[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-114180-arch_structure-26":3},{"question":4,"neighbors":27,"sameNumber":46,"prev":35,"next":38},{"id":5,"classKey":6,"session":7,"year":8,"subject":9,"number":10,"groupStem":11,"ownStem":12,"stem":12,"options":13,"answer":18,"answerKind":20,"answerS":11,"answerNote":11,"images":21,"explanation":23,"withheld":11,"deepChars":24,"freq":25,"indexable":26},"arch-114180-801-0102-026","architect","114180",114,"建築結構",26,null,"下列何者載重分布，使懸臂梁固定端彎矩最大？ 2w 2w w 0 0 L L L (a) (b) (c)",{"A":14,"B":15,"C":16,"D":17},"(a)","(b)","(c)","固定端彎矩值均相同",[19],"B","single",[22],"\u002Fimages\u002Farch-114180-801-0102-026.png","本題考點：懸臂梁固定端彎矩與分布載重的合力、形心位置——同樣大小的總載重，作用點離固定端越遠，彎矩越大。\n【正解理由】三根懸臂梁跨度都是 L，固定端在左。(a) 均布載重 w，合力 wL，作用在中點，力臂 L\u002F2，固定端彎矩 wL²\u002F2。(b) 三角形載重固定端為 0、自由端為 2w，合力 (1\u002F2) × 2w × L = wL，形心距大端（自由端）L\u002F3，也就是距固定端 2L\u002F3，固定端彎矩 (2\u002F3)wL²。(c) 三角形載重固定端為 2w、自由端為 0，合力同樣是 wL，形心距固定端 L\u002F3，固定端彎矩 (1\u002F3)wL²。三者總載重相同，但 (b) 的載重集中在離固定端最遠的一側，力臂最長，彎矩最大。故選 B。\n【逐項排除】\n(A) 不符。(a) 固定端彎矩 wL²\u002F2，合力力臂 L\u002F2，小於 (b) 的 2L\u002F3。\n(B) 符合。(b) 合力 wL 作用在距固定端 2L\u002F3 處，固定端彎矩 (2\u002F3)wL²，為三者最大。\n(C) 不符。(c) 載重集中在靠近固定端一側，合力力臂只有 L\u002F3，固定端彎矩 (1\u002F3)wL²，為三者最小。\n(D) 不符。三者總載重都是 wL，但合力作用點不同，力臂分別是 L\u002F2、2L\u002F3、L\u002F3，固定端彎矩並不相同；只看總載重相等就判斷彎矩相等，忽略了力臂。\n【演算步驟】（以 w = 1、L = 1 代入比較）\n1. (a)：M = w × L × L\u002F2 = 1 × 1 × 1 \u002F 2 = 0.5。\n2. (b)：M = (1\u002F2 × 2w × L) × (2L\u002F3) = 2 × 1 \u002F 2 × 1 × 2 \u002F 3 = 0.6667。\n3. (c)：M = (1\u002F2 × 2w × L) × (L\u002F3) = 2 × 1 \u002F 2 × 1 × 1 \u002F 3 = 0.3333。\n4. 比較：(b) 0.6667 ＞ (a) 0.5 ＞ (c) 0.3333，(b) 最大。\n【記憶點】總載重一樣時，比力臂：載重越往自由端集中，固定端彎矩越大。",520,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},23,"在圖示之三鉸拱結構中，A 點之水平反力為何？ 6P L A L L L",{"number":32,"session":7,"stem":33},24,"下圖框架之 A 點彎矩為何？ D 1 1 1 1",{"number":35,"session":7,"stem":36},25,"如圖所示剛構架，各構件 EI 值皆相等，基礎支承點 D 垂直下陷將使構件產生彎矩。若…",{"number":38,"session":7,"stem":39},27,"如圖所示的三鉸式剛架，A、E 為鉸支承，C 為鉸接，B、D 為剛接。則有關 A 點之…",{"number":41,"session":7,"stem":42},28,"如圖所示之剛構架，各桿件之 EI 值皆相同，於 B 點承受一集中載重 P 作用，下列…",{"number":44,"session":7,"stem":45},29,"依建築物混凝土結構設計規範，進行構材斷面強度設計時，混凝土最外受壓纖維之最大應變假設…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"113190","如圖所示之構架承受側力 P，兩柱分別高 L 及 2 L，柱頂皆為鉸接（pin），兩柱…",{"number":10,"session":51,"stem":52},"112190","下圖中之圖(i)所示為一單跨抗彎矩構架（moment-resisting frame…",{"number":10,"session":54,"stem":55},"111180","試分析下圖桁架結構，下列選項何者正確（T 為張力，C 為壓力）？ 10 m 10 m…",{"number":10,"session":57,"stem":58},"110180","一簡支梁跨距為 5 m，分別受到以下兩種載重形式：（A）跨距中央受到集中載重 10 …",{"number":10,"session":60,"stem":61},"109180","如圖示之均質矩形斷面，對於形心水平軸 x 之面積慣性矩記為 Ixx，而對於矩形底邊水…",1791863195548]