennaRSS/vienna-rss" target="_blank" rel="noopener noreferrer">Vienna</a><a href="https://wyatt180.com/blog/2026/04/11/%E5%A5%BD%E7%94%A8%E8%BB%9F%E9%AB%94#vienna" class="hash-link" aria-label="Direct link to vienna" title="Direct link to vienna">​</a></h2>
<p>一個很好用的RSS閱讀器，就這樣。<br>
<img decoding="async" loading="lazy" alt="va" src="https://wyatt180.com/assets/images/va-e2f460fa4ce87fea24eab72751eef615.png" width="483" height="338" class="img_ev3q"></p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="musicbrainz-picard"><a href="https://github.com/metabrainz/picard" target="_blank" rel="noopener noreferrer">MusicBrainz Picard</a><a href="https://wyatt180.com/blog/2026/04/11/%E5%A5%BD%E7%94%A8%E8%BB%9F%E9%AB%94#musicbrainz-picard" class="hash-link" aria-label="Direct link to musicbrainz-picard" title="Direct link to musicbrainz-picard">​</a></h2>
<p>一個幫音樂貼上標籤的軟體，對於買CD的人來說非常重要。他可以把CD中的每首歌貼上他的所有資訊，誰唱的誰寫的哪一年等等等等等等，非常好用。
<img decoding="async" loading="lazy" alt="mbpa" src="https://wyatt180.com/assets/images/mbpa-d638f61ecbd1c6497549e881126070f6.png" width="607" height="429" class="img_ev3q"></p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="obs"><a href="https://github.com/obsproject/obs-studio" target="_blank" rel="noopener noreferrer">OBS</a><a href="https://wyatt180.com/blog/2026/04/11/%E5%A5%BD%E7%94%A8%E8%BB%9F%E9%AB%94#obs" class="hash-link" aria-label="Direct link to obs" title="Direct link to obs">​</a></h2>
<p>應該也沒有人不知道，好用的串流錄影軟體。<br>
<img decoding="async" loading="lazy" alt="obs" src="https://wyatt180.com/assets/images/obs-a2dc7df0b688673ff3bec564772aa871.png" width="546" height="379" class="img_ev3q"></p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="終端機">終端機<a href="https://wyatt180.com/blog/2026/04/11/%E5%A5%BD%E7%94%A8%E8%BB%9F%E9%AB%94#%E7%B5%82%E7%AB%AF%E6%A9%9F" class="hash-link" aria-label="Direct link to 終端機" title="Direct link to 終端機">​</a></h2>
<p>當然還有很多終端機中的軟體，像是</p>
<ul>
<li>ffmpeg(音頻處理軟體)</li>
<li>ghostscript(壓縮pdf軟體)</li>
<li>imagemagick(壓縮圖片軟體)</li>
<li>yt-dlp(下載YouTube影片)<br>
<!-- -->還有很多，我就不依依列出來了</li>
</ul>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[畢業歌錄製]]></title>
