[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-114180-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-114180-801-0102-019","architect","114180",114,"建築結構",19,null,"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 8m y C x A 8m 500 N B 1200 N",{"A":14,"B":15,"C":16,"D":17},"FAB = 450 N（拉）","FBC = 1000 N（拉）","FAC = 800 N（壓）","Ay = 300 N（向上）",[19],"C","single",[22],"\u002Fimages\u002Farch-114180-801-0102-019.png","本題考點：三角形桁架的支承反力與節點法——先由整體平衡求反力，再在支承節點分解斜桿分量求各桿內力與拉壓。\n【正解理由】依題圖，A 為鉸支承、C 為滾支承（只提供垂直反力），AC 為水平上弦長 6 m + 8 m = 14 m，B 點位於 A 右方 6 m、下方 8 m，承受 500 N 向左與 1200 N 向下。整體水平平衡：Ax = 500 N（向右）。對 A 取力矩：Cy × 14 = 1200 × 6 + 500 × 8，得 Cy = 800 N（向上）；垂直平衡得 Ay = 1200 − 800 = 400 N（向上）。在節點 C，只有 AC（水平）與 BC（水平與垂直投影都是 8 m 的斜桿）兩桿：垂直方向由 BC 的分量平衡 800 N，得 BC = 800 × 1.4142 = 1131.4 N（拉）；水平方向 BC 的水平分量 800 N 必須由 AC 平衡，AC 推向 C 點，故 AC = 800 N（壓）。故選 C。\n【逐項排除】\n(A) 錯誤。AB 水平投影 6 m、垂直投影 8 m，桿長 10 m。節點 A 垂直平衡：F_AB × 8\u002F10 = Ay = 400 N，得 F_AB = 400 × 10 \u002F 8 = 500 N（拉），不是 450 N；方向（拉）正確，數值錯。\n(B) 錯誤。BC 的垂直分量要平衡 C 點反力 800 N，斜桿水平與垂直投影相等，F_BC = 800 × 1.4142 = 1131.4 N（拉）；方向（拉）正確，但數值不是 1000 N。\n(C) 正確。節點 C 水平平衡，BC 拉力的水平分量 800 N 由 AC 抵抗，AC 為 800 N 壓力。\n(D) 錯誤。Ay = 1200 − 800 = 400 N（向上），不是 300 N；方向向上正確，數值錯。\n【演算步驟】\n1. ΣFx = 0：Ax − 500 N = 0 → Ax = 500 N（向右）。\n2. ΣM_A = 0：Cy × 14 m = 1200 N × 6 m + 500 N × 8 m → Cy = (1200 × 6 + 500 × 8) \u002F 14 = 800 N（向上）。\n3. ΣFy = 0：Ay = 1200 N − 800 N = 400 N（向上）。\n4. 節點 C 垂直：F_BC × 8\u002F(8 × 1.4142) = 800 N → F_BC = 800 N × 1.4142 = 1131.4 N（拉）。\n5. 節點 C 水平：F_AC = F_BC × 8\u002F(8 × 1.4142) = 800 N（壓）。\n6. 節點 A 垂直：F_AB × 8\u002F10 = 400 N → F_AB = 400 N × 10 \u002F 8 = 500 N（拉）。\n7. 節點 A 水平檢核：500 N − 800 N + 500 N × 6\u002F10 = 0，平衡成立。\n【記憶點】先求反力再從只有兩根桿件的支承節點下手；拉壓看桿件是拉著節點還是推著節點。",592,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},16,"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…",{"number":32,"session":7,"stem":33},17,"圖中桁架結構有幾支零桿？",{"number":35,"session":7,"stem":36},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":38,"session":7,"stem":39},20,"圖示桁架 A、I 點為鉸支承，在 D 點受向下 4 kN 荷重，下列關於構件內力與方…",{"number":41,"session":7,"stem":42},21,"下圖桁架結構中 C、D 為鉸支承，BC 桿之受力狀況，下列何者正確（T 為張力，C …",{"number":44,"session":7,"stem":45},22,"桁架結構如下圖，a~d 桿件中何者軸拉力最大？ 1.5 m 3m 3m 1.5 m …",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"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":51,"stem":52},"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":54,"stem":55},"111180","關於無梁版（flat slab）結構系統，下列敘述何者錯誤？",{"number":10,"session":57,"stem":58},"110180","從永續性綠建築結構的角度，下列敘述何者錯誤？",{"number":10,"session":60,"stem":61},"109180","對鋼筋混凝土耐震柱的繫筋配置而言，下列何者為較適當的配置方式？ a b c d",1791863195473]