[{"data":1,"prerenderedAt":60},["ShallowReactive",2],{"q-114180-arch_structure-4":3},{"question":4,"neighbors":26,"sameNumber":44,"prev":33,"next":36},{"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-114180-801-0102-004","architect","114180",114,"建築結構",4,null,"一長度為 2 m 圓棒，直徑為 30 mm，彈性模數為 70 GPa，波松比（Poisson's ratio）0.3，當其受到 100 kN 拉力時，下列敘述何者正確？",{"A":14,"B":15,"C":16,"D":17},"軸向應力為 120 MPa","伸長量為 2 mm","軸向勁度為 20 kN\u002Fmm","直徑減少量為 0.018 mm",[19],"D","single",[],"本題考點：均勻斷面桿件受軸向拉力時的軸向應力 σ = P \u002F A、伸長量 δ = PL \u002F (AE)、軸向勁度 k = AE \u002F L，以及以波松比由軸向應變推得橫向應變與直徑變化量。\n【正解理由】先求圓棒截面積，再依序算出應力、伸長量、勁度與直徑變化。截面積 A = π × 30² \u002F 4 ≈ 706.86 mm²；軸向應力 σ = 100000 N \u002F 706.86 mm² ≈ 141.47 MPa；軸向應變為 σ \u002F E，橫向應變為波松比乘上軸向應變，約 0.0006063（直徑方向為縮小）；直徑減少量 = 30 mm × 0.0006063 ≈ 0.0182 mm，四捨五入後即 0.018 mm，與 (D) 相符。故選 D。\n【逐項排除】\n(A) 錯誤。軸向應力 = 100000 N \u002F 706.86 mm² ≈ 141.47 MPa，不是 120 MPa；選項數值比正確值偏小，正確敘述應為「軸向應力約為 141.5 MPa」。\n(B) 錯誤。伸長量 δ = PL \u002F (AE) = 100000 N × 2000 mm \u002F (706.86 mm² × 70000 N\u002Fmm²) ≈ 4.04 mm，選項的 2 mm 明顯偏小，正確敘述應為「伸長量約為 4.04 mm」。\n(C) 錯誤。軸向勁度 k = AE \u002F L = 706.86 mm² × 70000 N\u002Fmm² \u002F 2000 mm ≈ 24.74 kN\u002Fmm，不是 20 kN\u002Fmm；正確敘述應為「軸向勁度約為 24.7 kN\u002Fmm」。可用 P \u002F δ 交叉檢查：100 kN \u002F 4.04 mm 也落在約 24.7 kN\u002Fmm。\n(D) 正確。直徑減少量 = ν × (σ \u002F E) × d ≈ 0.0182 mm，即 0.018 mm；拉力使桿件軸向伸長、橫向收縮，所以是「減少」，方向也正確。\n【演算步驟】① 單位統一：P = 100 kN = 100000 N，L = 2 m = 2000 mm，E = 70 GPa = 70000 MPa = 70000 N\u002Fmm²，d = 30 mm。② 截面積：A = π d² \u002F 4 = 3.1416 × 30 mm × 30 mm \u002F 4 ≈ 706.86 mm²。③ 軸向應力：σ = P \u002F A = 100000 N \u002F 706.86 mm² ≈ 141.47 N\u002Fmm² = 141.47 MPa。④ 伸長量：δ = PL \u002F (AE) = 100000 N × 2000 mm \u002F (706.86 mm² × 70000 N\u002Fmm²) ≈ 4.04 mm。⑤ 軸向勁度：k = AE \u002F L = 706.86 mm² × 70000 N\u002Fmm² \u002F 2000 mm ≈ 24.74 kN\u002Fmm。⑥ 橫向應變：ε橫 = ν × σ \u002F E = 0.3 × 141.47 MPa \u002F 70000 MPa ≈ 0.0006063（無單位）。⑦ 直徑減少量：Δd = ε橫 × d = 0.0006063 × 30 mm ≈ 0.0182 mm ≈ 0.018 mm。\n【記憶點】拉桿「長向伸、橫向縮」：橫向應變 = 波松比 × 軸向應變，直徑變化量 = 橫向應變 × 原直徑。",588,1,true,[27,29,32,35,38,41],{"number":24,"session":7,"stem":28},"下列何者為材料彈性模數 E（modulus of elasticity）之單位？",{"number":30,"session":7,"stem":31},2,"下列有關混凝土性質的敘述，何者錯誤？",{"number":33,"session":7,"stem":34},3,"如圖所示，x 軸為作用力的反覆加載週期數目（N），y 軸為鋼所承受的應力（MPa）大…",{"number":36,"session":7,"stem":37},5,"關於圓球薄殼結構，下列敘述何者錯誤？",{"number":39,"session":7,"stem":40},6,"關於薄膜結構，下列敘述何者正確？",{"number":42,"session":7,"stem":43},7,"下列何種結構系統較不適用於超過 50 公尺之高層建築？",[45,48,51,54,57],{"number":10,"session":46,"stem":47},"113190","下列材料性質之敘述何者正確？",{"number":10,"session":49,"stem":50},"112190","有關材料性質，下列敘述何者正確？",{"number":10,"session":52,"stem":53},"111180","關於結構設計時之靜載重 D 與活載重 L，下列敘述何者錯誤？",{"number":10,"session":55,"stem":56},"110180","建築物設計風力之計算與所在地點之基本設計風速有關，依地況分成：地況 A：大城市市中心…",{"number":10,"session":58,"stem":59},"109180","若建築物之設計地震基底剪力為 V、基面以上的建築物重量為 W，下列敘述何者正確？",1791863195348]