[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-110180-arch_structure-26":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-110180-801-0102-026","architect","110180",110,"建築結構",26,null,"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 kN（B）全梁受到均布載重 2 kN\u002Fm。試問 A 載重形式下所產生的最大變形為 B 所產生的最大變形的幾倍？",{"A":14,"B":15,"C":16,"D":17},"8\u002F5 倍","4\u002F3 倍","1.5 倍","3\u002F4 倍",[19],"A","single",[],"本題考點：簡支梁在跨中集中載重與全跨均布載重下的最大撓度公式 Δ = P L³ \u002F (48 E I) 與 Δ = 5 w L⁴ \u002F (384 E I)，並以比值消去相同的 E I。\n【正解理由】兩種載重作用在同一根簡支梁上，E 與 I 相同，最大撓度都發生在跨中。A 形式：Δ_A = P L³ \u002F (48 E I)，P L³ = 10 kN × (5 m)³ = 1250 kN·m³，Δ_A × E I = 1250 \u002F 48 = 26.04 kN·m³。B 形式：Δ_B = 5 w L⁴ \u002F (384 E I)，w L⁴ = 2 kN\u002Fm × (5 m)⁴ = 1250 kN·m³，Δ_B × E I = 5 × 1250 \u002F 384 = 16.28 kN·m³。兩者相除 Δ_A \u002F Δ_B = 26.04 \u002F 16.28 = 1.6，也就是 8\u002F5 倍；直接化簡公式也可得 Δ_A \u002F Δ_B = 8 P \u002F (5 w L) = 80 \u002F 50 = 1.6，故選 A。\n【逐項排除】\n(A) 8\u002F5 倍：正確。依兩個撓度公式代入，比值為 1.6 = 8\u002F5，符合題目所問。\n(B) 4\u002F3 倍：小於正確比值 8\u002F5，數值與兩個撓度公式的計算結果不符。兩種載重的總載重都是 10 kN，差別只在分布方式，正確的放大倍數由公式係數與載重、跨距共同決定，應為 8\u002F5 倍。\n(C) 1.5 倍：與正確比值接近但仍偏小，代入撓度公式後算不出這個值；正確為 1.6 倍，也就是 8\u002F5 倍。\n(D) 3\u002F4 倍：小於 1，表示 A 的撓度比 B 小，方向就錯了。同樣總載重集中在跨中，彎矩比均布時大，撓度也較大，比值必須大於 1，正確為 8\u002F5 倍。\n【演算步驟】\n公式：跨中集中載重 Δ_A = P L³ \u002F (48 E I)；全跨均布載重 Δ_B = 5 w L⁴ \u002F (384 E I)\nA：P L³ = 10 kN × 5 m × 5 m × 5 m = 1250 kN·m³，Δ_A × E I = 1250 kN·m³ \u002F 48 = 26.04 kN·m³\nB：w L⁴ = 2 kN\u002Fm × 5 m × 5 m × 5 m × 5 m = 1250 kN·m³，Δ_B × E I = 5 × 1250 kN·m³ \u002F 384 = 16.28 kN·m³\n比值：Δ_A \u002F Δ_B = 26.04 kN·m³ \u002F 16.28 kN·m³ = 1.6\n化簡驗算：Δ_A \u002F Δ_B = 8 P \u002F (5 w L) = (8 × 10 kN) \u002F (5 × 2 kN\u002Fm × 5 m) = 80 \u002F 50 = 1.6 = 8\u002F5\n結果：A 載重形式的最大撓度為 B 的 8\u002F5 倍。\n【記憶點】簡支梁跨中撓度：集中 P L³ \u002F 48 E I、均布 5 w L⁴ \u002F 384 E I；同總載重時集中載重撓度是均布的 8\u002F5 倍。",681,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},23,"一纜索受到以下的均勻分布載重作用下，若不考慮纜索自重，其弧線會呈現何種線型？",{"number":31,"session":7,"stem":32},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":34,"session":7,"stem":35},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":37,"session":7,"stem":38},27,"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…",{"number":40,"session":7,"stem":41},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":43,"session":7,"stem":44},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…",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","下列何者載重分布，使懸臂梁固定端彎矩最大？ 2w 2w w 0 0 L L L (a…",{"number":10,"session":50,"stem":51},"113190","如圖所示之構架承受側力 P，兩柱分別高 L 及 2 L，柱頂皆為鉸接（pin），兩柱…",{"number":10,"session":53,"stem":54},"112190","下圖中之圖(i)所示為一單跨抗彎矩構架（moment-resisting frame…",{"number":10,"session":56,"stem":57},"111180","試分析下圖桁架結構，下列選項何者正確（T 為張力，C 為壓力）？ 10 m 10 m…",{"number":10,"session":59,"stem":60},"109180","如圖示之均質矩形斷面，對於形心水平軸 x 之面積慣性矩記為 Ixx，而對於矩形底邊水…",1791863205029]