[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-106180-arch_structure-30":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-106180-801-0102-030","architect","106180",106,"建築結構",30,null,"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？",{"A":14,"B":15,"C":16,"D":17},"A 點 B C","B 點 P E,I,L","C 點","D 點 E,I,L E,I,L A D",[19],"A","single",[22],"\u002Fimages\u002Farch-106180-801-0102-030.png","本題考點：靜不定門形構架受側向載重時的彎矩分布；固定端與鉸支端的束制差異，以及節點轉動如何削減柱頂彎矩。\n【正解理由】依題圖，A 為固定端、D 為鉸支承，兩柱與梁都是 E、I、L，P 水平作用在 B 點。以傾角變位法求解，令 k = EI\u002FL、側移角 ψ = Δ\u002FL。各桿端彎矩：M_AB = 2k(θB − 3ψ)、M_BA = 2k(2θB − 3ψ)、M_BC = 2k(2θB + θC)、M_CB = 2k(2θC + θB)、D 端為鉸，M_CD = 3k(θC − ψ)、M_DC = 0。B 節點平衡 2k(2θB − 3ψ) + 2k(2θB + θC) = 0 → 8θB + 2θC = 6ψ；C 節點平衡 2k(2θC + θB) + 3k(θC − ψ) = 0 → 2θB + 7θC = 3ψ。聯立得 θB = 9ψ\u002F13、θC = 3ψ\u002F13。代回得彎矩大小比 A ：B ：C ：D = 60 ：42 ：30 ：0（以 kψ\u002F13 為單位），再由柱剪力平衡 PL = 132kψ\u002F13，M_A = 60PL\u002F132 最大，故選 A。\n【逐項排除】\n(A) A 點：正解。固定端不能轉動，柱 AB 下端彎矩 M_AB = 2k(θB − 3ψ) 只被 θB 削減一次，是全構架最大值 60PL\u002F132。\n(B) B 點：柱頂 B 節點會順著側移方向轉動，M_BA = 2k(2θB − 3ψ) 被 θB 削減兩倍，大小 42PL\u002F132，小於 A 點。\n(C) C 點：C 節點連接下端為鉸的柱 CD，該柱側向勁度較低、分到的剪力較少，M_C = 30PL\u002F132，小於 A 點。\n(D) D 點：鉸支承不能傳遞彎矩，M_DC = 0，是全構架最小值。\n【演算步驟】\n① 桿端彎矩式（k = EI\u002FL、ψ = Δ\u002FL）如上。\n② B 節點：8θB + 2θC = 6ψ；C 節點：2θB + 7θC = 3ψ → θB = 9ψ\u002F13、θC = 3ψ\u002F13（弧度）。\n③ |M_AB| = 2(3 − 9\u002F13)kψ = 60kψ\u002F13；|M_BA| = 2(3 − 18\u002F13)kψ = 42kψ\u002F13；|M_CD| = 3(1 − 3\u002F13)kψ = 30kψ\u002F13；M_DC = 0（力 × 長度）。\n④ 柱剪力和 = P：PL = (60 + 42 + 30)kψ\u002F13 = 132kψ\u002F13 → M_A = 60PL\u002F132、M_B = 42PL\u002F132、M_C = 30PL\u002F132、M_D = 0。\n【記憶點】側推門形構架：固定柱腳彎矩最大，鉸接柱腳彎矩為零；節點會轉動的柱頂彎矩比固定柱腳小。",483,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},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":32,"session":7,"stem":33},28,"桁架結構受力如下圖，桿件 EC 之軸向力為多少 kN？",{"number":35,"session":7,"stem":36},29,"剛架結構受力如下圖，接點 C 之內力矩為多少 kN-m？",{"number":38,"session":7,"stem":39},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？",{"number":41,"session":7,"stem":42},32,"下圖之構架在 B 點受 4 tf-m 力矩作用，令材料性質 EI 為常數，則 BC …",{"number":44,"session":7,"stem":45},33,"對鋼構造建築物的設計，根據現行「鋼結構極限設計法規範」，D＝靜載重、L＝活載重、E＝…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","關於鋼筋混凝土柱，下列敘述何者正確？",{"number":10,"session":51,"stem":52},"113190","關於鋼筋混凝土梁桿件之「平衡鋼筋比」，下列敘述何者錯誤？",{"number":10,"session":54,"stem":55},"112190","以下鋼結構斜撐系統中，何者側向勁度最高？",{"number":10,"session":57,"stem":58},"111180","四組鋼造構架經耐震設計如下圖所示，其門型框架與斜撐斷面均同，僅斜撐配置不同，其中桿件…",{"number":10,"session":60,"stem":61},"110180","無梁版系統在我國較少應用於上部結構，大多僅應用在地下室結構，下列敘述何者錯誤？",1791863212039]