[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-105170-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-105170-801-0102-024","architect","105170",105,"建築結構",24,null,"梁結構受力如下圖，最大內力矩為多少 kN-m？ 5 kN A B 6m 4m",{"A":14,"B":15,"C":16,"D":17},"30","20","18","12",[19],"D","single",[22],"\u002Fimages\u002Farch-105170-801-0102-024.png","本題考點：簡支梁受單一集中載重時的支承反力與最大彎矩，最大彎矩出現在載重作用點，Mmax = P a b \u002F L。\n【正解理由】依題圖所示，A 為鉸支承、B 為滾支承，跨長 6 m + 4 m = 10 m，5 kN 集中載重作用在距 A 點 6 m、距 B 點 4 m 處。先求反力：對 B 點取彎矩，R_A × 10 m = 5 kN × 4 m，R_A = 2 kN；R_B = 5 kN − 2 kN = 3 kN。簡支梁受集中載重時，剪力在載重點由正變負，彎矩在載重點最大：M = R_A × 6 m = 2 kN × 6 m = 12 kN-m，也可由右側驗算 R_B × 4 m = 3 kN × 4 m = 12 kN-m。故選 D。\n【逐項排除】\n(A) 不正確。30 kN-m 是把載重 5 kN 直接乘以 6 m 的結果，等於把 A 點當成固定端、把梁當成懸臂梁計算。簡支梁的彎矩要以支承反力乘以距離計算，A 點反力只有 2 kN，正確值為 12 kN-m。\n(B) 不正確。20 kN-m 是把載重 5 kN 乘以 4 m，同樣是把 B 點當成懸臂梁的固定端。B 點反力為 3 kN，乘以 4 m 才是載重點的彎矩 12 kN-m。\n(C) 不正確。18 kN-m 大於載重點的實際彎矩。簡支梁最大彎矩發生在剪力為零的位置，也就是載重點，其值為 2 kN × 6 m = 12 kN-m，梁上任何位置都不會出現 18 kN-m。\n(D) 正確。載重點彎矩 = P a b \u002F L = 5 kN × 6 m × 4 m \u002F 10 m = 12 kN-m，為全梁最大彎矩。\n【演算步驟】\n跨長 L = 6 m + 4 m = 10 m。\nΣM_B = 0：R_A = 5 kN × 4 m \u002F 10 m = 2 kN；R_B = 5 kN − 2 kN = 3 kN。\nMmax = R_A × 6 m = 2 kN × 6 m = 12 kN-m（驗算：3 kN × 4 m = 12 kN-m）。\n公式：Mmax = P a b \u002F L = 5 kN × 6 m × 4 m \u002F 10 m = 12 kN-m。\n【記憶點】簡支梁單一集中載重：最大彎矩在載重點，Mmax = P a b \u002F L。",560,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},21,"在耐震設計時通常根據工址的水平加速度反應譜來計算工址的設計水平譜加速度係數，而在規範…",{"number":32,"session":7,"stem":33},22,"下圖所示桁架 A、B 兩端皆為鉸支承，D 點受水平外力 P 作用，則此桁架中有多少根…",{"number":35,"session":7,"stem":36},23,"剛架結構受力如下圖，支承 A 之水平反力為多少 kN？ 6 kN B C 10 m …",{"number":38,"session":7,"stem":39},25,"桁架結構受力如下圖，桿件 FC 之軸向力為多少 kN？ F G H 6m E A B…",{"number":41,"session":7,"stem":42},26,"桁架結構受力如下圖，桿件 EL 之軸向力為多少 kN？ 10 kN J 3m I K…",{"number":44,"session":7,"stem":45},27,"已知圖示系統之固端彎矩值分別為 M1 及 M2， W M1 M2 L 若其一端由固端…",[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},"112190","桁架於 E 點受力 P，DF 軸力為何？ B D F H A C E G G P",{"number":10,"session":57,"stem":58},"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":60,"stem":61},"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？",1791863213955]