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Advanced Stress Analysis Benjamin Liaw CUNY City College City University of New York (CUNY) CUNY Academic Works Open Educational Resources City College of New York Summer 6-5-2018 Advanced Stress Analysis Benjamin Liaw CUNY City College How does access to this work benefit ou?y Let us know! Follow this and additional works at: https://academicworks.cuny.edu/cc_oers Part of the Mechanical Engineering Commons Recommended Citation Liaw, Benjamin, "Advanced Stress Analysis" (2018). CUNY Academic Works. https://academicworks.cuny.edu/cc_oers/83 This Textbook is brought to you for free and open access by the City College of New York at CUNY Academic Works. It has been accepted for inclusion in Open Educational Resources by an authorized administrator of CUNY Academic Works. For more information, please contact [email protected]. FALL 2018 SYLLABUS Page 1/1 ME 54100: ADVANCED STRESS ANALYSIS Courses: ME I4200: APPLIED STRESS ANALYSIS Time & Tuesday & Thursday, 11:00 a.m. – 12:15 p.m. Place: Steinman Hall, Basement ST-B64 (Materials Science Lab) Course Stress and strain. Principal stresses & directions. Generalized Hooke's Law (constitutive relations) Description: for elastic materials. Plane-stress/plane strain formulations in Cartesian/polar coordinates. Failure criteria. Bending of straight & curved beams. Torsion of shafts. Thick tubes, rotating disks, shrink fits. Thermal stresses in rings, tubes, and disks. Energy methods in structural mechanics. Applications of finite element methods in stress analysis. Prerequisites: ME 24700: Engineering Mechanics II (Kinematics and Dynamics of Rigid Bodies) ME 33000: Mechanics of Materials ME 37100: Computer-Aided Design Instructor: Prof. Benjamin Liaw E-mail: [email protected] Office: Steinman Hall, Room ST-247 Tel: (212) 650-5204 Hours: Monday: 4:00 p.m. – 5:00 p.m. Fax: (212) 650-8013 Wednesday: 1:00 p.m. – 2:00 p.m. Textbook: B.M. Liaw, Advanced Stress Analysis, CUNY City College of New York, Open Educational Resources. References: 1. F.P. Beer, E.R. Johnston, Jr., J.T. DeWolf, D.E. Mazurek, Mechanics of Materials, 7th ed., McGraw-Hill, New York, NY, 2015. 2. A.C. Ugural, S.K. Fenster, Advanced Mechanics of Materials and Applied Elasticity, 5th ed., Pearson/Prentice Hall, NJ, 2012. 3. M.H. Sadd, Elasticity: Theory, Applications, and Numerics, 3rd ed., Academic Press (Elsevier), Waltham, MA, 2014. 4. A.P. Boresi and R.D. Schmidt, Advanced Mechanics of Materials, 6th ed., Wiley, New York, NY, 2003. 5. R.D. Cook and W.C. Young, Advanced Mechanics of Materials, 2nd ed., Prentice Hall, Upper Saddle River, NJ, 1999. 6. R.G. Budynas, Advanced Strength and Applied Stress Analysis, 2nd ed., McGraw-Hill, New York, NY, 1999. 7. A.E. Armenàkas, Advanced Mechanics of Materials and Applied Elasticity, CRC Press, Taylor & Francis, Boca Raton, FL, 2006. 8. R. Solecki and R.J. Conant, Advanced Mechanics of Materials, Oxford University Press, New York, NY, 2003. 9. J.T. Oden and E.A. Ripperger, Mechanics of Elastic Structures, 2nd ed., Hemisphere Publishing, Washington, DC, 1981. 10. S.P. Timoshenko, Strength of Materials, Part I: Elementary Theory and Problems, Part II: Advanced Theory and Problems, 3rd ed., Van Nostrand, Princeton, NJ, 1956. 11. S.P. Timoshenko, J.N. Goodier, Theory of Elasticity, 3rd ed., McGraw-Hill, New York, 1970. 12. J.R. Barber, Elasticity (Solid Mechanics and Its Applications), 3rd ed., Springer, 2009. 13. A.S. Saada, Elasticity: Theory and Applications, 2nd ed., Revised & Updated, J. Ross Publishing, Fort Lauderdale, FL, 2009. 14. W.D. Pilkey, Formulas for Stress, Strain and Structural Matrices, 2nd ed., Wiley, Hoboken, NJ, 2005. 15. W.D. Pilkey and D.F. Pilkey, Peterson's Stress Concentration Factors, 3rd ed., Wiley, Hoboken, NJ, 2008. 16. W.C. Young, R.G. Budynas, A. Sadegh, Roark’s Formulas for Stress and Strain, 8th ed., McGraw-Hill, New York, NY, 2011. 17. P. Kurowski, Engineering Analysis with SOLIDWORKS Simulation 2016, SDC Publications, 2016. Grading: 40% Homework (13 Assignments, 40%) 60% Term Project (3 Parts, 60%) Note: Grade may also be affected by your attendance record and participation in class discussion. ME 54100: ADVANCED STRESS ANALYSIS 06-05-2018 ME I4200: APPLIED STRESS ANALYSIS SECTION 1.1 INTRODUCTION PAGE 1/11 CHAPTER 1: ANALYSIS OF STRESS 1.1 INTRODUCTION (Lecture) Mechanics of Materials vs Theory of Elasticity elementary Mechanics of Materials MoM ~ theory for approximate yet practical solutions Solid Mechanics technical Theory of Elasticity ~ exact and rigorous solutions external force ~ body & surface forces internal force ~ normal & shear stresses loading quasi - static loading dynamic impact loading ~ vibration & wave propagation hygrothermal loading ~ humidity & temperature effects Def: body force: an external force acts throughout the