[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-109180-arch_structure-12":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-109180-801-0102-012","architect","109180",109,"建築結構",12,null,"圖示結構物為幾度靜不定？鉸接",{"A":14,"B":15,"C":16,"D":17},"1","2","3","4",[19],"B","single",[22],"\u002Fimages\u002Farch-109180-801-0102-012.png","本題考點：平面剛架的靜不定度判定——以「支承反力未知數 − 平衡方程式數 − 內部鉸接釋放的條件數」計算，並辨識內部鉸接對靜不定度的影響。\n【正解理由】依題圖所示，此為一座山形（人字形）門架：左右兩柱底端皆為固定端，兩根斜梁在屋脊處以一個鉸接相連，其餘接點（柱頂與斜梁交接處）為剛接。每個固定端可提供水平反力、垂直反力與彎矩三個未知數，兩個固定端合計 6 個反力未知數。整體結構在平面上只有 3 條平衡方程式（ΣFx = 0、ΣFy = 0、ΣM = 0）。屋脊的鉸接只連接左右兩根構件，該處彎矩為零，多提供 1 條條件方程式。因此靜不定度 = 6 − 3 − 1 = 2，此結構為二度靜不定，故選 B。\n【逐項排除】\n(A) 1：比正確結果少 1 度。兩個固定端提供的反力數與屋脊鉸接只釋放一個條件都已確定，扣除後剩下 2 個多餘未知數，不是 1；要得到一度靜不定，必須再多一個釋放條件（例如再增加一個內部鉸接或把一端改為鉸支承），與題圖不符。\n(B) 2：正確。6 個反力未知數扣掉 3 條整體平衡方程式，再扣掉屋脊鉸接提供的 1 條彎矩為零條件，剩下 2 個多餘未知數，符合題目所問。\n(C) 3：這是把屋脊的鉸接忽略、當成整體剛接門架時的結果，即 6 − 3 = 3。兩端固定的封閉剛接門架才是三度靜不定；題圖屋脊明確標示為鉸接，必須再扣 1，所以不是 3。\n(D) 4：比正確結果多 2 度，超過了兩個固定端所能提供的多餘反力數。此結構反力總數只有 6，即使不計鉸接也只到 3，不可能達到 4；要到四度靜不定需要更多支承束制或封閉構件迴路，題圖沒有。\n【演算步驟】\n1. 反力未知數：每個固定端 3 個（水平力、垂直力、彎矩），兩端合計 r = 3 + 3 = 6 個。\n2. 平面靜力平衡方程式：3 條（ΣFx = 0、ΣFy = 0、ΣM = 0）。\n3. 內部鉸接條件：屋脊鉸接連接 2 根構件，釋放條件數 = 2 − 1 = 1 條（鉸接處彎矩 M = 0）。\n4. 靜不定度 = 6 − 3 − 1 = 2 度。\n【記憶點】兩端固定的門架是三度靜不定，每加一個連接兩根構件的內部鉸接就減一度，所以「兩固定端＋屋脊一鉸」的山形門架是二度靜不定。",512,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},9,"如圖所示，鋼筋混凝土剪力牆因開口而形成短梁，如圖中圈選處。若此結構承受來自左方的水平…",{"number":32,"session":7,"stem":33},10,"若欲構築大跨距之多層建築，在規劃各層水平構件（樓版與梁）之結構系統時，下列敘述何者正…",{"number":35,"session":7,"stem":36},11,"有關基礎及地層之敘述，下列何者錯誤？",{"number":38,"session":7,"stem":39},13,"有關桁架結構之敘述，下列何者正確？",{"number":41,"session":7,"stem":42},14,"如圖所示，AB 為梁，BCDE 為桁架，B、C 及 E 均為鉸接，AB 長度為 2L…",{"number":44,"session":7,"stem":45},15,"如圖所示構架，A 點水平反力 Ax 及垂直反力 Ay 各為何？（A、C、E 為鉸接）…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","如圖所示之甲乙兩支梁承受相同垂直均布靜載重，若兩梁皆為鋼筋混凝土構造，斷面(1)、(…",{"number":10,"session":51,"stem":52},"113190","非結構物耐震考量，下列敘述何者錯誤？",{"number":10,"session":54,"stem":55},"112190","如下圖所示，一構件斜面之中心點受一水平力 P=1000 N 作用，此斜面與水平方向之…",{"number":10,"session":57,"stem":58},"111180","在結構系統的規劃上，下列敘述何者錯誤？",{"number":10,"session":60,"stem":61},"110180","圖示之鋼筋混凝土韌性構架，有關主筋搭接之敘述，下列何者正確？ D A B C",1791863206226]