[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-109180-arch_structure-33":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-109180-801-0102-033","architect","109180",109,"建築結構",33,null,"桁架結構之受力如下圖，則 B 點的反力為何？ P P 5m A B 5m 5m 5m",{"A":14,"B":15,"C":16,"D":17},"(1\u002F3)P","(1\u002F2)P","(2\u002F3)P","P",[19],"C","single",[22],"\u002Fimages\u002Farch-109180-801-0102-033.png","本題考點：靜定桁架的支承反力——以鉸支承 A 為取矩中心，同時考慮垂直載重與水平載重對 A 點的力矩，求滾支承 B 的垂直反力。\n【正解理由】依題圖，A 為鉸支承、B 為滾支承，A、B 相距 5 m + 5 m + 5 m = 15 m，桁架高 5 m。兩個 P 都作用在距 A 點水平 5 m 的上弦節點：一個向下、一個向右，該節點高 5 m。滾支承 B 只能提供垂直反力 By。對 A 取力矩：向下的 P 力臂為水平距 5 m，產生順時針力矩 5P；向右的 P 作用在高 5 m 處，力臂為垂直距 5 m，同樣產生順時針力矩 5P；By 的力臂為 15 m，產生逆時針力矩。平衡得 By × 15 = 5P + 5P = 10P，By = (2\u002F3)P（向上），故選 C。\n【逐項排除】\n(A) (1\u002F3)P：這是只計入向下的 P、漏掉水平 P 對 A 點力矩的結果（5P ÷ 15 = P\u002F3）。水平力作用在高 5 m 的節點，對 A 點有力臂，必須一併計入，By 應為 (2\u002F3)P。\n(B) (1\u002F2)P：小於正確結果。兩個 P 對 A 點都產生同向的順時針力矩，合計 10P，除以 15 m 得 (2\u002F3)P，不是 (1\u002F2)P。\n(C) (2\u002F3)P：正確。By × 15 = 5P + 5P，By = (2\u002F3)P，符合題目所問。\n(D) P：大於正確結果。B 點垂直反力只需平衡兩個 P 對 A 點的合力矩 10P，所需反力為 (2\u002F3)P；若 By 等於 P，對 A 點的逆時針力矩 15P 超過 10P，力矩不平衡。\n【演算步驟】\n1. A、B 跨距：L = 5 m + 5 m + 5 m = 15 m。\n2. 對 A 取力矩（ΣM_A = 0，順時針為正）：P × 5 m（垂直載重）+ P × 5 m（水平載重）− By × 15 m = 0。\n3. By × 15 m = 10P·m → By = 10P·m \u002F 15 m = 0.6667P = (2\u002F3)P（↑）。\n4. 檢核：Ay = P − (2\u002F3)P = (1\u002F3)P（↑）；Ax = P（←），水平力全部由鉸支承 A 承擔。\n【記憶點】求滾支承反力就對鉸支承取矩，水平載重只要作用點不在支承高度，就有力臂、要算進力矩。",536,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},30,"結構的軟、弱層造成勁度及強度的不連續性，為過去造成建築物震損的原因之一，「建築物耐震…",{"number":32,"session":7,"stem":33},31,"如下圖之梁結構，兩側懸臂端在集中力 P 作用下，下列敘述何者正確？",{"number":35,"session":7,"stem":36},32,"如圖示之剛構架，AB、BC、CD 之長度均為 L 且為相同斷面，EI = 撓曲剛度，…",{"number":38,"session":7,"stem":39},34,"如圖示之剛構架，AB、BC、CD 之長度及斷面均相同，A 為固定端，D 為鉸支承，E…",{"number":41,"session":7,"stem":42},35,"對於混凝土結構撓曲構材的耐震設計，在彎矩降伏會發生的範圍，鋼筋不允許搭接，因此「混凝…",{"number":44,"session":7,"stem":45},36,"矩形鋼筋混凝土梁斷面計算其彎矩強度時，混凝土受壓區之應力常簡化成一等效矩形壓應力區塊…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","下圖為一偏心斜撐構架（Eccentrically Braced Frame）之示意圖…",{"number":10,"session":51,"stem":52},"113190","下列鋼結構斜撐構架中，地震時何種耐震性能最差？圖(a) 圖(b) 圖(c) 圖(d)",{"number":10,"session":54,"stem":55},"112190","關於鋼梁桿件的鋼板「局部挫屈」，下列敘述何者錯誤？",{"number":10,"session":57,"stem":58},"111180","關於矩形斷面鋼筋混凝土簡支梁的設計與分析，下列敘述何者錯誤？",{"number":10,"session":60,"stem":61},"110180","有一簡支梁承受均布載重如圖所示，若梁自重不計，下列何者所得之最大正彎矩值與此梁相同？",1791863206416]