            <link>https://wyatt180.com/blog/2026/04/07/畢業歌</link>
            <guid>https://wyatt180.com/blog/2026/04/07/畢業歌</guid>
            <pubDate>Tue, 07 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[今天錄製鼓的部分，我們的鼓手真的很厲害也很賣力啊，竟然短短一次主歌副歌錄了超過50個take]]></description>
            <content:encoded><![CDATA[<p>今天錄製鼓的部分，我們的鼓手真的很厲害也很賣力啊，竟然短短一次主歌副歌錄了超過50個take</p>
<p>真的很享受製作音樂，太開心了，感覺這幾年學的編曲作曲錄音混音終於有實戰用到的感覺</p>
<p>我們的畢業歌真的很好聽，很好聽，很好聽</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[理想的日常]]></title>
            <link>https://wyatt180.com/blog/2026/04/01/理想的日常</link>
            <guid>https://wyatt180.com/blog/2026/04/01/理想的日常</guid>
            <pubDate>Wed, 01 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[這希望算是我的「BlogBlog 同樂會 - 2026 年 3 月」的投稿文章。上個月主題是「理想的日常」，由 Alex Hsu 主持。如果你有自己的部落格，歡迎一起來參加！]]></description>
            <content:encoded><![CDATA[<p><em>這希望算是我的「<a href="https://blogblog.club/party" target="_blank" rel="noopener noreferrer">BlogBlog 同樂會 - 2026 年 3 月</a>」的投稿文章。上個月主題是「<a href="https://alexhsu.com/perfect-days" target="_blank" rel="noopener noreferrer">理想的日常</a>」，由&nbsp;<a href="https://alexhsu.com/" target="_blank" rel="noopener noreferrer">Alex Hsu</a>&nbsp;主持。如果你有自己的部落格，歡迎一起來參加！</em></p>
<p>2/24是一個特別的日子，是個分科測驗模擬考的日子，但因為我沒有要參加分科測驗，就等於一整天在學校都沒事。</p>
<p>所以我決定一整天泡在圖書館，研究和聲(當然中間有溜出去打鏢啦)</p>
<p>今天研究的有兩個，第一個是The Jazz Harmony Book中的同調代替和弦、副屬和弦應用的練習，第二個是Take6 樂譜和聲進行的研究。因為我很懶惰，所以我就寫其中一點點就好。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="take6和聲">Take6和聲<a href="https://wyatt180.com/blog/2026/04/01/%E7%90%86%E6%83%B3%E7%9A%84%E6%97%A5%E5%B8%B8#take6%E5%92%8C%E8%81%B2" class="hash-link" aria-label="Direct link to Take6和聲" title="Direct link to Take6和聲">​</a></h2>
<p>選了三首，分別是A Quiet Place, Spread Love, If We Ever Needed the Lord Before。選這三首的原因很簡單，因為他們官方樂譜的免費試讀區就只有這三首的前兩頁(之後一定會買這本譜，太有趣了)</p>
<h3 class="anchor anchorWithStickyNavbar_LWe7" id="a-quiet-place">A Quiet Place<a href="https://wyatt180.com/blog/2026/04/01/%E7%90%86%E6%83%B3%E7%9A%84%E6%97%A5%E5%B8%B8#a-quiet-place" class="hash-link" aria-label="Direct link to A Quiet Place" title="Direct link to A Quiet Place">​</a></h3>
<p>他第一段的和弦進行是這樣的<br>
