Comprehensive Examination (structural engineering)
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Advanced Solid Mechanics Mathematics Methods in Structural Engineering Advanced Reinforced Concrete Matrix Methods in Structural Analysis Bridge Design Advanced Steel Structures Advanced Concrete Technology
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Comprehensive Examination (structural engineering)
- 2. ประธานกรรมการ ผศ.ดร. ธีรพงศ์ จันทร์เพ็ง กรรมการร่วม อ.ดร. รังสรรค์ วงศ์จีรภัทร ผู้แทนบัณฑิตวิยาลัย อ.ดร. ปารเมศ กําแหงฤทธิรงค์
- 3. Coursework Outline Advanced Solid Mechanics Mathematics Methods in Structural Engineering Advanced Reinforced Concrete Matrix Methods in Structural Analysis Bridge Design Advanced Steel Structures Advanced Concrete Technology วิชาเอกบังคับ วิชาเอกเลือก
- 5. Basic of Analysis Equilibriam Constitutive Law Kinematics
- 6. Basic of Analysis Displacement External Forces and Moments Strains Internal Forces And Moment Stress Static Equivalency ε = ∆L L σ = Eε σ = Mc I
- 7. Stress-strain relationship Stress Tensor 𝑇 = 𝜎𝑥𝑥 𝜎𝑥𝑥 𝜎𝑥𝑥 𝜎𝑥𝑥 𝜎 𝑦𝑦 𝜎𝑦𝑦 𝜎𝑥𝑥 𝜎𝑦𝑦 𝜎𝑧𝑧 Shear stress Normal stress 𝜎𝑥𝑥 Plane-x Direction-y Strain Tensor 𝑇 = 𝜀 𝑥𝑥 𝜀 𝑥𝑥 𝜀 𝑥𝑥 𝜀 𝑥𝑥 𝜀 𝑦𝑦 𝜀 𝑦𝑦 𝜀 𝑥𝑥 𝜀 𝑦𝑦 𝜀 𝑧𝑧
- 8. Failure Criteria Mode of failure 1. By excessive deflection 2. By general yielding 3. By fracture 4. By instability (Bucking) - Yielding of Brittle Metals - Yielding of Ductile Metals - Alternative Yield Criteria
- 9. 1. Maximum Principal Stress Theory 𝜎𝑒 = max 𝜎1 , 𝜎2 , 𝜎3 𝑓 = 𝜎𝑒 − 𝑌 Yielding of Brittle Metals 3. Strain Energy Density Criterion 𝜎𝑒 = 𝜎1 2 + 𝜎2 2 + 𝜎2 3 − 2𝜈(𝜎1 𝜎2 + 𝜎2 𝜎3 + 𝜎1 𝜎3) 𝑓 = 𝜎𝑒 2 − 𝑌2 2. Maximum Principal Stain Theory 𝜎𝑒 = max 𝑖>𝑗>𝑘 𝜎𝑖 − 𝜈𝜎𝑗 − 𝜈𝜎 𝑘 𝑓 = 𝜎𝑒 − 𝑌
- 10. Yielding of Ductile Metals 1. Maximum Shear-Stress Theory 𝜎𝑒 = max(𝜏1, 𝜏2, 𝜏3) ,𝑓 = 𝜎𝑒 2 − 𝑌2 2. Distortional Energy Density Criterion (Von mises) 𝜎𝑒 = 1 2 [ 𝜎1 − 𝜎2 2 + 𝜎2 − 𝜎3 2 + 𝜎3 − 𝜎1 2] , 𝑓 = 𝜎𝑒 2 − 𝑌2
- 11. 1. Mohr-Coulomb Yield Criterion 𝑓 = 𝜎1 − 𝜎3 + 𝜎1 + 𝜎3 sin 𝜙 − 2𝑐 cos 𝜙 2. Drucker-Prager Yield Criterion 𝑓 = 𝛼𝐼1 + 𝐽2 − 𝐾 𝛼 = 2 sin 𝜙 3(3−sin 𝜙) 𝐾 = 6𝑐 cos 𝜙 3(3−sin 𝜙) Alternative Yield Criteria
