[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-113190-arch_structure-19":3},{"question":4,"neighbors":26,"sameNumber":45,"prev":34,"next":37},{"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":22,"withheld":11,"deepChars":23,"freq":24,"indexable":25},"arch-113190-801-0102-019","architect","113190",113,"建築結構",19,null,"某懸臂梁長 3 m，承受均布載重 w。今將長度改為 6 m，仍承受均布載重 w，其他條件不變，則此梁之自由端變位為原來梁之幾倍？",{"A":14,"B":15,"C":16,"D":17},"4","8","16","32",[19],"C","single",[],"本題考點：懸臂梁承受均布載重時自由端變位 δ = wL⁴ \u002F (8EI)，變位與梁長的四次方成正比，用比例法求長度改變後的倍數。\n【正解理由】懸臂梁承受均布載重 w 時，自由端變位 δ = wL⁴ \u002F (8EI)。題目說 w、E、I 及其他條件都不變，只有梁長由 3 m 改為 6 m，因此兩者的變位比等於梁長比的四次方：δ₂ \u002F δ₁ = (6 m ÷ 3 m)⁴ = 16，自由端變位為原來的 16 倍，故選 C。\n【逐項排除】\n(A) 不符合。4 是梁長比的平方 (6 ÷ 3)²，等於把變位當成與梁長平方成正比；均布載重懸臂梁的變位與梁長的四次方成正比，正確倍數應為 16。\n(B) 不符合。8 是梁長比的三次方 (6 ÷ 3)³，那是懸臂梁自由端承受「集中載重」時變位與梁長三次方成正比的關係；本題是均布載重，載重總量也隨梁長增加，必須用四次方，正確倍數應為 16。\n(C) 符合。依 δ = wL⁴ \u002F (8EI)，梁長加倍、其餘不變，變位比為 (6 ÷ 3)⁴ = 16。\n(D) 不符合。32 比正確值 16 多了一倍，不是均布載重懸臂梁變位與梁長四次方成正比所得的結果；正確倍數應為 16。\n【演算步驟】\n① 公式：懸臂梁均布載重自由端變位 δ = wL⁴ \u002F (8EI)\n② 其餘條件不變，δ 只與 L⁴ 成正比：δ₂ \u002F δ₁ = (L₂ \u002F L₁)⁴\n③ 代入：δ₂ \u002F δ₁ = (6 m ÷ 3 m)⁴ = 16\n④ 結果：自由端變位為原來的 16 倍\n【記憶點】均布載重的梁變位看 L⁴，集中載重看 L³；梁長加倍，均布載重下變位放大為 16 倍。",456,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},16,"一剛架結構受外力作用如圖所示，下列何種梁上塑性鉸產生時，不會形成不穩定結構？",{"number":31,"session":7,"stem":32},17,"圖示之二懸臂梁，短梁與長梁於 a 點之垂直變位量分別為 Δ1 與 Δ2，兩者關係可表…",{"number":34,"session":7,"stem":35},18,"格子梁系統中，兩直交梁的斷面相同且端點支承亦相同。若直向與橫向的跨距比為 1：2，則…",{"number":37,"session":7,"stem":38},20,"根據尤拉挫屈公式（Euler equation），下列何種作法可降低柱子的有效長度，…",{"number":40,"session":7,"stem":41},21,"下列四種開口牆，其材料、外周尺寸、開口面積均相同，但開口位置或方式不同，何者抗震強度…",{"number":43,"session":7,"stem":44},22,"下列那種牆設計對於建築物耐震時水平強度的提升效果最好？圖中以網點圖樣填滿的部分為牆體…",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","圖示 B 點受力的桁架結構，下列構件內力與支承反力的大小與方向的敘述何者正確？ 6m…",{"number":10,"session":50,"stem":51},"112190","下圖中之圖(i)為一棟兩跨的單層鋼筋混凝土造建築物的結構示意圖。該建築物在遭受恐怖攻…",{"number":10,"session":53,"stem":54},"111180","關於無梁版（flat slab）結構系統，下列敘述何者錯誤？",{"number":10,"session":56,"stem":57},"110180","從永續性綠建築結構的角度，下列敘述何者錯誤？",{"number":10,"session":59,"stem":60},"109180","對鋼筋混凝土耐震柱的繫筋配置而言，下列何者為較適當的配置方式？ a b c d",1791863197886]