<strong>丨Dadd2 丨 F#9/A# 丨 Bm7 丨 F#9/A# Am7 D9#11/G# 丨 G6/9  F#m11 丨 F#m7 Bm7 丨 E9/G# 丨 A7 丨</strong></p>
<p>看起來超級複雜的，不是嗎。</p>
<p>但我仔細看看，發現其實這一切超級簡單，都是用第一個練習中用到的技巧所做出。我把和弦簡化後會長這樣。<br>
<!-- -->|和弦進行||||||
|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|
|和弦|D|Bm|G|F#m|Bm|A7|
|級數| I | VI | IV | III | VI | V7 |</p>
<p>真的很不可思議，竟然能把那麼基礎簡單地進行寫得那麼漂亮。</p>
<p>每個和弦之間放入不同的副屬和弦和神奇的變化音，再單獨分成一小節和加入一些251進行，竟然就變那麼帥氣。Bass音因為要進行的漂亮，所以很多和弦都變成了又酷又潮的轉位和弦，讓這整段看起來更奇怪，但其實都是功能性和聲的基礎！</p>
<p>其他兩首因為我懶得寫了，我就放著留在自己腦海裡。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="這就是我的理想日常">這就是我的理想日常<a href="https://wyatt180.com/blog/2026/04/01/%E7%90%86%E6%83%B3%E7%9A%84%E6%97%A5%E5%B8%B8#%E9%80%99%E5%B0%B1%E6%98%AF%E6%88%91%E7%9A%84%E7%90%86%E6%83%B3%E6%97%A5%E5%B8%B8" class="hash-link" aria-label="Direct link to 這就是我的理想日常" title="Direct link to 這就是我的理想日常">​</a></h2>
<p>這就是我理想的日常啊！</p>
<p>一整天沒有任何重要的事，能夠隨心所欲的做自己想做的事。像是2/24那天我一整天在學校沒事，我選擇在圖書館扎根，待了一整天，研究和聲，中午再出去打鏢。晚上回家耍廢。</p>
<p>這讓我想到國文課中的一個概念，奢侈。</p>
<p>我很喜歡其中<a href="https://linyutang.org.tw/" target="_blank" rel="noopener noreferrer">林語堂</a>在書中提到的概念</p>
<blockquote>
<p>「奢侈是在不妨礙他人的條件下，做一些逾越規矩的事」</p>
</blockquote>
<p>理想的日常，對目前的我來說即是一件奢侈的事</p>
<p>希望有招一日能把理想的日常變成真正的日常，而不奢侈</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[阿卡貝拉]]></title>
            <link>https://wyatt180.com/blog/2026/03/30/阿卡貝拉</link>
            <guid>https://wyatt180.com/blog/2026/03/30/阿卡貝拉</guid>
            <pubDate>Mon, 30 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[由於錄了一點之前寫的譜，發現這個譜有很大的問題，不適合阿卡貝拉，所以這邊統整出我學到的東西。]]></description>
            <content:encoded><![CDATA[<p>由於錄了一點之前寫的譜，發現這個譜有很大的問題，不適合阿卡貝拉，所以這邊統整出我學到的東西。</p>
<ol>
<li>每個人都要唱合音，不然只有六個人很乾</li>
<li>需要節奏性樂器的話用彈指或拍手或有Bass一人就好</li>
<li>音要拉長，不要太多短促音</li>
<li>大部分可以一起唱，但唱不同的音這樣</li>
<li>如果想要有伴奏有主旋律就至少需要三個人唱恆定的和弦音</li>
</ol>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[報平安]]></title>
            <link>https://wyatt180.com/blog/2026/03/29/報平安</link>
            <guid>https://wyatt180.com/blog/2026/03/29/報平安</guid>
            <pubDate>Sun, 29 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[感覺三月的更新頻率很低，所以我決定現在一定要報平安。]]></description>
