[{"data":1,"prerenderedAt":55},["ShallowReactive",2],{"q-112190-arch_structure-2":3},{"question":4,"neighbors":27,"sameNumber":39,"prev":25,"next":31},{"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-112190-801-0102-002","architect","112190",112,"建築結構",2,null,"下圖的門形構架，梁為剛體（EI=∞），若忽略構件的軸向變形時，當柱的 EI 值不變，但柱高由 h 增為 2 h 時，則頂層在相同外力下，其側向位移將會增加為原先的多少倍？",{"A":14,"B":15,"C":16,"D":17},"2倍","4倍","6倍","8倍",[19],"D","single",[22],"\u002Fimages\u002Farch-112190-801-0102-002.png","本題考點：梁為剛體（EI=∞）的門形構架受頂部水平力時，柱頂與柱底都不能轉動，單柱側向勁度為 12EI\u002Fh³；兩柱並聯後，頂層側向位移與柱高的三次方成正比。\n【正解理由】依題圖所示，兩根柱的柱底為固定端，柱頂與剛性梁相接。梁的 EI 為無窮大，梁本身不會彎曲，柱頂因此只能隨梁一起水平平移、不能轉動。這種「兩端都不轉動、兩端之間發生相對側移 Δ」的柱，其柱端剪力 V = 12EIΔ\u002Fh³，所以單柱的側向勁度 k = V\u002FΔ = 12EI\u002Fh³。題目又說忽略軸向變形，剛性梁把兩根柱頂綁成同一個側移量，兩根柱等於兩根並聯的彈簧，總勁度相加：K = 12EI\u002Fh³ + 12EI\u002Fh³ = 24EI\u002Fh³。頂層側向位移 Δ = P\u002FK = Ph³\u002F(24EI)。柱高由 h 改為 2h、EI 與外力 P 都不變時，Δ' = P(2h)³\u002F(24EI) = 8Ph³\u002F(24EI)，兩者相除 Δ'\u002FΔ = 2×2×2 = 8，側向位移變成原先的 8 倍，故選 D。\n【逐項排除】\n(A) 2 倍：不符合題目所問。柱高加倍時，位移放大的倍數取決於勁度式中 h 的冪次；本題勁度與 h³ 成反比，放大倍數是 2 的三次方 8 倍，2 倍遠小於正確值。\n(B) 4 倍：不符合題目所問。4 倍同樣低於正確值 8 倍；柱的側向變形由彎曲控制，勁度中的柱高是三次方，位移要放大到 8 倍才對。\n(C) 6 倍：不符合題目所問。柱高加倍時，側移倍數必為 2 的某個整數次方，6 倍不在這個序列中；依兩端不轉動柱的勁度式，正確值為 8 倍。\n(D) 8 倍：符合題目所問。勁度 24EI\u002Fh³ 與 h³ 成反比，同一外力下位移與 h³ 成正比，(2h)³\u002Fh³ = 8。\n【演算步驟】\n單柱側向勁度（柱頂、柱底均不轉動）：k = 12EI\u002Fh³（單位：力\u002F長度，如 kN\u002Fm）\n兩柱並聯總勁度：K = 12EI\u002Fh³ + 12EI\u002Fh³ = 24EI\u002Fh³（kN\u002Fm）\n原側向位移：Δ = P\u002FK = Ph³\u002F(24EI)（kN ÷ kN\u002Fm = m）\n柱高改為 2h：Δ' = P(2h)³\u002F(24EI) = 8Ph³\u002F(24EI)（m）\n位移倍數：Δ'\u002FΔ = (2h)³\u002Fh³ = 2×2×2 = 8（m\u002Fm，無因次）\n【記憶點】梁剛、柱底固定的門形構架，單柱勁度 12EI\u002Fh³，柱高變 2 倍、側移就變 8 倍。",634,1,true,[28,30,33,36],{"number":25,"session":7,"stem":29},"三維空間薄殼結構，係由厚度遠小於他向尺度之一個或多個曲型薄版或摺版所組成。若為混凝土…",{"number":31,"session":7,"stem":32},3,"下列敘述何者正確？①在同一場地震事件下，各地區震度相同，地震規模相異 ②某次地震 A…",{"number":34,"session":7,"stem":35},4,"有關材料性質，下列敘述何者正確？",{"number":37,"session":7,"stem":38},5,"關於材料波松比 ν（Poisson's ratio），下列何者錯誤？",[40,43,46,49,52],{"number":10,"session":41,"stem":42},"114180","下列有關混凝土性質的敘述，何者錯誤？",{"number":10,"session":44,"stem":45},"113190","一簡支梁斷面寬 100 mm，深度 150 mm，所在某一位置斷面的彎矩 100 k…",{"number":10,"session":47,"stem":48},"111180","有關高樓建築結構系統之特性，下列敘述何者正確？",{"number":10,"session":50,"stem":51},"110180","在結構系統中配置剪力牆作為耐震元件時，下列敘述何者正確？",{"number":10,"session":53,"stem":54},"109180","下列關於管式結構系統（tube structure system）之敘述，何者正確？",1791863194041]