- 12. Shear center 𝐹𝑙 = � 𝑞 𝑑𝑙 𝑏 0 𝑞 = 𝑉𝑦 𝑄 𝐼 𝑥 𝑒 = 𝐹𝑙ℎ 𝑉′
- 13. Linear Elastic 1. Symmetrical Bending : 𝜎𝑧𝑧 = 𝑀 𝑥 𝑌 𝐼 𝑥 , 𝜎𝑧𝑧 = 𝑀 𝑦 𝑋 𝐼 𝑦 2. Unsymmetrical Bending – Load : 𝜎𝑧𝑧 = 𝑀 𝑥 𝑌 𝐼 𝑥 − 𝑀 𝑦 𝑋 𝐼 𝑦 – Geometry : 𝜎𝑧𝑧 = 𝑀 𝑥(𝑦−𝑥 tan 𝛼) 𝐼 𝑥−𝐼 𝑥𝑥 tan 𝛼 , tan 𝛼 = 𝐼 𝑥𝑥−𝐼 𝑥 cot 𝜃 𝐼 𝑦−𝐼 𝑥𝑥 cot 𝜃 Fully Plastic 𝑀 𝑝 = 𝑌𝑏ℎ2 4 Bending
- 14. Torsion Linear Elastic •Circular Cross Section •Noncircular cross section Inelastic • Elastic-Plastic • Fully Plastic
- 16. Stiffness Method Flexibility Method 1. Equilibrium of force 2. Compatibility of deformations 3. Hooke’s low 1. Equilibrium of force 2. Displacement continuity 3. Linear force-displacement relationship
- 17. Stiffness Method 𝛿 = 𝐾 −1 𝐹 𝐹� = 𝐾� 𝛿̅ 𝐹 = 𝐾 𝛿 𝑆 = 𝜎 𝛿 หา 𝐾� ใน Local coordinate System Transform 𝐾� เป็น global coordinate System รวมเป็น 𝐾 หา Nodal Displacement หา Internal force จาก Stress matrix
- 18. Flexibility Method 𝑆 = 𝐵0 𝐹 + 𝐵1 𝑋 𝑆 = 𝑍 𝐹 𝑍 = 𝐵0 − 𝐵1(𝐵1 𝑇 𝐴𝐵1)−1 𝐵1 𝑇 𝐴𝐵0 𝛿 = 𝑍 𝑇 𝐴 𝑆 = 𝐵0 𝑇 𝐴 𝑆 หา 𝐵0 และ 𝐵1จากการตัดโครงสร้างให้เป็น Primary structure ที่มีเสถียรภาพ หา Internal force หา Nodal Displacement
- 20. Differential Equation Ordinary differential equations (ODE) Partial differential equations (PDE) Algebraic equations Differential equations 𝑎𝑥2 + 𝑏𝑏 + 𝑐 = 0 𝑚 𝑑2 𝑦(𝑥) 𝑑𝑥2 + 𝑐 𝑑𝑑(𝑥) 𝑑𝑑 + y x = sin(x) Find the numerical values Find the functions
- 21. Ordinary differentiale quations (ODE) Homogeneous Nonhomogeneous 0= f(x)= 𝑦 = 𝑦ℎ 𝑦 = 𝑦ℎ + 𝑦𝑝 General solution General solution + Particular solution
- 22. Partial differential equations (PDE) Fourier Series 𝑎0 = 1 𝑇 ∫ 𝑓 𝑡 𝑑𝑑 𝑇 0 𝑎 𝑛 = 2 𝑇 ∫ 𝑓 𝑡 cos 𝑛𝜔�𝑡 𝑑𝑑 𝑇 0 𝑏 𝑛 = 2 𝑇 ∫ 𝑓 𝑡 sin 𝑛𝜔�𝑡 𝑑𝑑 𝑇 0 𝑓 𝑡 = 𝑎0 + � 𝑎 𝑛 cos 𝑛𝜔�𝑡 ∞ 𝑛=1 + � 𝑏 𝑛 sin 𝑛𝜔�𝑡 ∞ 𝑛=1
- 23. Matrix Algebra Vector – Row vector : ∎ ∎ ∎ 1×𝑛 – Column vector : ∎ ∎ ∎ 𝑛×1 Matrix – Square Matrix : ∎ ∎ ∎ ∎ 𝑛×𝑛 – Rectangular Matrix : ∎ ∎ ∎ ∎ ∎ ∎ 𝑚×𝑛
- 24. System of linear equations A x b Uniqueness of solution 0 6 0 10 x1 x2 0 6 0 10 x1 x2 0 6 0 10 x1 x2 No Solution A = 0 Infinite Solution A = 0 Ill-condition A → 0