            <content:encoded><![CDATA[<p>感覺三月的更新頻率很低，所以我決定現在一定要報平安。</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[Whatever's Clever]]></title>
            <link>https://wyatt180.com/blog/2026/03/27/CP</link>
            <guid>https://wyatt180.com/blog/2026/03/27/CP</guid>
            <pubDate>Fri, 27 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[今天凌晨12:00 Apple Music上架了]]></description>
            <content:encoded><![CDATA[<p>今天凌晨12:00 Apple Music上架了<br>
<!-- -->真的好好聽啊<br>
<!-- -->超喜歡這張專輯的風格<br>
<!-- -->從聽到第一首歌Changes時就知道我一定會喜歡這張專輯<br>
<!-- -->真正出來時也真的很好聽<br>
<!-- -->目前最喜歡的是Don't Meet Your Heroes<br>
<!-- -->就是因為前副歌的和弦進行好好聽</p>
<p>他的投稿比賽我今天終於把譜打完了<br>
<!-- -->要在3/31之前錄完aca<br>
<!-- -->窩一定可以的</p>
<iframe src="/byun.pdf" width="100%" height="600px"></iframe>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[星期三，猴子去爬山]]></title>
            <link>https://wyatt180.com/blog/2026/03/25/星期三</link>
            <guid>https://wyatt180.com/blog/2026/03/25/星期三</guid>
            <pubDate>Wed, 25 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[嘿嘿嘿今天星期三]]></description>
            <content:encoded><![CDATA[<p>嘿嘿嘿今天星期三<br>
<!-- -->最近真的是忙到爆了<br>
<!-- -->現在每天都要做好多事情<br>
<!-- -->理想的日常<br>
<!-- -->就是跟現在相反的日常<br>
<!-- -->這樣可以算我的投稿文章嗎<br>
<!-- -->沒有啦<br>
<!-- -->之後還是會把文章丟出來<br>
<!-- -->已經寫好八成了<br>
<!-- -->但也只剩幾天了<br>
<!-- -->好的</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[第一台單眼]]></title>
            <link>https://wyatt180.com/blog/2026/03/22/Canon EOS 600D</link>
            <guid>https://wyatt180.com/blog/2026/03/22/Canon EOS 600D</guid>
            <pubDate>Sun, 22 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Canon EOS 600D]]></description>
            <content:encoded><![CDATA[<h2 class="anchor anchorWithStickyNavbar_LWe7" id="canon-eos-600d">Canon EOS 600D<a href="https://wyatt180.com/blog/2026/03/22/Canon%20EOS%20600D#canon-eos-600d" class="hash-link" aria-label="Direct link to Canon EOS 600D" title="Direct link to Canon EOS 600D">​</a></h2>
<p><img decoding="async" loading="lazy" alt="600d" src="https://wyatt180.com/assets/images/canon600d-4fc37ca151daf60b2dfbd4999c7af99e.jpg" width="2016" height="1512" class="img_ev3q"><br>
