[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-114180-arch_structure-16":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-114180-801-0102-016","architect","114180",114,"建築結構",16,null,"圖中所示一正三角形桁架，求可施加之最大負載 P，使得無任何桿件受力超過 3 kN 之張力或 2.5 kN 之壓力？",{"A":14,"B":15,"C":16,"D":17},"4.3","6.3","8.3","10.3",[19],"A","single",[22],"\u002Fimages\u002Farch-114180-801-0102-016.png","本題考點：對稱靜定桁架以節點法求桿件內力，再分別用「容許張力」與「容許壓力」反推載重上限，取較小者控制。\n【正解理由】正三角形桁架 A 為鉸支承、B 為滾支承，頂點 C 受向下載重 P，結構與載重左右對稱，兩支承垂直反力各為 P\u002F2。在節點 A 取力平衡：斜桿 AC 的垂直分量要抵抗向上的反力 P\u002F2，因此 AC 受壓；AC 的水平分量向左推 A 點，必須由底桿 AB 的拉力平衡，因此 AB 受拉。正三角形斜桿與水平的夾角使 sinθ = √3\u002F2、cosθ = 1\u002F2，可得 AC = BC = P\u002F√3（壓）、AB = P\u002F(2√3)（拉）。斜桿受壓的比例較大、容許壓力又較小，所以壓力條件先達上限：P\u002F√3 = 2.5 kN 得 P = 2.5 × 1.732 = 4.33 kN；拉力條件 P\u002F(2√3) = 3 kN 得 P = 3 × 2 × 1.732 = 10.39 kN，較寬鬆不控制。取兩者較小值 4.33 kN，取至小數一位為 4.3 kN。故選 A。\n【逐項排除】\n(A) 符合。4.3 kN 是斜桿壓力剛好達到 2.5 kN 時的載重，此時底桿拉力只有 P\u002F(2√3)，遠低於 3 kN，兩個條件都滿足。\n(B) 不符。6.3 kN 大於壓力控制上限 4.33 kN，代入後斜桿 AC、BC 的壓力會超過 2.5 kN，違反壓力限制。\n(C) 不符。8.3 kN 同樣大於 4.33 kN，斜桿壓力超過 2.5 kN；雖然底桿拉力仍未達 3 kN，但只要有任一桿件超限即不成立。\n(D) 不符。10.3 kN 遠大於壓力控制上限，斜桿壓力明顯超過 2.5 kN；只檢核拉力條件而忽略壓力條件，會漏掉真正控制的桿件。\n【演算步驟】\n1. 支承反力（對稱）：Ay = By = P\u002F2。\n2. 節點 A 垂直平衡：F_AC × sinθ = P\u002F2，sinθ = √3\u002F2 → F_AC = P\u002F√3（壓）。\n3. 節點 A 水平平衡：F_AB = F_AC × cosθ = (P\u002F√3) × 1\u002F2 = P\u002F(2√3)（拉）；同理 F_BC = P\u002F√3（壓）。\n4. 壓力條件：P\u002F√3 ≤ 2.5 kN → P ≤ 2.5 kN × 1.732 = 4.33 kN。\n5. 拉力條件：P\u002F(2√3) ≤ 3 kN → P ≤ 3 kN × 2 × 1.732 = 10.39 kN。\n6. 取小值：P_max = 4.33 kN，取至小數一位為 4.3 kN。\n【記憶點】正三角形頂點受載：斜桿壓 P\u002F√3、底桿拉 P\u002F(2√3)，兩個上限各算一次取小值。",504,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},13,"下列有關結構穩定性與靜定性之敘述，何者錯誤？",{"number":32,"session":7,"stem":33},14,"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":35,"session":7,"stem":36},15,"如圖所示的桁架，C 點承受一個集中載重 P 之作用，假設每一支桿件的彈性模數和斷面尺…",{"number":38,"session":7,"stem":39},17,"圖中桁架結構有幾支零桿？",{"number":41,"session":7,"stem":42},18,"如圖所示桁架結構，桿件 EJ 之軸力為多少 kN？ 4m 6 kN 12 kN 6@…",{"number":44,"session":7,"stem":45},19,"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…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"113190","一剛架結構受外力作用如圖所示，下列何種梁上塑性鉸產生時，不會形成不穩定結構？",{"number":10,"session":51,"stem":52},"112190","下列何種設計策略會增長建物基本振動週期？",{"number":10,"session":54,"stem":55},"111180","關於柱子的挫屈（buckling）破壞與臨界負載（critical load）之敘述…",{"number":10,"session":57,"stem":58},"110180","建築物耐震設計規範的鋼骨造結構系統中，常採用偏心斜撐結構系統。此系統的主要消能機制一…",{"number":10,"session":60,"stem":61},"109180","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…",1791863195452]