entire body V of a solid. It has a unit of force per unit volume. Examples of body forces include gravitational-weight force, inertial force, magnetic force, etc. Def: surface force: an external force, acts over the entire or part of the surface S of a solid. It has a unit of force per unit area. Examples of surface forces include pressure and aerodynamic lift/drag, etc. (a) body force: (b) surface force: cantilever beam under its own weight aerodynamic lift and drag over an airfoil FIGURE 1.1-A1 Examples of body and surface forces. ME 54100: ADVANCED STRESS ANALYSIS CHAPTER 1 – ANALYSIS OF STRESS ME I4200: APPLIED STRESS ANALYSIS SECTION 1.1 INTRODUCTION PAGE 2/11 Classification of Structures: Geometry & Loading (Self-Study) Def: structure: A collection of bodies arranged and supported so that it can resist and transmit loads. They can be classified into following groups, based upon a combination of geometric configurations and loading characteristics. A. 1-D Structures (or Bars): 1-D straight or curved structural member possessing one dimension significantly greater than the other two. rod (or tie member or tensile bar): a straight bar loaded in tension along the longitudinal axis. cable (or string): a flexible tie with zero or negligible flexural rigidity and can sustain only axial tensile forces. column (or compressive bar): a straight bar loaded in compression along the longitudinal axis. (Note: Slender columns are susceptible to failure in buckling.) torsional bar (or shaft): a straight bar loaded by twisting torques about the longitudinal axis. beam: a straight bar possessing one dimension significantly greater than the other two, bent flexurally in directions normal to the longitudinal axis. beam on elastic foundation: a loaded beam resting on an elastic foundation. beam-column: a beam loaded simultaneously by bending and compression. (Note: Slender beam-columns are susceptible to failure in buckling.) beam-tie (or tension-beam): a beam loaded simultaneously by bending and tension. curved beam: a curved beam subject to bending, twisting, shear and axial loads. arch: a curved beam supported at its ends and loaded primarily in direct compression. ring: a closed curved beam. truss: a structure consisting of two or more axial bars joined by frictional hinges and with each member loaded by an axial force only. frame: a structure made of two or more bars, which are rigidly attached and under bending, shear and axial loads. B. 2-D Structures: a 2-D flat or curved structural member possessing two dimensions significantly large in comparison with the third. panel: a 2-D flat structural member subject to in-plane loads, which act in directions tangent to the mid- surface. shear panel: a panel loaded only by in-plane shears. membrane: a flexible panel with zero or negligible flexural rigidity and can resist only in-plane tensions. balloon: a curved membrane. plate: a 2-D flat structural member subject to out-of-plane loads, which act in directions perpendicular to the mid-surface. shell: a curved plate, which can be loaded simultaneously by the in-plane stretching, compression and shear as well as out-of-plane bending and twisting. stiffened panel, plate or shell: a panel, plate or shell reinforced with bars. ME 54100: ADVANCED STRESS ANALYSIS CHAPTER 1 – ANALYSIS OF STRESS ME I4200: APPLIED STRESS ANALYSIS SECTION 1.1 INTRODUCTION PAGE 3/11 Rod (or Tie Member or Axially-Tensile Bar) Column (or Compressive Bar) Torsional Bar (or Shaft) Frame Beam Beam on Elastic Foundation Truss Beam-Column Curved Beam Beam-Tie (or Tension Beam) Ring Plate (Out-of-Plane) Panel (In-Plane) Shell (or Curved Plate) Arch ME 54100: ADVANCED STRESS ANALYSIS CHAPTER 1 – ANALYSIS OF STRESS ME I4200: APPLIED STRESS ANALYSIS SECTION 1.1 INTRODUCTION PAGE 4/11 (Axial-)Bar Tension (C0 member) Closed-Section Torsion ( member) EA P0 GKt T0 x,u x, L L y,v y,v T L T SL PL0 00 end elongation: uL end angle of twist: L or 2 EA GKt 4 G t normal stress distribution shear stress distributions: Px T x r Tx x x xr, & xs, x A J 2ts normal force vs axial-load intensity relation: twisting torque vs torque intensity relation: dP x dT x x sx mx dx dx t normal force vs axial displacement relation: twisting torque vs angle of twist relation: du x dx P x EA T x GK x dx t dx axial rigidity: EA torsional rigidity: GKt m (x) GK s(x) EA t t P P +dP T T+dT x x x x,u x,u ds R d dx dx y,v y,v d2 u x dx2 D.E.: EA s x D.E.: GK m x dx2 ttdx2 xu0: 0 0 x 0: 0 0 B.C.: @ B.C.: @ x L: Px L P0 x L: T L T0 ME 54100: ADVANCED STRESS ANALYSIS CHAPTER 1 – ANALYSIS OF STRESS ME I4200: APPLIED STRESS ANALYSIS SECTION 1.1 INTRODUCTION PAGE 5/11 Beam Bending (C1 member) (Thin-Walled) Open-Section Torsion ( member) B0 V0 EI & GK EIz t x,u x, T0 L L y,v y,v VL3 end deflection: vL 0 end angle
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