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第一部分：復習設計要考慮的問題
Section I: Review of Design Considerations |
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1; 2 |
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第一單元：介紹和設計概述
Unit 1: Introduction and Design Overview
為什麼結構力學？結構的類型，結構設計的步驟，成本因素。
Why Structural Mechanics? Types of Structures; Structural Design Process; Factors in Cost. |
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L1; L2 |
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R:第1章
Ch.1
M:7.1, 7.3, 7.4 |
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3; 4 |
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第二單元：載荷，設計要考慮的問題
Unit 2: Loads and Design Considerations
載荷／偏差的來源；載荷的種類和環境；載荷的限制和極限；安全裕度和因素；例子，V-n圖（上升離點陣圖）；失效的定義；故障分析報告。
Sources of Loads/Deflections; Types of Loads and Environments; Limit and Ultimate Loads; Factors and Margins of Safety; Example, the v-n Diagram; Definition of Failure; FAR's. |
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L3; L4, R |
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M: 7.2, 12.1, 12.2
7.2, 12.1, 12.2
G:1.7 |
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R－評價練習
R-Assessment Exercise |
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第二部分：一般彈性變形
Section II: General Elasticity |
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4; 5 |
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Unit 3: Language of Stress/Strain Analysis (Review)
應力和應變的定義；符號；張量規則；張量與工程符號；簡化符號；矩陣符號。
Definition of Stress and Strain; Notation; Tensor Rules; Tensor vs. Engineering Notation; Contracted Notation; Matrix Notation. |
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L4, R; L5 |
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BMP: A.2, A.3, A.6
A.2, A.3, A.6
R:2.1, 2.2
T&G: 第1章
Ch. 1 |
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指定作業1，設計問題1
HA1 out; DP1 out |
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6; 7; 8 |
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第四單元：彈性方程(複習)
Unit 4: Equations of Elasticity (Review)
彈性方程（均衡，應變置換，應力－應變）；靜態限定性；相容性；彈性張量；材料種類和彈性組成部分；材料軸和載荷軸的比較；應變性能和它的張量；形式上的應變張量；大應變和小應變的對比；線性和非線性的應變。
Equations of Elasticity (Equilibrium, Strain-Displacement, Stress-Strain); Static Determinance; Compatibility; Elasticity Tensor; Material Types and Elastic Components; Materials Axes vs. "Loading Axes"; Compliance and its Tensor; The Formal Strain Tensor; Large Strains vs. Small Strains; Linear vs. Nonlinear Srain. |
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L6; L7; L8, R |
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R:2.3, 2.6, 2.8
T&G:5.1-5.5, 5.8, 5.9, 7.1-7.4, 6.1-6.3, 6.5-6.7
J: 2.1, 2.2 （複合物）
2.1, 2.2 (for
composites) |
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8; 9; 10 |
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第五單元：工程常數
Unit 5: Engineering Constants
工程常數（縱向模型，Poisson比，剪切模型，交互關係係數，Chentsov係數）；互反關係；工程應力應變方程；適應性compliance 遵守和工程常數；實驗的目的；等級問題；對工程常數的測試；可變性和設計中的問題。
Engineering Constants (Longitudinal Moduli, Poisson's Ratio, Shear Moduli, Coefficients of Mutual Influence, Chentsov Coefficients); Reciprocity Relations; Engineering Stress-strain Equations; Compliances and Engineering Constants; Purposes of Testing; Issues of Scale; Testing for Engineering Constants; Variability and Issues in Design. |
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L8, R; L9; L10 |
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R:3.1-3.5, 3.9,
3.11
M:1.16
J:2.3, 2.4, 2.6 |
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提交作業1，指定作業2；
HA1 due; HA2 out;
提交設計問題1
DP1 due; |
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11; 12; 13 |
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第六單元：平面應力和應變
Unit 6: Plane Stress and Plane Strain
平面應力；平面應變；應用；近似值和模型極限。
Plane Stress; Plane Strain; Applications; Approximations and Modeling Limitations. |
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L11; L12; L13 |
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T&G:8-16
J:2.5
G:7.2, 7.7, 8.1, 8.2 |
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指定設計問題2
DP2 out;
提交作業2；指定作業3
HA2 due; HA3 out |
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13; 14 |
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第七單元：變換和其他坐標系統
Unit 7: Transformations and Other Coordinate Systems
