[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-106180-arch_structure-28":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-106180-801-0102-028","architect","106180",106,"建築結構",28,null,"桁架結構受力如下圖，桿件 EC 之軸向力為多少 kN？",{"A":14,"B":15,"C":16,"D":17},"2 2 E F G","4 2 4m","3 2 A B C D","2 6kN 3kN 4m 4m 4m 4m",[19],"C","single",[22],"\u002Fimages\u002Farch-106180-801-0102-028.png","本題考點：靜定桁架的支承反力與截面法；切開含 EC 的斷面，以垂直力平衡直接求斜桿內力。\n【正解理由】依題圖，A 為鉸支承、D 為滾支承，下弦 A、B、C、D 與右端點各間隔 4 m，上弦 E、F、G 高 4 m；B 點受向下 6 kN，右端點受向下 3 kN。對 A 取力矩求 D 點反力：RD = (6 × 4 + 3 × 16)\u002F12 = 6 kN；垂直力平衡 RA = 6 + 3 − 6 = 3 kN（向上）。在 B、C 之間切開，截斷 EF、EC、BC 三桿，取左半部：EF、BC 都是水平桿，垂直方向只有 EC 的分力。EC 由 E 到 C 水平 4 m、垂直 4 m，傾角 45°，垂直分力為 F_EC\u002F√2。ΣFy = 0：RA − 6 + （EC 垂直分力） = 0，EC 須提供向上 3 kN，F_EC = 3 × √2 = 3√2 kN（壓力），故選 C。\n【逐項排除】\n(A) 2√2：垂直分力只有 2 kN，與左半部需由 EC 補足的 6 − 3 = 3 kN 不符。\n(B) 4√2：垂直分力為 4 kN，比左半部的不平衡力 3 kN 大，平衡不成立。\n(C) 3√2：正解。EC 的垂直分力 3 kN 補足左半部 RA 與 B 點載重之差。\n(D) √2：垂直分力只有 1 kN，同樣無法滿足垂直力平衡。\n【演算步驟】\n① ΣMA = 0：RD × 12 m = 6 kN × 4 m + 3 kN × 16 m → RD = (6 × 4 + 3 × 16)\u002F12 = 6 kN。\n② ΣFy = 0：RA = 6 + 3 − 6 = 3 kN（向上）。\n③ 截面法（左半部）ΣFy = 0：3 kN − 6 kN + F_EC\u002F√2 = 0 → F_EC 的垂直分力為 6 − 3 = 3 kN。\n④ F_EC = (6 − 3) × √2 = 3 × 1.41421 = 4.243 kN = 3√2 kN（壓力）。\n【記憶點】平行弦桁架的斜桿內力 = 該節間剪力 ÷ sinθ；先求反力、再看切面左邊的淨垂直力。",460,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},25,"有一矩形梁斷面，梁寬 30 cm，梁高 60 cm。已知材料之彈性係數為 20,00…",{"number":32,"session":7,"stem":33},26,"下圖簡支梁之跨度為 L。已知材料之彈性係數為 E，梁斷面之慣性矩為 I。今於跨度中央…",{"number":35,"session":7,"stem":36},27,"下圖之懸臂梁，端點 B 承受一集中載重 P，則 B 點之垂直位移為： PL2",{"number":38,"session":7,"stem":39},29,"剛架結構受力如下圖，接點 C 之內力矩為多少 kN-m？",{"number":41,"session":7,"stem":42},30,"下圖門形構架在 B 點承受一水平載重 P，則下列何處有最大彎矩值？",{"number":44,"session":7,"stem":45},31,"下圖桁架受外力作用之情形如圖所示，則下列有關此桁架的敘述，何者正確？",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","如圖所示之剛構架，各桿件之 EI 值皆相同，於 B 點承受一集中載重 P 作用，下列…",{"number":10,"session":51,"stem":52},"113190","於「建築物混凝土結構設計規範」中，有關純混凝土之規定，下列敘述何者錯誤？",{"number":10,"session":54,"stem":55},"112190","下圖為一歷史建築的結構示意圖。該建築物的外牆為磚牆，大廳柱為實心的圓形木柱，屋頂則由…",{"number":10,"session":57,"stem":58},"111180","一桁架之載重及桿件尺寸如圖所示，每根桿件之軸向剛度（AE）值均相同，此桁架於 A 點…",{"number":10,"session":60,"stem":61},"110180","下列圖示的梁柱構架系統，在地震橫力作用下，地面層何處梁段較容易因地震而造成剪力破壞？…",1791863212028]