[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-109180-arch_structure-14":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-109180-801-0102-014","architect","109180",109,"建築結構",14,null,"如圖所示，AB 為梁，BCDE 為桁架，B、C 及 E 均為鉸接，AB 長度為 2L，BC、CD 及 CE 長度均為 L。下列敘述何者錯誤？",{"A":14,"B":15,"C":16,"D":17},"D 支承垂直反力為 3P\u002F4","CE 桿件承受拉力","A 支承垂直反力為 P\u002F2","A 支承力矩為 PL",[19],"A","single",[22],"\u002Fimages\u002Farch-109180-801-0102-014.png","本題考點：梁與桁架以鉸接相連的組合結構，先取桁架為自由體求支承反力，再把鉸接點的力傳回懸臂梁求固定端反力與力矩，並以節點法判斷桿件拉壓。\n【正解理由】依題圖所示，A 為固定端，AB 梁在 B 點以鉸接連到桁架 BCDE，D 為滾支承，P 向下作用在下弦中點 C，E 位於 C 的正上方。鉸接只傳遞力、不傳遞力矩，因此可先取整個桁架為自由體：對 B 點取力矩，R_D × 2L = P × L，得 R_D = P\u002F2；垂直力平衡，B 點對桁架提供的向上力 = P − P\u002F2 = P\u002F2；滾支承 D 沒有水平反力，B 點水平力為 0。再取 AB 梁為自由體：梁在 B 點承受桁架傳回的向下力 P\u002F2，A 端垂直反力 = P\u002F2，A 端力矩 = (P\u002F2) × 2L = PL。選項 (A) 寫 D 支承垂直反力為 3P\u002F4，與 P\u002F2 不符，是本題唯一錯誤的敘述，故選 A。\n【逐項排除】\n(A) 錯誤。D 點反力只由桁架本身的力矩平衡決定：P 距 B 點 L，D 距 B 點 2L，R_D = P × L \u002F 2L = P\u002F2。選項寫 3P\u002F4，比正確值偏大；改成「D 支承垂直反力為 P\u002F2」才對。注意 AB 梁的長度 2L 不影響 R_D，因為 B 為鉸接，梁對桁架只施加通過 B 點的力，對 B 點不產生力矩。\n(B) 正確。取節點 C 為自由體：BC 與 CD 都是水平桿，對垂直方向沒有分量，垂直方向只剩 CE 桿力與外力 P。ΣFy = 0 得 F_CE = P，方向是把節點 C 往上拉，也就是拉離節點，因此 CE 為拉力桿，大小等於 P。\n(C) 正確。桁架在 B 點需要向上 P\u002F2 的支撐力，依作用力與反作用力，AB 梁在 B 端被向下拉 P\u002F2。懸臂梁 AB 上沒有其他垂直載重，A 端垂直反力 = P\u002F2，方向向上。\n(D) 正確。A 端力矩 = B 端集中力 × 力臂 = (P\u002F2) × 2L = PL。傳到梁上的只有 P\u002F2，另一半 P\u002F2 由 D 支承承擔，不能把整個 P 當成作用在 B 點。\n【記憶點】鉸接點是「只傳力、不傳彎矩」的斷點：先解有滾支承的桁架求出鉸接力，再把它當成懸臂梁端點的集中載重。",704,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},11,"有關基礎及地層之敘述，下列何者錯誤？",{"number":32,"session":7,"stem":33},12,"圖示結構物為幾度靜不定？鉸接",{"number":35,"session":7,"stem":36},13,"有關桁架結構之敘述，下列何者正確？",{"number":38,"session":7,"stem":39},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）…",{"number":41,"session":7,"stem":42},16,"如圖所示為左右對稱之平面構架，承受垂直均佈載重。若將彎矩圖繪於張力側，最有可能為下列…",{"number":44,"session":7,"stem":45},17,"在圖中的門形構架，設梁為剛體（EI = ∞），而質量 m 集中於剛體梁上。若柱的 E…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","圖示之梁構造中 C 為鉸接，不考慮自重影響，在 B 出現微小垂直沉陷時，下列敘述何者…",{"number":10,"session":51,"stem":52},"113190","一般建築結構耐震設計時，下列敘述何者錯誤？",{"number":10,"session":54,"stem":55},"112190","下列有關纜索結構系統的敘述，何者正確？",{"number":10,"session":57,"stem":58},"111180","關於木質構造，下列敘述何者錯誤？",{"number":10,"session":60,"stem":61},"110180","下列有關鋼柱挫屈強度 Pcr 之敘述，何者錯誤？",1791863206243]