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Resistance to Accidental Explosions General principles

Resistance to Accidental Explosions General principles. Outline. Classification of explosion loads Dynamic response based on SDOF analogy Dynamic response charts ISO-damage (pressure-impulse) diagram Resistance curves for beams, girders and plates Ductility limitations

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Resistance to Accidental Explosions General principles

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  1. Resistance to Accidental ExplosionsGeneral principles

  2. Outline • Classification of explosion loads • Dynamic response based on SDOF analogy • Dynamic response charts • ISO-damage (pressure-impulse) diagram • Resistance curves for beams, girders and plates • Ductility limitations • Verification of simple design methods

  3. Simple (SDOF) vs. advanced methods • SDOF methods – Biggs’ (1964) (Elastic-plastic/rigid plastic methods, component analysis…) • Early Design • Screening of scenarios • Codes (NORSOK, IGN(UK)… • Advanced Methods – NLFEA • Large-scale simulations feasible • Detail Engineering • Critical Scenarios • Quality of analysis? Iso-damage curve for blast loading

  4. EXPLOSIONClassification of response • Impulsive domain - td/T< 0.3 Response independent of load magnitude • Dynamic domain - 0.3 < td/T < 3 • Quasi-static domain - 3 < td/T

  5. EXPLOSIONImpulsive domain - td/T< 0.3 Feq(t) • Conservation of momentum Feq(t) meq Y(td) keq(y) y(t) td t R(y)= keq(y)·y • Conservation of energy

  6. EXPLOSIONQuasi-static domain - td/T> 3 Feq(t) Feq(t) • Rise time small (1) External work Strain energy Feq(t) meq y(t) y(t) Y(td) keq(y) td trise td t trise t R(y)= keq(y)·y (2) (1) • Rise time large (2) Static solution

  7. Explosion response -1 DOF analogy

  8. Dynamic equilibrium- alternative formulation

  9. f(t) t ymax y(t) Load-mass transformation factor t EXPLOSIONSDOF analogy – Biggs’ method f(t) Feq(t) meq y keq(y) Dynamic equilibrium:

  10. F(t) Rel R(y) yel t t y Development of explosion response charts • Dynamic equilibrium • Explosion load history • Solve dynamic equation – numerical integration • Determine maximum deformation ymax • Perform analysis for different duration and load amplitude Fmax

  11. K2 K2 R R R R K2 K3 K1 K1 K1 K1 w w w w Elastic Elastic-plastic (determinate) Elastic-plastic (indeterminate) Elastic-plastic with membrane R K3 K2=0 Rel K1 Wel or yel w EXPLOSIONClassification of resistance curves

  12. Explosion response chartmaximum displacement versus load duration • Governing parameters: • Mechanisme resistance vs. maximum load Rel/Fmax • Load duration vs. eigenperiod td/T • Membrane stiffness, if any

  13. EXPLOSIONDynamic response chart for pressure pulse-[J.M.Biggs]Triangular load - rise time = 0.3 td

  14. Example yallow/yel =10 Development of ISO-damage curves from dynamic response charts for a given pressure pulse

  15. Example yallow/yel =10 Development of ISO-damage curves from dynamic response charts for a given pressure pulse Pressure = Fmax Impulse =1/2Fmaxttd

  16. EXPLOSIONIso-damage curve for yallow/yelastic =10. [W.Baker] Inadmissible domain Admissible domain

  17. EXPLOSIONResistance curves • Beams and girders • Tabulated values for elastic-plastic behaviour • Resistance curves based on plastic thory • Plates • Elastic and plastic theory

  18. Transformation factors for beams with various boundary and load conditions

  19. Transformation factors for beams with various boundary and load conditions

  20. New Revision II: Transformation factors for clamped beam with two concentrated loads

  21. Transformation factors for beams with various boundary and load conditions

  22. Ductility ratios( Ref: Interim Guidance Notes)

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