🏗️ 結構工程工具

🏗️ 回轉半徑（r = √(I / A)）Radius of Gyration 輸入截面對某軸的慣性矩 I 與截面積 A，計算回轉半徑 r=√(I/A)，反映截面面積分布離形心的遠近程度，用於壓桿穩定計算中長細比的求解。Radius of Gyration - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🏗️ 基底壓力（p = N / A）Bearing Pressure 基底平均壓力計算器：輸入豎向荷載 N 與基礎底面積 A，按 p = N/A 求基礎底面平均接觸壓應力，用於地基承載力驗算。Bearing Pressure - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🏗️ 慣性矩（I = b·h³ / 12）Moment of Inertia Rect 矩形截面慣性矩計算器：輸入寬 b 與高 h，按 I = bh³/12 求矩形截面繞中性軸的慣性矩，用於梁抗彎計算。Moment of Inertia Rect - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering... 🏗️ 截面模量（W = b·h² / 6）Section Modulus Rect 輸入矩形截面寬度 b 與高度 h，按 W=b·h²/6 計算抗彎截面模量，用於梁在彎矩 M 作用下彎曲正應力 σ=M/W 的快速校核，是截面抗彎能力的關鍵參數。Section Modulus Rect - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering t... 🏗️ 支座剪力（V = P / 2）Beam Shear Center 輸入簡支梁跨中集中力 P，計算兩端支座的反力與剪力，跨中單點荷載時兩支座各承擔 P/2，輸出支座剪力 V=P/2，用於簡支梁在跨中荷載下的支座受力分析。Beam Shear Center - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🏗️ 最大剪應力（τ_max = 1.5·V / A）Beam Shear Stress 輸入矩形截面梁所受剪力 V 與截面寬度 b、高度 h，計算平均剪應力並按 τ_max=1.5·V/A 求中性軸處最大剪應力，用於矩形梁抗剪強度校核。Beam Shear Stress - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🏗️ 最大應力（σ_max = K_t · σ_nom）Stress Concentration 應力集中計算器：輸入名義應力 σ_nom 與理論應力集中係數 K_t，按 σ_max = K_t·σ_nom 求孔、缺口等幾何不連續處的最大應力。Stress Concentration - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering t... 🏗️ 最大彎矩（M_max = w·L² / 8）Ss Udl Moment 簡支梁均布荷載彎矩計算器：輸入均布荷載 w 與跨度 L，按 M_max = wL²/8 求跨中最大彎矩，用於梁配筋與截面設計。Ss Udl Moment - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🏗️ 極慣性矩（J = π·d⁴ / 32）Torsion Polar J 圓截面極慣性矩計算器：輸入圓截面直徑 d，按 J = πd⁴/32 求抗扭幾何參數極慣性矩，用於圓軸扭轉計算。Torsion Polar J - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🏗️ 歐拉臨界（P_cr = π²·E·I / L²）Euler Buckling 歐拉臨界載荷計算器：輸入彈性模量 E、截面慣性矩 I 與計算長度 L，按 P_cr = π²EI/L² 求兩端鉸支壓桿屈曲臨界載荷。Euler Buckling - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. ↕️ 由伸長量與原長求應變Axial Strain 輸入杆件受力後的伸長量 ΔL 與原始長度 L，計算軸向線應變 ε=ΔL/L，衡量材料在拉壓下的相對變形大小，結果無量綱，常用於材料力學變形分析。Axial Strain - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🛢️ 由內壓求環向（周向）應力Hoop Stress 輸入薄壁圓筒的內壓 p、半徑 r 與壁厚 t，按 σ_h=p·r/t 計算環向（周向）應力，用於承壓管道、容器在內部壓力下的周向強度校核。Hoop Stress - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🛢️ 由內壓求縱向應力Longitudinal Stress 輸入薄壁圓筒內壓 p、半徑 r 與壁厚 t，按 σ_l=p·r/(2t) 計算縱向應力，用於封閉承壓容器在內部壓力下的軸向強度校核，數值恰為環嚮應力的一半。Longitudinal Stress - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering to... 📉 由均布載荷求懸臂樑自由端撓度Deflection Cantilever Udl 輸入均布載荷 w、梁長 L、彈性模量 E 與圓截面直徑 d，按 δ=wL⁴/(8EI) 求懸臂樑自由端撓度。Deflection Cantilever Udl - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineer... 