變換的回顧：方向余弦cosines；三維張量形式（軸，置換，應力，應變，彈性張量）；平面應力案例（和Mohr圓）；主應力／應變；不變數；最大剪切應力／應變；二維變形；其他坐標系統（比如：圓柱）；一般曲線坐標系統。
Review of Transformations: Direction Cosines; 3-D tensor form (Axis, Displacement, Stress, Strain, Elasticity Tensor); Plane Stress Case (and Mohr's Circle); Principal Stresses/ Strains; Invariants; Extreme Shear Stresses/Strains; Reduction to 2-D; Other Coordinate Systems (Example: Cylindrical); General Curvilinear Coordinates. |
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L13; L14 |
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R: 2.4, 2.5, 2.7, 2.9
BMP: 5.6, 5.7, 5.14, 6.4, 6.8, 6.9, 6.11
T&G: 27, 54, 55, 60, 61
J: 2.6
G: 7.3, 7.4 |
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15; 16; 17; 18 |
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第八單元：解答步驟
Unit 8: Solution Procedures
精確解答方法；空氣壓力函數；雙諧波方程；反轉方法(反分析方法)；半反推法；St. Venant原理；例子：單軸載荷平板，極座標形式和一個孔周圍的應力；應力集中；正交各向異性材料所要考慮的問題。
Exact Solution Procedures; Airy Stress Function; Biharmonic Equation; Inverse Method; Semi-Inverse Method; St. Venant's Principle; Examples: Uniaxiallyloaded Plate, Polar Form and Stress Around a Hole; Stress Concentrations; Considerations for Orthotropic Materials. |
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L15, R; L16; L17; L18 |
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R: Ch. 4
T&G: 17, Ch. 3, 4, 6 |
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提交作業3；指定作業4；
HA3 due; HA4 out;
提交設計問題2
DP2 due |
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18; 19; 20; 21; 23 |
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第九單元：環境的影響
Unit 9: Effects of the Environment
熱應變／應力從哪里來；熱膨脹係數；熱源；溫度的空間變化；自我平衡應力；對流，輻射，傳導率(傅立葉方程)；解答技巧；內應力；材料性能的降低；別的環境的影響；事例：潮濕；壓電現象
Where Thermal Strains/"Stresses" come from; Coefficients of Thermal Expansion; Sources of Heating; Spatial Variation of Temperature; Self-equilibrating Stresses; Convection, Radiation, Conductivity (Fourier's Equation); Solution Techniques; "Internal" Stresses; Degradation of Material Properties; Other Environmental Effects; Examples: Moisture; Piezoelectricity. |
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L18; L19, R; L20; L21; L22 |
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R: 3.6, 3.7
T&G: 第13章
Ch. 13
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提交作業4 ，指定設計問題3
HA4 due; DP3 out |
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22 |
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沒有課
No Lecture |
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後期測驗1；指定作業5
Evening Exam 1 ; HA5 out |
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第三部分：轉矩
Section III: Torsion |
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23; 24; 25; 26 |
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第十單元St. Venant撓理論
Unit 10: St. Venant Torsion Theory
橫截面的種類；St. Venant 撓理論；假定；正交各向異性材料所要考慮的問題；扭應力函數；邊界條件；過程摘要；解答；Poisson方程；事例：圓鑽杆；合成剪切應力；其他橫截面；翹面。
"Types" of Cross-Sections; St. Venant's Torsion Theory; Assumptions; Considerations for Orthotropic Materials; Torsion Stress Function; Boundary Conditions; Summary of Procedure; Solution; Poisson's Equation; Example:Circular Rod; Resultant Shear Stress; Other Cross-Sections; Warping. |
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L22; L23; L24, R; L25 |
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R: 8.1, 8.2
T&G: 10.1, 10.4, 10.5, 10.6
M: 3.1, 3.2
G: 3.1-3.4 |
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提交作業5 ；指定作業6
HA5 due; HA6 out |
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26; 27 |
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第十一單元：薄膜比擬法
Unit 11: Membrane Analogy
薄膜比擬法；運用；應用；窄矩形的橫截面；其他形狀。
Membrane Analogy; Uses; Application: Narrow Rectangular Cross-Section; Other Shapes. |
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L25; L26 |
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R: 8.3, 8.6
T&G: 107-110, 112-114
M: 3.1, 3.3, 3.4 |
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27; 28; 29 |
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第十二單元：轉矩（薄的）閉合斷面
Unit 12: Torsion of (Thin) Closed Sections
厚壁閉合斷面；特殊例子：圓形管道；剪切流；Bredt公式；轉矩小結。
Thick-walled Closed Section; Special Case -- Circular Tube; Shear Flow; Bredt's Formula; Torsion Summary. |
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L26; L27; L28, R |
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R: 8.7, 8.8