<!-- -->上了三次攝影課後受不了，二手買的7000，之後會好好學習怎麼使用它。</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[原子習慣]]></title>
            <link>https://wyatt180.com/blog/2026/03/21/原子習慣</link>
            <guid>https://wyatt180.com/blog/2026/03/21/原子習慣</guid>
            <pubDate>Sat, 21 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[---]]></description>
            <content:encoded><![CDATA[<hr>
<p><em>我記得我之前有講過這是我的國文報告內容，所以我決定把我的講稿改一改然後水一篇文章</em></p>
<p>相信幾乎所有人都讀過或至少聽過這本書和他的理論。但是，學會建立習慣，有了超級強大的動機後，要如何保持，就是另一門很深的學問了。</p>
<p>首先，跟大家講Steve Martin故事</p>
<p>Steve Martin是世界上最成功的喜劇演員、音樂家、作家之一，巔峰了將近半世紀的成功人士。他的童年並不輕鬆，他在十歲的時候便前往迪士尼樂園，但他的目的跟其他的同齡孩子不同，他是去應徵工作的。十歲的他得到了發傳單的工作，每發一個傳單可以得到0.5美元。三年後，他得到升遷，他開始在迪士尼的魔術商店工作，在這個商店他學了很多的魔術技巧和笑話，並且有了第一次的表演機會，成為了他未來變成明星的基礎。青少年時期他便開始在當地的俱樂部參加open mic，雖然當時他並不好笑，但Steve有感覺自己在進步。從一開始1分鐘、2分鐘，並循序漸進到最後有十分鐘的時間。後來他加入了電視台參與寫手，幾年後便開始了自己的節目，便在70年代開始紅遍美國，做巡演，並且一次比一次規模更大，並在2015年獲得終生成就獎。去年2025還推出了一張新專輯，但我沒有聽過。</p>
<p>在這個故事中我們可以得到一個簡單的結論，要得到人生的成功，最重要的是能夠長久持續的往目標努力。引用一句Steve Martin的話:「“I did stand-up comedy for 18 years. Ten of those years were spent learning, four years were spent refining, and four years were spent in wild success. I was seeking comic originality, and fame fell on me as a byproduct. The course was more plodding than heroic.”」這句話的翻譯是：「我說了18年的單口喜劇。其中前10年用於學習，4年用於精煉自己的段子，最後4年則迎來了輝煌的成功。我追求的是喜劇上的獨創性，而名和利只不過是隨之而來的東西。這段歷程與其說是波瀾壯闊，不如說是踏實篤定、腳踏實地。」</p>
<p>他的童年跟很多一般人一樣，對很多事情有興趣。但他與其他常人的差距就是，他在這半世紀得時間內保持了動力，維持了他練習講笑話、練習吉他、寫書的習慣。而我們這種普通人，常常做不到一半，就偏離軌道。</p>
<p>然而，要如何長期的維持這個動力、維持這個一開始微小的熱情，並不是一件容易的事。要做到這個說起來簡單但做起來超級難的保持動機，主要有兩個要點。</p>
<ol>
<li>短期目標不要簡單、也不要太難</li>
<li>享受無聊</li>
</ol>
<p>首先來說第一點，<strong>短期目標不要太簡單，也不要太難</strong></p>
<p>人腦喜歡挑戰，但是只喜歡有時候會贏、有時候會輸的挑戰。</p>
<p>舉一個我個人例子，我很喜歡丟飛鏢，我享受丟出飛鏢的瞬間，但如果我每次丟飛鏢都跟沒丟過飛鏢的新手比賽，那麼我很快就會就感到無聊，而且變得對飛鏢毫無熱情。為什麼呢，因為<strong>太簡單了</strong>，我每一場都贏的輕而易舉，得不到成就感；另一個方面，如果我每天都跟頂級職業選手比賽，雖然我會很開心，能夠與偶像比賽，但我也會很快就感到無聊，變得對飛鏢毫無熱情，因為<strong>太難了</strong>，還是得不到成就感。</p>
<p>但現在的狀況，我每天都在學校練習(也就是現在的情況)，有一些人比我強、有一些比我弱；我有時候贏、有時候輸，但如果我想要每一場都贏，我就必須盡我的全力專注在比賽。這個環境讓我能夠永遠保持練習的動機，這就是Goldilocks Rules的經典例子。</p>
<p>Goldilocks Rules源自於一個童話故事，一個私闖民宅的故事。這個故事荒謬的點有四個</p>
<ol>
<li>一個女孩敢闖入三隻熊的家？</li>
<li>還厚臉皮的把他們的粥喝掉</li>
