[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-113190-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-113190-801-0102-026","architect","113190",113,"建築結構",26,null,"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 EI 值相同，而梁為剛體。若假設柱水平變形主要為撓曲造成，剪力變形極小，則兩柱所分配水平剪力較大者約為較小者之幾倍？",{"A":14,"B":15,"C":16,"D":17},"1","2","4","8",[19],"D","single",[22],"\u002Fimages\u002Farch-113190-801-0102-026.png","本題考點：剛性梁連接各柱時，各柱側向變位相同，水平剪力依各柱側向勁度比例分配；柱底固定、柱頂鉸接的柱，其側向勁度為 k = 3EI\u002Fh³，與柱高三次方成反比。\n【正解理由】依題圖，兩柱柱底固定、柱頂以鉸接與梁相連，左柱高 L、右柱高 2L，兩柱 EI 相同，梁為剛體。梁為剛體，所以兩柱柱頂的水平變位 Δ 相同；柱頂為鉸接，柱頂不傳遞彎矩，每根柱都相當於底部固定、頂端受水平力的懸臂柱，側向勁度 k = 3EI\u002Fh³。短柱 k1 = 3EI\u002FL³；長柱 k2 = 3EI\u002F(2L)³ = 3EI\u002F(8L³)。各柱分配剪力 V = k·Δ，Δ 相同，故剪力比等於勁度比：V1\u002FV2 = k1\u002Fk2 = (3EI\u002FL³)\u002F(3EI\u002F(8L³)) = 8。較短的柱分到較大剪力，約為較長柱的 8 倍，故選 D。\n【逐項排除】\n(A) 不符合。1 倍代表兩柱平均分擔側力，這只在兩柱勁度相同時成立；本題兩柱高度不同，勁度與柱高三次方成反比，短柱勁度遠大於長柱，剪力比為 8 倍。\n(B) 不符合。2 倍等於兩柱的高度比，相當於把勁度當成與柱高一次方成反比；撓曲變形控制的柱，勁度與柱高三次方成反比，正確為 8 倍。\n(C) 不符合。4 倍等於高度比的平方，相當於把勁度當成與柱高平方成反比；撓曲變形下柱頂變位與柱高三次方成正比，勁度比應為 8 倍。\n(D) 符合。k1\u002Fk2 = (3EI\u002FL³)\u002F(3EI\u002F8L³) = 8，剪力依勁度分配，短柱剪力約為長柱的 8 倍。\n【演算步驟】\n公式：柱底固定、柱頂鉸接（懸臂柱）側向勁度 k = 3EI\u002Fh³；剛性梁使兩柱 Δ 相同，V = k·Δ\n短柱：k1 = 3EI\u002FL³（單位 kN·m²\u002Fm³ = kN\u002Fm）\n長柱：k2 = 3EI\u002F(2L)³，(2L)³ = 2 × 2 × 2 × L³ = 8L³，故 k2 = 3EI\u002F(8L³)（單位 kN\u002Fm）\n剪力比：V1\u002FV2 = k1\u002Fk2 = (3\u002F1)\u002F(3\u002F8) = 8（倍）\n【記憶點】剛性梁使各柱同變位，剪力依勁度分配；勁度與柱高三次方成反比，柱高加倍、剪力剩八分之一，短柱吃力。",550,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},23,"土壤液化會造成完工後的建築物下陷或傾斜，下列針對土壤液化現象的敘述，何者錯誤？",{"number":32,"session":7,"stem":33},24,"在靜態條件下，擋土牆可能之破壞型式不包括下列何者？",{"number":35,"session":7,"stem":36},25,"下圖剛架受地震力，最少出現幾個塑鉸時會發生崩塌？",{"number":38,"session":7,"stem":39},27,"下圖所示桁架中，a、c 兩桿互相垂直，在圖示水平力 P 作用下，那些桿件可能因受壓而…",{"number":41,"session":7,"stem":42},28,"於「建築物混凝土結構設計規範」中，有關純混凝土之規定，下列敘述何者錯誤？",{"number":44,"session":7,"stem":45},29,"關於預力混凝土梁之敘述，下列何者錯誤？",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","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…",{"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…",1791863197955]