T&G: 115, 116
M: 8.5
G: 3.10 |
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提交作業6，指定作業7
HA6 due; HA7 out |
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第四部分：一般樑理論
ection IV: General Beam Theory |
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29; 30 |
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第十三單元：一般梁理論的復習
Unit 13: Review of Simple Beam Theory
一般載荷的類型（復習）；一般樑理論的復習；正交各向異性材料要考慮的問題
eneric types of Loading (review); Review of Simple Beam Theory; Considerations for Orthotropic Materials. |
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L28, R; L29 |
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BMP: 3.8-3.10
T&G: 120-125
G: 5.1-5.9, 9.1-9.5, 10.1-10.4 |
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30; 31; 32; 33 |
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第十四單元：一般樑的特性和和工程梁理論
Unit 14: Behavior of General Beams and Engineering Beam Theory
幾何定義；假定；應力合力；變形；應變；一般的殼橫樑的應力；正交各向異性樑要考慮的問題；受力部分的性能；熱應力和力矩；選擇性強化；橫斷面的主要中軸；不對稱橫斷面的梁；工程樑理論的應用性；橫切力的作用；剪切中心；剪切偏轉的影響；工程樑理論的限制。
Geometry Definitions; Assumptions; Stress Resultants; Deformation, Strain, Stress In General Shell Beams; Considerations for Orthotropic Beams; Modulus-Weighted Section Properties; "Thermal" Forces and Moments; Selective Reinforcement; Principal Axes of Cross-Section; Beams with Unsymmetric Cross-Sections; Applicability of Engineering Beam Theory; Transverse Shear Effects; Shear Center; Contribution of "Shearing" Deflection; Limitations of Engineering Beam Theory. |
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L29; L30; L31; L32, R |
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R: 7.1-7.5, 7.7, 7.8
T&G: 126
M: 2.6, 8.1-8.3
G: 5.10-5.12, 6.1-6.8 |
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提交設計問題3
DP3 due |
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34; 35; 36; 38; 39; 40 |
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第十五單元：殼樑的特性（彎矩，剪力，扭力）
Unit 15: Behavior (Bending, Shearing, Torsion) of Shell Beams
殼樑的一般載荷；半硬殼式機身的構造；外殼／縱樑構建；一個單元的匣形樑；彎矩應力；節點平衡；純剪切力和純扭轉設計；一般解題方法；"無扭曲"情況；剪切中心；轉矩邊界條件；偏差；St. Venant假定；截面性能；撓度，剪切和剛度；多單元殼樑；勻等扭曲情況；開口斷面梁；厚皮殼；有效寬度。
General loading of a Shell Beam; Semi-monocoque Construction; Skin/stringer Construction; Single Cell "Box Beam"; Bending Stresses; Shear Stresses; Joint Equilibrium; Pure Shear and Pure Torsion Scheme; General Solution Procedure; "No Twist" Condition; Shear Center; Torque Boundary Condition; Deflections; St. Venant Assumption; Section Properties: Bending, Shear, and Torsional Stiffness; Multicell Shell Beams; "Equal Twist" Condition; Open Section Beams; Thick Skin Shells; Effective Width. |
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L33; L34; L35; L36; L37; L38, R |
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R: Ch.9, 8.7, 7.6
T&G: 126, 127
M: 7.3, 8.2-8.10, 9.3
G: Ch. 12 |
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提交作業 7；指定作業8（A部分，不用上交）；提交作業8（B部分）
HA7 due; HA8 (Part A) out (not for hand-in);
HA8 (Part B) due |
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37 |
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沒有課
No Lecture |
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後期考試；指定作業8（B部分）
Evening Exam 2; HA8 (Part B) out |
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第五部分：穩定性和縱向彎曲
Section V: Stability and Buckling |
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40; 41; 42 |
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第十六單元：（復習）分歧挫屈
Unit 16: (Review of) Bifucation Buckling
挫屈的種類；分歧挫屈的控制方程；邊界條件的應用；歐拉挫屈負載；邊緣固定性的係數；幾何參數；正交各向異性的／混合樑的問題；初始的非理想性；一階矩和二階矩。
Types of Buckling; Governing Equations for Bifucation Buckling; Application of Boundary Conditions; Euler Buckling Load; Coefficient of Edge Fixity; Geometrical Parameters; Considerations for Orthotropic/Composite Beams; Initial Imperfections; Primary and Secondary Moments. |
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L38, R; L39; L40 |
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R: 14.1, 14.2, 14.4
M: 6.1, 6.3
G: 11.1-11.4 |
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指定作業10
HA10 out |
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43; 44 |
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第十七單元：樑柱
Unit 17: The Beam-Column
樑柱定義；平衡方程；控制方程；軸向力的解答；樑柱的挫屈；一階矩和二階矩。