🛡️ 由平面應力狀態求等效應力Von Mises 2d 輸入平面應力 σx、σy 與剪應力 τ，按等效應力公式求馮·米塞斯應力，用於構件強度校核。Von Mises 2d - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🔀 由彈性模量與泊松比求剪切模量Shear Modulus 輸入材料彈性模量 E 與泊松比 ν，按 G=E/[2(1+ν)] 計算剪切模量 G，用於已知拉伸性能時換算材料的抗剪剛度，常見於各向同性材料的力學參數換算。Shear Modulus - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🔄 由扭矩、長度與剛度求扭轉角Angle of Twist 輸入圓軸所受扭矩 T、軸段長度 L、剪切模量 G 與直徑 d，計算極慣性矩 J 與扭轉角 θ=T·L/(G·J)，用於軸類零件在扭矩作用下的扭轉變形校核。Angle of Twist - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🔄 由扭矩與直徑求軸表面剪應力Torsional Shear Shaft 輸入圓軸扭矩 T 與直徑 d，按極慣性矩 J=πd⁴/32 計算軸表面最大剪應力 τ=T·r/J，用於傳動軸、轉軸在扭矩作用下的抗剪強度校核與尺寸設計。Torsional Shear Shaft - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering ... ⭕ 由直徑求圓截面抗彎模量Section Modulus Circle 圓截面抗彎模量計算器：輸入圓截面直徑 d，按 S = πd³/32 求抗彎截面模量，用於圓軸彎曲應力校核。Section Modulus Circle - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering... ⭕ 由直徑求實心圓截面慣性矩Moment of Inertia Circle 圓截面慣性矩計算器：輸入圓截面直徑 d，按 I = πd⁴/64 求繞中性軸的截面慣性矩，用於圓軸彎曲與穩定性計算。Moment of Inertia Circle - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineeri... ⭕ 由直徑求實心圓截面極慣性矩Polar Moment Circle 圓截面極慣性矩計算器：輸入圓截面直徑 d，按 J = πd⁴/32 求極慣性矩，用於圓軸扭轉剛度與強度計算。Polar Moment Circle - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering to... 📉 由端點集中力求懸臂樑撓度Deflection Cantilever Point 輸入端點力 F、梁長 L、彈性模量 E 與圓截面直徑 d，按 δ=FL³/(3EI) 求懸臂樑端點撓度。Deflection Cantilever Point - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engine... 🌡️ 由線膨脹係數與温差求熱應變Thermal Strain 輸入材料的線膨脹係數 α 與温度變化量 ΔT，計算熱應變 ε=α·ΔT，衡量構件因升温或降温產生的相對伸長或縮短，用於温度變化下的變形與應力預估。Thermal Strain - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. ⬇️ 由軸力與截面積求正應力Axial Stress 輸入杆件所受軸向力 F 與橫截面積 A，計算正應力 σ=F/A，判斷拉壓桿件截面上的平均受力大小，用於結構構件的強度校核與選材。Axial Stress - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🏗️ 端部彎矩（M = F·L）Cantilever End Moment 輸入懸臂樑自由端集中力 F 與梁長 L，計算固定端處的最大彎矩 M=F·L，用於懸臂結構在端部荷載下固定支座的彎曲受力分析與配筋參考。Cantilever End Moment - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering ... 🏗️ 許用應力（σ_allow = σ_yield / n）Allowable Stress 許用應力計算器：輸入材料屈服強度與安全係數，按 σ_allow = σ_yield / n 確定許用應力，用於結構構件強度校核。Allowable Stress - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools. 🏗️ 跨中撓度（δ = P·L³ / (48·E·I)）Ss Point Deflection 簡支梁集中力撓度計算器：輸入集中力 P、跨度 L、彈性模量 E 與慣性矩 I，按 δ = PL³/(48EI) 求跨度中點的撓度。Ss Point Deflection - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering to... 🏗️ 長細比（λ = L / r）Slenderness Ratio 壓桿長細比計算器：輸入計算長度 L 與回轉半徑 r，按 λ = L/r 求長細比，長細比越大越易失穩，用於壓桿穩定分類。Slenderness Ratio - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Structural Engineering tools.