[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-112190-arch_structure-8":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-112190-801-0102-008","architect","112190",112,"建築結構",8,null,"一結構如圖所示，上部為一個短柱，底部為兩個面積較小的長柱支撐，中間塗黑部分為剛體，當頂端受到一外力 P 作用時，最頂部的位移為多少？ P 2 AE 0.6 L AE AE L",{"A":14,"B":15,"C":16,"D":17},"PL\u002FAE","4 PL\u002F5 AE","3 PL\u002F2 AE","3 PL\u002F5 AE",[19],"B","single",[22],"\u002Fimages\u002Farch-112190-801-0102-008.png","本題考點：軸力構件的變形 δ = PL\u002F(AE)，以及串聯與並聯構件的位移疊加。上部短柱與下部兩根長柱為串聯；下部兩根長柱經剛體連結、縮短量相同，為並聯分擔載重。\n【正解理由】依題圖所示，上部短柱的軸向剛度標示為 2AE、長度 0.6L；下部兩根長柱各標示 AE、長度 L，中間塗黑的剛體把兩部分連在一起。頂端位移等於上部短柱的縮短量加上剛體的下移量。上部短柱承受全部的 P，縮短量 δ₁ = P×0.6L\u002F(2AE) = 0.3PL\u002FAE。剛體不變形，兩根長柱的縮短量必須相同；兩根柱的 AE 與 L 都相同，所以各分擔 P\u002F2，剛體下移量 δ₂ = (P\u002F2)×L\u002F(AE) = 0.5PL\u002FAE。頂端總位移 δ = δ₁ + δ₂ = 0.3PL\u002FAE + 0.5PL\u002FAE = 0.8PL\u002FAE = 4PL\u002F5AE，故選 B。\n【逐項排除】\n(A) PL\u002FAE：不符合題目所問。係數 1 大於正確係數 0.8，位移被高估；正確作法是上部短柱以 2AE 與 0.6L 計算、下部兩柱各承擔一半的力。\n(B) 4PL\u002F5AE：符合題目所問。上部短柱縮短 0.3PL\u002FAE，下部並聯長柱縮短 0.5PL\u002FAE，兩者串聯相加為 0.8PL\u002FAE。\n(C) 3PL\u002F2AE：不符合題目所問。係數 1.5 比正確值大很多，與「上部剛度較大、下部兩柱分擔載重」的條件都不相容，頂部位移應為 4PL\u002F5AE。\n(D) 3PL\u002F5AE：不符合題目所問。係數 0.6 小於正確值 0.8，位移被低估；串聯構件的位移必須把上段與下段的縮短量全部相加。\n【演算步驟】\n軸向變形公式：δ = PL\u002F(AE)（kN×m ÷ (m²×kN\u002Fm²) = m）\n上部短柱（承受 P，剛度 2AE，長 0.6L）：δ₁ = P×0.6L\u002F(2AE) = 0.3PL\u002FAE（m）\n下部長柱（兩柱並聯，各承受 P\u002F2，剛度 AE，長 L）：δ₂ = (P\u002F2)×L\u002F(AE) = 0.5PL\u002FAE（m）\n頂端總位移：δ = δ₁ + δ₂ = 0.3PL\u002FAE + 0.5PL\u002FAE = 0.8PL\u002FAE = 4PL\u002F5AE（m）\n【記憶點】上下疊放是串聯，位移相加；並排共用剛體是並聯，力依剛度分攤、位移相同。",556,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},5,"關於材料波松比 ν（Poisson's ratio），下列何者錯誤？",{"number":32,"session":7,"stem":33},6,"為抵抗拱結構支承處之外推力，下列設計策略何者不適當？",{"number":35,"session":7,"stem":36},7,"關於高層建築物的設計與建築物在地震中的反應，下列敘述何者正確？",{"number":38,"session":7,"stem":39},9,"一個微小的矩型六面體受到純剪力作用，下列敘述何者正確？",{"number":41,"session":7,"stem":42},10,"下列知名建築中何者最接近形抗結構？",{"number":44,"session":7,"stem":45},11,"圖示管狀結構（Tubular Structure）的外管受側力作用時，若管面為完全剛…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","有關高層建築結構系統與設計，下列敘述何者錯誤？①高層建築於設計風力下之層間位移角，不…",{"number":10,"session":51,"stem":52},"113190","關於設計載重組合，下列敘述何者正確？",{"number":10,"session":54,"stem":55},"111180","有關一般混凝土材料的敘述，下列何者正確？",{"number":10,"session":57,"stem":58},"110180","下列何者與土壤液化潛能之判定並無直接關係？",{"number":10,"session":60,"stem":61},"109180","根據「建築物耐震設計規範」，消能建築須按其消能元件之有效阻尼比，計算出中小度地震之設…",1791863199910]