[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-106180-arch_structure-19":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-106180-801-0102-019","architect","106180",106,"建築結構",19,null,"下圖剛架中，若梁的勁度趨近於無限大，則柱挫屈的有效長度係數 K 值為何？",{"A":14,"B":15,"C":16,"D":17},"0.5 EIb","0.7","1","2 EIc EIc H",[19],"C","single",[22],"\u002Fimages\u002Farch-106180-801-0102-019.png","本題考點：柱的有效長度係數 K，由柱兩端的轉動束制與是否允許側移決定；梁勁度無限大、柱底固定的門形剛架，屬於「兩端不轉動但可側移」的情形。\n【正解理由】依題圖，兩根柱 EIc、高 H，柱底為固定端；柱頂接一根勁度趨近無限大的梁 EIb，柱頂因而無法轉動。題圖的梁頂沒有任何側向支撐，整座剛架可以水平側移。於是每根柱的邊界是「下端固定、上端不轉動但可平移」。這種柱挫屈時，柱中高處出現反曲點，上下兩半各像一根長 H\u002F2 的懸臂柱，懸臂柱 K = 2，有效長度 KH = 2 × H\u002F2 = H，所以 K = 1，挫屈載重 Pcr = π²EIc\u002FH²，故選 C。\n【逐項排除】\n(A) 0.5：對應兩端固定且「不能側移」的柱，反曲點在四分點；本題剛架無側撐可側移，柱頂能水平移動，不符「無側移」這個要件。\n(B) 0.7：對應一端固定、一端鉸接且不能側移的柱；本題柱頂被無限剛的梁鎖住轉動（不是鉸接），且剛架可側移，兩個要件都不符。\n(C) 1：正解。下端固定、上端不轉動可側移，反曲點在中高，有效長度等於柱高。\n(D) 2：對應一端固定、一端完全自由（可轉動也可平移）的懸臂柱；若梁勁度趨近零，柱頂失去轉動束制才會接近此值。本題梁勁度無限大，柱頂轉動被完全束制，不符。\n【演算步驟】\n① 公式：Pcr = π²EIc\u002F(KH)²。\n② 邊界：柱底固定、柱頂不轉動可側移 → 反曲點在 H\u002F2 處（長度）。\n③ 半柱為懸臂柱：K = 2，有效長度 = 2 × H\u002F2 = H（長度）。\n④ K = H\u002FH = 1，Pcr = π²EIc\u002FH²。\n【記憶點】有側移剛架：梁無限剛 → K = 1；梁勁度趨零 → K = 2。無側移時才落在 0.5 到 1 之間。",473,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},16,"有關鋼骨材料之敘述，下列何者錯誤？",{"number":32,"session":7,"stem":33},17,"有關樁基礎之敘述，下列何者錯誤？",{"number":35,"session":7,"stem":36},18,"關於鉛心鋼板橡膠隔震器的敘述，下列何者正確？",{"number":38,"session":7,"stem":39},20,"建築結構除了耐風的強度設計外，規範仍要求檢討風力作用下建築物的容許層間變位角，其中耐…",{"number":41,"session":7,"stem":42},21,"下圖結構原為不穩定，擬於各節點間增加兩根桿件進行改善，則下列選項何者仍為不穩定結構？",{"number":44,"session":7,"stem":45},22,"型鋼會因製造過程產生殘餘應力（residual stress），下列敘述何者錯誤？",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"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":51,"stem":52},"113190","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…",{"number":10,"session":54,"stem":55},"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":57,"stem":58},"111180","關於無梁版（flat slab）結構系統，下列敘述何者錯誤？",{"number":10,"session":60,"stem":61},"110180","從永續性綠建築結構的角度，下列敘述何者錯誤？",1791863211966]