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THE DEGRADING EFFECTIVE STIFFNESS OF MASONRY NON SYMMETRIC MODEL

THE DEGRADING EFFECTIVE STIFFNESS OF MASONRY NON SYMMETRIC MODEL. John Nichols Texas A&M University Department of Construction Science. Introduction. Overview of the Problem Experimental Background Mathematical Basis ULARC Coding Example Conclusions. Overview of the Problem.

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THE DEGRADING EFFECTIVE STIFFNESS OF MASONRY NON SYMMETRIC MODEL

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  1. THE DEGRADING EFFECTIVE STIFFNESS OF MASONRY NON SYMMETRIC MODEL John Nichols Texas A&M University Department of Construction Science

  2. Introduction • Overview of the Problem • Experimental Background • Mathematical Basis • ULARC Coding • Example • Conclusions Texas A&M University

  3. Overview of the Problem • Masonry damage – growth of cracking • Experimental measurement of the damage • Finite Element Modelling • ULARC Coding • Example Texas A&M University

  4. Masonry Damage • The patron saint of bricklayers is St Stephen. Texas A&M University

  5. Theoretical Model Macchi 1982 Dynamic time varyingShear Load Non-proportional bi-axialCompression Masonry Panel Texas A&M University

  6. Experimental Background Load Cell The 25 tonne INSTRON provides a cyclic loading pattern The compression frame Strains measured using 700 mm rosette A 25 tonne rams Texas A&M University

  7. Final Damage Model Texas A&M University

  8. Mathematical Basis Damage Equation Beam Model for the Finite Element Development Texas A&M University

  9. ULARC Coding • Program developed by Powell – 1972 University of California (Berkeley) • Elasto-plastic analysis program • The K matrix elements can be calculated for a degrading element. Texas A&M University

  10. Universal Beam Model Texas A&M University

  11. Matrix co-efficients provide a general solution valid for any symmetric inverse function, f(n) Texas A&M University

  12. Example Texas A&M University

  13. Moment of Inertia Equations Texas A&M University

  14. Pont-y-Prydd Arch Pont – y – Prydd Bridge: 1755 Wales Failed in a flood, then in reconstruction Will be used for future research on the FEM technique Texas A&M University

  15. Slope Equations Texas A&M University

  16. Generalized Equation Texas A&M University

  17. Stiffness Co-efficients variation with Moment of Inertia Texas A&M University

  18. Masonry Arch The masonry arch is used because I have data on the deflected paths. Texas A&M University

  19. ULARC Results Texas A&M University

  20. Conclusions • A generalized equation for determination of the matrix entries has been provided • for an element that has a variation in the moment of inertia and the effective stiffness with applied strain Texas A&M University

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