Beam-column Definition; Equilibrium Equations; Governing Equations; Solution for Axial Force; Buckling of Beam-Column; Primary and Secondary Moments. |
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L41; L42, R |
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T: 第1章
Ch.1
M: 6.4
G: 11.5-11.6 |
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指定作業9
HA9 out |
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44; 45; 46 |
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第十八單元：挫屈和結構不穩定性方面的其他問題
Unit 18: Other Issues in Buckling/Structural Instability
挫屈的其他問題；壓碎；漸進式降伏；不均勻樑；平板挫屈；圓柱體；補強板；後挫屈；大撓度的曲率運算式；Galerkin法；挫屈破壞。
Other Issues in Buckling; Squashing; Progressive Yielding; Nonuniform Beams; Plate Buckling; Cylinders; Reinforced Plates; Postbuckling; Curvature Expression for large Deflections; Galerkin Method; Buckling and Failure. |
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L42, R; L43; L44 |
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R: 14.3, 14.5-14.7, Ch. 15, Ch. 16
T: （建議閱讀）
(Suggested)
J: Ch. 5
M: 6.2, 6.6-6.10 |
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第六部分：結構動力學的介紹
Section VI : Introduction to Structural Dynamics |
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46; 47 |
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第十九單元：動力學總則（復習）
Unit 19: General Dynamic Considerations (Review)
系統回應；方式和控制因素；彈簧-質量系統；慣性載荷；控制方程；原始條件；阻尼；多質量系統；矩陣方程形式；動力結構載荷的來源；動態結構反應的結果。
System Response: The Regimes and Controlling Factors; Spring-mass System, Inertial Loads, Governing Equation; Initial Conditions; Damping; Multi-mass System, Matrix Equation Form; (Sources of) Dynamic Structural Loads; Consequences of Dynamic Structural Response. |
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L44; L45, R |
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47; 48 |
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第二十單元：單彈簧-質量系統的解答（復習）
Unit 20: Solutions for Single Spring-Mass System (Review)
單自由度系統；自由震動和自然頻率；強迫振動；階梯函數；單位脈衝；Dirac ；任意力；Duhamel's摺積積分；正弦力；動力放大因素；共振。
Single Degree-of-Freedom System; Free Vibration and Natural Frequency; Forced Vibration; Step Function; Unit Impulse, Dirac Delta Function; Arbitrary Force, Duhamel's convolution) Integral; Sinusoidal Force; Dynamic Magnification Factor; Resonance. |
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L45, R; L46 |
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提交作業10；指定 作業11（不用交）
HA10 due; HA11 out (not for hand-in)
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48; 49 |
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第二十一單元：干擾係數
Unit 21: Influence Coefficients
總合成力和位移；彈性係數；Maxwell's 互易定理；例子；懸臂梁；剛度干擾係數；物理解釋。
Generalized Forces and Displacements; Flexibility Influence Coefficients; Maxwell's Theorem of Reciprocity; Examples: Cantilevered Beam; Stiffness Influence Coefficients; Physical Interpretations. |
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L46; L47 |
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R: 6.6, 6.13, 10.5
M: 4.10, 11.1, 11.2 |
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提交設計問題4
DP4 due |
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50; 51 |
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第二十二單元：多自由度系統的振動
Unit 22: Vibration of Multi Degree-of-Freedom Systems
控制矩陣方程；自由振動；特徵值和特徵向量－自然頻率和模式；例子；座位不連續品質系統的樑的表示法；模型的物理解釋；正交關係；運動的法線方程；模型回應的重合；強迫振動。
Governing Matrix Equation; Free Vibration; Eigenvalues and Eigenvectors--Natural Frequencies and Modes; Examples: Representation of Beam as Discrete Mass System; Physical Interpretation of Modes; Orthogonality Relations; Normal Equations of Motion; Superposition of Modal Responses; Forced Vibration. |
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L48; L49, R |
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51; 52 |
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第二十三單元：連續系統的振動
Unit 23: Vibrations of Continuous Systems
ㄧ般樑柱的慣性方程；自由振動；空間和時間分離的解答方法；例子：簡單支撐的樑；自然頻率和模型；正交關係；運動的法線方程；強迫振動；模型回應的重合；共振。
Generalized Beam-Column Equation with Inertia; Free Vibration; Separation of Spatial and Temporal Solutions; Example: Simply-Supported Beam; Natural Frequencies and Modes; Orthogonality Relations; Normal Equations of Motion; Forced Vibration; Superposition of Modal Responses; Resonance. |
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L49, R; L50 |
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