[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-106180-arch_structure-13":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-106180-801-0102-013","architect","106180",106,"建築結構",13,null,"下圖簡支梁受三角形載重，則 B 點反力為多少？",{"A":14,"B":15,"C":16,"D":17},"q0L\u002F6","q0L\u002F3 q0","q0L\u002F2 A B","2q0L\u002F3 EI L",[19],"B","single",[22],"\u002Fimages\u002Farch-106180-801-0102-013.png","本題考點：簡支梁受三角形分布載重時，以合力大小與合力作用位置求支承反力（力矩平衡）。\n【正解理由】依題圖，A 端為鉸支承、B 端為滾支承，三角形載重由 A 端的零線性增加到 B 端的 q0。三角形分布載重的合力等於三角形面積 W = q0L\u002F2，作用在三角形形心，也就是距小端（A）2L\u002F3、距大端（B）L\u002F3 的位置。對 A 點取力矩平衡：RB × L = (q0L\u002F2) × (2L\u002F3)，得 RB = q0L\u002F3。合力偏向載重大的 B 端，所以 B 端反力較大，故選 B。\n【逐項排除】\n(A) q0L\u002F6：這是 A 點反力。由垂直力平衡 RA = q0L\u002F2 − q0L\u002F3 = q0L\u002F6，A、B 兩端對調了；靠近載重小端的 A 支承分到的反力才是 q0L\u002F6。\n(B) q0L\u002F3：正解。對 A 點取力矩，合力 q0L\u002F2 乘上力臂 2L\u002F3 再除以 L。\n(C) q0L\u002F2：這是整個三角形載重的合力，等於 RA + RB 的總和，不是單一支承的反力；只有合力恰在跨度中央（如均布載重）時，兩端才各分一半，而本題的合力不在中央。\n(D) 2q0L\u002F3：大於合力 q0L\u002F2，單一支承反力不可能超過全部向下載重（梁上沒有其他外力），數值不成立。2\u002F3 是形心距 A 端的距離比例，不是反力的係數。\n【演算步驟】\n① 合力：W = (1\u002F2) × q0 × L = q0L\u002F2（力）。\n② 合力位置：距 A 端 2L\u002F3（長度）。\n③ ΣMA = 0：RB × L = (q0L\u002F2) × (2L\u002F3) → RB = (1\u002F2) × (2\u002F3) × q0L = q0L\u002F3（力）。\n④ 檢核：RA = q0L\u002F2 − q0L\u002F3 = q0L\u002F6（力），RA + RB = q0L\u002F2。\n【記憶點】三角形載重：合力 = 面積 q0L\u002F2，作用在距大端 L\u002F3 處；大端支承分 q0L\u002F3，小端分 q0L\u002F6。",426,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},10,"承上題，正方形斷面梁的最大應力為圓形斷面梁的多少倍？",{"number":32,"session":7,"stem":33},11,"依據「建築物耐震設計規範」之耐震設計目標，下列何者錯誤？",{"number":35,"session":7,"stem":36},12,"某十層樓建築物，其各層的質量皆相等，且各層的勁度與樓高亦相等。不考慮阻尼影響，在地震…",{"number":38,"session":7,"stem":39},14,"依「混凝土結構設計規範」耐震設計之特別規定，柱縱向鋼筋之鋼筋比不得大於多少％？",{"number":41,"session":7,"stem":42},15,"有一承受均佈載重之簡支梁，其最大拉應力在何處？",{"number":44,"session":7,"stem":45},16,"有關鋼骨材料之敘述，下列何者錯誤？",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","下列有關結構穩定性與靜定性之敘述，何者錯誤？",{"number":10,"session":51,"stem":52},"113190","下列關於建築物所使用被動消能元件之敘述，何者錯誤？",{"number":10,"session":54,"stem":55},"112190","下列有關「固定拱」、「雙鉸拱」和「三鉸拱」的敘述，何者錯誤？",{"number":10,"session":57,"stem":58},"111180","柱 1、柱 2、柱 3 之長度、材料、斷面均同，其最小挫屈載重分別為 P1、P2、P…",{"number":10,"session":60,"stem":61},"110180","鋼筋混凝土結構在耐震設計時，係依據鋼筋應力為 1.25 fy 所求得之彎矩強度以計算…",1791863211926]