[{"data":1,"prerenderedAt":54},["ShallowReactive",2],{"q-113190-arch_structure-2":3},{"question":4,"neighbors":26,"sameNumber":38,"prev":24,"next":30},{"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-113190-801-0102-002","architect","113190",113,"建築結構",2,null,"一簡支梁斷面寬 100 mm，深度 150 mm，所在某一位置斷面的彎矩 100 kN-m，關於此斷面的敘述，下列何者正確？",{"A":14,"B":15,"C":16,"D":17},"斷面模數 S = 325 cm3","斷面慣性矩 I = 2100 cm4","斷面最大應力為 266.7 MPa","斷面最小應力為-310.5 MPa",[19],"C","single",[],"本題考點：矩形斷面的斷面模數 S = bh²\u002F6、斷面慣性矩 I = bh³\u002F12，以及彎曲應力 σ = M \u002F S 的單位換算與正負號判讀。\n【正解理由】矩形斷面寬 b = 100 mm、深 h = 150 mm，先求斷面模數 S = bh²\u002F6 = 375000 mm³；再把彎矩 M = 100 kN-m 換成 N·mm，除以 S 得到斷面最外緣的最大彎曲應力約 266.7 N\u002Fmm²，N\u002Fmm² 即 MPa，因此最大應力為 266.7 MPa，與選項(C)的敘述相符，故選 C。\n【逐項排除】\n(A) 錯誤。S = bh²\u002F6 = 100 mm × 150 mm × 150 mm ÷ 6 = 375000 mm³，換成 cm³ 要除以 1000，得 375 cm³，不是 325 cm³。正確敘述應為「斷面模數 S = 375 cm³」。\n(B) 錯誤。I = bh³\u002F12 = 100 mm × 150 mm × 150 mm × 150 mm ÷ 12 = 28125000 mm⁴，換成 cm⁴ 要除以 10000，得 2812.5 cm⁴，不是 2100 cm⁴。正確敘述應為「斷面慣性矩 I = 2812.5 cm⁴」。\n(C) 正確。σ = M \u002F S = (100 × 1000 × 1000 N·mm) ÷ 375000 mm³ ≈ 266.7 N\u002Fmm²，即 266.7 MPa，為斷面最外緣纖維的應力，數值與選項完全一致。\n(D) 錯誤。矩形斷面上下對稱，中性軸通過形心，上緣與下緣到中性軸的距離相同，所以最大拉應力與最大壓應力大小相等、正負相反。斷面的最小（代數值最小）應力是受壓側的 -266.7 MPa，不是 -310.5 MPa；選項數值的絕對值與最大應力不同，本身就與對稱斷面的應力分布不合。正確敘述應為「斷面最小應力為 -266.7 MPa」。\n【演算步驟】\n① 斷面模數：S = bh²\u002F6 = 100 mm × (150 mm)² ÷ 6 = 375000 mm³ = 375 cm³\n② 斷面慣性矩：I = bh³\u002F12 = 100 mm × (150 mm)³ ÷ 12 = 28125000 mm⁴ = 2812.5 cm⁴\n③ 彎矩換算：M = 100 kN-m = 100 × 1000 × 1000 N·mm\n④ 最大應力：σmax = M \u002F S = (100 × 1000 × 1000 N·mm) ÷ 375000 mm³ ≈ 266.7 N\u002Fmm² = 266.7 MPa\n⑤ 最小應力：σmin = -M \u002F S ≈ -266.7 MPa（受壓側）\n【記憶點】矩形斷面 S = bh²\u002F6、I = bh³\u002F12，最外緣應力 σ = M \u002F S；對稱斷面上下緣應力大小相等、正負相反。",581,1,true,[27,29,32,35],{"number":24,"session":7,"stem":28},"下圖（左）為一簡支梁在均布荷載 q(x)作用下之示意圖，圖（右）則為該梁於 x 處截…",{"number":30,"session":7,"stem":31},3,"關於薄殼結構，下列敘述何者錯誤？",{"number":33,"session":7,"stem":34},4,"下列材料性質之敘述何者正確？",{"number":36,"session":7,"stem":37},5,"關於纜索結構（cable structures）的敘述，下列何者錯誤？",[39,42,45,48,51],{"number":10,"session":40,"stem":41},"114180","下列有關混凝土性質的敘述，何者錯誤？",{"number":10,"session":43,"stem":44},"112190","下圖的門形構架，梁為剛體（EI=∞），若忽略構件的軸向變形時，當柱的 EI 值不變，…",{"number":10,"session":46,"stem":47},"111180","有關高樓建築結構系統之特性，下列敘述何者正確？",{"number":10,"session":49,"stem":50},"110180","在結構系統中配置剪力牆作為耐震元件時，下列敘述何者正確？",{"number":10,"session":52,"stem":53},"109180","下列關於管式結構系統（tube structure system）之敘述，何者正確？",1791863194198]