[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-110180-arch_structure-27":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-110180-801-0102-027","architect","110180",110,"建築結構",27,null,"承上題，若材料的降伏強度為 50 MPa，梁斷面寬度與深度分別為 6 cm 及 12 cm，則上述兩種載重造成下列何種結果？",{"A":14,"B":15,"C":16,"D":17},"僅 A 載重造成彎矩降伏","僅 B 載重造成彎矩降伏","兩種載重都造成梁彎矩降伏","兩種載重下梁都維持彈性",[19],"A","single",[],"本題考點：比較簡支梁在兩種載重下的最大彎矩（跨中集中載重 P L \u002F 4、全跨均布載重 w L² \u002F 8）與矩形斷面的降伏彎矩 M_y = F_y × S（S = b h² \u002F 6），判定哪一種載重使梁彎矩降伏。\n【正解理由】先求斷面的降伏彎矩：S = b h² \u002F 6 = 6 cm × (12 cm)² \u002F 6 = 144 cm³ = 0.000144 m³，F_y = 50 MPa = 50000 kN\u002Fm²，M_y = 50000 kN\u002Fm² × 0.000144 m³ = 7.2 kN·m。再求兩種載重的最大彎矩：A 形式 M_A = 10 kN × 5 m \u002F 4 = 12.5 kN·m；B 形式 M_B = 2 kN\u002Fm × (5 m)² \u002F 8 = 6.25 kN·m。M_A = 12.5 kN·m 大於 M_y = 7.2 kN·m，最外緣纖維已達降伏強度；M_B = 6.25 kN·m 小於 M_y，梁仍在彈性範圍。因此只有 A 載重造成彎矩降伏，故選 A。\n【逐項排除】\n(A) 僅 A 載重造成彎矩降伏：正確。M_A 超過 M_y，M_B 未達 M_y，符合題目所問。\n(B) 僅 B 載重造成彎矩降伏：兩處都與計算結果相反。B 的最大彎矩 6.25 kN·m 低於降伏彎矩 7.2 kN·m，不會降伏；A 的最大彎矩 12.5 kN·m 高於降伏彎矩，反而會降伏。應改為「僅 A 載重造成彎矩降伏」。\n(C) 兩種載重都造成梁彎矩降伏：A 會降伏這一半成立，但 B 的最大彎矩 6.25 kN·m 小於 7.2 kN·m，B 載重下梁仍維持彈性，所以「兩種都降伏」不成立。\n(D) 兩種載重下梁都維持彈性：B 維持彈性這一半成立，但 A 的最大彎矩 12.5 kN·m 已超過 7.2 kN·m，A 載重下梁已降伏，所以「兩種都彈性」不成立。\n【演算步驟】\n斷面模數：S = b h² \u002F 6 = 6 cm × 12 cm × 12 cm \u002F 6 = 144 cm³\n單位換算：S = 144 cm³ = 144 \u002F 1000000 m³ = 0.000144 m³；F_y = 50 MPa = 50 × 1000 kN\u002Fm² = 50000 kN\u002Fm²\n降伏彎矩：M_y = F_y × S = 50000 kN\u002Fm² × 0.000144 m³ = 7.2 kN·m\nA 形式最大彎矩：M_A = P L \u002F 4 = 10 kN × 5 m \u002F 4 = 12.5 kN·m\nB 形式最大彎矩：M_B = w L² \u002F 8 = 2 kN\u002Fm × 5 m × 5 m \u002F 8 = 6.25 kN·m\n比較：M_A = 12.5 kN·m > M_y = 7.2 kN·m（降伏）；M_B = 6.25 kN·m \u003C M_y = 7.2 kN·m（彈性）\n結果：僅 A 載重造成彎矩降伏。\n【記憶點】判斷降伏就是比「最大彎矩」與「F_y × b h² \u002F 6」；同總載重下集中載重的跨中彎矩是均布的 2 倍，先降伏的必是集中載重。",742,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},24,"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？",{"number":31,"session":7,"stem":32},25,"建築物在抵抗側向地震力作用時，容許結構桿件產生破壞以損耗地震能量。依目前耐震設計原則…",{"number":34,"session":7,"stem":35},26,"一簡支梁跨距為 5 m，分別受到以下兩種載重形式：（A）跨距中央受到集中載重 10 …",{"number":37,"session":7,"stem":38},28,"下列圖示的梁柱構架系統，在地震橫力作用下，地面層何處梁段較容易因地震而造成剪力破壞？…",{"number":40,"session":7,"stem":41},29,"我國交通部中央氣象局於 109 年施行新的地震震度分級制度，讓地震震度分布與災害位置…",{"number":43,"session":7,"stem":44},30,"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？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","如圖所示的三鉸式剛架，A、E 為鉸支承，C 為鉸接，B、D 為剛接。則有關 A 點之…",{"number":10,"session":50,"stem":51},"113190","下圖所示桁架中，a、c 兩桿互相垂直，在圖示水平力 P 作用下，那些桿件可能因受壓而…",{"number":10,"session":53,"stem":54},"112190","在鋼筋混凝土結構設計中，關於構材斷面之平衡應變狀態與平衡鋼筋比，下列敘述何者正確？",{"number":10,"session":56,"stem":57},"111180","一桁架之載重如下圖所示，下列敘述何者錯誤？ 40 kN 3m 40 kN 3m 4m",{"number":10,"session":59,"stem":60},"109180","下列何者不屬於形抗結構？",1791863205034]