[{"data":1,"prerenderedAt":62},["ShallowReactive",2],{"q-112190-arch_structure-12":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-112190-801-0102-012","architect","112190",112,"建築結構",12,null,"如下圖所示，一構件斜面之中心點受一水平力 P=1000 N 作用，此斜面與水平方向之夾角為 θ=45°，若該構件垂直面之面積 A0 =100 cm2，則沿斜面之平均剪應力 τave 為多少？ P=1000 N P=1000 N A0=100 cm2 θ =45°",{"A":14,"B":15,"C":16,"D":17},"5 N\u002Fcm2","10 N\u002Fcm2","15 N\u002Fcm2","20 N\u002Fcm2",[19],"A","single",[22],"\u002Fimages\u002Farch-112190-801-0102-012.png","本題考點：軸向受拉構件斜截面上的應力轉換。斜面面積比垂直斷面大，作用力又要分解成垂直斜面與沿斜面兩個分量，平均剪應力 τ = (P\u002FA₀)·sinφ·cosφ（φ 為斜面法線與桿軸的夾角）。\n【正解理由】依題圖所示，構件兩端各受 P=1000 N 的水平拉力，屬軸向受拉；垂直斷面面積 A₀=100 cm²，斜面與水平方向夾角 θ=45°。設斜面法線與桿軸的夾角為 φ，斜面面積 A = A₀\u002Fcosφ，P 沿斜面方向的分量 V = P·sinφ，所以沿斜面的平均剪應力 τ = V\u002FA = (P\u002FA₀)·sinφ·cosφ。斜面與水平夾 45° 時，其法線與桿軸的夾角也是 45°，sin45° 與 cos45° 相等，sin45°×cos45° = 2\u002F4 = 1\u002F2，角度取哪一個量都得到同一個乘積。代入：P\u002FA₀ = 1000 N\u002F100 cm² = 10 N\u002Fcm²，τ = 10 N\u002Fcm² × 1\u002F2 = 5 N\u002Fcm²，故選 A。\n【逐項排除】\n(A) 5 N\u002Fcm²：符合題目所問。斜面面積放大與力分解各帶一個 45° 的三角函數因子，相乘得 1\u002F2，τ = 1000\u002F100×1\u002F2 = 5 N\u002Fcm²。\n(B) 10 N\u002Fcm²：不符合題目所問。10 N\u002Fcm² 是 P\u002FA₀，即垂直斷面上的正應力，不是斜面上的剪應力；要求斜面剪應力，還須乘上 sinφ·cosφ = 1\u002F2。\n(C) 15 N\u002Fcm²：不符合題目所問。軸向受力構件任一斜面上的剪應力最大只到 P\u002FA₀ 的一半（發生在 45° 斜面），即 5 N\u002Fcm²；15 N\u002Fcm² 已超過這個上限，也超過垂直斷面的正應力。\n(D) 20 N\u002Fcm²：不符合題目所問。理由同 (C)，20 N\u002Fcm² 比任何斜面可能出現的剪應力都大，也大於 P\u002FA₀，不可能是平均剪應力。\n【演算步驟】\n垂直斷面正應力：σ = P\u002FA₀ = 1000 N \u002F 100 cm² = 10 N\u002Fcm²\n斜面剪應力公式：τ = (P\u002FA₀)·sinφ·cosφ\n角度因子：sin45°×cos45° = 2\u002F4 = 1\u002F2（無因次）\n平均剪應力：τ = 10 N\u002Fcm² × 1\u002F2 = 5 N\u002Fcm²\n【記憶點】軸力構件 45° 斜面的剪應力最大，等於 P\u002FA₀ 的一半。",599,1,true,[28,31,34,37,40,43],{"number":29,"session":7,"stem":30},9,"一個微小的矩型六面體受到純剪力作用，下列敘述何者正確？",{"number":32,"session":7,"stem":33},10,"下列知名建築中何者最接近形抗結構？",{"number":35,"session":7,"stem":36},11,"圖示管狀結構（Tubular Structure）的外管受側力作用時，若管面為完全剛…",{"number":38,"session":7,"stem":39},13,"下列有關「固定拱」、「雙鉸拱」和「三鉸拱」的敘述，何者錯誤？",{"number":41,"session":7,"stem":42},14,"下列有關纜索結構系統的敘述，何者正確？",{"number":44,"session":7,"stem":45},15,"醫院欲加裝緊急發電機，業主要求該發電機需於強震後正常運作，下列敘述何者正確？①設置於…",[47,50,53,56,59],{"number":10,"session":48,"stem":49},"114180","如圖所示之甲乙兩支梁承受相同垂直均布靜載重，若兩梁皆為鋼筋混凝土構造，斷面(1)、(…",{"number":10,"session":51,"stem":52},"113190","非結構物耐震考量，下列敘述何者錯誤？",{"number":10,"session":54,"stem":55},"111180","在結構系統的規劃上，下列敘述何者錯誤？",{"number":10,"session":57,"stem":58},"110180","圖示之鋼筋混凝土韌性構架，有關主筋搭接之敘述，下列何者正確？ D A B C",{"number":10,"session":60,"stem":61},"109180","圖示結構物為幾度靜不定？鉸接",1791863199951]