[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-112190-arch_structure-24":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-112190-801-0102-024","architect","112190",112,"建築結構",24,null,"桁架於 E 點受力 P，DF 軸力為何？ B D F H A C E G G P",{"A":14,"B":15,"C":16,"D":17},"0","P\u002F2 3 （拉）","P\u002F2（拉）","-P\u002F 3",[19],"D","single",[22],"\u002Fimages\u002Farch-112190-801-0102-024.png","本題考點：靜定桁架的斷面法。切開含 DF 的斷面，取另外兩根被切桿件的交點為力矩中心，一條力矩平衡式就能求出 DF 的軸力。\n【正解理由】依題圖所示，所有桿件長度都是 ℓ，構成正三角形；下弦節點 A、C、E、G、I 間距 ℓ，C 為鉸支承、G 為滾支承，P 向下作用在 E。桁架高度 h = (√3\u002F2)ℓ。先求支承反力：E 位於 C 與 G 的正中間，兩支承各距 E 為 ℓ，由對稱得 R_C = R_G = P\u002F2（↑）。接著用斷面切過 DF、EF、EG 三根桿，取右半部（F、G、H、I）為自由體。EF 與 EG 兩根桿都通過 E 點，對 E 取力矩，它們不產生力矩，只剩 R_G 與 DF 的軸力。設 DF 以拉力為正，ΣM_E = 0：(P\u002F2)×ℓ + N_DF×(√3\u002F2)ℓ = 0，得 N_DF = −(P\u002F2)ℓ ÷ (√3\u002F2)ℓ = −P\u002F√3。負號表示 DF 為壓力桿，大小 P\u002F√3，故選 D。\n【逐項排除】\n(A) 0：不符合題目所問。零桿出現在「無外力節點只接兩根不共線桿件」等特定情況，例如 A、I 兩端點與其相鄰的 B、H 節點；DF 位於受載的中間跨，承受上弦壓力，不是零桿。\n(B) P\u002F2√3（拉）：不符合題目所問。大小只有正確值的一半，方向也錯：簡支桁架在跨中向下載重作用下，上弦受壓，DF 不是拉力桿。\n(C) P\u002F2（拉）：不符合題目所問。P\u002F2 是支承反力的大小，不是 DF 的軸力；DF 的大小為 P\u002F√3，而且是壓力，不是拉力。\n(D) −P\u002F√3：符合題目所問。對 E 取力矩，DF 軸力 = −(P\u002F2)ℓ ÷ (√3\u002F2)ℓ = −P\u002F√3，負號代表壓力。\n【演算步驟】\n桁架高度（正三角形高）：h = (√3\u002F2)ℓ（m）\n支承反力（E 位於 C、G 正中）：R_C = R_G = P\u002F2（kN，↑）\n斷面法，取右半部，對 E 取力矩（拉力為正）：ΣM_E = (P\u002F2 kN)×(ℓ m) + N_DF×((√3\u002F2)ℓ m) = 0\nN_DF = −(P\u002F2)ℓ ÷ ((√3\u002F2)ℓ) = −P\u002F√3（kN，壓力）\n【記憶點】斷面法取另兩桿交點為力矩中心；簡支桁架受向下載重，上弦受壓、下弦受拉。",605,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},21,"關於隔震系統，下列敘述何者錯誤？",{"number":32,"session":7,"stem":33},22,"對一個寬度為 b 深度為 h 的矩形斷面梁的斷面模數（S）及塑性斷面模數（Z），下列…",{"number":35,"session":7,"stem":36},23,"如下圖所示之四種桁架結構，各桿件之軸向剛度（AE）值皆相等。若溫度改變時，何者最有可…",{"number":38,"session":7,"stem":39},25,"下圖所示結構中，支承 A 與 B 的反力大小為何？ 100 kN 45 kN C 4…",{"number":41,"session":7,"stem":42},26,"下圖中之圖(i)所示為一單跨抗彎矩構架（moment-resisting frame…",{"number":44,"session":7,"stem":45},27,"在鋼筋混凝土結構設計中，關於構材斷面之平衡應變狀態與平衡鋼筋比，下列敘述何者正確？",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","下圖框架之 A 點彎矩為何？ D 1 1 1 1",{"number":10,"session":51,"stem":52},"113190","在靜態條件下，擋土牆可能之破壞型式不包括下列何者？",{"number":10,"session":54,"stem":55},"111180","如圖所示桿件受軸向外力作用，F1 = 100 kN，F2 = 500 kN，則 A、…",{"number":10,"session":57,"stem":58},"110180","建築結構之樓地版設計活載重，依據規範下列何種用途類別的單位面積活載重最高？",{"number":10,"session":60,"stem":61},"109180","如圖示，AC 及 BC 均為曲梁，A、B 為鉸支承，C 為鉸接，下列有關支承反力敘述…",1791863200055]