- 25. Eigenvalue Problems Ax = λ x Eigenvalues Eigenvectors A − λI x = 0 Trivial Solution x = 0 Nontrivial Solutions from det(A − λ𝐼) = 0Standard Form Ax1 = λ1x1 Ax2 = λ2x2 Ax3 = λ3x3 ⋮ Axn = λnxn
- 26. Roots of Equations Bracketing methods Bisection : 𝑥 𝑟 = 𝑥 𝑙+𝑥 𝑢 2 False-position : 𝑥 𝑟 = 𝑥 𝑢 − 𝑓(𝑥 𝑢)(𝑥 𝑙−𝑥 𝑢) 𝑓 𝑥 𝑙 −𝑓(𝑥 𝑢) Open methods Newton-Raphson Method 𝑥𝑖+1 = 𝑥𝑖 − 𝑓(𝑥 𝑖) 𝑓′(𝑥 𝑖)
- 27. Interpolation Assumption: Data are accurate and distinct. To do: Find a smooth curve through the data points. Curve fitting & Interpolation Curve fitting Assumption: Data contain scatter(noise), usually due to measurement errors. To do: Find a smooth curve that approximates the data.
- 28. Numerical Differential & Integration Differentiation 1. Finite difference approximations 2. Derivative by interpolation Integration 1. Newton-Cote formulas 2. Gaussian integration
- 30. พฤติกรรมการรับแรงดัด 1. ช่วงก่อนการแตกร้าว 2. ช่วงคอนกรีตใต้แกนสะเทินร้าวบางส่วน 3. จุดที่เหล็กเสริมถึงจุดคราก 4. ช่วงหลักการเริ่มต้นการครากของเหล็ก
- 32. ความสัมพันธ์ M−𝛟 แบบประมาณ 𝑀 𝑦 = 𝐴 𝑠 𝑓𝑦(𝑑 − 𝑘𝑑 3 ) ≤ 𝑀 𝑢 𝜙 𝑦 = 𝜀 𝑦 𝑑 − 𝑘𝑘 𝑀 𝑢 = 𝐴 𝑠 𝑓𝑦 𝑑(1 − 0.59 𝜌𝑓𝑦 𝑓′ 𝑐 ) 𝜙 𝑢 = 0.003 𝑘 𝑢 𝑑 ที่จุดเริ่มต้นการคราก ที่กําลังประลัย
- 36. 1. คานช่วงการเฉือนยาวมาก : a d⁄ = 6 2. คานช่วงการเฉือนยาว : a d⁄ = 3 หรือ 4 3. คานช่วงการเฉือนสั้น : 2.5 > a d > 1⁄ 4. คานลึก : a d ≤ 1⁄ พฤติกรรมการรับแรงเฉือน
- 40. Method of Plastic Analysis 1. Must have enough hinges to form mechanism 2. Moment diagram must be in equilibrium with applied load 3. lMl ≤ l 𝑀 𝑃l everywhere
- 41. Stiffeners
- 42. Torsion of I-Shape member 𝑇 = 𝑇𝑠𝑠 + 𝑇 𝑤 𝑇𝑠𝑠 = The portion of T resisted by torsional shear stresses 𝑇 𝑤 = The portion of T resisted as a result warping restraint
- 43. Bridge Design
- 44. Bridge Design 1. Aesthetics 2. Bridge types - Concrete bridge - Steel bridge - Wood bridge - Composite bridge 3. General design considerations 4. Loads 5. Bridge/system analysis
- 46. Cement hydration
- 48. Admixture in Concrete Mineral Admixture inexpensive and eco-friendly. Chemical control setting or water requirement Mineral improve some properties
- 50. Chloride Attack
- 51. Sulfate Attack
- 53. Thank you for your attention You can find me at: Anirut_decha@hotmail.com