Resistance to accidental explosions general principles
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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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Outline
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


Simple sdof vs advanced methods
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


Explosion classification of response
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


Explosion impulsive domain t d t 0 3
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


Explosion quasi static domain t d t 3
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




Explosion sdof analogy biggs method

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:


Development of explosion response charts

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


Explosion classification of resistance curves

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


Explosion response chart maximum displacement versus load duration
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


Explosion dynamic response chart for pressure pulse j m biggs triangular load rise time 0 3 t d
EXPLOSIONDynamic response chart for pressure pulse-[J.M.Biggs]Triangular load - rise time = 0.3 td


Development of iso damage curves from dynamic response charts for a given pressure pulse

Example yallow/yel =10

Development of ISO-damage curves from dynamic response charts for a given pressure pulse


Development of iso damage curves from dynamic response charts for a given pressure pulse1

Example yallow/yel =10

Development of ISO-damage curves from dynamic response charts for a given pressure pulse

Pressure = Fmax

Impulse =1/2Fmaxttd


Explosion iso damage curve for y allow yelastic 10 w baker
EXPLOSIONIso-damage curve for yallow/yelastic =10. [W.Baker]

Inadmissible domain

Admissible domain


Explosion resistance curves
EXPLOSIONResistance curves

  • Beams and girders

    • Tabulated values for elastic-plastic behaviour

    • Resistance curves based on plastic thory

  • Plates

    • Elastic and plastic theory






Ductility ratios ref interim guidance notes
Ductility ratios load conditions( Ref: Interim Guidance Notes)


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