Resistance to Accidental Explosions General principles

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Resistance to Accidental Explosions General
principles
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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

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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
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EXPLOSIONClassification of response

• Impulsive domain - td/Tlt 0.3
• Response independent of load magnitude
• Dynamic domain - 0.3 lt td/T lt 3
• Quasi-static domain - 3 lt td/T

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EXPLOSIONImpulsive domain - td/Tlt 0.3
Feq(t)
Feq(t)
meq
Y(td)
keq(y)
y(t)
t
td
R(y) keq(y)y

• Conservation of momentum

• Conservation of energy

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EXPLOSIONQuasi-static domain - td/Tgt 3
Feq(t)
Feq(t)
Feq(t)
meq
y(t)
y(t)
keq(y)
Y(td)
td
t
t
td
trise
trise
R(y) keq(y)y
(2)
(1)

• Rise time small (1)
• External work Strain energy

• Rise time large (2)
• Static solution

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Explosion response -1 DOF analogy
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Dynamic equilibrium- alternative formulation
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EXPLOSIONSDOF analogy Biggs method
f(t)
Feq(t)
meq
y
keq(y)
Dynamic equilibrium
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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
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EXPLOSIONClassification of resistance curves
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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

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EXPLOSIONDynamic response chart for pressure
pulse-J.M.BiggsTriangular load - rise time
0.3 td
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Development of ISO-damage curves from dynamic
response charts for a given pressure pulse
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Development of ISO-damage curves from dynamic
response charts for a given pressure pulse
Pressure Fmax Impulse 1/2Fmaxttd
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EXPLOSIONIso-damage curve for yallow/yelastic
10. W.Baker
Inadmissible domain
Admissible domain
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EXPLOSIONResistance curves

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

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Transformation factors for beams with various
boundary and load conditions
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Transformation factors for beams with various
boundary and load conditions
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New Revision II Transformation factors for
clamped beam with two concentrated loads
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Transformation factors for beams with various
boundary and load conditions
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Ductility ratios( Ref Interim Guidance Notes)