<li>這樣的劇情適合讓孩童閱讀？</li>
<li>這麼廢的故事可以寫出理論？</li>
</ol>
<p>金髮姑娘喝了三碗不同的粥，第一碗太燙、第二碗太冰，然而第三碗的溫度剛好在這兩碗之間，形成了黃金區域。這個聽起來很無聊的故事有一個核心觀念，<strong>控制在剛剛好的量</strong>。它可以應用在很多不同的領域，但以這本書的挑戰難度而言，要找到一個很小的黃金區域，能讓人保持在熱情狀態中，只要一點點太難或太簡單，都會導致失敗。要保持在不難、但也不簡單、剛剛好的狀態。</p>
<p>科學家想量化要抵達那個完美的區域，做出了一些些粗略的研究，並計算那個挑戰的目標最好要在你的能力的4%以上，雖然我們永遠不會知道比我們能力高4%在現實世界中是什麼意思，但這也能很好的佐證了Goldilocks Rules，要把挑戰控制在一個黃金區域，不太難也不簡單，剛剛好。</p>
<p>接下來第二點，<strong>享受無聊</strong></p>
<p>先講一個小小的故事</p>
<p>有一天，我們的作者詹姆士'透明(James Clear)，在健身房健身時，遇到了厲害的訓練師，是很多奧運國手的訓練師。James Clear非常好奇那些頂尖的運動員跟我們普通人到底有什麼差別於是展開了這段與訓練師對話：</p>
<p>「這些頂尖的運動員跟其他人有人麼不一樣」<br>
<!-- -->「其實沒什麼特別的，就是他們能掌握日復一日訓練的無聊，每天做一模一樣的事情」</p>
<p>這個答案讓作者非常震驚，也讓讀到這段的我非常震驚。</p>
<p>我們都聽別人說那些厲害的人都是<strong>超級有天份</strong>、<strong>熱情超級豐沛</strong>、<strong>對於勝利非常渴望</strong>，但結果呢，不是，那些厲害的人也會跟我們一樣，對於事情感到無聊、感到沒有動力，唯一的差別是厲害的人可以在無聊中持續努力。</p>
<p>想要在一個領域變得厲害，必須長時間持續的練習，然而長時間持續的練習，就會導致無聊，當我們感到無聊時，就很容易失敗。<strong>成功最大的敵人不是失敗，是無聊</strong>。無聊，換句話說，就是停止對短期結果感到愉悅，這個短期挑戰的結果變的每一次都可預期，減少了過程中的刺激感，減少了對成果的滿足感。</p>
<p>另一個方向，成癮式的產品就是利用這個心理，讓成功跟失敗控制在5050，讓一切事件的發生變得機率性，就能讓人長時間停留在這個產品。</p>
<p>最後總結剛剛講的所有東西，要提升自我，最重要的不是什麼超強的爆發力、也不是什麼異於常人的天份、更不是超乎常人的熱情，而是有把自己控制在4%區間、享受重複練習的無聊、死跟著計畫的能力。</p>
<p>用作者的話總結我的報告：「Professionals stick to the schedule; amateurs let life get in the way.」厲害的人選擇跟著計畫，普通人讓人生生活帶著自己走。</p>]]></content:encoded>
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        <item>
            <title><![CDATA[我喜歡]]></title>
            <link>https://wyatt180.com/blog/2026/03/18/我喜歡</link>
            <guid>https://wyatt180.com/blog/2026/03/18/我喜歡</guid>
            <pubDate>Wed, 18 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[今天是園遊會，也就是竹科實中的校慶大會。]]></description>
            <content:encoded><![CDATA[<p>今天是園遊會，也就是竹科實中的校慶大會。</p>
<p>跟其他學校最大的不同是，我們都辦在平日，搞到變成幾乎只有本校的人會參加，非常可惜。高三不用擺攤，但文組班還是有擺攤，我就幾乎整個上午待在那裡，跟著他們攤位的人玩，我也不知道為什麼，但我跟我們班的人都不太熟，熟的人都在其他班，就像文組班和另外一個普通班。接著就是一個叫做Raymond的人才(英文名字應該沒問題吧)(他有一個粉絲專頁：自然生態有意思)，找我跟一些他們班的人，臨時組一團合唱團，唱去年比賽的歌，在園遊會主舞台自由報名表演時間開唱。我就說，有譜我就唱，結果他們還真的有譜，我們就在短短的半小時內，不小心召集了約20人，湊成一組超厲害的合唱團(至少我這樣覺得)，組成的成員是去年班際合唱比賽冠亞軍的人，加上最佳指揮。上台唱時真的很興奮，最喜歡跟一群人一起唱歌了，尤其又是在這個奇妙的園遊會舞台。半小時湊合到所有人一起唱一起瘋一起玩是一個超級棒的體驗，這輩子很可能之後都沒機會了。這首歌叫做我喜歡，但目前沒有看到有人上傳影片，太可惜了。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="safari">Safari<a href="https://wyatt180.com/blog/2026/03/18/%E6%88%91%E5%96%9C%E6%AD%A1#safari" class="hash-link" aria-label="Direct link to Safari" title="Direct link to Safari">​</a></h2>
