[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-107180-arch_structure-22":3},{"question":4,"neighbors":26,"sameNumber":45,"prev":34,"next":37},{"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":22,"withheld":11,"deepChars":23,"freq":24,"indexable":25},"arch-107180-801-0102-022","architect","107180",107,"建築結構",22,null,"正方形斷面面積為 A，承受剪力 V，則此斷面之最大剪應力為何？",{"A":14,"B":15,"C":16,"D":17},"1.0 V\u002FA","1.5 V\u002FA","2.0 V\u002FA","2.5 V\u002FA",[19],"B","single",[],"本題考點：矩形（含正方形）斷面受剪力時的剪應力分布公式 τ = VQ\u002F(Ib)，以及最大剪應力發生在中性軸、為平均剪應力 V\u002FA 的 1.5 倍。\n【正解理由】梁斷面的剪應力並非均勻分布，而是依 τ = VQ\u002F(Ib) 計算：上下緣處 Q 為零，剪應力為零；中性軸處 Q 最大，剪應力最大。設斷面寬 b、高 h（正方形 b = h），中性軸以上面積對中性軸的一次矩 Q = b × h\u002F2 × h\u002F4 = bh²\u002F8，慣性矩 I = bh³\u002F12，代入得 τmax = V × (bh²\u002F8)\u002F[(bh³\u002F12) × b] = (12\u002F8) × V\u002F(bh) = 1.5 V\u002FA，故選 B。\n【逐項排除】\n(A) 1.0 V\u002FA：這是平均剪應力，相當於假設剪應力在整個斷面上均勻分布；實際分布是上下緣為零、中性軸最大的拋物線形，中性軸處的最大值大於平均值，應為 1.5 V\u002FA。\n(B) 1.5 V\u002FA：正確。矩形斷面中性軸處 Q = bh²\u002F8、I = bh³\u002F12，代入 τ = VQ\u002F(Ib) 得 1.5 V\u002FA；正方形是矩形 b = h 的特例，係數不變。\n(C) 2.0 V\u002FA：數值大於矩形斷面的最大剪應力；由 τ = VQ\u002F(Ib) 推得的係數是 12\u002F8 = 1.5，不是 2.0，正確為 1.5 V\u002FA。\n(D) 2.5 V\u002FA：偏大更多，與矩形斷面拋物線分布的峰值不符；正確為 1.5 V\u002FA。\n【演算步驟】\n① 公式：τ = VQ\u002F(Ib)，V 單位 kN、Q 單位 m³、I 單位 m⁴、b 單位 m，τ 單位 kN\u002Fm²。\n② 中性軸一次矩：Q = (b × h\u002F2) × (h\u002F4) = bh²\u002F8（m³）。\n③ 慣性矩：I = bh³\u002F12（m⁴）。\n④ 代入：τmax = V × (bh²\u002F8)\u002F[(bh³\u002F12) × b] = V × (12\u002F8)\u002F(bh) = 1.5 V\u002F(bh)（kN\u002Fm²）。\n⑤ 以 A = bh（m²）表示：τmax = 1.5 V\u002FA（kN\u002Fm²）。\n【記憶點】矩形（正方形）斷面最大剪應力在中性軸，為平均剪應力 V\u002FA 的 1.5 倍。",526,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},19,"關於薄膜結構之基本力學原理，下列敘述何者錯誤？",{"number":31,"session":7,"stem":32},20,"關於鋼筋混凝土結構之敘述，下列何者錯誤？",{"number":34,"session":7,"stem":35},21,"臺北 101 大樓（臺北國際金融中心）曾為世界最高的建築結構，有關此一地標性建築的結…",{"number":37,"session":7,"stem":38},23,"有關圓頂殼（dome shell）結構的敘述，下列何者正確？",{"number":40,"session":7,"stem":41},24,"下列有關傾角變位法之敘述，何者錯誤？",{"number":43,"session":7,"stem":44},25,"下列敘述何者正確？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","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":10,"session":50,"stem":51},"113190","下列那種牆設計對於建築物耐震時水平強度的提升效果最好？圖中以網點圖樣填滿的部分為牆體…",{"number":10,"session":53,"stem":54},"112190","對一個寬度為 b 深度為 h 的矩形斷面梁的斷面模數（S）及塑性斷面模數（Z），下列…",{"number":10,"session":56,"stem":57},"111180","有關建築物耐風設計規範的要求，下列敘述何者錯誤？",{"number":10,"session":59,"stem":60},"110180","以下關於材料力學中常用物理量之單位，何者錯誤？",1791863209369]