[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-114180-arch_structure-20":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-114180-801-0102-020","architect","114180",114,"建築結構",20,null,"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向的敘述何者錯誤？ I H G E 3m A B C 4 kN D 2m 2m 2m",{"A":14,"B":15,"C":16,"D":17},"HB 桿 = 4 kN（拉）","CE 桿 = 4.8 kN（壓）","AB 桿 = 5.3 kN（壓）","HG 桿 = 4.8 kN（拉）",[19],"D","single",[22],"\u002Fimages\u002Farch-114180-801-0102-020.png","本題考點：懸臂式桁架的節點法與截面法——從自由端無支承的節點逐點求內力，弦桿則以截面法取力矩求得。\n【正解理由】依題圖，下弦 A、B、C、D 與上弦 I、H、G、E 每格 2 m、高 3 m，斜桿 AH、BG、CE 由左下往右上，A、I 為鉸支承，D 點受 4 kN 向下。斜桿水平 2 m、垂直 3 m，桿長 √13 = 3.6056 m。在 H、G 之間切開，取右半部，對 B 點取力矩：F_HG × 3 m = 4 kN × 4 m，F_HG = 4 × 4 \u002F 3 = 5.33 kN，且為拉力；選項 (D) 說 HG 桿為 4.8 kN（拉），數值不符，是錯誤敘述。故選 D。\n【逐項排除】\n(A) 正確。H、G 之間截面右半部垂直平衡：斜桿 BG 的垂直分量須承擔 4 kN，F_BG = 4 × 3.6056 \u002F 3 = 4.81 kN（壓）；再看節點 B 垂直方向，BG 壓力的垂直分量 4 kN 推節點 B 向下，須由 HB 拉住，HB = 4 kN（拉），敘述正確。\n(B) 正確。節點 D 只有 DC（水平）與 DE（垂直），垂直平衡得 DE = 4 kN（拉）、DC = 0；節點 E 垂直平衡：F_CE × 3\u002F3.6056 = 4 kN，得 F_CE = 4 × 3.6056 \u002F 3 = 4.81 kN，CE 推著 E 點，為壓力，與 4.8 kN（壓）相符。\n(C) 正確。在 A、B 之間切開（截斷 IH、AH、AB，其中 IH 與 AH 都通過 H 點），取右半部對 H 點取力矩：F_AB × 3 m = 4 kN × 4 m，得 F_AB = 4 × 4 \u002F 3 = 5.33 kN，為壓力，與 5.3 kN（壓）相符。\n(D) 錯誤。HG 桿為 5.33 kN（拉），方向正確但數值不是 4.8 kN；4.8 kN 是 CE 斜桿的內力大小。\n【演算步驟】\n1. 斜桿長：水平 2 m、垂直 3 m，桿長 √13 = 3.6056 m。\n2. 節點 E 垂直平衡：F_CE × 3\u002F3.6056 = 4 kN → F_CE = 4 kN × 3.6056 \u002F 3 = 4.81 kN（壓）。\n3. H、G 間截面垂直平衡：F_BG = 4 kN × 3.6056 \u002F 3 = 4.81 kN（壓）；節點 B 垂直：F_HB = 4.81 kN × 3 \u002F 3.6056 = 4 kN（拉）。\n4. H、G 間截面對 B 取力矩：F_HG × 3 m = 4 kN × 4 m → F_HG = 5.33 kN（拉）。\n5. A、B 間截面對 H 取力矩：F_AB × 3 m = 4 kN × 4 m → F_AB = 5.33 kN（壓）。\n【記憶點】懸臂桁架上弦受拉、下弦受壓；弦桿力 = 載重 × 力臂 ÷ 桁架高。",565,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},17,"圖中桁架結構有幾支零桿？",{"number":32,"session":7,"stem":33},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":35,"session":7,"stem":36},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…",{"number":38,"session":7,"stem":39},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":41,"session":7,"stem":42},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 …",{"number":44,"session":7,"stem":45},23,"在圖示之三鉸拱結構中，A 點之水平反力為何？ 6P L A L L L",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"113190","根據尤拉挫屈公式（Euler equation），下列何種作法可降低柱子的有效長度，…",{"number":10,"session":51,"stem":52},"112190","關於承重牆結構系統特性，下列敘述何者正確？",{"number":10,"session":54,"stem":55},"111180","等跨長之連續梁受圖示向下等值均佈載重，下列那一種載重分布的第三跨梁中央 C 點之正彎…",{"number":10,"session":57,"stem":58},"110180","若降伏比定義為材料之降伏強度與抗拉強度之比值，其對於鋼結構耐震之影響，下列敘述何者正…",{"number":10,"session":60,"stem":61},"109180","鋼筋混凝土柱在相同斷面尺寸及淨高下，欲改善柱的耐震韌性行為，通常可以藉由下列何者來提…",1791863195489]