<p>最近看了2014 的Apple WWDC，看到負責macOS的人大吹特吹Safari有多快、有多輕量、有多美，害我有點被他騙到，決定開始一週使用Safari。結果今天才第二天，我就受不了了，馬上換回Brave。只能說蘋果的所有軟體只要開始跟Liquid Glass扯上關係就是超級重量，現在的Safari真的好爛喔，超級耗電的。26系列版本真的很差勁，希望27能改進，不然我的手機就永遠被這個爛Liquid Glass綁架了。</p>]]></content:encoded>
        </item>
        <item>
            <title><![CDATA[高三最快樂的三天]]></title>
            <link>https://wyatt180.com/blog/2026/03/16/最快樂的三天</link>
            <guid>https://wyatt180.com/blog/2026/03/16/最快樂的三天</guid>
            <pubDate>Mon, 16 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[這幾天是高三最快樂的三天，六日一，太快樂了]]></description>
            <content:encoded><![CDATA[<p><em>這幾天是高三最快樂的三天，六日一，太快樂了</em></p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="第一天師生盃day-one">第一天：師生盃Day One<a href="https://wyatt180.com/blog/2026/03/16/%E6%9C%80%E5%BF%AB%E6%A8%82%E7%9A%84%E4%B8%89%E5%A4%A9#%E7%AC%AC%E4%B8%80%E5%A4%A9%E5%B8%AB%E7%94%9F%E7%9B%83day-one" class="hash-link" aria-label="Direct link to 第一天：師生盃Day One" title="Direct link to 第一天：師生盃Day One">​</a></h2>
<p>去年拿冠軍的那個飛鏢比賽，今年我們來重新衛冕了。與去年最大的不同是，我們從原本的六人小組，到今年有13人參與比賽，陣容更大更豪華了，而且更有氣勢。</p>
<p>第一天的比賽有團體賽和單人賽。首先團體賽，我們在小組賽遇到了全明星組，而且還是三組!(小組賽總共只有四組)，那些全明星都是在網路上鼎鼎大名，代表過國家參與過飛鏢比賽，又或是長年冠軍的。但升級的我們，完全不怕，我們把那三隊誇張的明星隊全部2:0車過去，超爽的，能跟偶想比賽，還能打贏，太高興了。接下來進入八強，竟然遇到自己人！同校隊伍撞到！！！！！！！！！真的太可惜了，原本打算金包銀的。八強是整場比賽最輕鬆的一場，跟平常練習一模一樣。接下來四強遇到羅東高中(之後文章還常常會出現)，我們的狀況下滑了，沒像小組賽那麼威猛，所以很可惜的敗下陣來。季殿賽我們狀況下滑得更嚴重，竟然輸掉原本小組賽2:0的其中一隊明星隊，所以最後以第四名收場。很有趣的是立人高中握有歐子楷和施秉宏兩大巨星(這兩大巨星在第二天還會出現)，竟然連續兩年被我們擋下來，去年在八強，今年在小組賽就輸了。</p>
<p>下午是個人賽，這次個人賽一樣小組賽就淘汰，被羅東的淘汰。明顯感受到下午的體力和專注度都下滑非常多，尤其是手部的酸痛，導致發揮差勁。雖然我差勁，但是我隊友非常厲害，三個隊友打進16強，最驚豔的是那個只打半年的隊友，竟然能在比賽發揮的平時還好，真的是非常厲害。比賽要發揮到平常的實力就已經是非常困難的事情了，他不但沒變差，還能在關鍵時刻打出Hat Trick，真的太厲害了</p>
<p>晚上跟著一群好友去鏢店和吃晚餐，搞到快十點才回家，能夠跟這些原本沒有那麼熟悉的隊員打成一片是這趟旅程最高興的事情。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="第二天師生盃day-two">第二天：師生盃Day Two<a href="https://wyatt180.com/blog/2026/03/16/%E6%9C%80%E5%BF%AB%E6%A8%82%E7%9A%84%E4%B8%89%E5%A4%A9#%E7%AC%AC%E4%BA%8C%E5%A4%A9%E5%B8%AB%E7%94%9F%E7%9B%83day-two" class="hash-link" aria-label="Direct link to 第二天：師生盃Day Two" title="Direct link to 第二天：師生盃Day Two">​</a></h2>
<p>第二天是雙人賽和混合雙打賽，混合雙打我沒參加到，找不到女隊友，蠻可惜的。雙人賽則是跟我的死黨一起參加，平時會一起打棒球的那群，但打鏢也是很認真啦。雙人賽也是小組賽淘汰，這是我兩天覺得最可惜的比賽，前面團體賽雖然輸了，但我除了季殿賽都發揮得非常優異，但這雙打賽，我們最一局生死局領先對手150分左右，我們連續三次結鏢機會都沒結到，尤其是我最後一鏢single 9的機會，直接打到double葬送掉比賽。過了兩天我有稍微比較釋懷了。精彩的要來的，我們的其中一組隊友，過關斬將，打掉一堆鬼怪的準明星選手，打進決賽，遇到了巨星組合！歐子楷和施秉宏，其中歐子楷在這三戰兩勝的比賽中，完全沒有任何失誤，打了五個Hat Trick跟一個single 15結鏢。其中一個隊友表示，能跟完全沒失誤的偶像打真的太爽了，好興奮。</p>
<p>下午是混合雙打，完全沒打全程幫隊友加油，我超級喜歡這種氣氛，全部學校甚至全部新竹的飛鏢選手一起為新竹的選手加油。最後有一組打進八強，也是非常好的成績了。</p>
<p>接下來是慶功宴，我們14人(沒錯就是那麼多)擠進大埔鐵板燒，真的很開心原本某些沒那麼收悉的隊友經過這次比賽全部都靠更緊了，這是這比賽最大的收穫。</p>
<p>以我的文筆來說，真的很難用文字記錄下我想表達的情緒以及我的感動和快樂，但我會永遠記得這幾兩天的。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="第三天畢業歌編曲">第三天：<a href="https://www.youtube.com/watch?v=KjuJc5wfUag" target="_blank" rel="noopener noreferrer">畢業歌編曲</a><a href="https://wyatt180.com/blog/2026/03/16/%E6%9C%80%E5%BF%AB%E6%A8%82%E7%9A%84%E4%B8%89%E5%A4%A9#%E7%AC%AC%E4%B8%89%E5%A4%A9%E7%95%A2%E6%A5%AD%E6%AD%8C%E7%B7%A8%E6%9B%B2" class="hash-link" aria-label="Direct link to 第三天畢業歌編曲" title="Direct link to 第三天畢業歌編曲">​</a></h2>
<p>早上中午上午完全不重要，就是天平常的上課日，重點和精華都在晚上的編曲。</p>
<p>這是我第一次，跟我頻率對到的人一起做音樂，其中鍵盤手是我高中三年的同學，雖然不太熟，但都互相知道彼此這個人的能力，能被他邀請來一起製作畢業歌絕對是最開心的事。他也跟我們說他對於他這次組成的編曲組非常驕傲，找到了超厲害的鼓手，能夠隨時做到我們討論出來或在腦中的節奏；找到我這個不是很厲害的吉他手，但是是一個對於合聲、和弦進行有研究的吉他手，我和他都很開心能夠跟一個懂和聲的人一起討論，這邊到底要用A7 還是am7、要用tritone還是恆定結構銜接到下個和弦、要用b13音還是#5音。我超級興奮又開心，更好的是那個厲害的鼓手，她們家有完整的鼓組和一超厲害個吸音空間，完全沒有回音，之後一定會去哪裡完成畢業歌的錄製的。總之過程非常開心，對比兩年前參加熱音社的經驗是數十萬倍的更快樂。</p>
<h2 class="anchor anchorWithStickyNavbar_LWe7" id="這就是我最快樂的三天">這就是我最快樂的三天<a href="https://wyatt180.com/blog/2026/03/16/%E6%9C%80%E5%BF%AB%E6%A8%82%E7%9A%84%E4%B8%89%E5%A4%A9#%E9%80%99%E5%B0%B1%E6%98%AF%E6%88%91%E6%9C%80%E5%BF%AB%E6%A8%82%E7%9A%84%E4%B8%89%E5%A4%A9" class="hash-link" aria-label="Direct link to 這就是我最快樂的三天" title="Direct link to 這就是我最快樂的三天">​</a></h2>
<p>充實到不行的三天，都是從早上七點到晚上九點左右，但都是在做自己喜歡的事，原本在想說這能不能投稿到理想的日常，但想想這絕對不能算日常，也不會是我最理想的日常，因為連續三天超過13小時的外出是絕對沒法長久持續的，至於三月的理想的日常，之後會再公布哈。</p>]]></content:encoded>
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